ESRO SP-72 I. Proc. ESRO-GRI ESRO SP-72 I. Proc ESRO-GRI European Space Research Organisation Colloquium March 1971 European Space Research Organisation Colloquium March 1971 COLLOQUIUM ON WAVE-PARTICLE INTER II. ESRO SP-72 COLLOQUIUM ON WAVE-PARTICLE INTER II. ESRO SP-72 ACTIONS IN THE MAGNETOSPHERE HI. Texts in English ACTIONS IN THE MAGNETOSPHERE III. Texts in English September 1971 September 1971 iv + 284 pages iv + 284 pages
The Colloquium on wave-particle interactions in the magnetosphere held in The Colloquium on wave-particle interactions in the magnetosphere held in Orleans (March 17-19,1971) intended to review the outstanding problems still unsolved Orleans (March 17-19, 1971) intended to review the outstanding problems still unsolved in this field : in this field : — large-scale dynamics of the magnetosphere; — large-scale dynamics of the magnetosphere; — distribution of 'Oasma parameters; — distribution of plasma parameters; — decoupling of n..gnetospheric from ionospheric plasma; — decoupling of magnetospheric from ionospheric plasma; — acceleration and convection mechanisms; — acceleration and convection mechanisms; — substorms; — substorms; — polar wind..., — polar wind..., as well as the theoretical and experimental work needed to solve these problems in the as well as the theoretical and experimental work needed to solve these problems in the light of previous experiments (rocket launchings in auroral zone, Ariel 3 satellite...) light of previous experiments (rocket launchings in auroral zone, Ariel 3 satellite...) and of technical achievements (onboard computers, new sensors...). and of technical achievements (onboard computers, new sensors...). Ensuing discussions attempted to define types of missions which could be carried Ensuing discussions attempted to define types of missions which could be carried out in the future by the Small Scientific Satellites now being considered by ESRO. out in the future by the Small Scientific Satellites now being considered by ESRO. Such missions should be complementary to that of Geos and be implemented in the fra Such missions should be complementary to that of Geos and be implemented in the fra mework of the International Magnetospheric Studies Years (1975-1977), a world-wide mework of the International Magnetospheric Studies Years (1975-1977), a world-wide effort of coordinated studies on Sun-Earth elationships. effort of coordinated studies on Sun-Earth relationships.
ESRO SP-72 I. Proc. ESRO-GRI ESRO SP-72 I. Proc. ESRO-GRI European Space Research Organisation Colloquium March 1971 European Space Research Organisation Colloquium March 1971 COLLOQUIUM ON WAVE-PARTICLE INTER n. ESRO SP-72 COLLOQUIUM ON WAVE-PARTICLE INTER H. ESRO SP-72 ACTIONS IN THE MAGNETOSPHERE ACTIONS IN THE MAGNETOSPHERE September 1971 III. Texts in English September 1971 III. Texts in English iv + 284 pages iv + 284 pages
The Colloquium on wave-particle interactions in the magnetosphere held in The Colloquium on wave-particle interactions in the magnetosphere held in Orleans (March 17-19,1971) intended to review the outstanding problems still unsolved Orleans (March 17-19,1971) intended to review the outstanding problems still unsolved in this field : in this field : — large-scale dynamics of the magnetosphere; — large-scale dynamics of the magnetosphere; — distribution of plasma parameters; — distribution of plasma parameters; — decoupling of magnetospheric from ionospheric plasma; — decoupling of magnetospheric from ionospheric plasma; — acceleration and convection mechanisms; — acceleration and convection mechanisms; — substorms; — substorms; — polar wind..., — polar wind..., as well as the theoretical and experimental work needed to solve these problems in the as well as the theoretical and experimental work needed to solve these problems in the light of previous experiments (rocket launchings in auroral zone, Ariel 3 satellite...) light of previous experiments (rocket launchings in auroral zone, Ariel 3 satellite...) and of technical achievements (onboard computers, new sensors...). and of technical achievements (onboard computers, new sensors...). Ensuing discussions attempted to define types of missions which could be carried Ensuing discussions attempted to define types of missions which could be carried out in the future by the Small Scientific Satellites now being considered by ESRO. out in the future by the Small Scientific Satellites now being considered by ESRO. Such missions should be complementary to that of Geos and be implemented in the fra Such missions should be complementary to that of Geos and be implemented in the fra mework of the International Magnetospheric Studies Years (1975.1977), a world-wide mework of the International Magnetospheric Studies Years (1975-1977), a world-wide effort of coordinated studies on Sun-Earth relationships. effort of coordinated studies on Sun-Earth relationships. WAVE-PARTICLE INTERACTIONS IN THE MAGNETOSPHERE
Proceedings of H Colloquium held in Orléans, France, 17-19 March 1971 under the joint auspices of ESRO and Centre National de la Recherche Scientifique
ORGANISATION EUROPÉENNE DE RECHERCHES SPATIALES EUROPEAN SPACE RESEARCH ORGANISATION
114, avenue Charles-de-Gaulle. 92 - NEUILLY-SUR-SEINE (France) TABLE OF CONTENTS
OPENING ADDRESSES, /. Hiéblot and /. Ortner 1
Session I. T.R. Kaiser, Chairman
WAVE-PARTICLE INTERACTIONS IN THE. MAGNETOSPHERE, A. Eviatar 5 A THEORY OF VLF EMISSIONS, D. Nunn 17 INTERACTIONS BETWEEN MONOCHROMATIC WAVES AND PARTICLES (Abstract), G. Laval, R. Pellat and A. Roux 35 QUASI LINEAR CALCULATION OF VLF HISS SPECTRUM, J. Etcheto, A. Roux, R.P. Singh and J. Solomon 37 LOW FREQUENCY DRIFT WAVES IN THE MAGNETOSPHERE DURING SUBSTORMS (Abstract), K. Hagège, G. Laval and R. Pellat 41 RECENT WORK ON ION-CYCLOTRON WHISTLERS, D. Jones 43
Session II. N. d'Angelo, Chairman
WAVE-PARTICLE INTERACTION IN THE PLASMASPHERE, G. Haerendel .... 63 A NUMERICAL INVESTIGATION OF ELECTROSTATIC WAVES AT MHZ FREQUEN CIES IN THE UPPER IONOSPHERE AND THEIR INTERACTIONS WITH ENER GETIC PARTICLES (Abstract), B. Hultqvist 79 ON THE STRUCTURE OF THE GEOMAGNETIC TAIL, K. Schindler 81 A NON LINEAR THEORY OF " TYPE I " IRREGULARITIES IN THE EQUATORIAL ELECTROJET, A. Register 83 ON THE INTERACTION BETWEEN THE HOT MAGNETOSPHERIC PLASMA AND THE COLD IONOSPHERIC PLASMA OVER THE POLAR CAPS (Abstract), B. Hultqvist.. 93
Session III. G. Haerendel, Chairman
WAVES GENERATED BY A CONTROLLED BEAM OF ELECTRONS ARTIFICIALLY INJECTED INTO THE IONOSPHERE : THE ELECTRON ECHO EXPERIMENT, D.G. Cartwrighl and P.J. Kellogg 95 STUDIES OF VLF EMISSIONS IN THE SATELLITE ARIEL 3, T.R. Kaiser 109 EXPERIMENTAL STUDY OF ELECTRON PITCH ANGLE DIFFUSION IN THE PRESENCE OF VLF MODULATED HISS, /. Etcheto, R. Gendrin and D. Lemaire 123 CHARGED PARTICLES ASSOCIATED WITH VLF DAWN CHORUS EMISSIONS (Abstract), P. Rothwell, G J. Jenkins and H.L. Collin 135
iii SOME STUDIES OF CHORUS (Abstract), M. Rycroft. 137 CORRELATION BETWEEN VLF EMISSION FLUX AND ELECTRON PITCH ANGLE DISTRIBUTION AS DEDUCED FROM A ROCKET FLIGHT IN THE AURORAL ZONE, M. Hamelin 139 INTERACTION OF LONG-PERIOD WAVES AND ENERGETIC PARTICLES IN THE MAGNETOSPHERE (Abstract), G.K. Parks and J.R. Winckler 145
Session IV. B. Hultqvist, Chairman
PROBLEMS RELATED TO HIGH LATITUDE ELECTRIC FIELDS AND CURRENTS, C.G. FSlthammar and L.P. Block 147 MAGNETOSPHERIC STRUCTURE DEDUCED FROM WHISTLER OBSERVATIONS AT HALLEYBAY, J.L. Sagredo and K. Bullough. 157 DAWN-DUSK ELECTRIC FIELDS ACROSS THE MAGNETOSPHERE DERIVED FROM PLASMAPAUSE OBSERVATIONS, MJ. Rycroft 163 GYRORESONANT WAVE-PARTICLE INTERACTIONS IN A SPATIALLY VARYING MAGNETIC FIELD AND PLASMA DENSITY, /. Troughton and G. MartelH 175 WAVE AND BEAM LABORATORY EXPERIMENTS IN A MAGNETOACTIVE PLASMA, P.J. Christiansen, C. Christopoulos and G. Martelli 187 PARALLEL ELECTRIC FIELD, NEAR THE AURORAL IONOSPHERE, DEDUCED FROM ENERGY SPECTRA, ANGULAR DISTRIBUTIONS AND TIME VARIA TIONS OF LOW ENERGY AURORAL ELECTRONS AND PROTONS, H. Rème and J.M. Bosqued 197 GENERAL DISCUSSION (I) 209
Session V. A. Pedersen, Chairman
ONBOARD COMPUTERS FOR MAGNETOSPHERIC SPACECRAFT, A.C. Durney and T. Fokine 215 THE PHYSICS OF THE CHANNEL ELECTRON MULTIPLIER, C. Barat 231 FAST ANALYSIS OF PITCH ANGLE AND ENERGY DISTRIBUTION OF ENERGETIC PROTONS, /. Etcheto and B. de la Porte des Vaux 241 THE STUDY OF PLASMA RESONANCES WITH A SINGLE ANTENNA, M. Petit... 249 EXPERIMENTS WITH PLASMA WAVES (Abstract), J.O. Thomas, M.K. Andrews, T.A. Hall and C. Fang 259
Session VI. F. du Castel, Chairman
MAGNETOSPHERE STUDIES AT 10 EARTH RADII, G. Haskell .. 261 L'ÉTUDE DES INTERACTIONS DANS LA MAGNETOSPHERE ET LE PROGRAMME DE L'ESRO, F. du Castel '. 265 GENERAL DISCUSSION (II) 269 REFERENCES 271 iv Ladies and Gentlemen,
I am very happy indeed to welcome to Orléans, this French regional metropolis, the eminent specialists who, at the invitation of ESRO and the Groupe de Recherches Ionosphériques *, have come to take part in the Colloquium on wave-particle interactions in the magnetosphere.
Why did we arrange to hold this meeting in Orléans, in premises lent to us by the University, rather than in V-i.is ? Nations still occasionally have some difficulty in accepting in practice the existence of supranational Organisations. There is a closely allied problem with our French regions, which often have the same misgivings vis-à-vis their own national capital...
Following the general trend towards decentralisation, we have therefore chosen to move out of Paris everything that was not strictly indispensable to the life of the capital, and I have to admit that the G.R.I, is not absolutely necessary to the capital's life ! This laboratory was therefore transferred to Orléans a few months ago.
Before giving the floor to Dr Ortner, Head of ESRO's Space Missions Division, who originally proposed this Colloquium, I should like to thank him once again for having been good enough to entrust the G.R.I. — and particularly Dr Storey — with the honour of organising the Colloquium.
I hope this work will be as fruitful as possible. The high standing and professional competence of the people assembled here are already a guarantee of its success.
J. HlÉBLOT, Directeur du Groupe de Recherches Ionosphériques du Centre National de la Recherche Scientifique.
'Responsible for the scientific programme, and the organisation of the Colloauium with assistance from the University and the Municipality of Orleans. Ladies and Gentlemen,
Having the honour and the pleasure of representing ESRO at the opening of the Colloquium on wave-particle interactions in the magnetosphere, I should like to emphasise the importance of this meeting for the European space research programme.
But first of all I want to thank Dr. Hiéblot and the Ionospheric Research Group for all the trouble they have taken to make us so welcome in Orléans — and particularly Dr. Storey, who has undertaken the heavy task of preparing these meetings. I also wish to thank all the specialists who have been good enough to reply to our invitation to lecture on their work or to make an active contribution to the ensuing discussions.
The object of the Colloquium is clearly set out in the booklet you have been given :
" The purpose of the Colloquium is to try and answer the following questions :
— What are the outstanding problems that remain to be solved ?
— What theoretical and experimental work is needed to solve them ?
— What technical developments are needed for these experiments and what new experiments are suggested by recent technological advances ? "
Your work should culminate in the closing discussions of the last two days, during which we will endeavour to define the missions we consider it desirable to undertake with a view As you know, there is a tendency at the present time to restrict the part of the space budgets devoted to this type of purely scientific research, and competition between projects of this kind is therefore becoming increasingly keen. We shall therefore need to discuss in very great detail the projects we select so as to bring out all their potential value and so help to get them adopted as part of ESRO's future programme- This is precisely the purpose of this Colloquium. When you saw three satellite models on show in the reception hall, you must have wondered whether they represented future ESRO satellites ! I should make it clear at once that they are merely part of feasibility studies ordered from industry by ESRO for the definition of future satellites designed to study the magnetosphere, and no projects already adopted by the Council of the Organisation. In actual fact, ESRO has already adopted a geostationary satellite project in this field, known as Geos ; the onboard experiments have already been selected and the definition studies are to start shortly. The project will be implemented, we hope, towards the middle of 1975. 3 The projects under study may follow up the Geos project, with experiments complemen tary to those carried by Geos. Two of these projects concern a small satellite on a polar orbit, for the study of the near Magnetosphere, and the third one involves a Geos-type satellite on a highly eccentric orbit, carrying an onboard computer that would enable phenomena to be studied with a better resolution. These studies are not yet finished and — in the light of the proposals to be made during this Colloquium and the wishes expressed by you — we may reconsider some of the parameters we had selected and envisage other missions. After this Colloquium, we shall doubtless be able to complete the picture we have at present of the cause - and — effect relationships governing the dynamic phenomena of the plasma and fields in the terrestrial environment. At its next meeting, at the end of April 1971, ESRO's Launching Programmes Advisory Committee will probably take a decision on the nature of the supplementary projects designed to complete the Geos project, after hearing the opinion of the Organisation's Scientific and Technical Committee. The final decision, which lies with the Council, will possibly not be taken before next July, as at is the time — as you know — when the overall negotiations on the organisation of European space research are to take place. Your work will be carried out in a much more general context, in the light of the foreseeable future for the period from mid — 1975 to mid - 1977. Indeed, the International Union for Solar- Terrestrial Physics has taken the ii-'tiative of organising during that period the International Magne tosphere Studies Years, a world-wide effort of coordinated studies on Sun-Earth relationships. It should be borne in mind that, at its first meeting, in February 1971, in London, the preparatory Group selected ESRO's Geos satellite as the reference satellite for these measurements. While we have good reasons to hope that ESRO will include in its programme a new satellite for the study of the magnetosphere, we know that the period following the Geos launching in 1975 will be crucial for progress in the knowledge and understanding of phenomena governing the terrestrial environment. AU these factors further heighten the interest and importance of our meeting and lead us to wish it every success in its work. J. ORTNER, Assistant Director, Space Missions Division, ESRO. The projects under study may follow up the Geos project, with experiments complemen tary to those carried by Geos. Two of these projects concern a small satellite on a polar orbit, for the study of the near Magnetosphere, and the third one involves a Geos-type satellite on a highly eccentric orbit, carrying an onboard computer that would enable phenomena to be studied with a better resolution. These studies are not yet finished and — in the light of the proposals to be made during this Colloquium and the wishes expressed by you — we may reconsider some of the parameters we had selected and envisage other missions. After this Colloquium, we shall doubtless be able to complete the picture we have at present of the cause - and - effect relationships governing the dynamic phenomena of the plasma and fields in the terrestrial environment. At its next meeting, at the end of April 1971, ESRO's Launching Programmes Advisory Committee will probably take a decision on the nature of the supplementary projects designed to complete the Geos project, after hearing the opinion of the Organisation's Scientific and Technical Committee. The final decision, which lies with the Council, will possibly not be taken before next July, as at is the time — as you know — when the overall negotiations on the organisation of European space research are to take place. Your work will be carried out in a much more general context, in the light of the foreseeable future for the period from mid — 1975 to mid — 1977. Indeed, the International Union for Solar- Terrestrial Physics has taken the ii-'tiative of organising during that period the International Magne- tospheric Studies Years, a world-wide effort of coordinated studies on Sun-Earth relationships. It should be borne in mind that, at its firstmeeting , in February 1971, in London, the preparatory Group selected ESRO's Geos satellite as the reference satellite for these measurements. While we have good reasons to hope that ESRO will include in its programme a new satellite for the study of the magnctosphere, we know that the period following the Geos launching in 1975 will be crucial for progress in the knowledge and understanding of phenomena governing the terrestrial environment. AU these factors further heighten the interest and importance of our meeting and lead us to wish it every success in its work. J. ORTNER, Assistant Director, Space Missions Division, ESRO. 4 WAVE-PARTICLE INTERACTIONS IN THE MAGNETOSPHERE Aharon Eviatar Department of Environmental Sciences, Tel-Aviv University, Ramat-Aviv, Israel ABSTRACT A short introduction to the basic equations of linear and quasi-linear plasma kinetic theory is given. Some applications of these results to observed particle phenomena in the magnetosphere are reviewed. The creation of populations of energetic ions by magneto-hydrodynamic waves is considered and the effects of the existence of such ions on the stability of electromagnetic waves is discussed in the light of the obser vations made during the magnetic storm of April 18, 1965. Electrostatic ion waves are reviewed in the context of tUe polar wind. The state of knowledge of electron-wave interaction is surveyed. Various models involving whistlers, electrostatic modes and electromagnetic radiation normal to the field lines are discussed as means of explaining the observed particle lifetimes diffusion processes and the local accelera tion phenomena. The vast lacunae in our present understanding of magnetosphere plasma physics are delineated. 1. INTRODUCTION The hyphenated combination, wave-particle interaction, in the title of this Symposium is symptomatic of a fairly new and, in my opinion, positive trend in magnetosphere physics. The role of the magnetospheric plasma and its attendant wave modes has slowly won recognition as a major factor in determining the evolution of the high-energy radiation. During the early days of radiation- belt physics, the magnetosphere was considered to be a seething cauldron of energetic particles trapped in a constant magnetic field, whose sole loss mechanism was atmospheric scattering. As time went on and the level of sophistication of our knowledge rose, it became apparent that a constant magnetic field and an atmosphere could not suffice to explain the observed particle lifetimes as shown in Figure 1, which was published by [van Allen] *. At the same time and actually long before, others were diligently studying the propagation of waves in the magnetosphere. These studies go back to the early days of radio and ionosphere science and were a natural consequence of the development of radio technology. As a result, thj e was a tendency to concentrate on high frequencies and to regard the waves as propagating in a near-vacuum or at most in a zero temperature plasma. In spite of the obvious idealizations, a good deal of expe rimental material was elucidated by these methods and many practical considerations were advanced. The study of whistlers led to methods of remote sensing of the plasmaphere [Storey, Carpenter, 1966] 'All references appear in square brackets and are given in alphabetical order ai the end of the Vohme. 5 10,000 QUIESCENT ATMOSPHERIC LOSSES (WALT) INJUN m SpB 10 YEARS' STARFISH -[j INJUN m 302 ARGUS II -I YEAR " EXPERIMENTAL 100 CO 1 -I MONTH »- - '• ~i-T T 10 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Figure 1. — The L-dependence of observed values of the apparent mean lifetime of 2 MeV electrons from two US and two USSR nuclear detonations at high altitudes. Note the failure of atmospheric losses to duplicate the observations for L > 1.25 {after van Allen]. In the early 1960's, attention began to be paid to the possible consequences of the existence of a hot component in the magnetospheric plasma. To a large extent, this was a natural outgrowth of the remarkable progress in plasma kinetic theory which took place during the 1950's. The deve lopment of linear theory in plasma turbulence was aimed primarily at solving the problem of plasma confinement for thermonuclear fusion reactors. 2. LINEAR AND QUASI-LINEAR THEORY In order to clarify the concepts underlying wave-particle interactions, it appears useful to give a very quick and necessarily superficial introduction to the basic plasma physics involved. The basic equation describing a system comprised of plasma particles and fieldsi s the Vlasov- Maxwell equation : / 3 3 q 1 v x B\ 3 \ 3 ! 3B —- x E = — 3x c 3t 3 4 it 1 3E _X B = j+ — -r- 3x c e dt E = 4itlq [fdv 3x J — • B = 0 (1, 2) 3x These equations are highly non-linear and have not in general been solved. However, it is standard procedure to expand them in a perturbation series, linearize and take Fourier-Laplace transforms in space and time. The resulting algebraic equations lead to an existence condition involving the vanishing of a determinant of coefficients. This in turn implies a relation known as the dispersion relation between the real and imaginary parts of the phase velocity and the parameters of the plasma, such as temperature, density, isotropy, non-equilibrium, etc. The solutions of this dispersion relation determine the proper modes of the plasma. This fairly straightforward procedure has given birth to a plethora of predicted plasma wave phenomena, involving both wave growth and damping. The first of such phenomena is the damping predicted by [Landau] which bears bis name. It involves the absorption of electrostatic plasma oscillations. Since then many other linear damping effects — such as cyclotron damping, transit-time damping and others—have been discovered. In addition, a family of phenomena known as plasma instabilities has been investigated and criteria for the onset of instability have been derived, in terms of parameters of the plasma, by a large number of investigators. In principle, this linear theory cannot give the final amplitude of the waves or the ultimate fate of the plasma particles. It predicts something which is absurd on physical grounds, i.e. an infinite wave amplitude with all the energy sucked out of the plasma. Therefore, as the shortcomings of the linear theory became apparent, theorists on both sides of the Iron Curtain began to inquire into the nature of the non-linear mechanism which ensures that any unstable mode will ultimately attain a finite amplitude. The non-linearity enters in the lowest order via a wave-particle interaction in which the wave which had begun by drawing energy from one part of the velocity distribution of the particle population returns energy to the particles in another part of the distribution. This leads to a diffusion in velocity space which continues until a steady state is established [Drummond and Pines, 1962, 1964 ; Vedenov et al, 1962]. For example the manifestly unstable " bump-in-tail " distribution evolves by wave-particle interaction into a "plateau" which is neutral from the standpoint of stability. This is only one of many self-limiting processes involving wave-particle interactions. Let us consider the most simple case, that of purely electrostatic waves. The Vlasov equation can be written to second order in the form Ç!+T.Ç+^Eu,.Ç+^Ea,.Ç! = 0 (3) 3/ 3x m 3v m 3v 7 Note that one non-linear term is retained. Taking a Fourier expansion of the equation in space will lead to the linear equation plus a convolution term : The first term on the right represents wave-particle interaction and the second term represents coupling between the various modes. Quasi-linear theory ignores the mode coupling and tries to predict the final state of the plasma system on the bases of velocity space diffusion driven by wave-particle inter actions. In recent years it has achieved a degree of acceptance and has been extended to i 'dude elec tromagnetic waves in various frequency ranges [Shapiro and Shevchenko, Roulands et al.). It is still plagued by several problems such as the status of damped waves and the secularities that are asso ciated with all finite-order perturbation theories. More recent ventures into the non-linear domain appear promising [Dupree, Weinstock] and it is hoped that an analytical theory of plasma turbulence involving mode coupling will be forthcoming in the foreseeable future. 3. MAGNETOSPHERIC PARTICLE EFFECTS We have seen that the interaction of a particle and a wave can lead to the exchange of energy between them. We shall also see that " elastic " collisions can take place in which the particle can be scattered w thout appreciable change in energy. The acceleration of particles to high energies such as those observed in the van Allen belts was early ascribed to interactions between hydromagnetic waves and particles. However, as we shall see, the matter is by no means clear-cut and after more than a decade of activity, very little of a conclusive nature can be said about the problem. 3.1 Ions Since magnetohydrodynamic waves can propagate at frequencies up to the local ion cyclotron frequency, there is no reason to expect the adiabatic invariants of trapped protons to be conserved. This could be invoked as a reason for the absence of high-energy protons in the outer radiation zone, where there are magnetohydrodynamic waves and the ion cyclotron frequency is low. [Dragt] proposed such a mechanism and showed that a cyclotron resonance was necessary. This defined an energy threshold, since, as is well known, only protons whose velocities are somewhat greater than the local Alfvén velocity can attain cyclotron resonance. For all other protons, the interaction with MHD waves is one in which the mirror point is moved and the magnetic moment conserved. In all such interactions, the energy of the particle must be altered. If the mirror point moves down the field line, the energy must increase. [Parker] has discussed this mechanism in some detail. When a magneto hydrodynamic wave passes a mirror point, the magnetic field changes and the mirror point oscillates up and down the field line. The particles are reflected from moving magnetic fields and the net result is an acceleration of some particles. Parker has shown, however, that most particles are decelerated or lost and the net total energy of the system is decreased. Nonetheless, such events will appear to a particle detector as acceleration events. 8 The appearance of a population of energetic protons can have a profound effect on the energy density of the magnetospheric plasma and can give rise to instabilities normally associated with high- beta plasmas. A good example of such a case may be seen in the particle and field events associated with the great magnetic storm of April 18, 1965, and reported by [Brown et al. ; Lanzerotti et al. ; Sonnerup]. The April 18, 196S storm was a large one and had been preceded by an extended period of magnetic quiet. At the onset of the storm, the Explorer 26 satellite was fortuitously located at apogee near 5 Earth radii and stayed there for a sufficiently long time to observe a proton injection event and its consequence. The slow speed of the satellite at apogee enables us to interpret the observed pheno mena as temporal changes rather than spatial variations. The detectors observed sudden enhance ments of proton fluxes combined with a sharp decrease in the magnetic field. Figure 2 is a composite of the observations taken from the paper of [Lanzerotti et al.]. After the onset, the proton fluxes and the magnetic field continued to oscillate in antiphase. There was in general no coherent phase relation between the electron oscillations and the anticorrelated proton and magnetic field variations. This may be a result of poor pitch-angle resolution in the eiectron detectors. It is not totally clear what the relevant plasma phenomenon is here. [Sonnerup et al.] proposed the ion acoustic mode. However, this mode is subject to heavy Landau damping in the presence of hot protons. An alternative instability is the mirror instability proposed for this by [Hasegawa, a]. The mirror instability can appear in a high-beta plasma with a loss-cone distribution. It is of some interest to note that this instability which was predicted for laboratory plasma has never been observed in any laboratory device. This may be partially due to the fact that high-beta plasma has never been realized in the laboratory and partially due to the fact that the usual theory ignored drifts that arise from magnetic field and density gradients. The standard theory [Chandrasekhar et al.] predicts a non-oscillating mode for which : (5) Hasegawa's generalized mirror-drift mode is cverstable and has a growth rate given by : 1.1 XT* 1 3/2 1/2 vexpp / ' , , fi, /Tii\ /2\ //t||VXi\r /Tj. \ / kl\ " \ af I (6) The condition for instability is : •GMl' M Analysis of the experimental data of April 18, 1965 tends to indicate that the mirror drift insta bility can be responsible for the observed effects, although the evidence is not fully conclusive and one cannot make an unequivocal statement on the basis of the Explorer 26 data alone. It appears unlikely that the mirror drift mode is a major source of high-energy magnetospheric electrons, although, in the case under consideration, there apparently was some electron heating by transit-time damping. The role of electrostatic waves in the magnetosphere is also by no means insignificant. We shall discuss now an example of the involvement of ion acoustic waves in a phenomenon which involves 9 0620 0630 0640 0650 APRIL 18,1965, UT Figure 2. — A composite of Explorer 26 observations during the April 18, 1965 storm [after Lanzerotti et al.]. 19 both the upper atmosphere and the magnetosphere. Such ion waves can be generated in various regions of space and have indeed been observed by various investigators [Scarf et al. ; McPherson and Koons]. A theoretical treatment of electrostatic wave instabilities associated with the plasma outflow over the poles known as the polar wind has been given by [Koons et al.] and will now be reviewed. The characteristics of ion waves were analyzed in terms of plasma kinetic theory and magneto- hydrodynamics a decade ago by [Fried and Gould], The first prediction of such waves harks back to the early days of plasma physics [Tonks and Langmuir], The linearized Vlasov theory predicts damping unless rather stringent demands on currents and non-equilibrium between the charge species are satisfied. The laboratory observations [Alexeff and Neidigh] did not confirm this prediction. However, the results can be explained in terms of one-dimensional hydrodynamics. One way of self-consistent analysis is the application of quasi-linear diffusion theory as presented by [Vedenov et al., 1962]. This has been used by [Alexeff et al.] as a starting point to analyse the growth and damping properties of the observed mode. The method consists of taking the quasi-linear diffusion coefficient for resonant particles of species j, given by : •» -(f) (*)'#•«•— where k|2 is twice the mean-square magnitude of the oscillating electric field. This coefficient is then used to obtain the rate of energy absorption (power transfer) via a squared velocity moment of the diffusion equation. The absorption involved is that of plasma energy by the wave. The rate of such absorption is in turn related to the linear growth rate via the energy density. The final result is y O-fcv,) * 2 j?tn where Ct is the sound velocity and Vj the thermal velocity for particles of species j. This method was used by [Koons et al.] to analyze polar streaming phenomena. It is known that geomagnetic field lines in the polar regions are open to the tail and may even connect up to the interplanetary field. It has been shown [Axford, 1968; Banks and Holzer] that light ions in the thermal ionospheric plasma will be accelerated outward by the electric field created between the escaping electrons and the heavy oxygen ions. The flow of the light ions becomes supersonic at an altitude of a few thousand kilometres above the surface. The ion-wave instabilities are caused by relative streaming between the hydrogen and oxygen ions. The role of the electrons is not important. The theoretical analysis of [Koons et al.] involved treatment of a multicomponent plasma in which the choice of a frame of reference for the calculation of the growth rate is not obvious as in the case of a two-component plasma. The ui jdimensional hydrodynamic equations were used to obtain a dispersion relation, from which phase velocities and growth rates are found. The method is of course open to valid criticism in that it is not self-consistent in the usual sense of plasma kinetic theoiy. However, if we bear in mind the failure of linear Vlasov theory to predict ion waves as observed and the non-existence of a non-linear theory, this approach is worthy of consideration, with the above reser vations. It turns out that there are two distinct wave modes that can become unstable, one a hydrogen wave and the other associated with the oxygen ions. For typical polar ionosphere parameters, growth rates become quite large (60 sec-1) and linear hydrodynamics becomes inadequate to describe the situation. It would appear that a generalization of quasi-linear theory is in order. The plasma turns out to be so profoundly affected by the waves it generates that the linear theory breaks down very rapidly. 11 The ultimate spectrum is determined by non-linear processes including mode coupling and lies beyond the limits of our present-day theories. However, an estimate of the " frictional " coupling between the ionized components by wave-particle interactions indicates that the escape flux of the hydrogen ions is limited at about the threshold of the instability. Such a self-limiting process is typical of wave-particle interactions. 3.2 Electrons Wave-particle interactions involving outer-zone energetic electrons have aroused greater interest on the part of space-plasma physicists. [Scarf] was the firstt o suggest that the radiation-belt particles might have an effect on whistler propagation, followed by [Tidman and Jaggi]. In a thermal plasma I co ± Q I /KT\1/2 —T— M— (10) and there can be no resonant damping. Thus the approximation of low temperature is valid for such waves. However, if the plasma contains a population of highly supra-thermal particles, they can attain cyclotron resonance via Doppler shift and damp the transverse whistler mode. Thus, waves which would be expected to propagate with little or no attenuation in the magnetnsphere may be dam ped by the fast particle fluxes. These early gropings for the details of whistler mode propagation were hampered by a lack of experimental knowledge of the details of the electron distributions, in particular in regard to the aniso tropy in pitch angle. Consideration of the role of pitch-angle anisotropy leads to treatments of pitch-angle scattering by wave-particle interactions. They dealt with the results of violation of the first adiabatic invariant of outer-zone electrons by waves as a means of explaining the observed rapid untrapping of the electrons. Several mechanisms have been proposed by various workers to explain the observed lifetime and pitch-angle distributions. The earliest attempts by [Dungey, b; Cornwall, a] suggested that the lifetimes of energetic particles were determined by interactions with externally produced whistler-mode radiation, such as the atmospherics generated by lightning. Since the radiation was assumed to be excited externally, the full self-consistent fieldtheor y was not employed. The lifetimes against random- walk into the loss cone was found to be inversely proportional to the square of the whistler amplitude. Dungey found a typical scattering time of about five days for MeV electrons at L = 2.5. Cornwall, using the formalism of [Dragt] in which the variation of the square root of the action integral defined the scattering amplitude, estimated the lifetime against loss to be up to a month, with a lower limit of an hour at L = 2. It was pointed out by [Roberts, a] that there exist difficulties in obtaining cyclotron resonant scattering of electrons that mirror near the equator. Since such particles have small parallel velocities, they will have negligible Doppler shift and will resonate only with high frequency waves (SS kHz for 500 keV electrons at L = 2). This would require a flat VLF spectrum up to the cut-off at the electron cyclotron frequency, which is not observed. A falling frequency spectrum gives rise to a diffusion coefficient which is small for large pitch angles and leads to a pitch-angle distribution which is quite in disagreement with observation. The whistler mode is much more effective for particles mirroring well off the equator and if the noise band is wide enough can explain the observed lifetimes of such electrons. It is, of course, not quite correct to treat the particles as if they were interacting with a wave spectrum that fortuitously happens to exist in the magnetosphere. It is obvious that the waves and the energetic particles are intimately coupled. Any theory must involve a self-consistent kinetic treatment and give a valid description of the wave-particle interactions at least at the linear level. 12 One of the early efforts involved the interaction between stable electrostatic modes in particular, electron plasma oscillations and energetic electrons and the resultant scattering into the loss cone [Eviatar]. It is well known that if a plasma is far from thermal equilibrium, electron plasma oscilla tions can become greatly enhanced by the existence of suprathermal particle fluxes, even though the distribution is linearly stable [Tidman and Eviatar]. The waves are generated internally as the elec trostatic Cerenkov waves of fast particles passing through the thermal background plasma. The emission is reabsorbed by Landau damping which eventually leads to a steady-state spectrum deter mined by the balance between the emission and the damping. Since the waves are stable, it is possible to use the Balescu-Lenard kinetic equation to estimate the time required to scatter a " test particle " into the loss cone. The results show that such waves can be competitive with whistlers in the domain of validity of the theory. The magnetic field is ignored, which limits the validity to the outer magneto- sphere where the plasma frequency greatly exceeds the cyclotron frequency. The electron plasma oscillations, whose frequency is of the order of the electron plasma frequency, obviously violate the first adiabatic invariant. The role of whistler mode radiation was first treated in the framework of a self-consistent plasma kinetic theory by [Kennel and Petschek]. They showed that the loss-cone instability will cause the whistler mode amplitude to grow if the electron pitch-angle distribution is sufficiently anisotropic. Kennel and Petschek extended their analysis into the realm of quasi-linear theory. They were able to show that the quasi-linear velocity space diffusion which counteracts the linear growth rate is to a good approximation a pure pitch-angle diffusion. This diffusion, which monitors the aniso- tropy, tends to drive the particle distribution into a state of marginal stability. This holds for both electron whistler and ion cyclotron turbulence. The question arises as to how this idealized result relates to a finite plasma from which both particles and waves can escape. In such a case the approach to marginal stability must be understood as a steady-state diffusion equilibrium. There must be a steady replenishment of energetic particles to replace those lost through the loss cone. If ere is no such supply, there can be no regeneration of the waves that escap.. So far, the local acceleration mechanisms remain among the knottiest problems in space plasma physics. However, there must be such a mechanism operative and it is shown by Kennel and Petschek that its rate determines the magnitude of the precipitation flux and the lifetime of the trapped particles. This combination of acceleration or injection and loss maintains an effectively constant pitch-angle anisotropy. The problem of the small diffusion coefficient " of " (by whistler scattering) of particles having large equatorial pitch angles, i.e. which mirror near the equatorial plane, was studied by [Roberts and SchulzJ. They showed that particles which mirror within 5° of the equator can have bounce periods equal to the periods of magnetohydrodynamic wave modes which can exist in the magneto- sphere. Such bounue resonance can cause the second or " longitudinal " invariant to be violated. They found that a relative (to the ambient field) spectral density of 10"8 Hz-1 in the low-frequency turbulence is sufficient to supply the observed mirror-point diffusion along the line of force. Thus the scattering of particles trapped near the equator is visualized as a two-step process, whereby the particles are driven off the equator by bounce resonance and second-invariant violation into a region of equato rial pitch-angle space wherein the Kennel-Petschek whistler mode violation of the first invariant can become operative. The maximum flux of electrons that can be trapped stably is independent of the acceleration rate. Electrons which have high enough energies to resonate accumulate until the enhanced aniso tropy turns on the whistlers, which then proceed to scatter particles into the loss cone. Any further acceleration u. injection merely feeds more panicles into the precipitation flux. Kennel and Petschek calculated this limiting trapped flux by equating the wave growth rate to the rate of escape of the waves. The result compares fairly well with observations, although a few points remain unclear. In general, the trapped flux will be near the critical value wherever the acceleration is continuous and below i' 13 wherever the acceleration is sporadic. The observation that the observed fluxes are close to marginal stability implies that there exists an injection source which maintains the precipitation flux and the whistler mode amplitude. The nature of this acceleration is the major unsolved problem in space plasma physics. Very little has been done to investigate the nature of the local acceleration mechanism called for by observations [Frank, a]. One cf the pioneering efforts along this line is due to [Hasegawa, b]. Since the energy must come from the sun via the solar wind, Hasegawa proposes, as an acceleration mechanism, that the particles suffer a resonant interaction with electromagnetic waves which propa gate in from the magnetosheath. The generation of the waves is not considered in Hasegawa's model. Since the waves are driven by the solar wind they are regarded as propagating in the solar-wind direction. In the dayside equatorial magnetosphere, this amounts to propagation normal to the field lines. There are a few spécifie frequencies at which the wave will resonate with a cold plasma: m = k II «|| ± nil cyclotron frequencies V + Q\) \ co1 Q2 \* | hybrid frequencies <"»» = I Transit-time damping is not considered in this context since its major effect is to fill the loss cone. The above frequencies are the zeroes and singularities of the refractive index for perpendicular propagation in a cold plasma [Stix]. The dispersion diagram (Figure 3) shows three main pass bands. The narrowest band is band 2, whose width is proportional to the ratio of the electron cyclotron and plasma frequencies. Such a wave will not propagate far into the magnetosphere and will be reflected before it encounters any of the electron cyclotron harmonics. Therefore it will not be an important heating mechanism in the outer magnetosphere. The high-frequency band (band 3) undergoes a discontinuous change at the plasmapause where the cold plasma density increases sharply. Such a wave will be cut off, but it may tunnel through to band 2 and then suffer a hybrid resonance. Both bands 1 and 3 can and will encounter cyclotron resonance. The rate of dissipation of wave energy can be found by use of the plasma conductivity tensor and spectral density. It is found that under usual magnetosphere conditions, i.e. moderate anisotropy of a bi-maxwellian hot plasma, the absorption of these waves will be at the cyclotron harmonics. The power dissipated can be found by summing over these resonances and is to be equated to the energy gain of the particles. Hasegawa used observed electric field amplitudes and found the storm-time proton acceleration rate to be about 500 eV/sec and the quiet-time rate to be about 100 eV/h. However, these numbers, as well as the entire calculation, should not be taken too seriously for a variety of reasons. 1) We now have reason to believe that the proton temperature is much higher than previously accepted values and the assumption of zero temperature becomes suspect. 2) The damping increases the perpendicular energy and drives the plasma loss cone unstable. Thus energy will begin to be fed back to the waves, which will limit the attainable anisotropy. The main conclusion that can be drawn is the qualitative one that protons can be heated by cyclotron resonance more readily than electrons. Hasegawa finds that electrons can be heated within 100 km of the plasmapause by the tunnelling wave mentioned above which is cut off by the upper hybrid resonance. A rough estimate leads to a heating rate of about 60 eV/sec. 14 Z a)R=l/2(ile*(Û|'4wÊe)" ) + /Z wL=l/2(-Û8*(Jl! 4Wpe)' ) l/2 WuH=(il|+oj2e) _/n2 fa)P|^e\ Figure 3. — The dispersion diagram for propagation normal to a magnetic field in a zero temperature plasma [after Hasegawa]. This calculation is at the most primitive level of treatment of wave-particle interactions. It is a sad commentary on the state of magnetospheris plasma physics that this is one of the most sophisti cated treatments of the problem of local acceleration. 4. SUMMARY As we have seen, the theoretical understanding of the role of plasma waves and their interaction with particles in the magnetosphere is still in its infancy, although over 13 years have passed since the 15 advent of scientific satellites. Some small progress has been made, but there still remain several basic problems whose solution lies in the future : 1) The nature of the acceleration mechanism of the radiation belt particles is unclear. 2) The relative importance of pitch-angle scattering vs. radial diffusion in the repopulation of the belts after precipitation events remains in doubt. 3) We still lack a good non-linear theory of plasma turbulence which will include mode coupling and wave-particle interactions. Some promising starts have been made in that direction and it is to be hoped that new breakthroughs in plasma turbulence theory will lead to greater understanding of the plasma and particle physics of the Magnetosphere. DISCUSSION G. Haerendel. You mentioned a recent theory according to which the diffusion coefficient of particles is proportional to the growth rate of the waves generated by the particles in an instability process. What is the basis of this theory? Is it not necessary to consider the fate of the wave, i.e. whether it is damped by interaction with another particle component or not? It is the wave's amplitude that determines the diffusion. A. Eviatar. / was referring to the diffusion coefficient as found in a paper by Bernstein and Klotzenberg which was published in the " Journal of Plasma Physics " last year. It is called " A new derivation of quasi linear theory ".. They come up with a diffusion coefficient which is proportional to the growth rate. Recall that mode-coupling which must determine the ultimate fate of the wave is ignored in quasi linear theory. This is precisely what was criticised by Montgomery and Vahala, also in the " Journal of Plasma Physics ". In the past year, there has been a bit of almost acrimonious discussion on what happens to quasi linear theory, when you start looking at it very closely. I think it is true that quasi linear theory in principle cannot give you the whole answer. I believe I mentioned that one of its greatest failings is that, like all finite-order perturbation theories, it is subject to secularities and if you let it run long enough it too breaks down, leading to an unphysical result. As I said, if you try to explain your experiments with it, you may find results that indeed lead to difficulties. Quasi linear theory is now enjoying a vogue similar to that which linear theory enjoyed in 1956-1960. It is our hope that by 1975 we will have something better. 16 A THEORY OF VLF EMISSIONS D. Nunn Imperial College, London ABSTRACT The work attempts a theoretical explanation of the phenomenon of artificially triggered VLF emissions. First, resonant particle trajectories in a narrow-band whistler wave in an inhomogeneous medium are studied. It is found that second-order resonant particles become stably trapped in the wave. After one or two trapping periods, these particles can make a dominant contribution to the resonant particle current. A realistic zero-order distribution function is selected, involving a source of potential energy in the form of a loss cone. The resonant-particle currents are computed for the case of a constant-amplitude whistler crossing the magnetospheric equator. The results tend to explain many of the features of triggering. The equations governing the time development of the wave field due to the presence of a resonant-particle current are developed. Resonant-particle currents are computed for various generation region type field configurations. These results enable the problem of a self-consistent description of a generation region to be discussed. 1. INTRODUCTION This work is a theoretical study of the artificial triggering of VLF emissions by whistler morse pulses in the Magnetosphere. This fascinating phenomenon has been well documented [Helliwell, a, b] and the interested reader is referred to the literature. We will however point out several essential features of the process which a correct theory should be able to explain. Triggering tends to be confined to cases in which the morse frequency is about 0.5 times the equatorial gyrofrequency along the path of propagation. There is a definite delay—about 70 ms— between the front of the morse pulse and the start of the emission. The emission itself has an ampli tude typically 2-5 times that of the incident morse pulse, and often starts at a frequency 100-300 Hz higher. The "fully-developed emission usually exhibits a steadily rising or falling frequency, and " hook like " forms are not uncommon. 2. SETTING UP THE PROBLEM Ground-observed whistlers are believed to travel along a magnetospheric field line in a ducted mode [Helliwell, a, b]. The field-aligned density gradients guide the phase fronts of the wave in such a way that the wave vector k is nearly always parallel to the magnetic field. We thus assume that the 17 whistler morse pulse and the emission together form a continuous narrow-band wave train in which k is always parallel to B. When we come to give a more exact description of the emission process, it may be necessary to take into account effects such as Landau damping that result from the fact that k is not everywhere exactly parallel to B. As the wavetrain crosses the magnetospheric equator, energetic radiation-belt particles become cyclotron resonant with the wave, and give rise to resonant particle currents. Our task is to compute such currents and show that they modify the wave field in such a way as to produce emissions of the kind observed. 3. RESONANT-PARTICLE BEHAVIOUR The first task is to examine the behaviour of resonant particles in a whistler wave when the medium is inhomogeneous. Helliwell pointed out that resonant particles will tend to get quickly forced out of resonance because the resonance velocity will be changing. Using the usual notation, we have for the resonance velocity : V,a = (m-Q)/k • (1) A resonant particle will see a time variation in Si and k because of the inhomogeneity of the magnetic field, and in the field of an emission there will be a steady change in m. Thus we may write : d /. 3Q \ dk (2) We also have for the rate of change of velocity along the Bo direction : 2 dVz |V±| 3B eEk , , -^ = —-Lr±r^ Vx cosP (3) dt 2B 3z mm ' ' where |Vj is the perpendicular velocity of the particle and P is the phase angle between Vx and the electric field of the wave. We are particularly interested in particles which instantaneously satisfy the second-order resonance condition : ^Vz = ^Vr„ ; Vz = V„, (4) Such particles will clearly be able to stay in resonance with the wave for appreciable periods, and will thus play a dominant role. Substituting express::,is (2) and (3), we get : — A-CIVJ2 C0SP- |vj (5) where the coefficients A and C are related to the gradients in the system : , 3B/3z . 3(o/3/ A = a —r=j ha* |E| |E| 3B/3z C=a" |E| 18 0' Figure 1. — Some examples of second-order resonance lines for various values of the coefficients A and C. At a fixed time and place then, the second-order resonance condition is satisfied along a line in velocity space. The line lies in the Vx plane at Vz = V„, and the relationship between relative phase P and lvil («I- 5) is determined by A and C. It is interesting to note that if the magnetic field gradient is very large or the wave amplitude very weak, it will be impossible to satisfy (eq. 5) and there will be no second-order resonant particles. Some examples of second-order resonance lines are shown in Figure 1, using various values for A and C. We now pose the question : Supposing we take one of these second-order resonant particles and follow its trajectory, does it stay in resonance ? The appropriate analysis of the equations of motion is done in a published paper JNunn]. The key result is as follows : in an inhomogeneous medium, second-order resonant particles become stably trapped in the wave, just as in the homogeneous problem. In velocity space, such particles circulate around the instantaneous second-order resonance line, making a kind of ellipse in the coordinates P and Vz. The kind of motion is illustrated in Figure 2, where again P is the relative phase between \x and E. Another example is shown in Figure 3, which illustrates the time variation of relative phase P and pitch angle for a stably trapped particle. In an inhomogeneous medium trapped particles maintain an average relative phase P which is not ± TI/2 19 Figure 2. — Trajectories of stably trapped particles showing oscillations about the resonance line. The wave electric field is assumed to be in the x direction. The trajectories shown are the limiting ones, and the volume they enclose is the resonant particle trap. fj*n 1.190° Figure 3. — Computed examples of the time variation of relative phase P and pitch-angle a„ for stably trapped particles. The curves are two separate examples of the resonance line. 20 as in the homogeneous case, and as a consequence they undergo considerable changes in energy and magnetic moment. This can be seen in Figure 3, as a steady change in the particle's pitch angle. It is seen from Figure 2 that trapped particles oscillate about the left-hand branch of the second- order resonance line. It may be shown that if a particle goes beyond the right-hand branch of the resonance line, it will fall out of resonance. At any given point, we may now construct the region in velocity space that will be occupied by stably-trapped particles. One takes the second-order resonance line as defined by the local gradients, and constructs the set of limiting trajectories that just touch the right-hand branch of the resonance curve. The resultant surface encloses the trapping region in velocity space. A cross-section of the resonant particle trap for a particular case is shown in Figure 4. This illustrates the manner in v/hich the geometry of the particle trap depends upon the second-order reso nance line. It is important to note that this fairly simple picture of trapping behaviour is only valid if the resonance line itself— and thus the wave parameters —, is a slowly varying function of time as compa red to a trapping period. If this criterion is not met, resonant-particle behaviour will be infinitely more complex. ->—(- PARTICLE TRAJECTORIES Figure 4. — Cross-section of the resonant particle trap in the Vz = V„ plane for a particular form of the resonance line (a = 0.5; Ç/R = — 0.45, n/R = 0.6). The actual trap size is usually less than the theoretical maximum as particles near the outer edge of the trap are invariably lost. 21 If the wave parameters are in fact slowly varying, it is possible to obtain a good deal of infor mation about the resonant-particle current without doing a complete computation. Trapped particles which have ueen in resonance with the wave for long periods will be found in regions of velocity space that are determined by the local gradients at that point. This enables one to make a good estimate of the very large contribution to the resonant-particle current which comes from stably trapped particles. 4. COMPUTATION OF THE RESONANT-PARTICLE CURRENT The component of resonant-particle current perpendicular to the B direction is obtained by inte grating the resonant-particle distribution function over the whole of velocity space in the neighbourhood of the resonance velocity. 3 Ji = -e|(F„,-F0)Virf V (6) Here F0 (W, p) is the unperturbed energetic-particle distribution function, and is conveniently taken to be a function of energy W and magnetic moment only ((J.). Each point in the integration represents a particle. If SW, Sp. are the changes in energy and magnetic moment undergone by the particle as a result of interaction with the wave field,the n we may write, using Liouvilles theorem : 3F„ 9F0 • Clearly, in equation (6; the greatest contribution to J± will come from stably trapped particles for which S[i, SW are relatively large. Note however that stably trapped particles will only dominate the integral if they have been trapped for at least two trapping periods. It is not possible to compute the resonant-particle current without first specifying F0, and the results obtained will depend entirely upon the choice for F0. For example, a purely thermal-type distribution function for F0 will be found to give only wave damping. To obtain the growth rates necessary for triggering instability, one needs a source of potential energy in the form of a pitch-angle anisotropy or loss-cone distribution function. 5. THE INITIAL RESONANT PARTICLE CURRENTS IN THE WHISTLER PULSE We now enquire what are the currents which first appear in the whistler morse pulse when it enters the equatorial zone. These will obviously tell us when and how triggering is initiated. One assumes that the ambient magnetic variation has a parabolic variation with position 2 B = B0(l+I„z ) where z is the distance from the equator measured along the fieldlin e (2 it units equal one wavelength). The wave field is taken to be that of the unmodified morse pulse, and has a constant amplitude and a frequency fixed at onë-half the equatorial gyrofrequency. The zero-order distribution function F„ 22 Figure 5. — The zero-order distribution function F0 as a function of equatorial Vz and VL. used for the computations is shown in Figure 5, and is of the loss-cone type combined with an overall fall-off with energy as E"2. Using a variety of wave amplitudes the resonant-particle current is computed as a function of position, using the CDC 6600. On the graphs, the component of current in-phase with the wave electric field (Jr) and the reactive component of current (Ji) are plotted. The units of current are chosen such that at R = 0.00001, }r = 1 gives the ordinary linear growth rate for the distribution function chosen. Figure 6 plots the currents Jr, Ji for a fairly large amplitude field R = e Efc/mw2 = 0.00002 This corresponds to a wave electric field at the equator of 100 u.V/m, and to a full trapping period of about 20 ms. At these amplitudes, second-order resonant particles are stably trapped in the wave for several trapping periods, and the current is almost entirely due to these trapped particles. Most of the features of the graph are readily understandable. For \z\ > 8000, the gradient in magnetic field is sufficiently strong for second-order resonance to be forbidden, and Jx is conse quently small. At z = 8000, particles become stably trapped. The relative phase of trapping is at first P ~ 0, and the current is antiphase to the electric field at this point. As the equator is approached, the centre of the particle trap moves toPa — n/2, which explains the pronounced peak in Ji. At the equator phase, organisation of the trapped particles ceases, and the current falls to low levels but on the other side of the equator retrapping takes place to give a new peak in Jr and a generally positive component of Ji. 23 R= 0-00002 1=0 Figure 6. — The in-phase current 3r and reactive current 3i as a function of position for a pulse of constant amplitude and frequency. R =0-000005 Ï-0 -6000 Figure 7. — Computed currents for the intermediate amplitude case. Figure 7 is a similar plot for the case R = 0.000005, at which amplitude trapped particles do not dominate the current. However, the form of the curves is still similar to that of Figure 6. Figure 8 shows Jr, U for the case R — 0.0000005. This is the weak-amplitude case, when the equatorial E fieldi s about I pV/m, and the full trapping period is about 200 ms. Stable trapping does not occur and the currents are more or less locally generated. Note the completely different charac ter of the current curves, and that now there is only a single peak in Jr. 24 J Figure 8. — Currents computed in a weak-amplitude pulse. 6. TIME DEVELOPMENT OF THE WAVE FIELD We must now develop the equations which show how the whistler wave field is modified by the resonant-particle currents of the kind we have been considering. For simplicity, we suppose that the ambient plasma is of constant density, and that the magnetic field is constant. It is reasonable to suppose that the inhomogeneities in the system are only important as far as resonant-particle behaviour is concerned. The governing equations are Maxwell's equations and the equation of motion of the cold plasma particles. Neglecting the displacement current, these reduce to a single differential equation giving the time development of the wave electric field in terms of the resonant-particle current. r a2 / a \ /72 a i A 4 * / a \ a A Li?(-a7-/i2)-c^irJE^^(ir-/fi)irJi (7) A Here E± is the perpendicular electric field vector ; Ex = E* + iEy A and Ji is the resonant-particle current ; Jx = Sx + iiy At any given time the wave field will have a fast phase variation at a frequency CÙ0 say, and corres ponding wavelength k0. This rapid variation may be factored out, and we deal with slowly varying complex amplitudes s, and J. 25 ,| ,I E±= îe- ' """l (8) JL = J e-'Co—or, (9) Here of course k0, u0 satisfy the dispersion relation. 2 2 k%{Q — We assume that e and ï are slowly varying compared to the wave frequency. d? at We substitute eqs (8) and (9) into eq (7), and neglecting small terms obtain + Vg CS 2 2 2 (10) L-3T ^-] ii + fc c I This is a particularly simple equation and merely says that the current 2 generates a complex field s which is adverted away at the group velocity. We now divide s into an amplitude and a phase factor : s = |e| e* The current J is expressed in terms of the in-phase component Jr and reactive component Ji : Ï = Or + OO & Substituting again we finally obtain 3 d\i_i 4m» ( As expected, the rate of growth of field amplitude is directly proportional to the in-phase component of the resonant-particle current. An observer at a given point will see a rate of change of wave number k given by the expression 3k d 3 As we know, a generation region of the Helliwell type admits of solutions in which k, and thus wave frequency, steadily change. In such a case, it is necessary to redefine the quantities k0, <•>„ as often as is necessary to ensure that e, "S in fact remain slowly varying. 7. THE TRIGGERING PHASE The initial time development of the field is found by putting the currents Jr, Ji, computed in the constant-amplitude morse pulse, into the expressions (11) and (12). The strong morse pulse will show two distinct regions of large growth, one on either side of the equator. Either or both of these may develop into a self-sustaining generation region of the 26 Helliwell type, provided that the growth rates are sufficiently great. We shall see that a negative value for Ji in a generation region will cause the wave frequency to rise and vice versa. Thus the region of growth on the downstream side of the equator corresponds to the riser, and that on the upstream side to the faller. The weaker morse pulse only exhibits a single peak in ir accompanied by a positive ii, which suggests that these should only trigger fallers. There is a good deal of observational evidence to suggest that this is in fact the case. Figure 9 shows the maximum growth rates in the rising and falling zones as a function of morse amplitude R. It is seen that ir (max) remains roughly proportional to R over a wide range of amplitudes. Since wave-energy losses due to Landau damping and leakage from the duct are also AMPLITUDE Figure 9. — Maximum initial in-phase current ir in both rising and falling zones as a function of morse amplitude R. proportional to R, this graph suggests that triggering is just as feasible for weak amplitude signals as for strong. Thus there is nothing surprising about the fact that Omega pulses are able to trigger. It might have been expected that the growth rates would increase very rapidly above R = 0.000005, when stable trapping becomes possible. That this is not the case is due to the fact that the field varia tion is parabolic and not linear. The. time delay in the production of a triggered emission is readily explained. The currents in Figure 6, for example, arise as a result of particles interacting with the wave over a distance of about 1000 wavelengths. A resonant particle takes about 60 ms to traverse this distance and it will take about this time for the maximum currents to build up. Another factor is that there is an upper limit to the linear growth rate in the system, in order that the system shall not be absolutely unstable to whistler turbulence [Kennel and Petschek], One thus expects there to be an upper limit also to the non-linear growth rate experienced by the whistler morse pulse. There is nothing in the theory of wave-particle interactions to favour triggering at one-half the equatorial gyrofrequency. The f"'t that such a frequency is favoured is almost certainly a propa gation effect. Helliwell has suggested that ducting is most effective at this frequency, when loss of wave energy from the duct and Landau damping will be at a minimum. 27 J -10- R \lr \.-ooooi /-8- JC-2-I0"9 \-6 R •S^QOOZ -«• Vi -2 •00001- -6000 \ W / -2000 E Q 2000 «000 z 2- 4. Figure 10. — Currents computed in a Helliwell-type generation region with a rising frequency. X f =-000001 7C= MO-9 Figure 11. — Currents computed in a large-amplitude faller. £.-0.00001 Figure 12. — Current fields for a weak-amplitude faller. 8. LONG TIME DEVELOPMENT OF THE WAVE FIELD The continued development of the wave field and the production of a Helliwell-type generation region is a difficult problem in self-consistent wave-particle theory. It is really necessary to do a numerical time integration of eqs. (11) and (12), computing the resonant-particle current at each step. However, each computation of current takes 600 sees on the CDC 6600 and this approach is not prac ticable at present. One must try to understand qualitatively what happens. One of the most difficult aspects of the problem is the phase behaviour and the fact that the frequency of the emission changes steadily. Two important properties of the resonant-particle current make it possible for this to happen. In the strong pulse, the current arises from a beam of particles that have interacted with the wave over an appreciable distance. This current is slow to respond to quick changes in wave amplitude or phase, and owing to the inertia of the beam particles the wavelength of the current can only vary slowly. Indeed, if a beam is travelling into a region of decreasing wave amplitude, it will become almost independent of the wave field and any distinct phase relationship between the electric field and the current will tend to disappear. In the case of weak amplitude pulses, the current tends to be more locally generated and the phase relationship between J and E is much more rigid. Another important property of resonant-particle currents that distinguishes them from those due to cold particles, say, is that at a given place they are not time proportional to the wave amplitude, in other words, the wave field appears first and the currents may appear afterwards. Inspection of equation (12) reveals that if the resonant-particle current J has its phase tied to that of the electric field (as for weak-amplitude signals) then the overall time variation of phase One curious phenomenon associated with the early development of the wave field is the offset frequency. The morse field and that of the emission at a slightly higher frequency form a wave train with a beating amplitude. When resonant particles see this beating at the trapping frequency, trapped particles will resonate and be thrown out of resonance. There will then be a choking effect at this point. A full understanding of this problem will really require a full time integration. 9. THE GENERATION REGION The initial development of the wave field is very difficult to follow because of the rapid variation of parameters which takes place. However, once triggering has taken place the wave train settles down into a fairly stable configuration of the " generation region type ", with a roughly time-inde pendent wave profile and a steady rate of change of frequency. An obvious line of attack is to attempt a self-consistent wave-particle description of a stable generating region. The first task is to have a look at the currents which appear in a field approximating that which might be found in a generating region. The wave amplitude is taken to fall off upstream in a Gaussian fashion, and the location of the g.r. is made to coincide more or less with the known peak in growth rate Or). Wave frequency is assumed to be independent of position and to have a linear variation with time, the rate of change being chosen to be a typically observed value. The wavelength 29 is taken to be that which satisfies the local dispersion relation. The first deficiency in such a field is that little is known about the actual profile, and in any case it will not be exactly time independent. However it turns out that the exact details of the amplitude profile do not seem significant as far as the current is concerned. Also, the wavelength as a function of position will not be exactly as we have chosen it, and there will be some additional phase variations caused by Si. However our choice of field should tell us about the overall characteristics of the trapped-particle beam. Figure 10 shows the currents computed in a g.r. with exit amplitude R = 0.00002, and in which the frequency rises at a realistic rate : ç = —v3(ol3t- = o.ooooi or Note that the beam of stably trapped particles is again in evidence. There is now only a single peak in Jr located at the equator, with a pronounced peak in Ji at about z = — 2000. Note that at about z < — 2000 the wave field loses control of the trapped-particle beam, which then spirals freely, in fact undergoing a wavelength shift at its far end. Figure 11 shows the current field for the large-amplitude faller. Here Ji is positive at the upstream end. An interesting point is the secondary peak in Jr accompanied by negative Ji that exists downstream. These are the current fields appropriate to a riser, and if for instance the wave profile of a faller were to slowly sUp downstream, it could turn into a riser. Figure 12 is the case of the weak- ampiitudf. faller. The peak in Jr is upstream of the position predicted by Helliweil, and there is an overall positive Ji. The weak riser case is shown in Figure 13. Here the peak in Jr is well away from the equator, but note that Ji is also positive for this field. • $=0.00001 Figure 13. — Current fields computed for the case of a weak-amplitude riser. In the strong amplitude case, the in-phase component Jr will be a complex function of R, z, and rate of change of frequency (•; The dependence is illustrated in Figure 14, which plots y* on a z, Ç diagram for R = 0.00002. The quantity y* gives the growth rate to be expected from stably trapped particles Only. The whole y* pattern is linearly proportional to R along both axes. The 30 Figure 14. — Plot of y*, the estimated growth rate due to second-order resonant particles only: it is shown as a function of position z* and rate of change of wave frequency Ç*. blank regions on the graph are where second-order resonance is forbidden. The area labelled "rising zone " is where Si is negative, and the " falling zone " is where Ji is positive. The graph confirms that when stably trapped particles dominate, the maximum growth rate occurs at the equator for rising or falling frequencies, the optimum ratio being £/R = O.S. To achieve a self-consistent picture of a generation region we must first satisfy eq. (11). We note first that it is not physically realistic to suppose that the duct is completely lossless and free of Landau damping. In practice, there will be a substantial loss of energy from the duct, but the rate of this will be difficult to estimate. For a time-independent profile we may write eq. (11) as : The frequency behaviour of the entire g.r. will be controlled from the furthest point upstream at which the phase of the resonant-particle current is still effectively controlled by the wave field. For the large amplitude pulses, this will be where the field amplitude is about half the exit amplitude, but for the weaker pulses this will probably be nearer the tip. At this point, we may ignore the term in dfc/dz 31 and obtain a steady rate of change in wave number. The corresponding rate of change of frequency is then : 3o> 4i:Vgm0(a-w0) p 3 1 1T= (IÏ' + JÇC») Ll7a'/|6|)Jcp Consulting Figure 10 we see that û will be clearly positive provided the field is controlled from a posi tion z > — 2000. For self-consistency, clearly the rate of rise of frequency of the wave fieldactuall y caused by the current field must match that originally assumed in computing those currents. For the large amplitude faller, we see that fortunately à < 0 provided the control point lies between z=—1000 and z = — 3000. Similarly, the weak-amplitude faller shows (i < 0 for a control point at z < — 2000. Note that the currents computed in a weak-amplitude riser are not of a kind to make the frequency rise and thus a self-consistent picture in this case does not seem possible. Note that for self-consistency we must satisfy a complex series of interrelating equations. The rate of change of frequency depends strongly on Ji'andlessstronglyon|e|. The amplitude behaviour depends on Jr. Both currents, Jr and J(, are themselves strong functions of both amplitude and &. Observal>nil evidence seems to point to some kind of stability about the equilibrium condition, as amplitude and ù seem to remain quite stable during an emission. Phenomena such as hooks may presumably be interpreted as being the result of a déstabilisation of the g.r. and its rapid change to a more stable configuration. The present attempt to predict the nature of solutions to eqs. (11) and (12) is obviously rather unsatisfactory. A full understanding «11 only be obtained when numerical solutions to these equa tions are done, either using various trial prescriptions for the current or perhaps computing it in full. * See also [Abdalla; Stix]. DISCUSSION J. Rycroft. Can you produce a discrete emission in a frequency band 0J - 5 kHz with an input of, say, white noise over that frequency band? D. Nunn. No. Up to now, I have been working only with narrow-band signals around 15 kHz. I would consider the broad-band problem much easier as particle trapping does not take place, and the wave spectrum will merely grow at the linear growth rate. K. Schindler. If I understand you correctly, in your trapped-particle study you try to approach self- consistency by recomputing the magnetic field from your current and then compute the current again. I wonder how close you can get to self-consistency by this method with a reasonable effort of computation. D. Nunn. It takes a great deal of computation. Everv determination of the current field takes at least 600 sees pn the CDC 6 600. To do a tone integration of the fields is thus too costly. One possibility is to write a program to compute J very roughly (in say 50 sees) and then to time integrate the field. The resulting solution would then be self-consistent. Another possibility is to devise an analytic prescription for the current which embodies the essential features and then to time integrate the wave field. 32 K. Scbindler. // seems to be essential for a wave-particle >.. Ion phenomenon to really have a self-consistent solution. What is your justification then for believing these results? 1 realize of course that it is a very difficult problem and that a self-consistent solution is frequently just not available... but would you agree that there is still a gap ? D. Nann. Certainly. A lot of work remains to achieve self-consistency. I think though that the self-consistent problem is not as "pathological " as, for example, in the magnetotail... This is because the fields generated by the currents propagate out of the region of interest. G. Martelli. I notice that you have taken a parabolic variation for the magnetic field, using an appropriate expansion parameter. What assumptions have you made for the plasma density variation along a field line? Have you assumed a cold plasma approximation over the interaction region? D. Nunn. / have assumed that the cold plasma density is proportional to Bo. If one looks at the various terms in the second-order resonance condition, it turns out that the variation in cold plasma density is not very significant. So results will change slightly with different density models but not very much. 33 INTERACTIONS BETWEEN MONOCHROMATIC WAVES AND PARTICLES G. Laval, R. Pellat and A. Roux Section " Théorie des gaz ionisés ", Commissariat à l'Energie Atomique, Fontenay-aux-Roses, France ABSTRACT Many authors and especially Helliwell have reported that morse signals emitted from the ground in the VLF range can trigger new monochromatic signals, with a rapidly varying frequency, and a quasi constant amplitude. We will review previous theoretical interpretation of these artificially stimulated emissions (A.S.E.) and propose a new interpretation. We have studied analytically the trajectories of particles which go through the wave packet (morse signals) and deduced the distribution inside and behind the wave packet from their initial distribution function. Resonant particles remain trapped inside the wave packet during a short time because they travel in the opposite direction; when de-trapped, they give rise to a beam which can act coherently for a while. This beam, organized by the initial wave, will constrain the plasma to emit a wave satisfying the same resonance condition in a homogeneous medium, that is, a wave of same to andk. Then the length of the wave packet is growing. New particles meet this wave pocket, and lengthen it by the same mechanism, and so on. But in the inhomogeneous magnetospheric medium, one can obtain a varying frequency, the variation of which is directly related to the inhomogeneity. It has to be noted that this large frequency variation is due to free particles, moving in the inhomogeneous static field; conversely, trapped particles (inside the wave) cannot generate a frequency which differs from the initial one by more than the trapping fre quency (which is very low). The new frequency and wave number must satisfy simultaneously the dispersion relation and the reso nance condition; this is more easily satisfied when phase and group velocity are equal, providing a new interpretation to the fact that A.S.E. arc more likely observed at half the equatorial gyrofrequency. If the adiabatic force p. 3B/dz overcomes the trapping force, the resonant particles may be de-trapped before they have completely crossed the wave packet, so that A.S.E. can begin before the end of the initial wave packet. The triggered modes may be amplified by cyclotron instability when they propagate towards the Earth. The non linear saturation of this instability (due to the trapping of particles inside the triggered wave) occurs when the trapping frequency (which is proportional to the square root of the wave amplitude) is equal to the linear increment of the involved frequency. This non linear saturation is reached rapidly because at these high frequencies (z. half the equatorial gyrofrequency), the linear increment is relatively low. From this we can understand the quasi constant amplitude of the triggered modes. 35 QUASI LINEAR CALCULATION OF VLF HISS SPECTRUM J. Etcheto, A. Roux, R.P. Singh and J. Solomon* Groupe de Recherches Ionosphériques, Saint-Maur-des-Fossés, France ABSTRACT In this work, we assume that emission of VLF waves is the result of a cyclotron interaction of energetic electrons with the whistler mode. If the wave frequencies are much smaller than the electron gyrofrequen- cy, we can neglect energy diffusion for the particles. In this case, the distribution function of the ener getic electrons and the wave magnetic field have to satisfy the coupled equations of pitch-angle diffusion and wave energy conservation. We consider the steady-state case and we assume that a given aniso tropic source of particles maintains a constant anisotropic distribution function of energetic electrons. We take into account the inhomogeneity of the medium and we calculate the equilibrium spectrum of the waves for different values of the anisotropy and of the mean velocity of the energetic electrons of the source. This case is applicable to continuous emissions of low level VLF hiss associated with continuous electron precipitation. The spectra which are obtained are similar to the ones recently measured by OGO 3 and Ariel 3. 1. INTRODUCTION We consider here the steady-state diffusion case like in the Kennel and Petschek's work but we take into account the inhomogeneity of the medium and instead of computing the limiting flux of the trapped particles, we focuse our attention on the VLF spectrum of the waves. We assume that the emission of these VLF waves is the result of a cyclotron interaction between the energetic electrons and the whistler mode. We neglect the energy diffusion for the particles and we consider waves propagating parallel to the Earth magnetic field. 2. EQUATIONS As we consider an inhomogeneous medium we use, as variables, a — ^-5—"Î , a quantity pro- portional to the first adiabatic invariant and D = (»j| -f- D*)1'2 the total velocity of the particles ; Bj. and I),, are the velocities of the particles respectively perpendicular and parallel to the Earth static * Communication presented at Orléans by J. Solomon. 37 magnetic field B0. We can then write the diffusion equation in pitch-angle and the wave energy conservation equation under the following forms : •+ &=*>*• -5--^ ^Sr^ * l*"-*] + s(""° (1) , «tf B0 r r+- 3F i m* A LJo 3/t JB|| = C yt is the growthrate of the cyclotron instability (the integration has to be performed with 2 o,, = J v — 2 [i B0 = ronstauf). F (», [i, z, 0 is the distribution function of the particles. B0 (z) is the Earth static magnetic field and z the distance along B0 from the equator. B£ (z) is the spectral density of the wave energy per wave number k. S (», |i) is the source term ; qe and me are the charge and the mass of the electron ; \g is the group velocity of the waves. 9 F 3 B2 Now we consider the steady-state case and the terms -5- and -=-i- disappear in (1) and (2). oi at We can then integrate the coupled equations (1) and (2) and so obtain an expression which connects the wave energy density B* (zt) getting out of the amplifying zone, and the source term S. The principle for this integration is the same as the one that two of us used for computing the final spectrum of the waves in the relaxation case [Roux and Solomon]. We suppose that the amplifying zone extends symmetrically around the equator between zt and — zt. We obtain the following expression : . . 2* r" BÎ r r+- / f'w sfr.nW \ 1 (ri) The indexes v and v„ indicate that integrations have to be performed respectively with v and vn constant. R is the reflexion coefficient for the waves at the end of the line of force. In order to per form the integration in (4), we suppose that n0/B0 is constant, n0 being the cold plasma density and B0 a dipolar field. In fact, we take B„(z) = B0e [l + 1 -L-j (5) r0 being the distance from the Earth centre to the furthest point of the line of force and B0c the value of the field at the equator for a given L value. We also take for the source : •«•••-HSSH-S»" where » is the usual pitch angle of the particles ; p0 is connected to the mean velocity of the energetic particles ; K (m) is a normalization coefficient so that : f" f+c0 n 1 2jt I sin arfa | »2S(a,u)do = — — (7) Jo Jo no *L The parameter m gives the anisotropy of the source ; ^ is the density of the trapped energetic electrons (energy E > 40 keV) and TL is the life time of these energetic particles, as defined by Kennel and Petschek. 38 3. NUMERICAL RESULTS We have done computations by using (4) and we have taken the following experimental values 3 8 3 for the densities and the life time for L =: 5 : n, =; 10*m~ ; n0 = 10 m" ; TL ~ \0*s [Hess]. In (4) we have choosen z, so that BÔ' (zj =; 2 B0-e. This value of z, corresponds roughly to the region where the growthrate ft vanishes. \ORM.\LIZH) IRUJLIMT I Figure 1. — Normalized frequency (flf„). The first result obtained is that the wave spectra depend very little on the source anisotropy. On the Figure 1, we have plotted spectra of the wave magnetic field versus frequency/norma lized to the equatorial gyrofrequency/^o for two values of the mean energy of the energetic electrons. We notice that the frequency of the maximum of the spectra depends very much on this mean energy, as expected. On the Figure 2 we compare two spectra computed with the same values of the parameters but one (solid line) in an inhomogeneous medium and the other (dashed line) in a homogeneous medium. In the case of the inhomogeneous medium where B0 (z) increases with z from the equator we get a spectrum displaced towards higher frequencies. This is roughly due to the fact that the electron gyro- k v frequency f increases with z ; therefore the resonance condition/„ = f + -=-**• which has to be satis ce 2n fied, gives rise to higher frequencies. 39 a* r / i 7 \\ i / ^ \ i / ^ \ i / v \ i // ^\ \ \ i \ \ i \ \ t I \ \ i 1 \ \ i I \ \ i a*' i l - . r 1 1 1 1 1 1 T T _I_J 1 < 1 | I-J_1.|J ^ VlHMALIZLD (;BtOUHNfY ir/f l Figure 2. Finally, we notice that the spectra so obtained roughly agree with the observations both in spectral shape and in intensity [Russel et al, a; Roberts, b]. Furthermore all the spectra computed here are decreasing towards higher frequencies approxi mately like f'2. This is in agreement with observation of VLF spectra obtained on Ariel 3 [T.R. Kaiser; private communication]. In conclusion, we would say that to carry.on this theory, it would be interesting to get satellite measurements of VLF spectra correlated with measurements of sources or distribution function of the energetic electrons. DISCUSSION 3. ."roughton. Could you give some more Indications on the effect of varying anisotropic sources on the spectrum of waves? You said you have a given anisotropic source of particles. How does the way you change the anisotropy of this source of particles change the spectrum? 3. Solomon. In this computation, we have taken a source term given by formula (6). The influence of m, the anisotropy coefficient of the source, is very small if we consider both the frequency of the maximum and its amplitude. 40 LOW FREQUENCY DRIFT WAVES IN THE MAGNETOSPHERE DURING SUBSTORMS K. Hagège, G. Laval and R. Pellat, Section " Théorie des gaz ionisés ", Commissariat à l'Energie Atomique, Fontenay-aux-Roses. France ABSTRACT We give a possible explanation of low-frequency modulations which have been observed on particle distri bution functions, particle precipitations and magnetic field measurements during substorms. We assume that the hot plasma coming into the magnetosphere has a pressure gradient with a characteristic scale of about one Rc. The dispersion relation for drift waves is established by taking into account the pressure and magnetic field gradients as well as the particle motion in the non-uniform field. The wave frequencies may be larger or smaller than the ion bounce frequency but are always smaller than the electron bounce frequency. For small B the waves are quasi electrostatic. For a finite value of 8, the polarisation of the electromagnetic field is analysed and compared with observations. The electron Landau effect is too small to be an efficient excitation mechanism. We show that it can be replaced by a high frequency turbulence of whistler waves. The parallel electric field of the drift wave gives rise to an anisotropy of the electron distribution function. Pitch-angle scattering acts like collisions and the drift wave becomes unstable with an appreciable growth rate. Since the drift wave generates anisotropy, the high frequency noise level may increase when the low frequency electric field is present and we consider the non-linear regime associated with the corresponding increase of the growth rate. Finally, it is suggested that these waves provide a very fast radial diffusion mechanism. As consequences, the destruction of the pressure gradient and particle injection into the inner magnetosphere are expected. 41 « RECENT WORK ON ION-CYCLOTRON WHISTLERS Dyfrig Jones European Space Research and Technology Centre, Noordwijk, Holland ABSTRACT A considerable amount of experimental and associated theoretical research has recently been concen trated on the mechanisms that affect electromagnetic waves propagating in the upper ionosphere at frequencies in the region of the local ion gyrofrequencies. It is found that both polarisation reversal and mode-coupling manifest themselves in the phenomena observed in this VLF range by satellite receivers. In addition, reflection of the ion cyclotron mode at an altitude which is dependent on frequency is also important in the case of waves propagating downwards into the ionosphere from above. On investigating these effects in detail, interesting new phenomena can be postulated on theoretical grounds. 43 1. UPWARD PROPAGATING WAVES Figure 1 [Gurnett et al.] shows the familiar picture of a short fractional-hop electron whistler and an associated proton whistler. The important frequencies to observe are the following : a) the proton gyrofrequency, towards which the ion cyclotron trace is asymptotically approaching, b) the cross-over frequency, where the electron and ion whistler traces are coincident in time, and c) the frequency at which the electron whistler trace disappears before the commencement of the ion whistler trace. This frequency has unfortunately been called the electron whistler cut-off frequency. In radio propagation theory, the term " cut-off " is usually reserved for when the refractive index of the wave goes to zero, which is not the case here. It will there fore be called the " maximum coupled frequency " for reasons which will be given later. 1000- * ; ï -* -* * J ^» 800- «. * to Q. f « 600. \ iAr*<«M* .» O S 400- k* U- *** 200- ^ - \ *" * * * * -• î»i.i I 2 TIME (sec) 1000- -ELECTRON WHISTLER e eoor- -PROTON WHISTLER a. 3 600 - a. £ 400 Û, 200 0 I TIME (sec) Figure 1. — Spectrogram showing a proton whistler and nomenclature. 44 1.600- FMCTHWAL HOP WHISTLER PROTON WHISTLER Time (sec) Figure 2. — A proton and heliu '/lustier observed in the Alouette II satellite. The lower part of the figure shows the spectrum of this Jgnal as produced by a " Sonagraph " spectrum analyser. The upper portion of this figure is an idealized representation of this event (Ororal, Australia, December 3, 1965; 1221.15 UT; 132° E long., 32° S lot.; 2007 km height). Figure 2 [Harrington et al.] shows both proton and helium ion whistlers associated with the same electron whistler. In the Northern hemisphere the polarisation of an upgoing electron whistler has a right-handed sense, whereas that of an ion whistler has a left-handed sense. If the refractive indices of the two waves in an ionosphere consisting of electrons, protons, helium ions and oxygen ions are calculated, Figure 3 is arrived at [Gurnett et al.]. In this diagram the vertical plane corresponds to longitudinal propagation (0 = 0) and the horizontal plane to transverse propagation (8 = n/2). The abscissa is scaled in frequency A, which is the wave frequency, normalised to the proton gyrofrequency Q„ so that A = 1 at O, ; Q2 and Q3 represent the helium and oxygen ion gyrofrequencies respectively ; a, p and y in the caption of Figure 3 are the fractional abundances of protons, helium ions and oxygen ions respectively. Considering the longitudinal case, it is seen that for frequencies below the oxygen gyrofrequency, both right-handed (R) and left-handed (L) waves can propagate. As the oxygen gyrofrequency is approached, the refractive index of the left-handed wave tends to infinity, and at the gyrofrequency itself, this mode becomes evanescent. The right-handed wave is unaffected at the oxygen gyro frequency. Above the oxygen gyrofrequency, it is only the right-handed wave that can propagate, until a frequency mc is reached, above which both modes may again propagate. It is seen that coc is indeed a true cut-off frequency, since it is the frequency at which the refractive index of the left-handed 45 Figure 3. — Refractive index squared for the R, L, and X waves and wave-normal surfaces in each bounded volume (a = 0.8; P = 0.15; y = 0.05). wave goes to zero. Between this cut-off frequency and the helium gyrofrequency is the cross-over frequency at which the refractive indices of the two waves are equal. Above the cross-over frequency one has a repetition of what occurred below the oxygen gyrofrequency, with the left-handed mode refractive index tending to infinity as the helium gyrofrequency is approached, the right-handed wave being unaifected. Between the helium gyrofrequency and the proton gyrofrequency the refractive indices vary in a manner similar to those between the oxygen and helium gyrofrequencies. It is therefore seen that only the right-handed wave is continuous over the whole range of frequencies shown. The refractive index equation for these waves contains the parameters R, L, D and S, which are in turn functions only of the gyrofrequencies, the plasma frequencies and the wave frequency in the absence of collisions : n2 = (B + F)/2A, where n is the refractive index, B = RL sin2 B + PS (1 + cos2 0) F = (RL — PS)2 sin*fl + 4 P2D2 cos2 0 A = S sin2 0 + P cos 0 0 = angle between wave normal and terrestrial magnetic field vector R = i — y ^* f co (a + ekQJ 46 L = i _ y 'M f (o(co — ekQt) f CO2 S = i (R + L) D = i(R-L) k = number of constituents 2 2 h IT = 4in, q /mk = plasma frequency squared of the k' constituent h Q» = l?*B0/mtc| = gyrofrequency of the k' constituent ek = qk/\qk\ = — 1 for electrons and + 1 for ions e» = wave frequency nk = number density of the ^constituent 1 qk = electric charge of the k" constituent mt = mass of the k"' constituent B0 = terrestrial magnetic field strength c = velocity of electromagnetic radiation in free space. It is deduced from these equations and illustrated in Figure 3 that L = oo corresponds to the case where the wave frequency equals a gyrofrequency ; that L = 0 corresponds to the case where the wave fre quency equals a cut-off frequency; and that D = 0 corresponds to the case where the wave frequency equals a cross-over frequency. The condition S = 0 appears as a boundary in the case of transverse propagation, and it occurs where the wave frequency equals a hybrid resonance frequency [Stix]. It is also possible to treat the abscissa of Figure 3 as an altitude axis, since the terrestrial magnetic field, and therefore the gyrofrequencies, decrease in magnitude as altitude increases. (Such an inter change of units is obviously only qualitative, since a, P and y — the ion fractional abundances — also vary with height). As an illustration, consider a right-handed wave of frequency less than the value of the oxygen gyrofrequency in the lower ionosphere. This point will lie on the curve marked R in Figure 3, somewhere below fi3. As the wave propagates upwards in height, it will, at a certain alti tude, become equal to the local oxygen gyrofrequency and on continuing to propagate upwards will, at a greater altitude, become equal to the local cross-over frequency ca23. In the absence of collisions, polarisation reversal occurs at this altitude, which is called tho cross-over level, the wave switching over to become left-handed. This left-handed wave will propagate upwards until it reaches an altitude at which it becomes equal to the local helium gyrofrequency 02. At this height, it becomes evanescent. If collisions are included and provided the wave normal angle satisfies a certain condition (which will be discussed later), it is possible for some right-handed wave to be generated at the cross over level, and this wave will propagate upwards independent of the left-handed wave until it reaches the a>13 cross-over level. Above this level, it is again possible to have both left-handed and right- handed waves propagating upwards, by virtue of polarisation reversal and mode-coupling respectively. The left-handed wave reaches a height at which its frequency equals the proton gyrofrequency and here it becomes evant~cent. The right-handed wave propagates to greater altitudes and, possibly, to the opposite hemisphere in the usual electron whistler mode. Figure 4 [Gurnett et al.] illustrates the actual variation of gyrofrequencies, cross-over frequency and cut-off frequency with altitude for the model ionosphere shown. Consider a satellite receiver at 47 1700 km, at which height the proton gyrofrequency is 400 Hz. The cross-hatched areas denote regions where the left-handed wave can propagate, and it is seen that no propagation of this mode is possible between a gyrofrequency and the cut-off frequency (L = 0) above it, as was shown of Figure 3. Consider firstly a right-handed longitudinal wave of frequency 600 Hz propagating upwards from the ground. It will first reach the level S = 0, but will not be affected, since S = 0 is a boundary only for transverse propagation. It next reaches the level L — 0 but is again unaffected, since L = 0 influences only left-handed waves. On proceeding upwards past the level where D = 0, polarisation reversal will occur (neglecting collisions) and the wave will propagate upwards until it reaches 7S0 km, "i I I I I i I I I I I I 1 I I I I I I I I I I I I ALTITUDE KM Figure 4. — Various critical frequencies versus altitude for a typical model ionosphere. 48 at which level L = oo and the wave becomes evanescent. Thus this frequency will not be teceived at the satellite. Secondly, consider a frequency of 300 Hz. It is seen that this can reach the satellite since it will not become evanescent until 2400 km — well above the satellite height. The upper diagram in Figure 4 shows how the phase velocity of a 400 Hz wave varies with altitude, and it is seen that at the satellite altitude, the phase velocity of the left-handed wave becomes zero, thus making the phase refrac tive index (n) and group refractive index (n, = n + codn/dœ) infinite. This explains the long time delays of ion cyclotron whistlers as the local ion gyrofrequency is approached. Because of the importance of polarisation reversal in the formation of ion cyclotron whistlers, Figure S illustrates the way in which the polarisation changes with altitude. (See also [Rawer and Suchy]). This diagram [Jones, a] includes the effect of collisions. The effect of collisions may be included by replacing mk in the refractive index equation by tnk (1 + (Zt), where Zk = vjm and vk is the collision frequency of the k'H constituent. In the absence of collisions, polarisation reversal is possible for all wave-normal angles not equal to zero. Including collisions, there is a certain angle 9C, cajed the critical coupling angle, below which no polarisation reversal should occur. This angle may be obtained from the polarisation equation : sin2 6 RL — PS 2ip + 1 = 0 cosfl P(L — R) where p is the polarisation. Complex o plane Frequency 400 Hz -10 -ip -1-5 770 770S -2-01 Figure 5. — Variation of polarisation with angle 0 and height. Curves AA', BB' are for 9 = 8° and 8.8° respectively; curve CC is for 9 = 0C = 8.9°; curves DD\ EE' are for 9 = 9° and 10° respectively. Heights are marked on the. curves. The cross-over level is seen to be between 771.9 and 772 km. 49 Critical coupling occurs when the two roots of this equation are zero, that is when : P(L —R) sin2 8 G = — - = ± i . RL — PS cos 9 This requires that the real part of G shall be zero, and when this is so, the imaginary part gives 2 the value of sin 0,,/cos 0C. It is readily seen that in the absence of collisions, since all quantities are real, 6e is zero. In Figure 5 the critical coupling angle is 8.9°. Consider a wave-normal angle of 10". A right-handed circularly polarised wave will lie at — 1.0 on the ordinate of the Argand diagram. As the cross-over level (771.9 km) is approached, the polarisation changes as indicated by curve EE' and it is seen that by the time 772 km is reached, the polarisation has switched over co the positive half of the complex plane, that is the wave has become left-handed. On such a curve, the large change in polarisation for a small height change is evident. This large gradient of polarisation can itself make Fôrsterling's coupling parameter ii large. Fôrsterling's coupled equations for vertical incidence in an inhomogeneous, anisotropic medium may be written [Budden] : K + Fo ("o + where F0 and Fx are proportional to the fields in the ordinary (left-handed) and extraordinary (right- handed) modes, respectively. The prime denotes l/K9/3z, where K = nmjc is the wave number and z is the vertical co-ordinate. The indices of refraction for the respective modes are n0 and nx, and >p is the coupling parameter, so called because when i/< = 0, the equations are independent and the two modes propagate independently; but when $ # 0, the equations are coupled and there is interaction between the modes. i/r is a function of ths polarisation : .,. Po P* (Pi-D &Ç-D Thus coupling will be large if the polarisation gradient is large. In Figure 5, as the angle 8.9° (the critical coupling angle) is approached, not only is the polari sation gradient large, but also the polarisation itself approaches unity on the real axis. This serves to further increase the coupling parameter \j/, as can be seen from the equation. Therefore for wave- normal angles greater than, but fairly close to, the critical co» iling angle 8C, it is possible to have both left-handed and right-handed waves above the cross-ove- " vel by virtue of polarisation reversal and mode-coupling respectively. For very large wave-normal angles, no coupling is to be expected, the initial right-handed wave switching over completely to left-handed at the cross-over level. For wavç- normal angles 8 much less than the critical coupling angle, the polarisation remains left-handed as the cross-over level is passed, as shown by the curve for 8 = 6° in Figure 5. Again, the closer one gets to 0C, the greater the possibility of coupling, and some left-handed wave could be generated at the cross-over level. Figure 6 [Jones, 6] shows how the critical coupling angle varies with frequency. Consider a VLF receiver at 1000 km, and suppose that a whistler signal is travelling upwards- from a lightning flash near the ground. Because the refractive index is large for all frequencies considered here, it may be assumed (as a result of Snell's law) that the wave normals are vertical and also that the angle between the wave normal and the magnetic field vector is the saine for all frequencies. 1000 km is the cross-over level for a frequency of 288 Hz for which 8e is 7°12\ For slightly greater frequencies, the cross-over level is below 1000 km. The proton gyrofrequency at llwu km is 443 Hz and for this frequency the cross over level is at 650 km and the value of 8C is 12°. Thus frequencies in the range 288 to 443 Hz have 50 0 500 1000 1500 2000 Altitude, km Figure 6, — Variation of cross-over frequency with altitude for local night-time model. The numbers by the curves are the values of the critical angle Bc. cross-over levels at or below the receiver. The greatest 6C for this range is 12°. If, then, 6 exceeds 12°, the whole of this frequency range will be converted to a proton whistler. The smallest 6C is 7° 12'. Iffl is less than 7° 12', no waves will be converted to a proton whistler. If7°12' < B < 12°, onlythose frequencies for which 0 > Oc will show conversion and it is said that the proton whistler is partially formed. If the wave-normal angle had been 15° 18' say, then the frequency 480 Hz would suffer pola risation reversal at 600 km, and as the waves travel on upwards, successively lower frequencies will have suffered reversal, 410-480 Hz at 700 km, 370-480 Hz at 800 km, and so on. But no frequency greater than the local gyrofrequency of 443 Hz can be received at 1000 km. Thus there is a gap between 443 Hz and 480 Hz in the whistler trace recorded at 1000 km. The frequency 480 Hz is therefore the " maximum coupled frequency " (previously called the " cut-off " frequency) Cic at 1000 km for a wave travelling upwards with a wave-normal angle of 15° 18'. Figure 7 [Jones, a] illustrates the expected forms of proton whistlers. Because the angle 0C increases above 1700 km, Figure 7 (d) shows a more complicated type of partially-formed proton whistler expected at altitudes greater than this. Figure 8 [Shawhan, private communication] is one example of such a partially-formed ion whistler observed on the Injun III satellite. Since the wave normals of whistlers incident from below on to the ionosphere are refracted to the vertical, it is possible to determine the wave-normal angle 0 at every latitude = TT/2, and 0 = 0, which is less than all the values of 8C in Figure 7 resulting in no proton whistlers. In the low-latitude limit, tj> = 0 and 9 = n/2, which is greater than all values of t)c in Figure 7 resulting in fully-formed proton whistlers. Between the two limits, one would expect the partially-formed proton whistlers, and these regions are shown in Figure 5 [Jones, b]. Also shown in this Figure is the boundary of observed pioton whistlers taken from [Gurnett et al. Fig. 5]. However, more recent results by [Rodriguez and Gurnett], who looked at the progression of coupling types with latitude, are shown in Figure 10. It is seen that proton whistlers actually cut off at lower 51 (a) PLOloiLjgVPA'SSifZDSYJlQQW&Sl-- Time Time Time Hz 600 \ (d) !"«» •\ 3 \ Proton gïro-frequency__(2A00Kms)__ i? 200 - -x^ Figure 7. — Expected forms of proton whistlers depending on height and the angle between the wave- normal and magnetic field, (a) height — 1000 km; 0 :> 12°, fully-formed proton whistler, (b) height = 1000 km; 7°12' < 9 < IT. (c) height =•• 1000 km; 0 < 7"12', no proton whistler. (d) height = 2400 km; 0 = 6°; partially-formed proton whistler. latitudes than is predicted from theory, although the progression of coupling types is correct : at low latitudes, we have fully formed proton whistlers ; at higher latitudes, the proton whistlers become weaker until at latitudes above about 55° they completely disappear. It was seen from Figure 5 that even for angles greater than the critical coupling angle, the polarisation gradient was very large. This is further illustrated in Figure 11 [Jones, a], which is for the case of no collisions, i.e. the critical coupling angle is zero. It is seen that even for an angle of 10° the polarisation switches rapidly from right-handedt o left-handed. Thus one would expect a large amount of energy to be coupled into the right-handed mode above the cross-over level resulting in only weak ion cyclotron whistlers. This was recently confirmed by [Wang] who considered a colli- sionless stratified model ionosphere, and computed the reflection and transmission coefficients of a normally, incident plane wave, taking into account the multiple reflections at the slab interfaces. He showed that for small angles (0 < 10°), the intermode coupling is strong in the vicini'.y of the cross over level, and the wave is dominated by the right-hand mode for an incident right-hand wave. For Figure 8. — Partially-formed whistler [Shawhan, private communication}. 52 FREQUENCY whistlers 30- 6Ô1" Magnetic latitude Figure 9. — Regions of fully-formed, partially-formed and no proton whistlers, using the night-time model of [Gurnett et al.]. The full line curves are the boundaries assuming constant magnetic field with latitude. The dotted lines are the boundaries corrected for magnetic field variations. Approximate boundary of observed proton whistlers is taken from [Gurnett et al. (Fig. 5)]. large angles (0 > 30°) inteonode coupling around cross-over is small and the wave is dominated by the left-hand mode for an incident right-hand wave. Figure 12 shows the variation with wave-normal angle of the normalised vertical energy flux of a coupled upgoing wave as obtained by [Wang]. It is therefore possible to shift the theoretical boundaries to lower latitudes by taking into account both the polarisation gradient near the cross-over level, and the condition.for critical coupling. JMTMJJ^ T " °fP°,ar>°atwn P w'tl> oMtudefor an upgoing wave initially polarised with a fc. nf.SrJ^if°7arWUSan?'ei^en the»a»e-™<™>l <>"d the magnetic field vector. Collisions are neglected. The frequency is 400 Hz and the model used 1 that of [Gumett et al.]; X is the wavelength in the medium at the crossing. 54 2800 2400 2000 1600 I 1200 800 SYMBOL COUPLING TYPE c, 400 c ,c .c vvv 2 3 4 \ cs X 10 20 30 40 50 60 70 80 90 MAGNETIC LATITUDE (degrees) Figure 10. — Observed transition latitudes (A — A') in coupling types compared with Jones' plot. «so Km 55 X I- os hi ,6* a 0.6- HI _l 0. a J HI N < S \ OS i o -r- —1— 10 30 SO ao ANGLE (degrees) Figure 12. — Variation with angle of the normalized vertical energy flux of a coupled upgoing wave. f(Hz) L 'H | L^~ — *B ^•—'Linear t 200 - »c """ L *0 m>Om~**~ASÇ&*.ff to 15 USecs) Figure 13. — Expected form of spectrogram from complex ray-tracing calculations [Terry]. Concluding the section on upward propagating waves, we have the computations of [Terry] shown in Figure 13, which are complex ray-tracing results, that is, ray tracing in which collisions are included, thus making the refractive index complex. At first sight it appears that the electron and ion cyclotron whistlers are not coincident in time at the cross-over frequency. However, due to the inva lidity of ray tracing in the immediate vicinity of a coupling point, a full wave treatment in terms of Airy integral functions is required. 56 2. DOWNWARD PROPAGATING WAVES Interesting ion effects also occur on downward propagating long fractional-hop whistlers, that is, whistlers that have propagated from the opposite hemisphere to the satellite receiver. Figure 14 [Muzzio] shows an apparent turning up of the whistler trace at a frequency below the local proton gyrofrequency at atsut 900 km. Figures 14 (a) and (b) are for a geomagnetic latitude of 40° and (c) and (d) for 21°. Figures 15 and 16 fEgeland et al.] show a similar effect at about 700 km at 11° and at 4° geomagnetic latitude respectively. The dispersions of these whistlers indicate that they have propagated from the opposite hemisphere. This type of phenomenon has been called an " ion cut-off 0G0-4 (ACT) 3 AUG 67 0819:10 UT 0820:10 UT a) tr f 0G0-4 (SNT) 5 AUG 67 2218:30UT 2218:50 UT kHz 1.25- 0- c) t t isec Figure 14. — Spectrograms of Ion cut-off whistlers detected by OGO 4. Examples (a) and (b) were detected at Ororal, Australia and examples (c) and (d) at Santiago, Chile. In all four examples, the satellite height was about 900 km. Examples (a) and (b) show multiflash events, in contrast to the isolated ones in examples (c) and (d). The arrows at the bottom of each spectrogram indicate the pro bable origin, based on the Eckersley law, of the components indicated by the arrowheads at the top. The great difference in the minimum frequencies ht the 2 passes is due mainly to differences in the magnetic field intensities at the 2 sites. 57 whistler " as it is profoundly affected by the L = 0 cut-off for the left-hasd wave. Figure 17 will illustrate this point. Figure 17 (a) once more shows the variations of the proton gyrofrequency (L = oo), the cross-over frequency (D = 0) and the cut-off frequency (L = 0) with altitude. Consi der a satellite receiver at 1000 km and a whistler propagating downwards from iibove. This must have propagated from the opposite hemisphere as a right-banded wave. Figure IS. — Data recorded 1920 LT at geomagnetic Figure 16. — Spectrogram recorded 2 May 1967, latitude 11° N, altitude 704 km. 1923 LT, at geomagnetic latitude 4" N, altitude 713 km. ALTITUDE KH. TIME Sees. a b Figure 17. — a) Variation of proton gyrofrequency, cross-over frequency and cut-off frequency with altitude, b) Expected form of spectrogram when polarisation reversal and mode-coupling are included. 58 2.1 Firstly, consider a frequency of 800 Hz say, which is greater than the maximum gyrofrequency in the lower ionosphere. This will propagate down past the satellite and as it never encounters any cross-over level, it will continue down to the ground. Hence this frequency is only recorded once at the satellite (neglecting ground reflections). 2.2 Secondly, consider a frequency of 600 Hz say, which is greater than the proton gyrofrequency at the satellite. This right-hand wave propagates down from high altitudes, past the proton gyro frequency level, which only affects left-handed waves, until it reaches the cross-over level. 2.2.a In the absence of coupling, only polarisation reversal occurs and the wave propagates downwards from the D = 0 level as a left-handed wave. However, as it approaches the L = 0 level, it is reflected and will propagate back up to D = 0 where again polarisation reversal occurs and the wave becomes right-handed, which will be received at the satellite once more. Hence, this frequency would be recorded twice at the satellite. 2.2.6 If coupling is included, and this depends on the critical coupling angle, then it is possible that if the downcoming wave-normal angle is less than the critical coupling angle, this results in no pola risation reversal at D = 0 and hence no reflection can occur at L = 0. Figure 6 (which was obtained at a different latitude from Figure 17 a) showed how the critical coupling angle increased towards lower altitudes. Therefore it is easily seen that the " reflected " trace at frequencies of 600 Hz and above should not appear if 8 is less than the 6C for 600 Hz. If 0 is very large — approaching 0cmax shown in Figure 17 a — then all frequencies up to the maximum proton gy frequency along the path will undergo polarisation reversal and reflection. Therefore the maximum frequency reached by the reflected trace should correspond to the maximum coupled frequency observed on upgoing electron whistlers, and these could both give some indication of the wave-normal angle of the whistler wave. 2.3 Thirdly, consider a frequency of 400 Hz say, which is less than the local proton gyrofrequency at the satellite. In exactly the same way as in the previous case, we have a right-handed wave pro pagating down to the cross-over level where it is possible, for a certain range of wave-normal angles in the presence of collisions and a large polarisation gradient, that both right- and left-hand modes will propagate down — the right-handed wave to the ground, and the left-handed wave to be reflected at the cut-off level. Similarly, when the reflected left-handed wave reaches once more the cross-over level, both right-handed and left-handed waves will propagate up, and in this case where the wave frequency is less than the local proton gyrofrequency, both will be recorded at the satellite, to produce the compound trace shown in Figure 17 (b). As explained earlier, if the wave-normal angle is less than a certain angle, the ion cyclotron whistler may only be partially formed and the trace will not reach the local proton gyrofrequency. 2.4 Consider a frequency of 300 Hz, which lies between the cut-off and cross-over frequencies at the satellite. Such a right-handed wave propagating down will possibly undergo polarisation-reversal and mode-coupling at the cross-over level (which is now above the satellite), to produce both right- handed and left-handed waves, which are recorded as they propagate past the satellite. The left- handed wave will be reflected at the cut-off level and hence will be recorded twice at the satellite. It is easily seen that the minimum frequency of the left-handed wave to be recorded at the satellite will be the cut-off frequency, since lower frequencies have their cut-off (reflection) levels above the satellite. The right-handed whistler trace can obviously be continuous to lower frequencies. That the right-handed wave just below the cross-over frequency at the satellite and the left- handed vave above the cross-over frequency at the satellite (i.e. the ion cyclotron whistler) have not yet been observed, may be due to the wave-normal angles not being suitable for mode conversion. In the foregoing discussion it has been assumed that the wave-normal angles at all frequencies are equal, which may not be realistic for waves which have propagated from the opposite hemisphere. 59 The absence of the increasing trace on Figure 15 seems to indicate that in this case the reflected waves had travelled back along a different path, which did not include the satellite [Egeland et al.]. Since the ray path near a reflection point is symmetric about a magnetic field line [Helliwell, c], it seems that in the case of Figure 15, the angle between the ray direction and the magnetic field vector must be fairly large. The reflection of electromagnetic waves at the cut-off level in the ionosphere is also manifest in the low-frequency cut-off of VLF radio noise observed both on the ground and in satellites [Gurnett & Burns]. This is demonstrated in Figure 18, which is a spectrogram obtained from Injun 5 records PROTON WHISTLER CROSSOVER FREQUENCY LOW FREQUENCY (FROM PROTON WHISTLER) CUTOFF Figure 18. — Simultaneous low-frequency cut-off and proton whistler illustrating the relationship of the cut-off frequency to the cross-over frequency (Injun V, sept. 1968). and which also sho vs proton whistlers. It is seen that the low-frequency cut-off of the noise is just below the cross-over frequency of the proton whistler, which is strong evidence that it is related to the cut-off frequency, and that the noise (right-handed) has been generated above the satellite height and, having propagated down to suffer polarisation reversal at the cross-over level, is reflected at the cut-off level. That this type of noise sometimes has no low-frequency cut-off indicates that coupling has occurred at the D = 0 level so that the right-handed wave can propagate down past the cut-off altitude. In other cases, the low-frequency cut-off of the noise can be above the cut-crf frequency and even above the local gyrofrequency. This indicates that the waves are being reflected well above the cut-off level due to the increasing refractive-index gradient as illustrated in Figure 3. Such an effect should be most marked at the lower altitudes where the cut-off frequency, cross-over frequency and gyrofrequency are close together, giving a large refractive-index gradient in this region. The refrac tion and ultimate reflection of such waves obviously also depend on the initial wave-normal angle. Figure 19. — A sonograph record and a beat frequency oscillograph record ( 60 WMe» 409.4 (CPS) 3. SUMMARY It has been shown that ions profoundly affect both upward and downward propagating waves in the ionosphere, at frequencies in the region of the ion gyrofrequencies. All the comments which have been made concerning proton whistlers hold equally well for helium whistlers. [Gurnett et al.] have shown how the cross-over frequency can be used to obtain good estimates of the local plasma composition. Also, it ir. possible to obtain estimates of irregularities of proton density from the cyclo tron damping of proton whistlers [Gurnett & Brice, Lucas & Brice]. This attenuation manifests itself in the disappearance of the proton whistler trace before it reaches the proton gyrofrequency (Fig. 19 from [Gurnett & Brice]). Recent polarisation measurements on OGO 6 by [Smith] and on a Nike-Tomahawk rocket by [Maynard et al.] have confirmed that the polarisation of electron whistlers is right-handed and that of proton whistlers if left-handed. 62 WAVE-PARTICLE INTERACTION IN THE PLÀSMAPHERE G. Haerendel Institut fur extraterrestrische Physik, Max-Planck-Institut fur Physik und Astrophysik Garching bei Mûnchen, Germany 1. INTRODUCTION Among the many wave-particle interaction processes we will discuss only gyroresonant inter actions. A great number of publications has dealt with this subject. So, we will not be concerned with details of the processes, but rather ask how far the observed particle populations inside the plasma- sphere and their variations are governed by the gyroresonant interaction with electromagnetic plasma waves of low frequencies. Four topics will be covered. As an introduction (Section 2) we shall throw a side glance on the mathematics describing the gyroresonant wave-particle interactions. The formal advantage of a special choice of momentum variables will be demonstrated. Section 3 deals with the penetration of protons through the plasmapause, i.e. with the sudden transition from a hot to a cold plasma background. This subject has recently attained much attention. Enhanced pitch-angle scattering and the emission of certain ULF waves has been attributed to it. The stationary distribution of electrons inside the plasmasphere and the origin of the „ slot " are discussed in Section 4. Finally, in Section S we shall consider the interaction of electrons and protons by means of emission and absorption of whistler mode waves (ELF-waves). 2. MATHEMATICS OF WAVE-PARTICLE INTERACTIONS The gyroresonant wave-particle interaction comes about if by the particle motion £*.ong magne tic field lines a circularly or elliptically polarized wave appears Doppler shifted to the local gyro- frequency or multiples thereof. In this case the first adiabatic invariant of the particle motion, the magnetic moment, is violated. Pitch-angle as well as energy of the particle can change. It depends on the phase relation between particle and wave in which direction energy and momentum are trans ferred. With a random distribution of initial phases of the gyromotion it is the gradient of the particle distribution in velocity space that determines wave growth or absorption. Two fundamental relations are needed to describe wave-particle interacikms, one for the conser vation of wave energy and one for the conservation of particles in velocity space. We shall follow the quasi-linear approach, i.e. we neglect mode coupling of waves and the effects of finite amplitude waves on the particle orbits. 63 The particle velocity parallel to the magnetic field («y) and the wave frequency (to) are related by the resonance condition expressing the Doppler shift. We do not treat resonances other than at the gyrofrequency (_Q). Furthermore, we consider the simple case of propagation of waves in the direction of the magnetic field. The resonance condition is 2 2 with vph being the phase-velocity and y = [1 — (i^/c )]"" . The polarization of the waves can be expressed, by the sign of to, positive for left-handed (posi tive ion mode) and negative for right-handed (electron mode) waves. The dispersion relation expresses vph as a function of w. For ion cyclotron waves (L) and electron whistler waves (R) propa gating in the direction of B we have : U-WÛ/'2 (L)(2a) [1 - (oi/QJ]1'2 [1 + K/m«) ( (pA is the Alfvén velocity). If we look at the wave-particle interaction from a frame of reference moving with the phase- velocity, we find a pure elastic scattering, since in this frame of reference the electric vector of the wave vanishes. Formally this is expressed by [Brice, 1964] : Pi dPx + 0>n — y mvjù #|| = 0 (3) [Gendrin, 1968] noticed that this relation combined with the dispersion and resonance relations can be integrated to yield an invariant of this process. We shall write it down for the three types of intr étions that will be discussed subsequently (e and/) stand for electrons and protons respectively) : myAtn D-0£/bjH />-L(4a) P'2 = p\ + On — ymVfii2 + \ nfy\ In [(D^/oJb — 1] p — R (46) \ — mjn/Atn[(v%lB^—ï\ e — R (4c) The equation for the e — R interaction is an approximation for the case co/Qt -4 1. The magnetosphere is a very inhomogeneous system. Wave-particle interaction processes may occur for the same L-value at quite different values of »A and Q. Only if the particle species under consideration is dominated by processes characterized by a narrow range of values for these background parameters, can we regard p' as an invariant for the whole range of pitch-angles attained by many random scattering processes. The neighbourhood of the equatorial plane is a preferred region for such interactions because of the relatively slow variation of DA and Q along the field-lines. However, interactions at higher latitudes may be essential in certain cases. Because of this property of p' the particle distribution function (F) is conveniently defined in terms of the variables p' andpN [Haerendel, 1970, " On the balance... "], whereby these values apply to the momentum when traversing the wave-particle interaction region (in many cases the equatorial plane). Outside this region the local value of the momentum follows from adiabatic theory; p' and/>g are canonical variables. Therefore, the expression describing diffusion in p^ rather than in pitch- angle is particularly simple : -57F(rti||) = —(D—)+*-£ (5) 3t » 3p,, \ dp,, J 64 s and / symbolize any source and loss terms as far as the population of an L-shell is concerned. In many situations J would be equivalent to the (negative) divergence of the transport process in L-space. The absence of a corresponding term in p' expresses the above mentioned restriction to nearly constant background parameters for the wave-particle interaction region. The present form of the diffusion term can be easily obtained from the form derived by {Gendrin, 1968, his equation A22] by noticing that 3 1 1 / 3 3 \ -5— , = — lPi "3 '?« — ymv>*) T~) (6) dp| It «<">«• PL V 4*1 °PL! A and by replacing the diffusion coefficient for pitch-angle scattering, D, by : D=/iD (7) A According to [Kennel and Petschek] and [Gendrin, 1968], D depends only on the parallel velocity, vn : A 1 Q2 bl D = T^TF" <8> bl is the spectral power density of the magnetic field for the wave-number interval k, k + dk. The resonance and dispersion relations define m and k as a function of BJ. In the quasi-linear approach the diffusion equation is to be supplemented by an equation expressing the conservation of wave energy, as for instance : 3Z>2 —± = _div(62v,) + 2(y-d)fc2 (9) v, is the group velocity, y the growthrate and d the damping rate of the waves; y is again easily expressed by the variables p' and p g [Haerendel, 1970, " On the balance... 'Tas : j.-.-pp.J*»,-4jtVai f ., , î 3F. (10) These equations provide the mathematical fundamentals for describing wave-particle mteractions in the magnetcsphere. 3. PENETRATION OF PROTONS THROUGH THE PLASMAPAUSE 3.1 Variation of energy spectra with L Since the work of [Dungey, Hess and Nakada] it is widely believed that protons are supplied to the inner regions of the magnetosphere by transport across L-shells under conservation of the first two adiabatic invariants. Between magnetic storms the transport may be described as diffusion. A recent review of observational evidence for diffusion and of the magnitude and L-dependence of the diffusion coefficient was given by [Walt]. [Dungey, Hess and Nakada] noticed that the integral energy spectrum of protons if approxi mated by an exponential law : /(> E) = exp(E/Eo) (11) 65 shows a systematic dependence on L, namely Eo = EL- (12 a) with E ranging between about 10 and 20 MeV. This was later confirmed by [Mihalov and White] and [Fritz and Krimigis]. [Pizzella and Randall], however, in comparing differential spectra found another relation : Eo=:L- (126) These discrepancies show that the approximation of the energy spectra by exponential laws is rather poor. Therefore, the answer about the characteristic energy (Eo) depends on the energy range used. All the same, there are enough indications of a systematic increase of energy as protons are transported into the inner magnetosphere. The starting point of the present discussion is the observation that the differential proton spectra at high L-values (L > 4.5) are significantly broader than at lower L-values (L < 4.5). This is demon strated by Figures 1 and 2 a, b which were taken from [Pizzella and Frank] and [White], respectively. ii | j uii iiiii| | ||ii| = ' ji|i[ i6S;L - ^^ iL. 4y i i v - .E =8 kev L-5.0 SF E^».6 kev VH S 10 I „--" ^h*-"KO~l *0-+H3*« 2 \ U .0 \ "S* L«6.0 *\" E =3.5 kev •ft 2 e\^ I0 N \ I—H o A-, \ ^ « \ * = z EQUATORIAL DATA ce a. =- il = dE ri-Jl) \ ^ Z 0G0 3 \ \ EXPLORER 12 MARINER 4 \U \\ \\z _ \ - I I I llllll I I I llllll I I I llllll I I IrVrnt 0.1 I 10 100 1000 PROTON ENERGY, kev Figure 1. — Time averaged differential proton spectra near the magnetic equator for th'ee L-values after [Pizzella and Frank]. Figures 2a and 2b. — Differential proton spectra for eight L-values at B = 0.10 gauss after [White] 66 01 Ot 01 MM I 114 ENERGY, MtV 10 = IM nun—i i i uni]—i i IIIIIII—TT- rmj—n = l«3.0 3,5 4fl 5.0 10' I «o» I 2 *ï I04 g I03 B> 0.10 Own' «AUG 15-25. 1964 •NOV 19-DEC 2,1964 Q0EC28,1964-JAN3, 1965 ti 'ilM 111 *FEB 2-8, 1965 »* •i i i.uni l 1,1 M 0*00 I • I • • "tl • « ' 1 J ' "lint J 01 02 04 0(011 ENERGY, MtV Although the latter data were obtained at low altitudes, they should give a good indication of the form of the spectrum at higher altitudes at the same L-shell, since Eo is found not to vary much for constant L inside L x 4 [King]. Allowing for a systematic increase of the mean energy with decreasing L according to 12 a or 12 b, we must conclude that the lower energy portion of the proton spectra at high L is strongly reduced as compared with the higher energies upon transport towards the Earth. This change seems to occur rather abruptly near L = 4, pointing towards an effect related to the plasmasphere. [Haerendel, 1968] showed that the stationary proton distribution in L-space cannot be under stood as a pure diffusional equilibrium without significant losses. Loss and diffusion time scales must be of comparable magnitude. He ./ever, a sudden change of the slope of the flux-versus-L contours near L = 3.5 indicates a relative increase of the loss rate in the inner magnetosphere. With the data of Figures 1 and 2 we must conclude that this increase in the ratio of loss and L-diffusion rates is particularly strong at the low energy end. Two different reasons may be invoked for this observation. Either the transport in L (diffu sion) is reduced inside the plasmasphere, or new loss processes that are not efficient outside become available inside the plasmasphere. A combination of both possibilities may as well exist. The first hypothesis looks attractive when we think of the d.c. electric fields as measured by [Heppner] and [Caufifman and Gurnett]. At latitudes below a sharp boundary which runs close to the equatorward boundary of the auroral oval the electric field is on the average about an order of magnitude weaker than at high latitudes. The same may apply to those Fourier components that result in the transport of trapped particles in L-space by violation of the third adiabatic invariant. Diffusion coefficients as derived empirically by several authors and compiled by [Walt], however, do not give any evidence for an abrupt change near L = 4. The possibility of enhanced losses inside the plasmasphere by pitch-angle scattering has achieved some attention recently. We shall discuss the evidence in more detail. 3.2 Particle precipitation at the plasmapause The energy range in which protons appear to be missing in the time averaged spectra at L < 4 is the range of ring current protons. During magnetic storms it is strongly populated. [Russel and Thome] noticed the close coincidence of the peak of the ring current belt and of the plasmapause. Figure 3 shows their observation taken from the paper of [Cornwall et al.]. The outward motion of the ringcurren t belt in the recovery phase of the storm in accordance with the expansion of the plasma- pause is suggestive for the action of an additional loss process inside the plasmasphere. [Cornwall et al.] have attributed the decay of the ring-currentproto n belt to the ion cyclotron instability. They argue that outside the plasmasphere protons are not sufficiently anisotropic to be subject to this instability. When, however, after the main phase of a magnetic storm, the cold plasma background is building up again, their anisotropy suffices to destabilize ion cyclotron waves, by which process the protons suffer from enhanced pitch-angle scattering. Although this theory may describe essentially the cause of the ring-current decay inside the plasmasphere, there are several difficulties in detail. Formally [Cornwall et al.] base their argument for the stability of the ring-currentbel t ou»side the plasmasphere on the lack of sufficient anisotropy. What could keep the protons from being sufficiently anisotropic ? There could be another loss process dominating. O* .*rwise the proton distribution should build up ju.». to the marginally stable distribution, i.e. to the aniutropy that is sufficient to create enough waves, and thereby pitch-angle scattering, as is necessary to balance the influx of new ring-current protons. 68 Figure 3. — Distribution in L-space of the thermal ion concentration and the proton flux at 31 [Haerendel, 1970, " On the balance... "] derived marginally stable pitch-angle distributions with vanishing flux at the loss cone. He found for a given L-shell a family of solutions depending on the ratio : U = p'2/m2v\ (13) where p' is the momentum invariant of the wave-particle interaction process as defined in Section 2 (Equations 4). Figure 4 shows one such example. The undetermined constant, K, normalizing the flux,_/, depends on the relative loss of wave energy from the system. Apart from this factor, we find lower stably trapped fluxes for smaller values of U, i.e. of the density of the cold plasma background, although the anisotropy grows with decreasing U. This behavior is caused by the energy transfer accompanying pitch-angle scattering. At small values of U the particle velocity approaches the wave phase velocity, and energy transfer becomes important. For a given pitch-angle anisotropy, the gradient, 3F/3p||, which determines the growth rate according to Equation 10, is enhanced if energy loss is taken properly into account. Therefore, the absolute flux can be lower in order to create the same growth rate as in the absence of energy loss. Looking at Figure 4 one would expect higher fluxes of ring current protons to be trapped in the cold plasma environment of the plasmasphere, rather than a reduction as suggested by [Cornwall et al.]. However, this argument is misleading. The problem lies in the inapplicability of the cold plasma theory as developed by [ Cornwall, c] and [Kennel and Petschek] to the ring-current protons outside the plasmasphere. Waves that would become destabilized in the cold plasma theory are actually damped, because the resonant protons are close to the thermal peak of the plasma. The dispersive medium is constituted by the ring-current particles themselves. No theory of the limiting trapped fluxes without cold plasma background has come to the attention of the author. The argu ment of [Cornwall et al.] as well as the similar arguments of [Brice, 1970] and [Brice and Lucas] are not applicable. 69 90 70 50 Figure 4. — Solutions of the stably trapped proton distribution at L = 4.5 assuming a sharply peaked differential spectrum for different values of parameter U (Equation 13) after [Haerendel, 1970, " On the balance... "]. The normalization constant, K, is given by the right-hand side of Equation 16. In the light of this discussion it is suggested that the ring current protons are in fact at the stable trapping limit outside the plasmasphere. Observational evidence can be found in the little variation of the ring-current flux outside L » 6 through the different phases of a storm (Figure 3) and in the coincidence of ring-current and proton aurora in L-space [Eather and Carovillano]. This means that the ring-current is maintained in the presence of proton precipitation. During magnetic storms it extends closer to the earth and builds up to higher levels roughly proportionally to the equatorial magnetic field. The decay of the ring current inside the plasmasphere appears now in a different light. Although with the cold plasma background new modes of plasma waves become available, which may lead to the decay of the ring current, it is not clear that the rate of precipitation is actually higher than outside 70 the plasmasphere. Several open questions remain. Why are the lower energy protons more effi ciently depleted than the higher energies that constitute the peak of the differential spectrum in Figure 2 ? Is it the combination of reduced transport in L-space and losses by charge exchange ? Why is the total proton flux inside the plasmasphere below the stable trapping limit as pointed out by [Haerendel, 1970, " On the balance... "\ ? Unless we find quantitatively satisfying answers to these questions we cannot claim to understand the trapped proton population of the magnetosphere. 3.3 Emission of Pc 1 geomagnetic pulsations The ion cyclotron waves which can be excited in the cold plasma environment of the plasma sphere may grow to quite substantial amplitudes if the transition of the protons from the external hot plasma-low density region occurs rather suddenly. The build-up of the cold plasma at a certain L-shell outside the plasmasphere by diffusion from the ionosphere is probably so slow that the adjust ment of the energetic particles to this environment via pitch-angle scattering does not lead to large amplitude ion cyclotron waves. The grade B-drift of the more energetic particles ( > 1 keV), how ever, will result in a relative motion with respect to the thermal plasma and enable occasional sudden transitions through the plasmapause where it intersects L-shells favorably. Since protons are drifting westward this is expected to occur more often between midnight and late morning hours (Figure 5), in particular during outward expansions of the plasmapause. fmld = 0.1 fg AVERAGE PLASMAPAUSE CARPENTER 1966] Figure 5. — Location of the source of Pc I micropulsations derived by two different assumptions on the Doppler shift experienced by the emitting protons; fmU = 0.1 fg corresponds to emitting protons close to the peak of the differential energy spectra of Figures 2a and 2b 71 The waves that can be excited follow from the resonance condition (1) once the particle energy A is known. If we choose the characteristic energy, Eo, as defined in Equation 12 a, with E — 16 MeV [Mihalov and White] and a cold plasma density varying with L as : n„ « 7.5 .10* IT* (14) as derived from whistler data of [Angerami and Carpenter], we find for the parameter U : U = 500/L (15) At the plasmapause U is typically 100 for these particles. This means that the excited wave fre quency, 4. ELF-HISS AND ELECTRON SLOT Interactions of electrons with whistler mode emissions have been discussed by [Kennel and Petschek] to account for the pitch-angle diffusion of electrons above about 40 keV. The precipita tion of low energy electrons (0.1-10 keV) in the auroral oval is not likely to be caused by whistler mode 72 turbulence, but rather by the electric field emissions, probably electrostatic waves, near the equator that were observed with the electric field detector on board OGO S [Kennel et al.]. Inside the plasmasphere the situation may be quite différent. The phase velocity of electro magnetic whistlers is much lower, so that relatively low energy electrons can interact easily with these waves. [Russel and Holzer] found strong ELF hiss inside the plasmasphere in the frequency range from a few 100 Hz to a few kHz. The distribution of this sort of steady banded noise is shown in Figure 6. What is the origin of the ELF hiss ? Is it related to the trapped electrons ? Figure 6. — Distribution of ELF hiss in the frequency range from 100 to 1000 Hz with amplitudes greater than 3 my for four local time sectors. Data from OGO 3 after [Russel and Holzer]. Little has been published about low energy electrons inside the plasmasphere. Figure 7 taken from [Vette] reviews the equatorial distribution of electron fluxes. At low energies the fluxes appear to have a minimum near L a 4, but this minimum is not comparable to the so-called slot which appears at higher energies and at somewhat lower L-values. Inside this minimum the electron fluxes (> 40 keV) increase towards the Earth in a manner compatible with the L~* law that was derived for the limiting fluxes of stable trapping by [Kennel and Petschek] and [Cornwall, d]. Therefore, it is tempting to understand the low energy electrons as being stably trapped and to relate the origine o the ELF hiss to the whistler mode instability that keeps them at the stable trapping limit. The fre quency range observed agrees well with the resonance condition and the dispersion relation of whistlers with plasmaspheric parameters. According to [Haerendel, 1970, " On the balance... " ] the total stably trapped flux,y,.t., can be described by : itl « io« \^P\ /^^om-^c-'sterad-']. (16) 73 ELECTRON RADIAL PROFILE AT EQUATOR AT VARIOUS TIMES OF THE SOLAR CYCLE EXPLORER 14 •GO la OGOlb ERS 17 ATS1 1234 56 789 10 11 12 L (EARTH RADII) Figure 7. — Profiles of the integral electron flux for various energy thresholds near the equator after [Vette]. AX is the latitude interval in which the wave-particle interaction takes place, and R the reflec tion coefficient of the waves at the end of the " system " (In this case only field-aligned propagation of waves was assumed. The " system " is a flux tube). Comparing Equation 16 with the flux of electrons with E > 40 keV in Figure 7 and assuming that this is a substantial fraction of the total flux, we derive — tn R/JA > 10. With reasonable values for AX (» 0.15 radian) this would suggest R< 0.2. That means that the waves are not particularly well trapped in the magnetosphere. They get absorbed or propagate out of.the volume under consideration. The most intriguing question arising now is that for the cause of the slot that is so prominent at energies above about 100 keV. [Russel and Thorne] suggest to relate it to ah increasingly better reflection of whistlers with decreasing frequency. The higher the energy of the particle the lower the frequency with which it resonates. This argument seems to be supported by the result of [Thorne and Kennel] that whistlers tend to be reflected where the lower hybrid resonance frequency is close to the wave frequency. This occurs well above the lower ionosphere and is more effective at the lower frequencies. 74 However, reflection must be very perfect if this were really the cause of the slot. A drop of the flux by three orders of magnitude in the center of the slot as seen in Figure 7 would imply — In R x 10~3. That means that in each reflection the wave amplitude is maintained to an accuracy of 10"3. This appears to be somewhat unlikely. Another suggestion would be that the higher energy electrons interact also with the ELF hiss that appears to be emitted by the low energy electrons. Resonance can be achieved somewhat off the equator, where the local gyrofrequency is higher and larger Doppler shifts are needed. In the termi nology of [Kennel and Petschek] these electrons would suffer from parasitic diffusion, i.e. they do not generate their own wave field. From the resonance condition (1) and the dispersion relation (2 6) of whistlers we derive for w/Qe < 1 : »||r * »A V0./» (17) As waves propagate along the magnetic field, w will remain constant and : s/2 B||, s B /Vïï. (18) This relation shows that the resonant energy increases very strongly with increasing magnetic field strength, B. Resonance will only be possible over a small latitude interval, but it may be suffi cient to create substantial pitch-angle scattering. Such a suggestion could only account for the drop of electron flux at the high altitude side of the slot. The steep recovery at low L must be attributed to quite a different process. Furthermore, the parasitic diffusion at the higher energies must be accompanied by a somewhat reduced transport rate across L-shells for such an effective decrease of the fluxes to occur. As in the case of the protons which were discussed in Section 3 many open questions remain. Our suggestions are still awaiting careful quantitative checking. 5. INTERACTION BETWEEN PROTONS AND ELECTRONS Interactions of protons with right-handed waves (p — R) and of electrons with left-handed waves (e — L) are also possible. In these interactions energy is absorbed by the particles if they have an anisotropy typical for trapped particles. This way one particle component can act on the other. One such possibility is that energetic protons in the plasmasphere interact with the ELF-hiss and gain energy that way. [Gendrin, 1968] has derived the paths of protons in velocity space for (p — L) and (p — R) interactions (Figure 8). They are defined by Equations 4 a and 46 using Equa tions 1 and 2a. The heavy dashed curves applying to p — R interactions with m > 2 Qp deviate strongly from lines of constant energy (circles). The energy grows with increasing »j or decreasing pitch-angle. That means that protons must be strongly accelerated before-they can be scattered into the loss cone by right-handed waves. The reason is that in order to fulfill the resonance condition with a frequency well above Qp the protons must travel at nearly the phase velocity. In this case the scattering is inelastic. If we assume interaction only near the equator and adopt a model for the cold plasma density such as Equation 14, we can calculate the parallel velocities of the electrons and protons that resonate with a right-handed wave of a given frequency. In Figure 9 we plotted the parallel kinetic energies of resonant particles for a few L-shell- and 75 1 2 3 4 5 LONGITUDINAL BEAM VELOCITY (l/>//Va) Figure 8. — Paths in velocity space of protons interacting (I) with left-handed ion cyclotron waves (p—L), (2) with right-handed whistlers at m <2Qp(p—R). (3) with whistlers at 6. SUMMARY Our discussion of wave-particle interactions in the plasmasphere was rather qualitative and sketchy. More work has to be done to persue the validity of most of the suggestions. The problems pointed out can be summarized as follows : 1) Protons in the energy range of some tens of keV outside the plasmasphere are less efficiently transported into the plasmasphere than for the higher energies. It seems to be doubtful that losses by ion cyclotron turbulence at the plasmapause can solely account for the observed 76 10 100 1000 E„e [KeV] Figure 9. — Parallel kinetic energies of protons and electrons interacting with whistlers in the frequency range 0.01 Qm < m < 0.3 Qe at the equator for 4 values ofL. Density model according to Equation 14. The trace 15 MeVjLz indicates characteristic trapped proton energies as a function ofL (Equation 12a). reduction of the flux as suggested by [Cornwall et al.], since these particles should already be subject to pitch-angle scattering outside the plasmasphere [Eather and Carovillano]. 2) During the sudden transition of several 100 keV protons through the plasmapause ion cyclo tron waves may be generated with substantial amplitudes. Pearl-type micropulsations have been related to this process. 3) Electrons at a few tens of keV inside the plasmasphere appear to be at the stable trapping limit and to generate the ELF hiss observed in the plasmasphere. 4) Two hypotheses for the origin of the slot in the electron distribution at higher energies were discussed : — either it indicates nearly perfect trapping of the emitted whistler waves, whereby the limi ting electron fluxes are lowered [Russel and Thorne], — or these electrons are subject to parasitic diffusion by interacting with the ELF field off the equator. This means they fall below the stable trapping limit. 5) It was pointed out that protons in the several 100 keV range can absorb energy from the whistler wave field set up by electrons at somewhat lower energies. The significance of this process to the proton population remains unclear. It thus appears that wave-particle interactions, in particular with the electromagnetic cyclotron waves, are important processes also in the inner magnetosphere. The causal relations with the obser ved particle populations are far from being clarified and deserve a much closer investigation. 77 A NUMERICAL INVESTIGATION OF ELECTROSTATIC WAVES AT MEGAHERTZ FREQUENCIES IN THE UPPER IONOSPHERE AND THEIR INTERACTIONS WITH ENERGETIC PARTICLES* Bengt Hultqvist Kiruna Geophysical Observatory, Kiruna, Sweden ABSTRACT A numerical study of the warm plasma dispersion relation for conditions corresponding to the upper ionosphere and exosphere will be reported. The wavelength range of existence for megahertz electrostatic waves will be discussed. Solutions of dispersion equation are given as function of direction of propaga tion relative to the magnetic field lines and of wavelength for a stationary plasma as well as for combina tions of stationary and streaming plasmas. A number of graphs will be produced by means of which the solutions of the warm dispersion equation can be deduced for a wide range of values of wavelength, plasma density and streaming velocities without any further computer work. 'Publ. in Plasma waves in space and laboratory, J.O. Thomas and B. Landmark éd., Edinburgh Univ. Press, 1970, vol. 2, p. 199. 79 ON THE STRUCTURE OF THE GEOMAGNETIC TAIL Karl Schindler European Space Research Institute, Frascati, Italy It seems widely accepted that the plasma sheet in the tail of the geomagnetosphere [Vasylhmas; Bame et al.] plays an important role in a number of magnetospheric processes. For instance, magneto- spheric substorms seem to involve considerable changes in the plasma sheet configuration [Hones]. The plasma sheet is also an important reservoir of particle energy which conceivably can govern a variety of processes, for instance particle precipitation [Axford, b]. The importance of the plasma sheet for the magnetosphere has been the motivation for a number of investigations which I shall briefly summarize. For details, I have to refer to the original literature. It seems reasonable to explore the consequences of a model [Cole and Schindler] where the domi nant contributions to the momentum balance of a volume element inside the plasma sheet are the gra dient of a scalar pressure P balancing the stresses exerted by the magnetic field B : V/> + — B x (V x B) = 0 (1) Clearly, a more refined picture would have to take into account a number of other effects which are presently neglected, such as pressure anisotropy, fluctuations, convection and possibly external forces. A simple picture of the magnetic configuration in the tail consists of field lines which are pulled- out dipole lines, keeping their dipole topology. Such a model seems to suggest itself in view of obser vations using time averages over periods larger than, say, 10 minutes [Speiser and Ness]. Applying (1) to such a picture, one finds that it requires a pressure gradient along the tail. The pressure profiles along and across the tail are strongly coupled. The magnetic structures observed on time scales > 10 minutes can reasonably be explained in this way. (Whether or not the resulting pressure gradient is consistent with the observations seems not yet clear.) This picture, however, has a number of drawbacks : — Since, at least in a model where th•) magnetic field lies in the x, z-plane (solar-magnetospheric coor dinates), the current density y' is constant along field lines, it is not possible to have the current concen trated in a neutral sheet which is thinner than the plasma sheet. At present, it is not clear how serious this point is. — There is experimental evidence for negative values of Bj provided by [Mihalov et al.] and [Schindler and Ness] on time scales < 100 seconds. — On the same time scale, the magnetic-field magnitude becomes locally considerably smaller than one would expect it to be from the picture of pulled-out dipole lines. 81 — Theoretical studies of ideal neutral sheets are subject to a number of instabilities such as tearing (e.g., [Schindier and Soop]). One can expect that, since the situation discussed so far is fairly close to the exact neutral-sheet configuration, perturbations of sufficiently large amplitude will give rise to unstable formation of concentrations of the electric current. There seems to be a simple way in which these difficulties would be avoided, namely if the magnetic field projected in the .Y, z-plane allowed for the presence of closed loops. These loops would not necessarily be stationary. In order to obtain more experimental information and to see whether this concept is consistent with observations [Schindier and Ness] analyzed data from the Explorer 34 satellite. It was concluded that the observations are in fact consistent with the picture of loops imbedded in the neutral sheet. The picture of pulled-out field lines can be applied on time scales > 100 seconds, but has to be aban doned for smaller averaging times because neutral points appear. Although the magnetic fine structure may not be important for various global aspects of the magnetosphere, it seems very important for those problems involving the detailed particle orbits. This is the case, for instance, in particle acceleration processes. Neutral-point instabilities can accele rate particles much more effectively than neutral-sheet instabilities [Biskamp and Schindier]. The ratio of the electric fields is : t ±*B*\JL.y[K(±)n (2) E„s \_ae V m, \aJ j (np = neutral point; ns = neutral sheet; L = characteristic length of the equilibrium considered; ae = electron Larmor radius measured in the full tail field: mjm-, = electron to ion mass ratio). Several problems concerning the plasma sheet arise from this model. For instance, the following points would require more experimental work. — Neutral sheet fine structures at time resolution 2; 1 second or better. — Particle acceleration processes. •— Ion pressure tensor (anisotropy, directed motion). •— Pressure profiles along and across the tail. — Discrimination between space and time dependence. It seems necessary to understand the above points before the role that the plasma sheet plays in the magnetosphere can be safely evaluated. Although there are other interesting questions to answer, I feel that evaluation of the properties of the plasma sheet is one of the more urgent problems in current magnetospheric physics. DISCUSSION P. Rothwell. Can you give an idea of the distance between neutral points ? You said you can rule out the idea that it is oscillating phenomenon because this would require the neutral points to have too high a velocity. K. Schindier. The answer is : honestly no ! I have shown a model which gave the best agreement with the observational material and there of course we have a number, and this I can quote. If we assume that the current sheet is one Earth radius thick, then the lateral extent of the loop one third of this, and the length of this should be 2% that is several Earth radii. But I would not like to be quoted on this as a firm number because, you have seen all the difficulties involved. What I would like to claim is that the topology I showed is consistent with the observations. That is really all we can say... 82 A NONLINEAR THEORY OF " TYPE I " IRREGULARITIES IN THE EQUATORIAL ELECTROJET André Rogister European Space Research Institute, Frascati, Italy ABSTRACT This paper is concerned with the nonlinear development of the Farley- Buneman instability in the equatorial electrojet. The stabilization mechanism is as follows : a turbulent (negative) vertical electron flux < Si^Sn > develops in the turbulent layer; in order to preserve charge neutrality, the (positive) vertical ion flux n vitX decreases accordingly. Hence the secondary electric field Es = niiViV^/q, and the electrojet electron current qenvety also decreases, thereby quenching the instability. The predictions of the theory agree quite well with what experimental evidence is available. 1. INTRODUCTION Experimental studies of the equatorial ionospheric E region have revealed the presence of an assortment of non-thermal plasma motions in the equatorial electrojet referred to as Type I [Bowles, Balsley and Cohen] and Type H [Balsley] irregularities. The linear theories of [Farley; Buneman] describe an instability mechanism which can plausibly explain the generation of Type I irregularities : the current flowing in the equatorial ionosphere in the East-West direction can drive longitudinal ion-acoustic waves whenever the electron drift velocity in the wave direction exceeds 11 — * ' I times the velocity of sound in the ionospheric plasma ; fl,(e) and v,M are the ion (electron) gyrofrequency and ion (electron)-'-eutral collision-frequency respectively. A major argument which favours these theories is that the theoretical threshold drift velocity agrees well with observational data. The linear theory of [Rogister and d'Angelo] appears to explain well the origin of Type II irregularities : a universal-like instability [Simon ; Hoh ; Morse, a] sets in in an inhomogeneous plasma immersed in crossed electric and magnetic fields. In favour of the theory is, first among others, the fact that the splitting of the echoing region observed by [Balsley] (at least under day-time conditions) can be explained. It should be recalled that [Dougherty and Farley] have also attempted to explain the characteristics of Type II irregularities assuming that these result from non linear coupling of Type I waves; the theory is thus unable to explain Balsley's experimental result that Type II irregularities are also observed when the electrojet current density is lower than the Farley- Buneman threshold. 83 With linear theories, one can merely decide when a wave will go unstable. The ultimate level of the irregularities, energy spectrum and phase velocities, among other characteristics, can only be found from nonlinear theory. This paper is concerned with the nonlinear theory of the Farley- Buneman modes; the nonlinear theory of Type II irregularities will be the subject of a forthcoming paper. The major nonlinear results of Part I can be summarized as follows : a) The r.m.s. density fluctuation,squared , is, after stabilization : where Ep (< 0; see Figure 1) is the electrojet primary electric field which has its origin in the tidal 3 motion of the atmosphere; the other notations are standard. With B = 0.3 emu, Ep = (—) 2.510 emu and c, =: 350 m/sec, we findtha t the maximum (v, and v„ varying with height) rjn.s. density fluctuation, squared, is of order : 3 • 10- ff) iî, (Vertical) ySouih) 'ij(West) Figure 1. This figure agrees fairly well with [Booker's] estimate of 10_ 3 quoted by [Bowles et al.]. One should, however, bear in mind that Booker's evaluation is necessarily crude and was made for auroral irregu larities (which are supposed to be of the same nature [Balsley]). Furthermore, we should note that the strength of the primary electric field itself is not easily evaluated, at present. It is here suggested that accurate measurements of the fluctuationleve l could be used tc evaluate Ep when the ionospheric plasma is turbulent (i.e. under midday conditions). 84 b) The phase velocities of Type I irregularities after nonlinear stabilization has occurred, are essentially independent of the electrojet velocity (vt) (in contrast to results of linear theory) but are, in fact, equal to the velocity of sound in the plasma (c5). The turbulence is drifting horizontally ; hence the phase velocity measured by an observer looking at an angle 0 to the horizontal should be : c, cos 8. Furthermore, the electron drift velocity is given by the formula :«, = cs 11 — Jf' I ; this value is about 2 c, at the altitude where the turbulence level is largest, but is a function of height. Therefore, the phase velocity is near the sound speed c„ although the electrojet speed vc is greater than e,. That conclusion is confirmed by the observations. It has been shown (see e.g. [Sugiura and Cain] and references herein) that at the dip equator, the secondary (vertical) electric field is related to the primary (in the East-West direction) field, under quiet conditions, by : (EJ„. = ( "i>t,x+ <5n5ve^> =nvliX+ ^ônSv^ (4) (/, in the vertical direction) where the brackets are the correlations of the density and velocity turbulent fields. This relation directly leads to 2 B p v, / v„v, \-'f v? / v.v(\- <.5nènyY (5) instead of (3). Equation (5) shows that the secondary electric field decreases with increasing turbu lence; hence the East-West electron drift which drives the instability will also decrease until marginal stability is achieved, i.e. f, .0, = c, 11 ' ' I ; (/, is the unit vector in the East-West direction); this result, combined with (5), leads to the asymptotic turbulence level given by (1). Recently [Skadron and Weinstock] have advanced another theory of nonlinear, stabilization of Type I turbulence in the equatorial electrojet. Their results will be contrasted to ours in the last section of this paper. In Section 2, we describe our macroscopic approach to the problem and the mathematical apparatus which will be used to solve the equations. The solution is given in Section 3. The nonlinear stabilization is described in Section 4. 2. DISCUSSION OF MACROSCOPIC EQUATIONS In the framework of a two-fluid theory, taking into account collisions with a neutral background (ion-ion and electron-ion collisions are negligible in the equatorial electrojet), the equations to be 85 considered are the following : on -^ + V • (mj) = 0 (6) nj {-£. + Vy • vv;j = - VPj + nq, {v. + -^ x Bj - vpmj,, (7) where y* (i, e) refers to the ions and electron fluids, respectively. In considering the Farley-Buneman instability, we adopt the simplified model of a uniform equilibrium electrojet layer, with equal ion and electron fluxes flowing across the upper and lower (horizontal) boundaries (see Fig. 1). Thus, the net ionization-recombination rate inside the layer vanishes for each species. The net momentum change Q, resulting from these processes is in general not zero. The corresponding term, to be intro duced in equation (7), has however negligible effect both on the equilibrium and on the irregularities, as was shown previously [Rogister], and has therefore been dropped here. We have also neglected charge separation and finite Larmor radius effects in equations (6, 7). These approximations have been justified in [Register]. In order to proceed, we split each variable 0 according to * = 0 + 5* (8) where 0 is the spatial average of 0 and 5, * is a fluctuation. Since long parallel (to B) wavelengths are more favorable to resistive instabilities [Rosenbluth], we shall consider, in the following, fluctuations with very small parallel wave numbers; we shall further assume one-dimensional propagation for -\ convenience : i.e., we let V = s -5-; clearly, that hypothesis has no effect on the results as long as mode coupling is negligible. We are now in a position to split equations (6, 7) as follows Get s be the direction of propa gation of the waves) : *-. • + <<5v, • s — 5v,> = — s <— Sp,/m,(n + &i)> + — (E + — x B) — v,v, (10) as as Bij \ c I and 3 _ A 3 \ _ 3 A _ 3 A _ ( (11) IF + y>- s IF) Sn + " "aT ' '5v'+17(5 ' ** *° = ° , A A I 3 _ A3 A3 1A Of >x • s x —- 5v, + (v, + 5vj) • s y- Sv, — <(5vj • s — <5v,> + v,5v, = s • 5v, (12) ^",J* ' [it&y'+ ^'+ 5v,) ' " ~ès Sy'+ v'5y'} = — ^ "aTSp''^ + 5n) + Z <4~ «(« + 3")> + I ?;B • Î X i^ (13) J OS j C 2 _For low p plasmas \fi = 4 n {pe + />i)/B ], the perturbations are essentially electrostatic, hence, B = B = — B /,. We have also defined Q, as qs B/m,c and, e.g., < S y, S v, > as the autocorrelations (which are spatially homogeneous) of the fluctuating velocity fields. To obtain (I3),we have assumed q. = — ?, ; note also that s • <6v, • s —- 5v,-> = — —- <(5vj • s)2> = 0. as 2 OS 86 Considering two-dimensional flows across the magnetic field, one sees that then: are five equations for eight average variables. Since the geomagnetic field B and the East-West primary electric field E, ty are given, we need another relation to complete the description of the system. The electrojet layer being of finite vertical extend, we require (see Figure 1) that >><>M+ <5n &>„> = n vltX + <<5» Sv, ,~> (14) since the plasma must be charge neutral on a length scale of the order of the layer thickness. The system "f equations (11-13), on the other hand, can be closed by assuming some equation of state, or by considering the equations of pressure transport. As in [Rogister], we introduce the following expansion parameters v v —i ~e ; —e -~e ; —-~O, E ; CO— ~e ; A s 2sC. — ; C. —=1 (15) v„ Qt v, v, a ve which describe both the actual conditions, in the electrojet at the altitude x a 100 km and the expe 3 3 rimental results. In fact, »,Ï8X 10* cps, v, ~ 5 x 10 cps, Ep ~ 2.5 x 10 emu, E,~ 5 x 10* 6 2 -1 emu, B =: 0.3 emu, Qe ~ 5x 10 cps, Q, m 10 cps (average atomic mass M ~ 31), c, ~ 360 m.sec (after [Sugiura and Poros]); furthermore, the observed angular frequency of the irregularities was o> ~ 5 x 102 cps for a wavelength iï3m. Therefore, e < I0-1. Note that the relations (15) imply^, ~ —ve~ Eve(?, is however essentially in the vertical direction whereas ve is almost horizontal) and mjm, a e3. Equations (9-14) are nonlinear. Since the asymptotic turbulence level (2) is rather small, it is appropriate to assume ô n a e n in the following. (It is however interesting to note here that equations (9-14) can be solved exactly for fully developed turbulence). As one might infer by scaling the equations, or merely by inspection of the results obtained in [Rogister], it follows that Sve ~ ve , ôvi 2: vt if on ~ en (16) The nonlinear theory of type I irregularities is easily worked out by expanding equations (9-14) in powers of e, using the scaling relations (15, 16). To lowest order, it is found that the waves merely propagate without changing form; i.e. the growth rates and dispersive effects are small compared to the real part of the frequencies and thus proceed on larger time scales (> I/eu>). It is thus natural to use the [Krylov-Bogolubov] multiple time scales expansion scheme to solve to next order in e. That is, we let, for instance : •5n(0 s &!(/„;«,;...) (17) so that : ^5flWs(_L+e_L+...)5„(,o;«i:...) as) and we expand : 5n = Snm + eon11' + - (19) It is customary, although improper, to drop the subscripts (0, 1,...) appearing in (17, 18); we find it convenient to adopt that convention. Note that the correlations are independent of a> but grow in time; hence < èn5n> = < ôniny (et;...). Therefore the average quantities Vj and È, are also func tions of et (see 10 and 14), 87 3. NONLINEAR THEORY OF THE FARLEY-BUNEMAN INSTABILITY In the aim of clarity, this section is written in a concise mathematical style. For every equation we consider, we firstgiv e the order of magnitude of the different terms (with the help of 15-16) and then solve. The different terms of (12), with J = e, scale as follows (in order) : 1 : 1 : 1 : 1 : e"2; B"3. (12 a) We conclude that A-*v<0) = 0 and î.fc«..-S-£.îx*?) (20) Consider (11) with J = e; we find(wit h the help of 20) the ordering 1 : 1 : 1 : e. (11a) Thus O .— A 3 \ . mi . - o A (^ + Ve.^n.o> + B-^. = 0 (21) (1) <0) To obtain a dispersion relation, we must thus obtain <5ve (or <5ve ; see equation 20) in terms of «5»<°>. The terms of equation (13) scale as follows (using 20) : e(B3) : e2(e*) : 82(e5) : 1(e); e(e) : 82(e2) : e(l) (13 a) where we have indicated the relative order of magnitude of the electron contributions in paren thesis. There results that »,*•*?"« fl,<£x 3 •*»?" (22) The ordering appropriate to (11), with J = /, is : 1 : 8 : 1 : B. (U6) It follows that : 3 A -(»). .0» (23) at as Combining (20-23), we thus find : l\ a,a,/ 3t T a*} (24) Equation (24), which is equivalent to a dispersion relation, has the solution - A V, • 5 ôn°(s; t; et ;...) = &i° s — t ; fir;... (25) O.Q, which shows that the profile of the density wave propagates without distorsion on the " fast " time scale. If one Fourier analyses equation (24), one find, indeed that all modes move at the same speed; as a consequence, the " random phase approximation " (the phases of the modes are assumed to be at random), which is the basic ingredient of all statistical theories of turbulence [Frieman and Rutherford; Kadomtsev; Rogister and Oberman; Dupree; Weinstock], is here invalid; formulated another way, statistical theories deal with the weak coupling limit (the Fourier modes moving at different speed) whereas the present situation is one of strong coupling. We shall now assume that all variables Sn(m, Sv,lm), aie of the form given by (25). Equation (11) to next order in s : 3 A * (2) , 3 A , / 3 A 3 ^ ^.S^ ^.(1^Sn^^(±^^±)) 0) ^ del 5 + + ( S (26) i2} {0) will describe, after elimination of 6ve . s, the " slow " behavior of ôn . From equation (12) : î-ôv? = ±t.îxSv<» (27) Furthermore, from (13) : 0 i- ? • 5v< ' + v, Î • OS» = - ± l ôp?>lmÂ- C, % • ? x *<» + Q, % • £X *v»> (28) at as j Scaling the terms of equation (12) with J ~ /, one shows that A A /n. t, • s x 5v,' = 0 (29) (2) (I) To obtain s. <5ve , there remains to eliminate £. 5v, from equation (28). From (11), we findth e required expression : A _ ; * . 5vJ"= 1. &,"> + » 5n Since we find 1 ^> = i^L(1_^L)- v.. J. fac (3,) n 0,0, \ Q.Q,/ by combining (20, 22, 23) and (24), equations (27, 28) yield - 3 A "IIs m w Introducing (32) in (26) we finally obtain after elimination of?. Sy, , $. 5ve , and with the help of the dispersion relation (24) : /l V'V' \ 3 J! («J V'V> ~ A 3 J! (») I *— „ - I •=— OB1 = • V, • S -r- Off \ atQ,I Set lifit 3s -ïà£[•ç^-fc>(I-S)-a*'•] (33> 89 The first term of equation (33) merely represents a renormalization of the propagation velocity. If we assume an isothermal equation of state, the second term agrees with our previous result [Rogister], although the present calculation is nonlinear (see 32). Instability then sets in whenever - A ve • s > c, 4. NONLINEAR RELAXATION OF THE INSTABILITY (0) l (0) The calculation of Section 3 reveals that 5ve =s e~ âv, . By inspection of (14), one then finds that the turbulence cannot develop beyond a level such that < 5«&CiI> ~ nvtx; this estimate of the turbulent flux is compatible with our scaling (16). For such a weak turbulence « ônân y/nn ~ s2), it is justified to assume an isothermal (or adiabatic) equation of state. One easily shows that (see 20, 31) <&„*»> = - s • %•%. (l --gL) Ï. • î Furthermore, and still with the ordering defined by (15, 16), we find : 9i s Vi.x = • m,v, Inserting (34, 35) in (14) yields : i--^('-ar['+*-*,(i)'('-s)^^fcr - Note here that — —• 11 ' ' 1 is the ratio of the Pedersen and the Hall conductivities for Hi \ »'«*«i I the parameters appropriate to the central electrojet layer; assuming v,/ve constant, it can readily be shown that CT2/°'I is maximum at the altitude where v(!v,/Q(.f2i = — 1. The following picture of the nonlinear relaxation of the instability thus emerges from our calculation. As the turbulence level increases, a (negative) vertical electron flux < SuM5n >, given by equation (34), develops in the electrojet layer. Thus, in order to preserve charge neutrality, the (positive) vertical ion flux nvl-x must decrease (since < SvltX5n > ^ < àvt%j&n ». The secondary electric field, Ej = Ex = wi{V,JJ,iX/^f, decreases accordingly. Hence the hori zontal East-West electron drift also decreases until the most unstable modes, corresponding to hori zontal propagation, are stabilized. At this stage, / u.v. "\ (37) *(-•&) Thus all waves, except those propagating in the East-West direction, are damped away; mode- coupling effects, however, could play a role and make it possible for waves to propagate in directions close to the East-West axis. To avoid ambiguity, we note here that the phase velocities that one should observe from ground stations are given by the formula (V#)0bs = cs cos 0 where 8 is the angle between the direction of observation and the horizontal (see Fig. 1). 90 The equilibrium secondary electric field is given by the relation (see 35 and 37) /. v.v, \ c - (38) which, combined with (33), leads to equation (1) in view of the above discussion (/y .î = 1). Furthermore, equation (37) shows that i>„ = 2 r, at the altitude where a1joi is maximum (see the discussion following equation 36); lower down in the ionosphere, i>w > 2r„ whereas higher up va < 2 c,; these considerations of course only apply to those layers where type I irregularities are excitef1. Tj summarize, it seems that our results agree quite well with what is available of experimental evidence. The '* strong turbulence " approach of [Skadron and Weinstock) on the other hand does not seem able to explain at least one important point, namely that the observed phase velocities of the irregularities are of the order of the sound speed (we recall that this result contrasts with what one might infer from linear theory). We suggest that their solution violates the " constraint " (14) given the large turbulence level ÇJ < SnSn >/n =: 0.6) they find. A CKNO WLEDGEMEST It is a pleasure to thank Dr. N. a"Angela for discussion of the results obtained in this paper. DISCUSSION L.R.O. Storey. To what extent are the classical formulas for the bulk conductivity of the plasma modified in the presence of turbulence ? A. Rogister. The formula which governs the equilibrium of the equatorial electrojet in the presence of <.ônôn>~ turbulence is EJE, = ffj/ff, I / + | —. - " 2 ; since o2/ff, g> /, even a small turbulence level can modify appreciably the ratio EJEr This modification comes about because, to preserve charge neutrality in the layer, we now require <<5n ôv^y + hv^ = <&i &„> + nvrx instead of nhix = nê„ However, the relations between average electric field and average velocities are not modified by the presence of turbulence. Therefore, I would think it is improper to speak here of anomalous resistivity, G. Haerendel. J did not quite understand how your theory is related to the observation which you quoted initially, that when the electric field becomes weaker, in the evening or so, you see a bifurcation of the level where you have the enhanced scattering. One could make a simple suggestion : what is expressed by the electric field is the drift velocity of the electrons in the frame of reference of the observer on the Earth. What counts for the instability is the drift velocity with respect to the ambient ions. Now the ambient ions in that layer are attached to the neutrals and we know that a neutral wind in the E layer rotates in direction with varying altitude about twice between 90 and 130 km. So, it could just be that at two levels (or more) the neutral wind and the ions are moving oppositely to the drift velocity of the 91 electrons and that in these layers the relative velocities of ions and electrons exceed the critical velocity. The neutral winds are of the order of 100 m/s and the difference between observed and critical velocities which you mentioned was something like 50 or 60 mis. So, at this time of the day, you can easily get neutral wind velocities which will Just do it. A. Rogister. The mechanism you suggest is quite a plausible one, although it requires sufficiently large velocities for the neutral winds, especially when the electron drift velocities are small, say of the order of, or below, 100 m/s (which should be compared to the critical relative velocity of 360 mis). Furthermore, that mechanism would require a persistence of the wind patterns for at least a few hours at two given periods of the day : in the morning and in the evening. 92 ON THE INTERACTION BETWEEN THE HOT MAGNETOSPHERIC PLASMA AND THE COLD IONOSPHERIC PLASMA OVER THE POLAR CAPS * B. Hultqvist Kiruna Geophysical Observatory Kiruna, Sweden ABSTRACT The interpretation of recent observations of field-aligned ions with energies in the keV range in terms of m. electric field parallel to the geomagnetic field lines between the hot plasma from the plasma sheet, in its horns going to the atmosphere, and the cold ionospheric plasma, is discussed. Some quantitative results, based on the assumption that some kind of diffusion dominates the propagation through the horns of the plasma sheet, show that magnetic-field-aligned electric fields may sometimes exist and that] the total potential difference between the ionosphere and the plasma sheet may even exceed 10 kilovolts. The effects on the voltage difference of the detailed shapes of electron density and equivalent temperature distributions between the ionosphere and the plasma sheet are discussed, as well as the dependence of the electric field on various other parameters. *See " On the production of a magnetic field-aligned electric field by the interaction between the hot magnetospherlc plasma and the cold Ionosphere ", Plan. Space Sd., (1971), in press. 93 DISCUSSION H. Rème. Did you see any variation in the pitch-angle of low energy electrons at the time of proton alignment ? b. Hultqvist. In fact, we have only measured in two directions, perpendicular to magnetic field lines and in the loss cone. So we could not look in detail at the pitch-angle distribution. But we have seen another interesting thing in the electrons. We have seen detai.d anticorrelation between the flux of the low-energy electrons and the flux of the hot electrons, which directly fits with this mechanism; because, when you have large fluxes of hot electrons, when you have an increasingly hot plasma in contact with the ionosphere, your potential difference increases and that retards your electrons and you see the effect of this, for reasonable shapes of your spectrum, as a reduction in the flux of the low-energy electrons. That, we have seen but this is very preliminary. H. Rème. Yes, because, in my rocket flight, the ratio of low-energy e jctron fluxes of some degrees of pitch-angle over the same energy electron fluxes with a 90° pitch-angle changes and takes an increasing value in the presence of the electric field, because of the action of this field. P. Rothwcll. You said that you saw this phenomenon over the whole polar cap on a very quiet time. Does this mean that you generally observe it when it is quiet and not when it is disturbed, or is it distributed evenly to all types of events ? B. Hultqvist. / should say that we have not yet studied well the dépendance on disturbance level but we certainly have seen it in quiet as well as in disturbed situations. So it is not a clear dependence, so to say. I should however perhaps point out that this case where we saw it all over the polar cap was one single case in half a year of satellite operation and it was in many ways an unusual case. So it is not representative. I think it is related to the long-known fact that the polar cap aurora is anticorrelated to kp. 94 WAVES GENERATED BY A CONTROLLED BEAM OF ELECTRONS ARTIFICIALLY INJECTED INTO THE IONOSPHERE : THE ELECTRON ECHO EXPERIMENT D.G. Cartwright and P.J. Kellogg School of Physics and Astronomy, University of Minnesota, Minneapolis, U.S.A. ABSTRACT The Electron Echo Experiment injected about 3000 pulses of energetic electrons into the ionosphere at pitch-angles between 65° (down the field) and 115° (up the field) from an Aerobee 350 sounding rocket launched from the Wallops Island Firing Range, Va. The pulses were 16 ms long, spaced 1110 s apart; th'i beam current was 70 m A, the electron energy varied between 35 and 45 ke V. This paper presents the observations in the frequency range 16 Hz to 10 MHz of the electric component of waves generated by the experiment. Wave generation by the beam electrons was observed at frequencies near the plasma frequency and the upper hybrid resonance frequency of the ambient ionospheric electrons, at frequencies below the electron cyclotron frequency (whistler mode) and at frequencies near twice the electron cyclotron frequency (possibly Bernstein mode). Also a 200 m A beam of argon ions of 50 eV energy generated waves near the lower hybrid resonance frequency. All of these waves have phase velocities low enough to interact strongly with the emitting particles; to within an order of magnitude we can account for the observed amplitude of all except tite Bernstein-mode waves, by Cerenkov-like emission from the energetic particles. However, the variation of the observed amplitudes with injection pitch-angle and with time from the beginning of the pulse show peculiarities which are not yet understood. 1. INTRODUCTION The Electron Echo Experiment was conceived by Professor J.R, Winckler of the University of Minnesota. A rocket-borne accelerator was to inject pulses of electrons at pitch-angles near 90° to the Earth's magnetic field, so that the electrons would travel to the conjugate point, mirror there and return to the vicinity of the rocket. By choosing the rocket trajectory and the energy of the elec trons appropriately, it is possible to match the eastward component of rocket velocity to the eastward drift velocity of the electrons caused by the curvature and gradient of the Earth's magnetic field. Thus electron detectors carried on the rocket can be used to analyze the electron beam returning from the conjugate area. 95 One of the problems to be investigated in this experiment was the neutralization of a current- emitting vehicle in the ionosphere. In vacuum, the rocket would charge up within a fraction of a millisecond to a potential which would prevent the electrons from escaping. In the ionosphere, the rocket can collect a current of thermal electrons which will at least partly compensate for the electrons emitted by the gun. Some aspects of this problem have been analyzed by [Linson]. In the Electron Echo Experiment three different means of neutralizing the rocket were tried : 1) the conducting skin of the rocket alone was used to collect thermal electrons; 2) an attempt was made to establish a conducting bridge between the rocket and the ionosphere by emitting from the rocket a beam of argon ions of about 50 eV energy and 3) the area for collecting thermal electrons was increased by deploying an aluminized mylar disc of about 75 square metres area. The electrons were emitted in 16 ms pulses at the rate of 10 pulses/s for 12 s, then 1 pulse/s for 6 s. A total of about 3 000 pulses was emitted during the flight. The electron energy varied between 35 and 45 keV along a ramp of 1 ms duration; the beam current was about 70 mA. During the time that the eastward component of rocket velocity was accurately matched to the electron drift velocity and the rocket was also moving along a shell of constant L (Ah < 10"* per electron bounce; one Larmor radius is about Ah = 10"5), at least one and as many as three echoes were detected. The preliminary results of the Electron Echo particle experiments have been reported by [Hendrickson, McEntire and Winckler]. The present authors realized that the Electron Echo Experiment also offered an opportunity to investigate wave-particle interactions in the ionosphere under controlled conditions. During flight through the atmosphere, the electron accelerator payload was protected by a fiberglassnos e cone about 3 metres long which, after motor burn-out, was ejected to expose the accelerator and particle detectors. This nose cone has obvious advantages as a vehicle for the wave detectors : 1) the receivers are removed from the noisy environment close to the accelerator payload; 2) the nose cone follows the trajectory of the accelerator payload much more closely than a separately launched rocket could; 3) because it is ejected ahead of the accelerator payload, the nose cone is ilways close to some part of the injected electron beam; 4) the nose cone is launched at the same time as the accelerator payload. We therefore attached to the outside of the nose cone two stainless steel bands, each of 1 000 cm2 area, the forward one of radius 22 cm, the aft one of radius 58 cm, separated by 167 cm, to serve as electric antennas. We fitted into the nose cone a number of receivers covering the frequency range from dc to 10 MHz and provided a package with its own telemetry transmitter, telemetry antennas, batteries, and associated instrumentation. Because calculations (T. Jones, M.S. thesis, University of Minnesota, 1970, unpublished) had shown that the beam causes only weak instabilities, the receivers were designed for high sensitivity, determined ultimately by the noise of the preamplifiers. The preli minary results of the observations of waves generated during the Electron Echo Experiment have been reported by [Cartwright and Kellogg]. The results which will be discussed here were obtained from two of the receivers. One was a broad-band receiver which covered the range 16 Hz to 10 kHz with automatic gain control in 8 steps of 10 dB each. The other was a sweep frequency receiver which swept from about 100 kHz to 10 MHz 80 times per second with a resultant frequency resolution of about 30 kHz. The sweep rate was chosen to ensure that we looked at each frequency at least once during every gun pulse. The limiting noise was about 5 uV r.m.s. for the broad-band receiver and about 10 /tV r.m.s. for the other receiver. 96 The Electron Echo payload was successfully launched on an Aerobee 350 sounding rocket from the National Aeronautics and Space Administration's Wallops Island Firing Range in Virginia at 1631 UT, 13 August, 1970. 95 seconds after launch the nose cone was ejected at a speed of 10 m/s and about 10 seconds later the gun started firing. The rocket reached apogee of 350 km 5 mn 16 s after launch. 2. HIGH-FREQUENCY OBSERVATIONS Figure 1 shows a section of data from the sweeping receiver. Because of the high sweep rate, this data must be recorded at high chart speeds, in this case 300 cm/s. The 1 kHz tone burst at the bottom of Figure 1 shows when the gun was firing. The beginning of individual sweeps is marked by a large-amplitude synchronizing pulse. On the sweep which occurred just before the gun fired, the only remarkable feature is the small peak near the high-frequency end of the sweep. This is a signal from a short-wave transmitter on the ground near Wallops Island, which has traversed the lower layers of the ionosphere to reich the nose cone. Similar signals from four different transmitters were seen during the flight; some of the others can be seen at the high-frequency end of the next sweep. This next sweep, which starts at almost the same time as the gun pulse, illustrates the main features of the high-frequency emissions which we want to discuss. At the low-frequency end of the sweep is a band of noise extending beyond 1 MHz. This noise band always lies below the electron cyclotron frequency; so we believe it is whistler mode emission. The most conspicuous and most common feature is the large-amplitude, fairly narrow peak at about 5 MHz on this particular record. We shall show later that the frequency of this emission band is closely related to the electron plasma frequency of the ambient ionosphere; so we shall refer to this emission as the " plasma frequency emission ". Between these two emission bands is a small, narrow spike at about 2.5 MHz. SIGNAL FREQUENCY MHz > 3 z «Wt»wv»'rf«.*<-'»yYwJ rr J° °El LU 100 > 300- LU 1000 - O Id 3000-1 a: z< S2 in GUN PULSE (16ms ) Figure I. — Chart record at 300 cm/s of data from 1C 9 kHz-10 MHz sweeping receiver. Two complete sweeps are shown. Lower trace is 1 kHz tone burst to show when electron accelerator is firing. 97 We see this emission, which is at a frequency close to the second harmonic of the electron cyclo tron frequency, during an appreciable fraction of the flight. No waves can propagate at this frequency in a cold plasma, but the emission has the frequency characteristics of the first Bernstein mode in a hot plasma. We will refer to this emission as " Bernstein-mode emission ", but it should be understood that the identification is only tentative, because we cannot explain the intensity of the emission. With a chart speed of 300 cm/s, we accumulate in a 10 minute flight almost 2 km of chart records; to compress this amount of data to manageable proportions we have used an intensity- modulated display, with time along the X-axis and frequency along the Y-axis. By this method we can vary the time scale of the data, but detailed information contained in the amplitude of the signal is lost. Figure 2 shows a section of data presented in this way. The time scale is expanded so that individual sweeps of the receiver are resolved. The features pointed out in Figure 1 are clear. It is also clear that radiation is observed only when the gun is firing, at 1/10 second intervals. Also, the 0-10 MHz SPECTRUM AT 1633104 Z •\ ' i *"••• t-ffii •NNpMfcJM: VMM 8 •\ ••••«<•• n >• . -.. i ,6 i x S ; >• 5 fH .>f.if";:!-"|Vi]i oz O cc 3 mi le i < I s I I m !• 0 p-H- ' ! :* !• I • rtfclN»Hll.l-«l ' ' ' J I l__l I i ' i ~ i 0 0.5 1.0 TIME (SECONDS) Figure 2. — Intensity-modulated display of data front 100 kHz-10 MHz sweeping receiver. Time scale is expanded so that individual sweeps are resolved. Q8 intensity of the emissions appears to be modulated at some period greater than 1/10 of a second; this period turns out to be 1/2 the spin period of the electron accelerator payload, that is, the emission depends on the pitch-angle at which the electrons are injected. The spin axis of the rocket made an angle of about 25° with the Earth's magnetic field and the electrons were emitted perpendicular to the rocket spin axis; so during one spin period the injection pitch-angle of the electrons varied between about 65° (down the field) through 90° to 115° (up the field). The short horizontal bars towards the right of the figure are in-flight frequency markers, 1 MHz apart, generated automatically at about 10-second intervals during the flight. Figure 3 is a similar intensity-modulated display but the time scale is much more compressed and as a result the time resolution is only about 1 second. The 8 minutes of the flight after nose cone ejection are shown. The apparent gaps in the data occur when the gun is firing once per second. The most conspicuous feature of this diagram is the double-humped profile of the plasma frequency radia tion, between about 5 and 7 MHz. The frequency labelled Fl is the electron plasma frequency at the peak of the F layer, determined from the ground-based ionosonde at Wallops Tsiand. The frequency labelled F2 is the upper hybrid resonance frequency at the peak of the F layer, calculated using the F layer plasma frequency and the local electron cyclotron frequency. Thus the plasma frequency emis sion band extends from below the local electron plasma frequency to above the local upper hybrid resonance frequency. We interpret the double-humped profile as follows : as the rocket ascends, the electron plasma frequency it "jst increases until the rocket reaches the peak of the ionospheric F layer. From then until apogee, tue electron plasma frequency decreases. The profile is approximately sym metrical about apogee. The dispersion relation for a cold plasma shows that there are two bands of frequencies within which the refractive index is greater than 1. One such band occurs for the extraordinary mode and frequencies between'the electron plasma frequency and the upper hybrid resonance frequency. (The electron plasma frequency is much greater than the electron cyclotron frequency). The other is the whistler range of frequencies, that is, below the electrou cyclotron frequency. Since the speed of 40 keV electrons is about c/3 and since we observe radiation in both these frequency bands, we suggest that the simplest interpretation of the radiation is that it is generated as Cerenkov-like emission from the beam electrons. We have calculated, in the electrostatic approxima tion, the expected amplitude for spontaneous emission in the neighborhood of the plasma frequency for conditions appropriate to the Electron Echo Experiment; it agrees to within about an order of magnitude with the maximum amplitudes observed in this frequency range. Exact calculations show that the condition for emission of radiation is : w — kTvz = n 99 ALTITUDE (KILOMETERS) 200 250 300 350 300 250 100 ———• 1—r—i—r J L J L 23456789 TIME SINCE LAUNCH (MINUTES) Figure 3. — Intensity-modulated display of data from 100 kHz-10 MHz sweeping receiver. Time scale is compressed to show most of the flight. FI, F2 are electron plasma frequency, upper hybrid resonance frequency at region of maximum F layer electron density. We have started detailed analysis of the chart records from the sweeping receiver. For the plasma frequency emissions we have scaled the ampUtude for about 360 pulses when the rocket and the hose cone were near apogee. The results are shown in Figure 4, in which the X axis is injection pitch-angle, the Y axis is the time at which radiation was observed, measured from the beginning of the gun pulse, and the blackness of the dots represents the amplitude of the emission according to the scale on the bottom of the figure. 100 ELECTRON ECHO PLASMA WAVES PLASMA FREQUENCY RADIATION M,N,8 O SERIES (360 PULSES) • i •• i T •( - I- • -i i --i -i • J 18 16 0 - o J 14 O «o iOa ' o • • e o 0 o •• 12 O O- Oo • e o ' °° ° ° 10 — O Oeooe o o MOD fl00S • «O O o o 0 • A 8 — •• oO- • •* O o O ° •£) O O00" " 6 -oo OO» QfB* o o- 0 0 O oô« • M' *•# OÔ O o-0 4 • • $* • • » o • o cb 2 o •• • Q> I-- I " I t I • -1 - [• • • I :_L: L ' •• ' ' 110 100 90 80 70 UP INJECTION PITCH ANGLE DOWN FIELD FIELD AMPLITUDES IN p\J • >I60 • 140-160 • 120-140 • 100-120 O 80-100 o 60-80 o 40-60 Figure 4. — Amplitude of radiation near the plasma • 20-40 frequency for 360 gun pulses near apogee, as a function of injection pitch-angle and time from the start of the • <20 pulse. We expected a strong dependence on injection pitch-angle. The heating current for the filament of the electron accelerator was a 20 kHz square wave. This deflected the electron beam emerging from the accelerator by about 5° either side of perpendicular to the rocket axis, in a plane parallel to the rocket axis. Thus we would expect any emissions which depend on the beam electron density to have a maximum amplitude for pitch-angles about 5° on either side of 90°. In any case, electrons which are injected at 80° pitch-angle (down the field) look just like electrons which were injected at 100° pitch-angle (up the field) after they have mirrored below the rocket; so any variation with pitch-angle should be symmetrical about 90°. A section through Figure 4 at 4-5 ms after the start of the gun pulse is shown in Figure 5. While there is considerable scatter in the data, we think that the smooth curve of the figure is a valid representation of the behavior of the emission amplitude with injection pitch-angle (the data from other periods in the flight show a very similar pattern). The two peaks, spaced about 10° apart, represent the profile of the injected electron beam, but the pattern is shifted from 90° by about 10-12°. Such a displacement could be caused by an electric field in the vicinity of the rocket, along the magnetic field or along the rocket axis. However, in such a field, electrons collected by the rocket from the ambient ionosphere would acquire an energy of about 4 keV, but a Faraday cup mounted on the accelerator payload showed no electrons of this energy. We do not yet understand the apparent displacement of the pattern from 90°. ELECTRON ECHO PLASMA WAVES PLASMA FREQUENCY RADIATION. M.N.a 0 SERIES -l—r- -r ' ,| ' ' ' ' I ' DELAY TIME 4-5 MILLISECONDS • • I IIO 100 90 80 70 UP INJECTION PITCH ANGLE DOWN FIELD FIELD Figure 5. — Section through Figure 4 for 4-5 ms after the start of the pulse. The displacement of the symmetry axis of the pattern from 90° is not understood. 102 The dependence of the emission amplitude with time after the beginning of the gun pulse is an even bigger surprise. Figure 6 shows a section of Figure 4 for pitch-angles between 104 and 108°. (Reference to Figure 3 shows that a section along a different pitch-angle, for instance 100-102°, would show a different detailed behavior but the general features would be the same). We expected that this figure would show a fairly short rise time of the order of 1 or perhaps 2 ms, corresponding to the time taken for the beam to travel from the accelerator to the vicinity of the nose cone and then for slow waves to travel from the beam out to the nose cone. Then would follow a plateau 16 ms long and a decay period of 1 or 2 ms. The observed pattern reveals that some collective process in either the electron beam or the background plasma modifies the emission mechanism or the propagation of waves from the beam to the nose cone, or possibly both, in a way which depends on the number of electrons which have been emitted by the rocket. At this time we do not understand this collective process. ELECTRON ECHO PLASMA WAVES PLASMA FREQUENCY RADIATION M,N, a 0 SERIES -1—i—|—.—|—i—|—i—|—i—| i | i— PITCH ANGLE 104°-108° (UP FIELD) 320 280 w 240 GUN O > PULSE o 200 or ENDS o 160 UJ a => ZJ a. <2 1 «i-""• "--1—i—i—|—•—• I i I 6 8 10 12 14 16 18 20 DELAY TIME (MILLISECONDS) Figure 6. — Section through Figure 4 for 104-108" pitch angles. We expected the amplitude to show a plateau 16 ms long. 103 3. LOW-FREQUENCY OBSERVATIONS Figure 7 is an intensity-modulated spectrum, covering the frequency range 0-10 kHz, of noise detected by the low-frequency, wide-band receiver. The noise started precisely when the argon plasm." generator was turned on. (The plasma generator was used for about I minutes of the flight to keep the rocket neutral. It emitted continuously about 200 mA of argon ions of about 50 eV energy, together with the appropriate cunrent of electrons of about 1 eV energy to maintain neutrality.) The spectrum of the noise shows intense blobs centered at about 8 kHz, deeply modulated at exactly the spin period of the accelerator payload. The ratio of the maximum to minimum amplitude is at least ' I ! I ! I I I 0 12 3 4 5 t TIME (SECONDS) Figure 7. — Intensity-modulated spectrogram of radiation in the frequency range 16 Hz-10 kHz. Centre frequency of radiation is near lower hybrid resonance frequency. Modulation period is spin period of argon plasma generator. 300 to 1 ; the modulation envelope is accurately a cardioid pattern, the amplitude proportional to sin 9/2, where 9 is the spin angle of the rocket measured from the instant that the plasma generator is directed away from the nose cone. The center frequency of the spin-modulated hiss corresponds to the lower hybrid resonance frequency of the ambient ionosphere. Taking into account the effects of collisions and thermal motions of the ions and electrons, the maximum refractive index at this lower hybrid resonance fre quency is about 20 000. Since the speed of 50 eV argon ions is about c/20 000, we suggest that this emission is Cerenkov-cyclotron radiation by the argon ions. The minimum in the modulation envelope always occurs when the plasma generator is pointing away from the nose cone. This suggests to us that the argon ions leave the rocket as a jet rather than travelling in helices about the magnetic field. (The Lannor radius of 50 eV argon ions in the Earth's magnetic field is about 150 metres.) Thus the beam of slow electrons and energetic argon ions emitted by the plasma generator apparently sets up a polarization electric field which cancels the effect of the Earth's magnetic field on the ions and the electrons. This behavior was predicted by [King and Knauer] in their feasibility study for the plasma generator. The vertical lines on the spectrum of Figure 6, spaced 1/10 of a second apart, are thought to be caused by the dc electric field resulting from polarization of the background plasma as the electron beam traverses it. 104 4. THE BLACK CLOUD At the right-hand side of the spectrum of Figure 7 is a sudden sharp increase in noise This is the first of the phenomena which we associate with the Black Cloud. The noise reaches an amplitude of over 10 mV r.m.s., with a I//2 spectrum in intensity, down to a low-frequency limit of about 80 Hz, and persists for the remainder of the flight, masking any other events such as whistlers. The brief blank period near the beginning of this noise has been attributed to a large dc spike or step of about 1 volt amplitude which temporarily blocks off the pre-ampliners. The fading of the high-frequency stations, described earlier, starts 4-5 seconds after the sudden increase in the low-frequency noise. We now consider, but reject, several of the most obvious mechanisms which might explain these events : 1) The high-frequency signals would be excluded from the nose cone if it were suddenly enveloped in a cloud of dense plasma with plasma frequency high enough to reflect the sign, is from the high-frequency stations. This cannot be the explanation because : a) Onboard measurements of the antenna impedance did not show the large change which would be associated with such a dense cloud surrounding the antennas. b) The frequency of the plasma frequency emissions did not change appreciably at the time of the Black Cloud. c) Assuming that the source of the dense plasma is the argon plasma generator on the accelerator payload, it cannot fill the required cylindrical volume to a plasma density high enough to exclude the high-frequency stations. 2) We next conjecture that the fade-out of the high-frequency stations could be caused by increased absorption due to heating of the ionospheric plasma either by the electron beam or by the plasma source. However, any such heating decreases rather than increases the elec tron collision frequency and hence will reduce absortion rather than increase it. 3) Scattering of the high-frequency signals from a turbulent cloud with dimensions of the order of 1 km is not tenable either, because of the sudden decrease in signal strength. Some of the events could be explained if the nose cone had become enveloped in a slowly expanding volume of turbulent plasma with a sheath region of enhanced plasma density a few tens of metres thick. The low frequency 1//noise is evidence of electrostatic turbulence within the volume. Such a turbulent region has been predicted by [Linson] for a spacecraft which is emitting a beam current much greater than the thermal current of electrons which it can collect, whereas the Electron Echo payload was emitting a beam current only about 1/10 the thermal electron current while the mylar disk was deployed and only about twice the thermal current when the skin alone was used to collect thermal electrons. 5. SUMMARY We find that, as predicted by Kellogg and Jones, the beam loses no significant energy to insta bilities. In fact the beam loses no significant energy to all radiation processes combined. (This is shown much more directly by the particle experiment, of course.) Even so, within a few kilometies of the beam, the radiation can easily be detected. We believe that the main features of the radiation can be accounted for by Cerenkov-cyclotron emission by the beam electrons and the plasma generator ions. 105 ACKNO WLEDGMENTS We thank Professor J.R. Winckler for the opportunity to take part in the Electron Echo Experiment. Pitch-angle and electron gun data from the accelerator payload were provided by R.A. Hendrickson and R.W. McEntire. The electronics package was built, tested and calibrated by R.L. Nichols. The wave observations of the experiment were supported under Grant NGL-24-005-008 from the National Aeronautics and Space Administration. DISCUSSION A. Eriatar. / should like to comment with respect to the previous question. Your considerations on the tenuous beam are by means of a test particle approach : a test particle in a plasma creates a wake with which the second test particle interacts. This is a perfectly legitimate way of considering wave- particle interactions in the plasma. The second thing is with respect to the stabilisation. The fn t is that two-stream instability, which one would expect to tear such a beam apart, is not observed. hu~e you analyzed that in terms of thermal effects? In other words, have you considered the existence of a hot plasma which would cause the waves or particles to be scattered over several wavelengths before the instabii.'y could build up ? Your experiment would show this better than anything else. We know what is enough to stabilize the two-stream instability and your current measurements should give you an indication about what thermal energy density in the plasma is, i.e. what the temperature is in the surrounding plasma into -which the beam may flow. This should put a limit on the temperature. I just wondered whether you may be overlooking something of this kind when you do a cold plasma analysis on something which had been stabilized by thermal effect, which would be unstable in the cold plasma situation. D. Cartwright. When this experiment was first proposed, in about 1965, Tom Jones (Univ. of Minnesota, M.S. Thesis, unpublished), a graduate student of Professor Kellogg, worked on this problem and came out, we think, with the correct results. He analyzed this beam plasma situation for all kinds of instability and, of course, he started with the two-stream instability. The two-stream instability has a growth rate something like the plasma frequency, only for an infinite plasma with beams of the same intensity. It turns out that the main limiting effect is that you have to fit the wave into the transverse dimensions of the beam. This places a severe restriction on the kind of waves which can grow and in fact they propagate out of the beam system before they have grown even one e-folding time from the thermal background. This, we will not be able to detect and it would have essentially no effect on the beam. Incidentally, they found that with this boundary condition of the wave hnving to fit across the beam system, the fastest growing instability was a whistler mode instability. C. Oddou. Have you an explanation concerning the interpretation of the HF noise by Cerenkov emission and the delay time observed? D. Cartwrigkt. What we can explain is the beginning of the delay time in terms of wave-group velocity but what we do not understand is the immediately decreasing amplitude. C Oddon. How do you justify the delay time you observed with Cerenkov emission? D. Cartwrigjit The radiation is into a wave mode with very low group velocity, near the upper hybrid resonance frequency and the delay time of about 3 milliseconds is more or less what we would expect for the time that it takes for the waves generated near the beam to propagate out to the nose cone. What 106 we do not understand is why the amplitude falls off after 3 milliseconds. That is very difficult. We would expect it to go up to some kind of a" plateau " and stay that way until about 16 milliseconds after the pulse. We do see radiation for about 3 milliseconds after the pulse... I have no explanation for what is going on... B. Holtqrâf. / would like to ask about the direction of propagation relative to the magnetic field. If I understood you right, you were observing radiation propagaling practically along the magnetic field. D. Cartwright. We cannot tell and that is what makes it difficult to calculate the radiated power, too. Our antennas were aligned with the axis of the nose cone; so, if the antennas were symmetrical, we would have zero response for waves propagating perpendicular to the axis of the nose cone. In fact, the antennas are highly unsymmetrical, so we do have a response even for waves propagating exactly per pendicular to the axis. The axis of the nose cone made an angle of about 20° with the magnetic field. But we just do not have enough instrumentation to determine what the propagation angle is. However, at the upper hybrid resonance frequency, the group velocity goes to zero for propagation perpendicular to the magnetic field; so the electric field becomes very large. R.P. Singh. How do you justify considering the electrons twice, once when they are emit'.ing electro magnetic waves and then again when they are undergoing interaction with these waves ? D. Cartwright. / do not think we are considering them twice. The way we have calculated the Cerenkov radiation is simply as single-particle radiation and then we have considered the waves propagating in the background plasma. The electron density in the beam is only about 1110 th at most and at other limes about 1/100 th of the ambient electron density near the F-layer peak. So we think that it is more or less justified not to take too much notice, at least at this stage, of the collective effect of the electrons. We have just calculated single-particle radiation in a background plasma. 107 STUDIES OF VLF EMISSIONS IN THE SATELLITE ARIEL 3 T.R. Kaiser Department of Physics, University of Sheffield, Great Britain ABSTRACT Ariel 3 was a near-Earth satellite (altitude 500-600 km) with a high-inclination orbit. Tape recorder storage provided almost continuous data over a period of 10 months at all magnetic latitudes and local times. VLF emissions were observed primarily in two regions at high invariant latitudes (70 to 80° A) and at medium latitudes (50 to 60° A). Medium-latitude emissions are generated close to the equatorial plane by the transverse resonance instibility and have a strong storm-time dependence. They also exhibit a marked longitudinal structure which co-rotates with the Earth. High-latitude emissions are an auroral-oval type of phenomenon with pronounced maxima at 23 and 14 h MLT. These are attributed, respectively- to precipitation of soft electrons from the magnetospheric tail and from the cusps on the solar side. 1. INTRODUCTION The Ariel 3 VLF experiment was designed to study the characteristics and world-wide distribu tion of VLF phenomena. The satellite orbit (inclination, 80° ; altitude 500 to 600 km ; period, 96 min) was chosen to optimise the global coverage; it surveys the whole range of geomagnetic latitudes and, in a period of some SO days, covers all local times. Data storage was by means of an onboard tape recorder which was read out once per satellite revolution. Signals, received on a single 14-turn screened loop aerial (3.0 m2 in area, coaxial with the spin axis), were distributed to three channels each of 1 kHz bandwidth to 3 dB points on 3.2, 9.6 and 16.0 kHz respectively; an additional channel on 16.0 kHz with 100 Hz bandwidth facilitated the identi- 109 fication of CW signals from GBR (Rugby). The minimum detectable signal levels were approxima tely 6.1(TU, 6.10"13 and 6.10"'*/Hz"' at 3.2, 9.6 and 16 kHz respectively and the receivers bad a logarithmic response with a dynamic range of 75 dB. On the three 1 kHz bandwidth channels, the peak, mean and minimum signals in each 28 s period (~ 2° along the orbit) were recorded. The peak and minimum reading circuits had time constants of 0.01 s and 0.1 s respectively and were reset imme diately after read-out. The mean reading circuit actually provided a ' running mean ' with a time constant of 30 s. This arrangement enables information to be obtained concerning the nature of the signals. For instance, impulsive signals such as whistlers are easily distinguished from broad band noise such as hiss; the receiver parameters were such that white noise produced approximately the same levels from the peak, mean and minimum outputs. Figure I. — Natural VLF emissions at 3.2 kHz, 1967 May 26, 1253 to 1423 UT. Ordinate : measured signal level in dB above 10~"y1Hz~x. Abscissae: minutes of time along the orbit; A: invariant latitude; X : geographic latitude; H ii r | ii ii , ii ITI i n i ,T i 11 11 rti | i i M 11 .TTTTTTTTTTr.-ni i ,, i n i (in i ,•! in | riio \ t / :Jj |lil']i ;i 60- n 20 30 <0 50 SO 70 80 90 1 ' J 3D 30 60 60 30 30 A . I . .1 1 . . 1 . . l . i . . 'eV ' 30 ' EO ' -30 -50 -60 -30 EQ 30 60 t> • • . .1 !•• i 300 0 60 120 180 LI io l o's ' "Mi" ' 18 ' 'ai' ' MJ i • 12 18 ' ' 'oo' SZA « 'it ' ' +W •*' 110 Ariel 3 also carried an experiment provided by the University of Birmingham (Professor J. Sayers) which measured local electron density and temperature. The VLF measures of r.m.s. magne tic field can thus, on the assumption of quasi-longitudinal propagation, be converted into a power flux using the local refractive index calculated from electron density and the terrestrial magnetic field strength. Results in this paper will, where appropriate, be given as free space equivalent r.m.s. magnetic field, i.e. the field strength in a plane wave in free space having the same power flux as the wave measured at the satellite. The satellite, and the VLF equipment, functioned continuously from launch (May 5, 1967) until re-enf-y (December 13, 1970) after 20090 revolutions. Tape-recorded data were available for approximately 10 months from launch and. after failure of the tape-recorder, real-time data were avai lable when the satellite was within range of a tracking station. A 3.2 kHz record obtained during the great magnetic storm which commenced on May 25, 1967, is shown in Figure 1 (peak, mean and minimum outputs are given). In the equatorial regions, low, mean and minimum with high peak outputs indicate impulsive signals originating in thunder storm activity. In the northern polar region, the satellite passed twice through an intense high- latitude hiss zone (at approximately 84 and 86 min) while, at medium latitudes, intense zones of emis sion are apparent on both morning and evening sides of the Earth (maxima at 0, 30, 50 and 76 min). Many individuals and organisations contributed to the successful outcome of the Ariel 3 project and the data analysis and interpretation leading to the results described in the following are the work of a number of members of the Sheffield Space Physics Group, especially Doctors K.. BuUcugh and A.R.W. Hughes. The work of reducing the observations is still far from complete and the results presented here refer especially to the period 5 May to 24 July, 1967, i.e. to northern hemisphere summer and southern hemisphere winter. During this period, all magnetic latitudes and local times were sampled. 2. fflGH-LATITUDE EMISSIONS The high-latitude zone, occurring at invariant latitudes above 60°, was observed on Injun III [Gurnett]. At the Ariel 3 sensitivity levels, it is identifiable on almost all high-latitude passes. The occurrence and intensity do not correlate strongly with magnetic activity (K„) and the latitudinal zone width (to 10 dB points) decreases with increasing signal intensity, being of the order of 5° for strong emissions. The spectrum shows a diurnal variation, linked to the diurnal variation in occurrence (see below). The averaged spectrum is flat (to within about 1 dB free space equivalent - f.s.e.) at 06 and 18 h (minimum occurrence) while the 3.2 kHz emissions average 5 dB more intense at midnight and 4 dB free space equivalent less intense at noon than those at 9.6 kHz. These spectral features are not inconsistent with Cerenkov emission from low-energy electrons [Jôrgensen]. The morphology of the zones of emission, as obtained from Ariel 3, has been described by [Hughes et al., b]. Emissions occur at all local times but are most frequent near midnight and in the early afternoon. At midnight, the frequency of occurrence at 3.2 kHz of emissions greater than 10-11y2Hz'1 free space equivalent (mean signal) is approximately the same in both hemispheres (80 %) but, in the afternoon, the peak occurrence in the northern hemisphere (summer) is 90 % com pared with 50 % in the southern hemisphere (winter). Ill Figure 2. — High latitude emissions. Percentage frequency of occurrence of VLF emissions at 3.2 kR*., mean intensity > 10~l2y2 Hz'1 free space équivalent, in the northern hemisphere (1967, May 5 to July 24). The coordinates are invariant latitude and magnetic local time (centred dipole). These data are illustrated in Figures 2 and 3, which show the frequency of occurrence of emis sions at 3.2 kHz in the northern hemisphere with mean intensity greater than 10~12 and 10_IO72Hz~1 free space equivalent respectively. Thus, the emissions have maximum occuirence at — or just after — magnetic midnight and at 14 to IS h MLT at invariant latitudes of 72 and 78° respectively. There are two well-defined sectors of minimum occuirence between 05-06 h and 19-21 h MLT, 112 Figure 3. — High latitude emissions. Percentage frequency of occurrence of VLF emissions at 3.2 kHz, ?if iH!?ns"y > 10~ y Hz'1 free space equivalent, in the northern hemisphere (1967, May 5 to July 24). The coordinates are invariant latitude and magnetic local time (centred dipote). separating the active regions. A band of Minimum occurrence at about A = 68° separates the high- latitude emissions from those at medium latitudes. It is possib'e to define a locus of maximum occur rence (the broken curve in Figure 2) which varies in latitude from 79°A at noon, 76°/i at 18 h and 78°/i at 06 h to 72°J1 at midnight, giving the familiar oval shape which is characteristic of many auroral phenomena. Figure 4 shows the relationship between this locus and other high-latitude phenomena. 113 Il II II lui" " '-' }l I I l I l I I I 1 1 -I r"- 0 2 A 6 8 10 12 14 16 18 20 22 24 MAGNETIC LOCAL TIME Figure 4. — High latitude emissions. Location and occurrence of 3.2 kHz emissions in relation to other high latitude phenomena. A : locus of maximum occurrence of emissions obtained from Figure 2. B : limit of closed field lines, 35 keV electron " background " boundary, Alouette 2. C : locus of minimum occurrence of emissions (dividing the high and medium latitude activity). D : stable trapping region, 280 keV electron boundary [Williams and Mead]. E : percentage frequency of occurrence of VLF emissions (> I0~I2y2 Hz'1 free space equivalent) at the locus of maximum occurrence. Shaded region : auroral oval [Feldstein]. It is seen to lie a few degrees poleward of Feldstein's auroral oval [Feldstein] and of the boundary of the closed magnetic field lines given by [McDiannid and Burrows]. It is noteworthy that the locus of maximum occurrence in the southern hemisphere is more circular than that in the northern hemi sphere, being at 15° A at 12 h and 24 h, and at 74 and 72''A respectively at 06 and 18 h. This difference in shape could be associated with the orientation of the dipole axis to the Earth — Sun line during the period of observation [Hughes et al, a]. 114 Figure 5. — The location of the high latitude emissions in invariant latitude (A) as a function of Kp for various magnetic local times. IIS In order to study the relation between the high-latitude emissions and magnetic activity, the data were divided into four magnetic local time ranges : 00 ± 03 h, Ot +03 h, 12 + 03 a and 18 + 03 h. The location of a zone of emission was taken as the invariant latitude of the zone maximum. Figure 5 shows its variation with K„ for both hemispheres, the solid lines representing least squares fits. It is clear that there is a significant equatorwards displacement with increasing Kp, the shift per unit Kp interval (AA) being given in Table 1. Table 1 MLT (± 03 h) AA° (North) AA° (South) 00 — 0.7 — 0.7 06 — 1.0 — 1.3 12 — 1.6 — 1.9 18 — 1.0 — 1.7 Note that the equatorwards displacement is significantly greater at noon than at midnight, in agreement with the results of [Feldstein and Starkov] for the mean position of the auroral belt. As stated previously, no general pattern of occurrence or intensity as a function of K, has emerged. There appears, however, to be a tendency for the more intense emissions (> 10"9v2 Hz-1 free space equivalent) to be relatively less frequent when K, exceeds 4. This is consistent with the behaviour of other phenomena such as the polar radio-aurora [Bullough, a]. 3. VLF EMISSIONS AT MEDIUM LATITUDES Unlike the high-latitude phenomena described above, the medium-latitude emissions, occurring on closed field lines, are strongly correlated with magnetic disturbances. The evolution of the emissions during the great magnetic storm of May 2S/26, 1967 has been described in detail by [Bullough et al., a, b]. During this period, the satellite was in a favourable dawn-dusk orbit and before the Storm Sudden Commencement (SSC) the mean intensity at zone maximum on 3.2 and 9.6 kHz was typically 10"" to 10"9y2Hz-1. The effect of the solar wind enhancement is first observed at 3.2 kHz on the morning side ; shortly afterwards the SSC occurs and enhanced 9.6 kHz morning emission appears. These morning emissions reach a relatively steady mean intensity (of about 10"7 and 10"6y2Hz_1 on 9.6 and 3.2 kHz respectively) which is maintained until, during the initial recovery phase of the storm, the solar wind pressure drops, when the morning emissions fall to the pre-storm level. The evening emissions remain low until the initial recovery period, when they rise to intensities comparable to those observed in the morning. This is in agreement with the establishment of the symmetrical ring current. The evening emissions decay, following the drop in solar wind pressure, somewhat more slowly than the morning ones. During this period of decay of the ring current, there is some recovery of the 3.2 kHz emis sions from their sharp drop to background level and moderately strong emissions continue, in both morning and evening, at 3.2 kHz and, to a lesser extent, at 9.6 kHz. 116 During intense emissions the high-latitude boundary is usually well denned with a decrease in intensity of 5-15 dB per observing interval (~ 2° along the orbit) towards the pole. In the pre-storm period the 3.2 kHz boundary (denned as 10 dB down on the zone maximum) was typically at 64-65°A, while that for 9.6 kHz was centred around 57-59°A. During the main phase, both boundaries moved to a lower latitude of about 52°A (L = 2.6). The first displacement and final recovery of the morning boundary appear to be associated with the onset and termination of the solar wind enhance ment. The evening boundary moves to lower latitudes approximately in phase with the decrease in DST. [Bullough et al, a, b] have shown that the emissions, on a given shell, are limited to frequencies somewhat below the minimum gyrofrequency encountered on the field line; thus, the source must lie close to the geomagnetic equator. From this we conclude that the mechanism is that of cyclotron resonance, since [Kennel and Petschek] have shown that the wave growth in this case is restricted to the vicinity of the equator. Their weak diffusion theory also predicts a limiting trapped particle flux associated with a wide-band whistler-mode field of the order of 10~2y at the equator. The equi valent field at low altitudes is of the order of 0.1 y. If we take the saturation levels stated above and assume that, because of the minimum gyrofrequency cut-off, the bandwidth is approximately that of the observing frequency, we find that the mean signals at zone maximum obtained during the May 25/26 storm correspond to a wavefield strength at the satellite of about 0.05 y. Having regard for the uncertainties in the theoretical prediction, this is in good agreement with [Kennel and Petschek]. From the observations on frequencies {/) of 3.2, 9.6 and 16 kHz, it appears that the emissions during this disturbed period have a spectrum such that the wavefield in y2Hz_1 varies as/"" where n ~ 2. When corrected for the variation of local refractive index with frequency, this would indicate a power spectral index n ~ 1.5. [Thome and Kennel] have shown that, in the absence of duct guiding, emissions will be largely reflected at an altitude where the wave frequency equals the lower hybrid frequency. This would usual ly occur at altitudes above the satellite for the Ariel 3, 3.2 kHz channel. [Bullough et al, a, b] have con cluded, from this and other evidence, that these emissions have been duct-guided down to an altitude close to the satellite. During quiet periods (K„ > 2+), the 3.2 kHz signal is often weaker than that at 9.6 kHz, suggesting non-ducted propagation on these occasions. [A.R.W. Hughes] has analysed data from the first 80 days of Ariel 3 (1967, 5 May to 24 July) to produce maps of occurrence of emissions as a function of invariant latitude and magnetic local time. An example is given in Figure 6 which shows the frequency of occurrence of medium latitude emissions at 3.2 kHz with intensity greater than 10""y2Hz"' free space equivalent for magnetically quiet periods (Kp < 2+). The most significant features are the zones of emissions in the dawn and dusk sectors; the former is surely related to the ' chorus ' observed at ground level but there do not appear to be well established ground-level observations of the latter zone. Although Figure 6 suggests somewhat dissimilar distributions in the two hemispheres, this could be misleading since a given local time zone in, say, the southern hemisphere will have been sampled during a different period of the 80-day interval than the same time zone in the North. Recent analysis of a subsequent period (13 Aug.- 31 Oct., 1967) gives a similar distribution in latitude; the dawn sector zone is still clearly apparent (although less than during the previous period) bur the evening zone is much less pronounced. Although for both periods the data referred to here were for Kp < 2+, it is important to note that the earlier period was generally more magnetically disturbed than the later one. A most significant feature of the medium-latitude behaviour is the occurrence of zones at particular longitudes which corotate with the Earth and may persist for a day or so. They occur at somewhat higher latitudes (5-10° polewards of the more normal zones of emission shown in Figure 6) and have a width in invariant longitude of the order of 10° to 10 d.î below maximum intensity. For this reason, they frequently appear on a single pass and not on adjacent ones. On occasions, when the satellite closely followed a magnetic meridian, conjugate peaks were observed in both hemispheres. 117 MAGNETIC LOCAL TIME Figure 6. — Medium latitude emissions. Percentage frequency of occurrence of VLF emissions at 3.2 kHz with intensity above 10~ui*Hz~l free space equivalent for the period 1967, May 5 to July 24, during magnetically quiet conditions (Kp < 2+J. The intensity frequently approaches the peak saturation level observed during the great storm of May 1967 (see above). [Bullough and Lefeuvre, unpublished] have studied a number of occasions when this occurred and have, from a composite of the data, derived the representative longitude profile shown in Figure 7. It has tentatively been suggested [Bullough and Lefeuvre, private communication] that these zones first occur, following a substorm, in the dusk and/or dawn sectors. A further feature is the occurrence, on a significant number of occasions, of a zone of emission localised at 340° East magnetic longitude in the southern hemisphere; this occurs at latitudes somewhat equatorwards of the normal zones shown in Figure 6. 118 -20 -15 -10 -5 0 5 10 15 20 Relative Invariant Longitude (degrees.) Figure 7. — Representative profile of localised (in longitude) zone of mid-latitude emissions. Enhanced VLF signals are also observed at or near the equator. These are a night-time pheno menon with a sharp boundary at dawn and dusk; it is, therefore, suggested that they are initiated by equatorial thunderstorm activity. 4. SUMMARY AND CONCLUSIONS The location of the zones of high-latitude emissions places them on tte poleward side of the trapping boundary, associating them with the precipitation of low-energy electrons of 1 keV or less [O'Brien]. The maximum near midnight seems likely to be associated with particles originating in the plasma sheet, while that on the sunward side would appear to be due to particles from the neutral points or cusps [Hughes et al., a]. The deviation from symmetry about the noon — midnight magnetic meridian is interestin't, suggesting an associated asymmetry in the magnetosphere. It bears similarity with the model of [Brice] based on plasma convection in the outer magnetosphere with the rotation of the Earth causing the re-connection of terrestrial and interplanetary field lines on the day-side to be displaced post-noon. These re-connected field lines then convert over the polar caps and merge downstream in the tail. The equatorward movement of the high-latitude emission zones during magnetic activity presumably follows the move jent of the trapping boundary. Medium-latitude emissions occur on the closed field lines inside the plasmapause and their behaviour is closely related to magnetic activity. During a great storm, the emission intensities satu rate, reaching a limit which agrees well with the prediction of [Kennel and rttschek] based on the theory 119 of weak diffusion of electrons into the loss cone, due to wave-particle interaction. The variation with frequency of the high-latitude boundary agrees with the hypothesis of a rninirnum gyrofrequeucy cut off as is expected if the transverse cyclotron resonance is the generating mechanism. During quiet periods, the mid-latitude zones maximise at 50-60°/l with enhancements in the dawn and dusk sectors. Localised zones, which have relatively narrow longitudinal width and which co-rotate with the Earth, are frequently observed. Detailed discussion of the observations of man-made signals from GBR (invariant latitude, 50.9°) is beyond the scope of this paper (see however [Bullough et al., a, b, e]). The following are, nevertheless, some salient features. The wavefield in the northern hemi sphere has a broad maximum in intensity near 5Q°A and a high-latitude boundary (or minimum) coincident with the medium-latitude trough. Superimposed is a sharp maximum (=: 10"3 to 10"2v field strength at the satellite) centred on the field line passing through GBR. In the conjugate hemi sphere, the whistler-mode signal is generally comparable in intensity to that in the North, except that the main peak is broader and displaced about 6° to the West of the computed geomagnetic conjugate point. The maximum intensity in the South is about 12 dB less than that in the sharp peak in the North. DISCUSSION B. Hnltqvist. You did not say anything about the relation between your observations of hiss at the equator and the recent observations of large fluxes of particles there. You talked about trapped radiation, but I understand you meant trapped VLF radiation. T. R. Kaiser. / am speaking of enhanced VLF signals observed at the satellite during equatorial crossings. As I have said, this is a daytime phenomenon, with a sharp cut-off at dawn and dusk. It therefore seems reasonable to conclude that the emissions are initiated by radiation penetrating from below the ionospheric D-region. We still have to look more carefully at the ratios between our peak, mean and minimum reading channels, to see if this is just a superposition of a high spheric rate from equatorial thunderstorms. We suggest that the post-noon maximum is associated with precipitation from the neutral points (or cusps). As 1 have said, the displacement to post-noon may be related to the asymmetry produced when the effect of Earth rotation is included in the pattern of magnetospheric convection. G. HaerendeL. Do you think that the VLF emissions are emitted at low altitudes or at high altitudes? T. S. Kaiser. We hate concluded that the medium-latitude emissions are generated at or near the equator, that is at the top of the field line. On the other hand, it seems most likely that the high-latitude emissions are generated at lower altitudes. 6. HaerendeL The only particles that could generate this noise are roughly one-keV electrons. There are not many high-energy particles at these latitudes. So I think it is a simple exercise to see what the electrons can do. T. B. Kaiser. [Jargenseh] has shown that observed fluxes of soft electrons could just about produce the observed intensities by the Cerenkov mechanism. 120 G. Haerendel. / have another comment on the observations : you mentioned the persistence of certain longitudes with enhanced VLF power over 2 days. What was the latitude of this emission? T. R. Kaiser. These isolated peaks occur some 5 to 10° polewards of the background activity, which itself maximises between 50 and 60°. There may also be some frequency dependence due to the minimum gyrofrequency cut-off. G. Haerendel. / just wanted to mention in that connection measurements by [Bewersdorff et al.] of the ion current, which have shown that the plasmapause can have a quite irregular shape and strong gradients in longitude. It looks as if sometimes deformations of the plasmapause are corotating and are persisting for at least many hours, perhaps even 2 days. I would like to suggest an interpretation of the persistence of enhanced VLF emissions at certain longitudes as being due to a strong distorsion of apart of the plasmapause corotating with the Earth. When electrons by the VB drift go through this surface and enter the cold plasma, they may become subject to the instability causing the VLF emission. Could you briefly indicate what kind of antenna you have used? T. R. Kaiser. We used a loop antenna supported near the boom extremities of the spacecraft. Great care was taken to screen the loop and arrange its geometry to reduce interaction with other experiments, especially to minimise interference form the 6 kHz square wave on the Birmingham plasma probes which were only a short distance from our loop aerial. In the event we found in orbit that any such interference was below our receiver noise level, while the sensitivity was sufficient to observe emissions on all revolutions, filling the 80 dB dynamic range of the receivers. A. Babnsen. Concerning the auroral or the northern VLF emissions, I want to ask what the altitude of the satellite and whether there is any indication on where the noise came from, below or above. T. R. Kaiser. This satellite has a near-circular, high-inclination orbit with altitude between 500 and 600 km. The instrumentation did not allow us to obtain wave normal and Poynting vector directions. 121 EXPERIMENTAL STUDY OF ELECTRON PITCH ANGLE DIFFUSION IN THE PRESENCE OF VLF MODULATED HISS J. Etcheto, R. Gendrin and D. Lemaire Groupe de Recherches lonosphériques, Saint-Maur, France ABSTRACT We present results obtained during a rocket experiment (Kerguelen Islands, March-April 1968) in which particles and VLF wanes were measured simultaneously. VLF modulated hiss was present during the flight. The electron precipitation if as observed to increase at the same time as the amplitude of the VLF waves. Assuming a gyroresonant interaction to be the cause of this phenomenon, the region of resonance has been located. It is found to be wide in latitude. The distribution function of the electrons in the vicinity of the loss cone was measured partially. The anisotropy was observed to decrease when the VLF field increased, so increasing the pitch angle diffusion, and to increase when the field decreased. From this measurement of the anisotropy, we are able to deduce values for the diffusion coefficient at the maxima and minima of the modulation. The values obtained in this way are consistent with those obtained independently from the amplitude of the VLF waves. At the same time a ULF wave was present, with approximately the same periodicity as the VLF hiss modulation. We can place our observations in the framework of Coroniti and Kennel's theoretical work. The case is one of succession of weak and near-strong diffusions. The ratio of the flux at the maxima and minima of diffusion is of the order of 2, as predicted by theory. In order to study wave-particle interactions in the magnetosphere between electrons and the whistler mode, rocket experiments were performed at Kerguelen Islands (L » 3.7) in March-April 1968. The description of this experiment and the preliminary results that are related with wave pro pagation phenomena have already been published [Meyer; Berthomier; Gendrin et al., 1970 a; Sukhera], In two other papers [Gendrin et al., 1970 6; Etcheto et al., 1971], hereafter referred to as Papers 1 and 2, we reported the preliminary results which were obtained with the particle detectors and we described a VLF associated particle precipitation event that occurred during the third flight (April 1, 1968). The purpose of the present paper is to give a more refined picture of this phenomenon and to correct the slight errors that appeared concerning this event in Papers 1 and 2 (See Appendix). 123 1. PERTURBING EFFECTS ON THE PARTICLE DETECTORS AND THEIR ELIMINATION A more precise analysis of the particle data has shown that there were two perturbing effects. The first one is due to the sensitivity of the detectors to the light : this effect introduced errors in the counting rates of the low energy channels. The second effect is due to the relatively large integration time of the detectors (=; 0.4s) as compared to the spin period of the rocket (~ 1 s); this effect produced an apparent attenuation of the particle distribution anisotropy. 1.1 Perturbations due to the light In spite of the precautions which were taken, part of the sunlight or of the Earth albedo was able to penetrate the detectors after reflexions inside the apertu™ system. The generated noise corre sponds to pulses of small amplitude : therefore, the counting rates of the low energy channels were most disturbed. This effect was more important for the nroton detectors than for the electron detectors (because of differences between the two types of scintillators) and more important for longi tudinal detectors than for transverse detectors (which sometimes did not see at all either the Sun or the Earth). A careful analysis of the data, which was made with the help of a computer program [Lemaire], allows us to draw the following conclusions - — Contrary to what has been published in Paper 1, Figure 1, the energy spectra do not present a breaking: of the slope. For instance, at the culmination of the rocket (=c 400 km), the electron spectrum fits well an exponential law : J (> E) = k exp. (— E/E0). (1) TUK5VEK5E DETECTOIS i VFIULLEL DETECTOTS Figure 1. — Mean energy spectra of electrons at the rocket culmination f =: 400 km), during the third flight. 124 The characteristic energy E0 is of the order of 75 keV (Figure 1), in agreement with the measurements of [Pizzella et 3/.] for L = 4. — Contrary to what has been published in Paper 1 (p. 6174), the longitudinal electrons do present also a quasi periodic modulation, associated with the transverse modulation (Figure 2). However, the absolute values of the longitudinal fluxes remain questionable. Figure 2. — Modulations in the mean transverse and parallel electron detectors during the third flight. 1.2 Perturbations due to the duration of the measurements Due to misalignment of the rocket spin axis with respect to the local geomagnetic fieldan d due to the anisotropy of the electron distribution function, the flux which is received by the transverse detectors should be modulated at twice the spin frequency (s: 2 Hz). The integration time of each energy channel being 0.4 s*, the net result is a smoothing of the anisotropy effect. We define the anisotropy coefficient by the equation : a = 1 _ J (76°)/J (90°) (2) in which J (90°) and J (76°) correspond to the extreme values which were sampled during one spin period. Therefore a smoothing of the observed angular variation of the fluxes leads to a smaller value of the anisotropy coefficient. Corrected values of this coefficient are presented on Figure 3 and 4 for two different energy channels. One notices that these fluctuations are anticonelated with the fluctuations of the mean value of J (90°), and that the anisotropy is greater for higher energy particles. Besides, the absolute values of a are approximately two times larger than the ones which were presented in Paper 2, Figure 1. *lnitially this integration time was choosen equal to 0.1 s; but due to interferences produced by the telemetry commutators on the VLF experiment, we were obliged to increase this integrationt time. 125 ELECTBDK5 55 < ï. < 110 U-V — —r — —r i i I 1 10 - 1 KEBCUELEH WttH. '. , 19ÉQ I.S - \ A r\ - - WVJ^y V _/. r y 01) ^—<^ ^— ~~~~~ \ i i i.^AfVVYV-: 03.^9 0.1 JU 03J1 CJJ.î 03 1-1 TTHE D T Figure 3. — Variation of the mean perpendicular flux J (90°) and of the partial anisotropy a = 1 — / (76°)JJ (9(f) for electrons of energies between 55 and 110 keV. The two variations are clearly anticorrelated, indicating a tendency towards isotropy during periods of increased fluxes. Figure 4. — Variation of the mean perpendicular flux J (90°) and of the partial anisotropy a = 1 — J (76°)IJ (90°j for electrons of energies between J10 and 210 keV. 1LHIKU\5 l)(xLc:)0UV 1 1 1 \ |l KLRtiL'LLfcN APRIL . I'lWJ " - 1 1 . 1 1 1 126 2. STUDY OF THE VLF ASSOCIATED PRECIPITATION EVENT 2.1 Description of the event and its interpretation During the third flight (April 1, 1968, near 03.30 UT), the flux of trapped electrons (a =; 90° at 400 km) presented a quasi periodic modulation, in phase with a similar variation of the intensity of a VLF hiss near 4 kHz (Figure 5). This modulation concerning electrons and right-handed waves [Gendrin et al., 1970 a], we are dealing with an (e, R) wave-particle interaction taking place at a higher altitude [Gendrin et ai, 1970 b]. The backward interaction of the waves upon the particles leads, for such an interaction, to a diminution of the electron pitch angle in the region ot interaction, hence to a lowering of their mirroring altitudes [Brice, a; Gendrin]. The flux increase that we observed at low altitude during the peaks of the modulation is a consequence of such an effect. Figure 5. — Simultaneous variation of the mean perpendicular flux of electrons (55 < E < 110 keV), the integrated VLF noise (3.5 < f < 4.5 kHz) and the integrated VLF noise (0.08 < f < 0.5 Hz). The first two phenomena appear clearly in phase, the propagation time between the equatorial region and 400 km being approximately the same for the electrons and for the VLF waves. The origin of the phase shift that appears on the VLF envelope is not yet understood. 03.30 03.35 1 1 1 1 1 1 1 1 it . "• 1- g §1 - zs" *•£• ~ o 1 1 1 1 1^- > 1 127 The variation of the anisotropy that we observed at 400 km between 76 and 90° corresponds to an anisotropy variation of a very small part of the angular distribution function in the equatorial region. But this part is the most interesting one, because it is situated in the vicinity of the loss cone angle, a value around which any increase of the diffusion leads to a large decrease of anisotropy. This is precisely what we observe. The maximum values of the mean perpendicular flux (at 400 km), which are associated to an increase of the diffusion, are correlated with both an increase of the parallel flux (Figure 2) and a large decrease of the anisotropy near 90° (Figures 3 and 4). 2.2 Localization of the region of interaction For an (e, R) interaction, the emitted frequency to/2re is related to the local electron gyro- frequency toB/2n and to the parallel component of the particle velocity ny : in which k is the wave number, given as a function of frequency by the dispersion relation for the whistler mode by : 2 2 c fc = a>o o)/(coB — with local plasma frequency f0 = co0/2 n . Let A be the latitude, along the line of force, of the interaction region. The rough constancy of the magnetic moment of the particles allows us to compute tig (A) for particles that have a total velocity v and that mirror at 400 km. Using the so-called magnetic model for the cold electron density distribution, fl = fa .fB (in which fa is a constant approximately equal to 1 MHz), it is possible to compute the ratio w0/coB at every point along the magnetic field line, and therefore to deduce the value of the emitted frequency as a function of A, the total energy of the particle being a parameter (Figure 6). For the observed frequency range of the emission (3.5-4.5 kHz), and for a total energy of 100 keV, one sees that the interacting region is not situated at the equator but slightly off, a result which is in agreement with [Liemohn's] theoretical computations. One could argue that there is an interaction region associated with each value of the total energy and consequently that there is no reason for attributing any specific latitude to the interacting region. However, the frequency for which the amplification is maximum is in fact the frequency which satisfies equations (3) and (4) in which the parallel velocity of an individual particle is replaced by the mean parallel velocity of the whole distribution function. This has been demonstrated explici tly for interactions between protons and ULF waves [Gendrin et al., I971] but the argument can be transposed easily to interactions between electrons and VLF waves. As the mean electron energy is of the order of 80 keV (See Section 1), it is perfectly justified to take A = 25° as the latitude, along the line of force, at which the observed interaction took place. 2.3 Computation of the diffusion coefficients There are two methods for computing the pitch angle diffusion coefficients. The first one is based upon the measurement of the VLF field intensity both on the ground and on board the rocket [Gendrin et a/., 1970 a, b] : 1 2 B/ = 6.10-*y.Hz- ' (5) GEOMUaiEIlC LATITUDE (DEGKEBS) Figure 6. — The emitted frequency as a function of the geomagnetic latitude of interaction and of the total energy of an individual particle mirroring at 400 km. For a distribution function varying like exp [— EIEB], the parameter is equal to E0. The dotted area corresponds to the frequency range of the observed hiss, indicating that for an e-folding energy of 80 keV, the interaction was maximum at a latitude of the order of 25°. Bf being the spectral density per unit of frequency of the wave. The diffusion coefficient D can be written [Gendrin, 1968] : (6) pu VB0/ in which Bt is the spectral density per unit of wave number and B0 the static magnetic field intensity. One has : (7) ' Ak 2nAf Ak 2B ' ' in which V, is the group velocity of the waves. But for the whistler mode at frequencies which verify equations (3) and (4), one has : a) (8) so that D = to • o)g ©' (9) 129 6 Considering an interaction at a latitude }. = 25° where B0 m 1.4 x 10 T and with a frequency / = 4 kHz, one gets * : 3 2 _1 D0 = 10- rd s (10) The second method uses the measurements of the anisotropy of the distribution function [Etcheto et al.]. [Theodoridis and Paolini] have compu'ed numerically the distribution function of electrons inside and outside the loss cone, according to the theoretical formulas of [Kennel and Petschek]. We did similar computations for the specific parameters which were valid during our experiment (Figure 7). EQUATORIAL PITCH ANGLE! (DEGREES! Figure 7. — Equatorial pitch angle distribution for different values of the diffusion coefficients. a0 is the equatorial value of the loss cone angle. Two of the vertical arrows correspond to the extreme values of the équivalent equatorial pitch angles which were sampled by the transverse detectors at 400 km; the last one corresponds to the equivalent equatorial pitch angle which was sampled by the longitudinal detector. From such curves, it is possible to get the anisotropy as we defined it by equation (2). This anisotropy depends on the diffusion coefficient D. Consequently, the measurement of a gives us directly the value of D. Of course, we have to take into account the change of pitch angle with latitude. When trans posed to the equator, equation (2) becomes : a =1-J„(6.98°)/J„ (7 •20°) (11) */n Papa 1, p. 6176 and in Paper 2, formula (2), a factor 2 71 was forgotten, so that the diffusion coefficients were overestimated. 130 AHlSOnOFI COETTICIDR Figure 8. — The curve giving the variation of (DTE)~AI1 with a, as deduced from Figure 7. 2 Figure 8 gives the variation of a as a function of (DTE)"" , TE being the time of escape of particles (roughly a quarter of the bounce period) which, for 80 keV particles, amounts to = 0.15 s. By looking at Figure 3 or 4, one sees that a is approximately equal to at K 0.2 during the peaks of the flux modulation and 2 3 (13) (D2TEr" > 10 so that Di = 7.10-*rd2.s-' (14) 5 2 D2 < 10~ rd . s~' (15) One sees that D0 and D„ both evaluated at the peaks of the flux modulation and computed by two diffe rent methods are very similar. Moreover, for the value of DTE given by equation (12), the corre sponding " longitudinal " flux for ««o = 14° is 500 times less than the transverse flux, as can be see from Figure 7. This is approximately the ratio that we have measured experimentally (see Figure 1). 2.4 Diffusion strength A useful parameter for defining the strength of the diffusion is [Kennel and Petschek] : I = (DTa)"2/^. 131 If i > 1, we are in the strong diffusion limit. If ( < 1, we are in the weak diffusion limit. Putting the values obtained for D, one obtains : £, = 0.08 at the peak of the flux modulation 2 i2 < 10~ at the minimum. The diffusion lifetime during the peaks TLi = JL,np_) "•' D, \ exB ! is of the order of 2600 s, as compared to the minimum lifetime : 2TE The small value of both Ç, and the ratio T„/TL1 shows that we are not in a case of strong diffusion, a result which is compatible with the fact that the rocket was fired during a VLF event of relatively small intensity. 3. MODULATION BY ULF WAVES As it is shown in Figure 5, a ULF wave was present during the phenomenon. Therefore, it was tempting to interpret this effect within the framework of [Coroniti and Kennel's] theory : the ULF waves are perturbing the diffusive equilibrium reached between the particle precipitation and the VLF waves, and they modulate these two effects at their own frequency. But a problem remains in our case : the VLF hiss and the particle precipitation are not modu lated at the proper period of the VLF waves O 10 s) but at the modulation period of the ULF waves (= 80 s). This notwithstanding, the orders of magnitude of the fluxes during the peaks of the modula tion and during the valleys agree well with [Coroniti and Kennel's] formulas, taking into account the measured values of the wave intensities, anisotropy, amplification coefficients, etc. [Etcheto el al.]. Other mechanisms have been proposed which could be responsible for such associated ULF and VLF waves. [Cornwall, b] described the indirect interaction of a drift wave and a whistler wave, which could lead to a kind of relaxation. Both the ULF and VLF waves would be modulated at the relaxation frequency. Unfortunately, he studied only this effect for drift waves, which, being electrostatic in nature, are not observable, on the ground. [Hagège et a].] have studied the mutual destabilization of particles in the simultaneous presence of a whistler wave and of a drift wave. The VLF should be modulated at the frequency of the ULF wave. Here also, the drift wave is (inobservable on the ground. Another possible interpretation is that the drift wave (of an 80 s periodicity) modulates the distribution functions of both electrons and protons. This will lead to a modulation of both the VLF wave at 4 kHz and the ULF wave at 0.1 Hz. The simultaneous variation of the proton flux that we have observed [Lemaire] could be an argument in favour of such an interpretation. (The corresponding results, which are not yet fully analyzed, will not be presented here.) 132 4. CONCLUSIONS We have observed a modulated precipitation event, associated with a VLF hiss. This event is fairly well interpreted within the framework of the quasi linear theory of gyrotesonant wave-particle interactions between electrons and the whistler mode. The frequency of the VLF emission and the latitude of the interaction region are in good agreement with well-established theories involving a complete distribution function with a given e-folding energy and a given anisotropy. The pitch angle diffusion coefficients which can be deduced from the measurements of the wave intensity or of the particle anisotropy are in good agreement together. Our results show that we were below but near the strong diffusion limit, as one would expect from the relatively small value of the VLF field at the time of the experiment. Therefore, we can conclude that the [Kennel and Petschek's] mechanism is surely the dominant one for determining the limiting flux of particles during intense VLF emissions. On the contrary, the origin of the modulation at 80 s is far less clear : modulation of the electron anisotropy by a ULF wave, mutual interaction of a ULF and a VLF wave, or simultaneous modula tion of these two waves by a third one ? Our own measurements do not allow us to conclude. Only in situ measurements of ULF waves, both electromagnetic and electrostatic, would shed some light on this interesting problem. APPENDIX Due to refined analysis of the data, it has been possible to improve some figures and to correct some assertions which were presented in Paper 1 [Gendrin et al., 1970 b] and in Paper 2 [Etcheto el a!.]. These corrections are summarized as follows : Paper 1. Figures 1 and 6 must be replaced by Figures 1 and 6 of the present Paper. For " The longitudinal detectors do not present a modulation effect " (p. 6174) and " The value of D " (p. 6176), see Figure 2 and equation (10) of the present Paper. Paper 2. Figures 1 and 2 and equations (2) and (9) have to be replaced by Figures 4 and 8 and equations (10) and (14) of the present Paper. 133 CHARGED PARTICLES ASSOCIATED WITH VLF DAWN CHORUS EMISSIONS P. Rothwell, G.J. Jenkins, H.L. Collin Department of Physics, University of Southampton, Great Britain ABSTRACT Six sounding rockets, instrumented to detect charged particles over a wide range of energies (^ 2 key to > 350 key) have been launched from South Uist (L = 3.5), two during VLF " dawn chorus " events, one during a magnetic storm, and three at magnetically quiet times when no VLF emissions were observed at the ground. A feature of the results is that while bursts of enhanced high energy particles were observed in the pre sence of dawn chorus and during the magnetic storm (up to ^ I03 particles cm ~ 2 sec ' ' ster ~ ', a factor of = 103 up on fluxes observed at quiet limes) the low energy (few keV) electron fluxes (typically s 10s electrons cm'2 sec'1 ster'1, keV) did not vary much all through the various firings. Most of the energetic electrons in the enhanced fluxes associated with the VLF chorus had energies > 350 keV. An estimate of around 50 electrons/cc for equatorial electron density on the field line through South Uist during a chorus event made on the assumption that a resonant interaction between waves in the chorus frequency band (1-3 kHz) and the energetic electrons observed from the rocket had taken place near the equatorial plane, agrees well with the direct measurement of the equatorial electron density at L — 3.5 at a similar local time, made from OGO 5 a few hours later than one of the rocket flights. 135 DISCUSSION B. Hultqrist Do you think the L = 3 precipitation mechanism is the same as the L = 6 or 7 auroral precipitation mechanism ? P. Rothwell. No. The precipitation mechanism for low energy ' auroral ' particles (few keV) seems to be different from the precipitation mechanism for higher energy electrons at L — 3, and is probably different at higher latitudes as well. B. Holtqvist What about the anisotropy in the energy range of particles you are working with ? P. Rofiiwen. Satellite observations indicate thai the pitch-angle anisotropy of high energy electrons in the equatorial plane near L = 6 or 7 is much less than near L = 3. B. Hnltqvist. But the anisotropy does increase with energy in the auroral zone too. P. Rothwell. Most chorus emission is observed in the morning and at latitudes somewhat lower than the auroral zone. The wave-particle interaction generating chorus and precipitating particles probably can occur in the auroral zone too, but I think to a lesser extent than at latitudes just beyond the plasma- pause and in the morning, where we know that the energetic particle pitch-angle anisotropy in the equa torial plane is greatest. 136 SOME STUDIES OF CHORUS M.J. Rycroft Department of Physics, University of Southampton, Great Britain ABSTRACT With reference to ground-based observations of the VLF emissions known as chorus made in South-Uist, Outer Hebrides (I = 3.4) and in central Iceland (I = 6.2), some salient features of the signals are review ed. Preliminary findings are presented of a rocket experiment, launched from South-Uist, to investigate one component of the magnetic field of the wave at five frequencies within the chorus band. Possible physical causes for the different periodicities found in both types of observation are discussed. It is assumed that the whisiler-mode signals are generated and amplified by the transverse resonance instabi lity, in which the pitch angles of energetic electrons are decreased : some trapped electrons are thereby precipitated into the atmosphere, both inside and outside the plasmapause. 137 CORRELATION BETWEEN VLF EMISSION FLUX AND ELECTRON PITCH ANGLE DISTRD3UTION AS DEDUCED FROM A ROCKET FLIGHT IN THE AURORAL ZONE M. Hamelin Groupe de Recherches lonosphériques, Orléans, France ABSTRACT We present preliminary results from a rocket experiment launched in the auroral zone with a VLF receiver and energetic electron detectors on board. These detectors were aimed roughly in the direction of spin axis and perpendicularly to this axis. The energy detected was divided into several channels between 10 and 300 keV. A VLF emission — auroral chorus—was detected between 400 and 1000 Hi during two separate periods. The data show a strong enhancement of precipitated and trapped electron fluxes occurring during the chorus events; the correlation seems to be best for the 50-170 keV energy channels. These events are associated with an increase of amplitude of the PC 3-4 magnetic disturbances delected on the ground. 1. INTRODUCTION The rocket experiment reported here was performed by the Group of Pr. Mozer (Service d'Aéro- nomie du C.N.R.S., Verrières-le-Buisson, France), in 1966 with the purpose of studying wave normal direction of VLF emissions and their correlation with energetic electron fluxes. The launching conditions, the onboard equipment and the data analysis are briefly reported here; then we present the experimental results, VLF chorus received, electron precipitated and trapped fluxes. 139 2. THE EXPERIMENT 2.1 Launching conditions The rocket, a Dragon type, v/as launched at Andôya, in Norway, at 00.12 UT; the corresponding Mcllwain parameter L is 6.3. The rocket was fired just at the beginning of a strong magnetic event (Figure 1). The magnetic activity was quiet up to 30 mn before firing; the rocket started just at the end of the large oscillation of more than 100 y peak to peak. Figure 1. — East-West component of the magnetic field detected on the ground. We can see during the flight large amplitude PC 4 oscillation. On the large scale original record, there are also some smaller amplitude oscillations of higher frequency. 2.2 Onboard equipment The VLF equipment is the same as the one launched by [Béghin] in Iceland. The detector is a magnetic antenna at 45° from the spin axis. Waves being assumed in quasi parallel mode with quasi circular polarisation, the spin modu lation of the signal gives us the wave normal direction in space (Figure 2). Figure 2. — Sonogram showing the spin modulation of the VLF signal. 140 As in the Iceland experiment, the wave normal is found to be within 30° of the magnetic field. The other equipment on board was two electron detectors, as described by [Mozer], perpendi cular and near parallel to the spin axis. 2.3 Data analysis The electron detectors were protected from the sunlight by an aluminium sheet. In spite of this protection, the measurement of electron fluxes was disturbed, not only in direct sunlight but also by reflection on the aperture cone of the detectors. So we have only taken into account the measure ments picked up on the dark side. 3. RESULTS 3.1 VLF results The spectrum of VLF emission received on board shows two important level periods of chorus in the upper figure, suddenly followed by hiss (Figure 3). The differences in darkness are caused by an AGC in .he spectrum analyser. In the middle figure, VLF has been filtered around 500 Hz. 3.2 Electron fluxes and correlations We have plotted on the same time scale the horizontal component of the magnetic field detected on the ground, the VLF signal filtered around 800 Hz and the directional fluxes perpendicular and parallel to the magnetic field in an interval of pitch angles of about 15° (Figure 4). The dashed line, symmetrical with respect to the culmination, represents the background distribution of flux. We must consider three regions for the perpendicular flux plot : — below 190 km, particles are lost at the conjugate point; — above 240 km, particles can drift around the whole Earth; — between 190 and 240 km, particles were injected no more than an hour before. We can notice first that there is a very good correlation between trapped and precipitated fluxes, the precipitated flux being larger. There is a peak to peak correlation between VLF and the fluxes. However, there is a peak of fluxwithou t VLF after the first sequence of chorus ; it corresponds to the sharp extinction of chorus followed by hiss (Figure 3). The chorus emissions occur at the times of strong magnetic oscillation. These results, obtain-d during a strong magnetic event, are in agreement with the 1968 Kergue- len experiment [Cendrin et al., 1970 a, b] for the correlation of chorus with trapped particles. However, we notice two differences : the ratio between parallel and perpendicular fluxes is inverted and the precipitated flux is now modulated. 141 I kHz 150 200 High} fime 250 s / Figure 3. — VLF signal filtered around 500 Hz and sonograms corresponding to the two large amplitude sequences. 142 100 200 300 400 50901, 4Q. GROUND MAGNETOMETER flight lime s' 30 20 10- 30- VLF 800 Hz dB 20 10 0 f ELECTRON FLUX (//) 100 200 300 400 432 400 300 ALTITUDE km Figure 4. — Correlation between Magnetic activity, VLF and directionnal fluxes of energetic electrons. 143 100 2Ç0 300 400 S 30 VLF 500 Hz flight time dB 20- 10' A Jfn vn ^ V^/ >--Aa^Av^js/^V . 0' —^/Ai vv^vl i ANISOTROPY NEAR THE LOSS CONE 1.4- 1.2' 1 0.8 100 200 300 4Ô0 432 400 h Figure J. — Correlations between VLF signal and anisotropy of the electron distribution. Evidence of wave-particle interaction is also shown by Figure 5 : we have defined the anisotropy as the ratio between the flux of electrons mirrored at the rocket altitude and the flux of electrons mirrored at 100 km. If one considers the curves above the altitude of 190 km, the former are trapped and the latter precipitated at the other end of the line of force. An increase of this ratio means that the mechanism of filling the 100 km mirroring level is stopped. The data seem to indicate that such a mechanism is correlated with wave-particle interaction. It is especially evident for the first sequence of VLF; for the second sequence, there is a strong modulation of anisotropy during the VLF event. Our preliminary results show evidence of wave-particle interaction with energetic electrons as the mechanism of chorus generation. 4. ACKNOWLEDGEMENTS The advice of Dr. C. Béghin, under whose direction this work was performed, is greatly appreciated. We should like to thank Dr. Bruston (ServU - d'Aéronomie) for his help. We also thank M. Cazenave and M. Le Hénaff (CNES) and the computing Centres of CNES and C.N.R.S. for the data processing. This experiment was supported by the CNES t.: a collaboration programme between the Groupe de Recherches Ionosphériques ani the Service d'Aéronomie du C.N.R.S. 144 INTERACTION OF LONG-PERIOD WAVES AND ENERGETIC PARTICLES IN THE MAGNETOSPHERE G.K. Parks Faculté des Sciences, Université de Toulouse (France) and J.R. Winckler School of Physics and Astronomy, University of Minnesota (U.S.A.) ABSTRACT Particle and field variations of a few minutes period are frequently observed in the magnetosphere daring storms and substorms. Detailed studies of such variations observed at synchronous altitudes indicate that the magnetic field waves are linearly polarized in the meridian plane. The amplitudes of these waves can be as large as 25 y in the average geomagnetic field of 50-80 y, giving AB/B of 0.2 to 0.5. These waves are observed predominantly in the noon to midnight sector. Presence of such waves gives rise to complicated wave-particle interactions. In studying the correlated particle variations, we find that generally electrons of energies ^ 50 keV oscillate In phase with the H-component field but the percent modulation is not related in a simple way to the amplitude of the waves, indicating non-adiabatic pro cesses are involved. In one event, the protons oscillated 180° out of phase with both electrons and the magnetic field. In another event, a factor of two modulation in trapped =; JO keV electrons was observed in the absence of any significant magnetic field oscillations. The observational characteristics are consist ent with predictions of drift instabilities with varying fl values as reported in this Colloquium by Laval Pellat, and Hagège. The example of particle oscillations in the absence of magnetic field oscillations corresponds to the low fi case where the waves approach the electrostatic mode. 145 PROBLEMS RELATED TO HIGH-LATITUDE ELECTRIC FBELDS AND CURRENTS C.G. Fâlthammar and L.P. Block Division of Plasma Physics, Royal Institute of Technology, Stockholm, Sweden ABSTRACT SUMMARY OF PROPOSED EXPERIMENTS PHENOMENON PROPOSED EXPERIMENTS Decoupling of magnetospheric and iono Dc E-fields (£|| and EL) at various altitudes, spheric plasmas ( Unipolar dynamo, magne including equatorial plane at L > 4. tospheric convection, substorm induction Plasma experiments (electron density and tempe fields) rature, bulk plasma velocities, polar wind) Softer particle precipitation poleward of Particle experiments, including measurements of auroral zone due to unipolar dynamo upgoing fluxes at various altitudes Magnetospheric convection De E-fields (EJ and their correlation with v X B in the solar wind Configuration of field-aligned currents (in Three-component low frequency B-field measure particular build-up of substorm current ments to locale field-aligned currents system) Anomalous resistivity caused by field- High-frequency E- and B-field measurements and aligned currents simultaneous low-frequency B-field measurements for correlation with field-aligned currents Electron density anomalies in topside iono High resolution electron density measurements and sphere due to field-aligned currents simultaneous low-frequency B-field measurements and simultaneous measurements of He, O, and N ion concentrations Formation of electric potential sheaths Laboratory sheath experiments. Particle experiments (both precipitation and up- going fluxes) with high pitch-angle resolution. High-frequency E- and B-fields. Low frequency B-fields (to locate field-aligned currents causing the sheaths). Electron density and temperature measurements. 147 1. INTRODUCTION As a consequence of the progress in experimental SDace research in recent years there is no longer any doubt that electric fields in the magnetosphere and electric currents along geomagnetic field lines play an important role in connection with auroral and geomagnetic activity. This raises a series of new questions, which are important as well as difficult. Many of them can be combined under the heading : What properties does the plasma above the ionosphere have as a circuit element ? The response of this plasma to electric fields has a direct bearing on the electrical and dyna mical coupling between the magnetosphere and the ionosphere, on the creation of density anomalies and on the acceleration of charged particles. I; has, however, also a fundamental plasma physical interest, because some of the " anomalous " properties exhibited by the ionosphere reflect a behaviour of low-density plasma which is still far from well understood. Therefore, progress in understanding these phenomena is not only necessary in order to understand certain high-latitude geophysical pheno mena, but may also represent an advance in basic physical knowledge. In view of the subject of the present Colloquium, the discussion below will be essentially limited to aspects where information of interest can be gained from non-eccentric polar-orbiting satellites. 2. LARGE-SCALE ELECTRIC FIELDS One of the many difficulties in studying the response of the magnetospheric plasma to electric fields is the insufficient knowledge of the electric fieldsan d how they are applied. The electromotive force in the magnetosphere may be considered as arising from four main sources (although a strict distinction between them is not possible) : a) ionospheric winds; b) the unipolar dynamo action of the ionosphere rotating with the Earth; c) the magnetospheric convection, which is in its turn driven by an external dynamo, the solar wind; d) induction fields associated with magnetic substorms. The ionospheric winds, being relatively unimportant [Bcôtrôm, b\ will not be discussed here. 2.1 The unipolar dynamo field An electric-field source that has attracted rather little attention is the unipolar-dynamo action of the rotating ionosphere — although it has been named as a possible energy source [Mclhvain, b]. This relative lack of attention is not surprising, because in the idealized magnetohydrodynamic models that have commonly been used so far, this field has rather uninteresting or even trivial consequences (corotation of plasma on near-Earth magnetic field lines, " twisting " motion of the plasma oi the more extended ones). However, as the high-latitude part of the unipolar e.m.f. is applied to a low-density plasma with far from simple electrical properties, the effects of this e jn.f. are neither obvious nor uninteresting. One circumstance of importance is that, provided the ionospheric electric field is known (cf. eq 1 and 2 below), .this e.mS. is entirely well defined, and therefore well suited for studying how low-density magnetospheric plasma responds to applied electric fields. 148 If the ionospheric electric field in a frame rotating with the Earth is E', the ionospheric electric field in a non-rotating frame [Alfvén and Falthammar, a, § 1.3.2] can be written : E = E' — (w x r) X B (1) where w is the angular velocity vector of the Earth, r is the position vector, and B the local magnetic field vector. E' in turn is related to the height-integrated horizontal current jx and conductivity tensor a by : Ji = « • E' (2) In quantitative analysis one may need to account for the non-alignment of the magnetic and rotational axes in using the expression (1). Explicit formulas for the case of an inclined dipole can be found in the work of [Hones and Bergeson]. However, in the present qualitative discussion of the possib'e consequence of the field (1), we shall for simplicity disregard the non-coincidence of the magnetic and geographic axes so that both E and E' can be discussed in terms of potentials V and V, related by : V = V — V„ (1 — cos2 X) (3) where X is the latitude and V0 is a function of altitude. In the ionosphere, V0 has the value 94 kV. If the magnetospheric plasma were an ideal magnetohydrodynamic medium, the ionospheric potential distribution (3) is simply mapped along magnetic field lines, each of these being an electric equipotential line. This implies simple corotation in the inner magnetosphere and " twisting " or cellular convection motion in the distant regions. In the real magnetospheric plasma, simple corotation probably prevails inside the plasmapause, where the plasma is still of medium density. The more interesting region, however, is that of high latitudes, where the " load " of the unipolar generator is a low-density plasma. The voltage applied over this region is of the order of 10 kV (Fig. 1). Figure I. — A conductor rotating in the presence of a magnetic field acts as a unipolar dynamo. A simple example is a rotating permanent magnet. The ionosphere rotating in the geomagnetic field also acts as a unipolar dynamo. 149 The polar-cap magnetic field lines, especially those on the dayside, reach deep into the geo magnetic tail. If the field lines were equipotentials, it would mean that, as the ionospheric end of a field line makes one revolution, the plasma at the other end of the field line would at the same time describe a path of huge dimensions. Just poleward U the closed-field-line region, the plasma at the far end of the field-line would have to describe a path length of thousands of Earth radii within a small fraction of a day \— if the frozen field conditions were valid all along the field lines. There is little reason to believe that such motion occurs. The alternative is that a certain amount of " slippage " occurs between the two ends of the field line. This means, physically, an electric decoupling by means of electric fields somewhere along the magnetic field lines. The region of polar-cap field lines may, in fact, be closer to the other extreme where the tail plasma is essentially decoupled and not constrained to move in the way dictated by the polar-cap rotation. The amount of decoupling that occurs in reality should be determined observationally. This might be done by experiments on polar-orbiting satellites. For a decoupling of the corotational field to occur, a necessary condition is the presence of an electric field with a non-vanishing component Ej = B (E. B/B2) [Alfvén and Fàlthammar, a, §§ 5.1 and 5.4] which must, furthermore, be non-conservative, i.e. : curl Eg ¥= 0 • (4) (cf. e.g. [Fàlthammar, a]). Note that the condition (4) may well be satisfied in a static case, i.e. a case where curl E s 0 (curl Ex = — curl Ej). This is illustrated schematically in Figure 2 for the special case where the external field is zero, i.e. total decoupling and no externally applied field. (In general, there will in addition be an external electric field applied across the tail region.) Figure 2. — Decoupling of the plasma on polar-cap magnetic field lines from corotation with the lower ionosphere requires that the magnetic field lines are not electric equipotential lines, i.e. that E|| = E. B/B = 0. The figure shows qualitatively the spatial variation of £j in the case of zero field above, and smooth transition. If the decoupling occurs via a sheath, there will he sharp knees in the equipotentials. Decoupled region I 150 Conceivable ways in which the decoupling electric field can be maintained have been discussed by several authors [Alfvén and Fâlthammar, a; Swift; Sagdeev and Galeev, a, p. 122; Ossakov; Coroniti]. If the plasma in the polar plumes is sufficiently thin and hot, it may separate itself from the cooler polar-cap ionosphere by means of a space-charge sheath somewhat analogous to that at a wall in a laboratory plasma [Block]. The wall sheath serves to equalize the fluxeso f electrons and positive ions by a potential that retards the former and accelerates the latter. Under such a sheath there would occur precipitation of both ions and electrons, the latter being high-energy tail electrons of sufficient energy to overcome the retarding barrier. The decoupling may also occur via a space-charge sheet associated with electric-current flow (for a review, see [Block, &]) corresponding to the free space-charge sheaths sometimes seen in labo ratory gas discharges. The amount of decoupling that may occur depends very much on the properties of the polar- plume plasma. If a polar wind is flowing, the plasma is rather cool and probably not very thin. Then the decoupling, if any, is likely to occur at great altitudes. If the plasma is stationary, it may be hot and thin, and the separation sheath may be situated not very far above the F-layer. To clarify the problems mentioned here, several types of experiments can be made from small polar-orbiting satellites : a) Plasma experiments should reveal what density and temperature characterize the polar-cap plasma at high altitudes and preferably also whether it has a systematic outward bulk velocity. b) Electric field experiments would directly reveal whether any decoupling takes place below the satellite orbit, provided that, simultaneously, the ionospheric electric field is sufficiently well known. Such decoupling would reveal itself by a deviation from the field obtained by simple mapping of the ionospheric field (1) upward along magnetic field lines. The strength of the corotational field is of the order of 7 mV/m. The precision of measurement must therefore be better than that. Notice, however, that in the special case illustrated in Fig. 1 the edge of the decoupled region is also associated with a large field-strength spike, which may be more easily detectable. Furthermore, it is worth mentioning that the electric field is known in the low-latitude part of the orbit (where (1) and simple mapping hold), and this gives an opportunity of calibration twice in every orbit. c) Particle experiments may also provide interesting clues. For example, below decoupled region, a field configuration such as in Figure 1 would tend to give a systematic latitude variation in the energy of the precipitating particles. It must, of course, be realized that superposed external fields will also influence the space variation of particle energy, but as the contribution from the unipolar field is systematic in a simple and known way, it might still be detectable. 2.2 The magnetospheric convection field The electric field associated with magnetospheric convection is ultimately driven by the solar wind. There are several hypotheses about how this occurs. A review has been given by [Axford,4]. More recently [Coleman] has developed a model for the interaction, and [Alfvén and Fâltham mar, b] have discussed the role of these fieldsfo r tapping energy from the solar wind. Attempts to map the electric fieldsassociate d with the convection fields have been made on the basis of ground-based magnetometer records [Taylor and Hones] and balloon-borne electric measurements [Mozer and Serlin, Mozer and Manka]. Any mapping of this kind will depend on assumptions which may not be well fulfilled at high latitudes. A direct check is needed, and, because of a possibly imperfect electric coupling, measurements should be made both in the distant magneto- sphere and at more moderate altitudes above the ionosphere. 151 , i .!,«,„, ii ,„,,.,„„,,„,,i. ni ni uu it Ill til. Due to their comparatively moderate strength, the quiet convection fields are more difficult to measure than the substorm fields, which are discussed in § 2.3, and which should be the prime target in the near future. In connection with the non-substorm fields, therefore, a less ambitious but still useful goal would be to study in a rather crude way how their general properties correlate with those of the interplanetary plasma and in particular with the southward magnetic-field component. Another interesting problem in this context is that of the plasmapause. It has been argued [Nishida; Brice,ê] that the plasmapause is the result of a superposition of the Earth's corotation field with the general convection field. If that is correct the electric field should be continuous across the plasmapause. However, [Karlson; Block, a] have found that a plasmapause must be present even if the Earth would nave no rotation at all. This is due to charge accumulation which excludes any externally impressed electric fieldsfro m a region of the order of the size of the plasmasphere. Hence, a sudden change in EL should be observed at a satellite traversal of the plasmapause. Such a dis continuity of the right order of magnitude has been observed by [Gurnett, 6; Cauffman and Gurnett], but more measurements are needed. 2.3 Electric induction field during substorms Particularly strong electric fields occur in connection with substorms. From whistler obser vations it has been inferred [Carpenter and Stone] that electric fields of the order of 0.3 mV/in are present on closed field lines prior to magnetic substorms. The appearance of an appreciable field strength before the substorm may be due to the rearrangement of magnetic flux prior to the onset [Fairfield and Ness; Aubry et al.; Fairfield]. Still stronger electric fields are induced at the onset of substorms, when the slowly accumulated tail field is suddenly destroyed. The sudden transition from a stretched-out, largely radial tail-field configuration to a more dipole-like one is reported to be a typical feature of the substorm [Cummings et al. ; Fairfield and Ness ; Coleman and McPherron ; Russell et al.,b; Camidge and Rostoker]. These observations indicate that a sheet current of the order of 30 mA/m disappears within minutes. This tail-current interruption may be analogous to the Alfvén-Carlqvist process for solar flares [Alfvén and Carlqvist; Carlqvist (1968, 1969)] which has also been invoked in connection with the asymmetric ring current [Akasofu]. It is tempting to think that part of the current that used to flow as a sheet current in the tail is instead rerouted via the ionosphere where it appears as the characteristic westward electrojet. (In addition to die primary westward electrojet there would be created a transverse — polarizing — Hall current and corresponding — depolarizing — sheet currents). Such an inter ruption will explain not only the rerouting of the current via the ionosphere, but also the appearance of sudden induction fields of sufficient magnitude to cause injections of energetic particles into the trapping region [Lezmak and Winckler; de Forest and Mcllwain]. (A change of the order of 10 gammas over a region of the order of 3.107 m and occurring within minutes could induce electric field strengths of the order of a few mV/m). Whatever is the actual cause of the change in the tail current, the electric induction fields produ ced are a very important part of the substorm process. Rather little can be deduced theoretically about these electric fields. Even if the magnetic field change (3B/3*), and so curl E, were known in all detail, the actual field distribution could not be calculated. The reason for this is that unlike idealized models with infinite conductivity along field lines, realistic models of the magnetospheric plasma do not allow easy assessment of charge distributions and boundary conditions. This makes an experimental study of substorm-electric fieldsver y important. As the magnetic field lines cannot be assumed to be equipotentials, measurements are needed not only near the equatorial plane, but also at various altitudes above the ionosphere. 152 3. PROBLEMS RELATED TO FIELD-ALIGNED CURRENTS 3.1 Configuration of field-aligned currents As has been emphasized by [Bostrôm, a, b, c] ground based measurements are inadequate for exploring the configuration of the overall current systems in the ionosphere and magneto- sphere, and magnetic measurements above the ionosphere are needed. Some measurements of this kind have already been made [Zmuda et al., 1966, 1967; Armstrong and Zmuda; Cloutier et al.] by which the existence of field-aligned currents has been confirmed. However, much more comprehen sive measurements of this kind are needed. In particular it is important to make three-component magnetic field measurements in order to map the distribution of upward and downward field-aligned currents. This would be one important task to be undertaken ty mtans of the kind of satellites with which this Colloquium is concerned. In particular, it would be interesting to study the build-up of the field-aligned current system during a magnetic substorm. As already discussed in § 2.3, a key part of the substorm process may be the switching of a large current (of the order of a MA) from a cross-tail path to a path via the iono sphere. Theoretically, one would expect that the current path via the ionosphere initially consists of two adjacent field-aligned paths of opposite direction, which are then gradually separated until the inflow to the ionosphere and the rc*ura flow are at either end of the nightside auroral oval. This is also in agreement with the observation [Bostrôm, c] that the auroral electrojet starts in a very localized region from which it spreads in an east-west direction (and is simultaneously displaced northward). However, very little can be said on theoretical grounds about this transition. A main difficulty is the limited knowledge of how the plasma above the ionosphere responds to the sudden imposition of large field-aligned currents. For example, creation of anomalous resistivity (§ 3.2), depletion of the topside ionosphere (§ 3.3), and the formation of space charge sheaths (§ 3.4) will influence the build-up and the spreading of the current. Simultaneous density and magnetic-field measurements from a polar- orbiting satellite would provide information of great interest in this context. 3.2 Field-aligned currents and anomalous resistivity As already emphasized by [Alfvén and Fâlthammar, a; cf. also Persson, 1963, Î966] the low- density plasma of the magnetosphere can be expected to behave in a way that cannot be described in terms of ordinary conductivity. In addition to the possibility discussed by these authors there are various other ways in which the plasma can behave abnormally with respect to current conduction [Swift; Sagdeev and Galeev, a; Ossakov; CoronitiJ. These latter processes are generally based on wave- particle interaction, and will be discussed in other papers at this Colloquium. They are not, therefore, further treated here except for the remark that the high-frequency electric and magnetic field measu rements that are needed to search for microfields associated with anomalous resistivity should of course be coordinated with low-frequency magnetometer measurements for detecting the field-aligned current responsible for causing the anomalous state. 3.3 Field-aligned cm-rents and density anomalies The currents that are found to flow along geomagnetic fieldline s reach current densities of the order of 10"5 or 10"* Am""2 [Zmuda et at., 1967; Cloutier et al.]. Current density of this order may, under circumstances discussed by [Block and Fâlthammar, 1968, 1969], cause substantial depletion of charge carriers in the topside ionosphere. Large-scale density depletions will also follow from the presence of a polar wind [Banks and Holzer, 1968], Both these mechanisms may be present, and could explain the large depletions that are known observationally to occur at high latitudes. The regions of depletion sometimes have sharp boundaries [Calvert] and can be of very limited width, as in 153 the case of the microtroughs reported by [Herzberg and Nelms]. Especially in this latter case, field- aligned currents may be the cause. To improve the understanding of how these density anomalies ate created, and what role they may play in the electrodynamics of the magnetosphere, it would be useful to make high-resolution electron density surveys from polar-orbiting satellites that also contain magnetometers for detection of field-aligned currents and instruments suited for detection of field-aligned plasma Sow. As the processes creating density anomalies can also be expected to cause anomalous ion composition, simultaneous measurements of helium, oxygen and nitrogen densities would be desirable. The creation of density anomalies in a magnetic flux tube may considerably change the ability of the plasma in that flux tube to carry field-aligned currents. It is therefore an interesting question, whether anomalous depletion of the ionospheric plasma may be a factor of importance in determining the rate at which the field-aligned current system of a substorm develops in its early phases. Much information relevant to this question should be obtainable from the coordinated magnetic-field and density measurements already mentioned. Finally, the formation of density depletion will create conditions that are particularly favourable for formation of space-charge sheaths (§ 3.4). Therefore, a systematic study of the concurrence of sheaths (detectable by particle measurements) and density depletions, using instruments on the same satellite, could also be an inportant contribution towards a better understanding of the complicated electrodynamics of the topside ionosphere. 3.4 Field-aligned currents and sheath formation The suggestion by [Alfvén] more than one decade ago, that electric potential sheaths may occur in or above the ionosphere was based on an analogy with the experimentally known, although theore tically not well understood, behaviour of laboratory plasma. The suggestion was not widely accepted at its time, but the recent progress in rocket- and satellite-borne observations has rather suddenly changed its status from heresy to high fashion. This is a healthy reminder that, in spite of obvious limitations, laboratory plasma experiments should not be neglected as a complementary guide to the understanding of the cosmical plasma. The study of space charge sheaths is one of the most challenging fields of plasma physics, but also one of the most difficult. The efforts towards progress in this area should therefore include both space and laboratory experiments as well as theoretical analysis. A possible analogy of the wall-sheath of a gas discharge has already been mentioned in § 2.1. However, the sheaths of which indications have so far been seen are probably more similar to the free space-charge sheaths sometimes occurring in gas discharges. These sheaths have long been known to occur at places where there is a more or less abrupt change of plasma parameters. The typical example is sheath formation at a cross-section discontinuity (where a change of electron density and temperature occurs because of the change in current density). However [Babic et al.] have recently performed experiments where sheaths are created in a discharge with a gradually varying neutral-gas pressure, and where the position of the sheath can be adjusted by changing the pressure distribution. A major remaining difference between this experiment and the ionosphere is the influence of the walls, which are important in the experiment, especially for the relaxation oscillations in which the sheath is alternately extinguished and recreated. (Fresh neutral gas is supplied from the wall to the 1S4 depleted discharge column on the anode side of the sheath, and ionized by the discharge electrons.) However, it is perhaps worth noting that in the ionosphere too, there may be something at least remotely similar to a wall. The narrow field-aligned troughs that are known to exist [Herzberg and Nelms] and may be created by the currents themselves [Block and Fâlthammar, 1968, 1969] are likely places for sheaths to be created. The sheath would then be situated at the bottom of the trough, and the depleted flux tube would be surrounded by " walls " of denser plasma from which additional charge carriers could be supplieu by diffusion or E x B-drift. The evidence for sheaths in the ionosphere is now fairly well-known and is not repeated here. For a recent review the reader is referred to [Block, c\. The review mentioned also contains new original contributions. Among these is the prediction that the plasma in a polar magnetic AMX tube has a " weak spot " in the altitude range 5 000-10 000 km, where a sheath is most likely to form. This particular prediction depends on an assumed density distribution. A study of sheath formation by small ionospheric satellites should therefore include both particle measurements to detect the pre sence of sheaths, and plasma measurements to explore the conditions in which the sheaths exist. As [Carlqvist and Bostrôm] have shown, indications of space charge sheaths can also be found in records of visible aurorae, which should therefore be a valuable complement to the satellite obser vations in the search for, and study of, sheaths above the ionosphere. The electric space charge sheaths will accelerate particles both upward and downward. Pro vided the satellite altitude is not very low (say less than 500 km), the particle experiments should also contain detectors measuring upward-directed fluxes; this, unfortunately, has not been common practice. Although the sheaths will primarily create well-collimated particle beams, the velocity distribution in these beams may become dispersed much more rapidly than expected from binary collisions. At least this is known to happen in the laboratory. A striking example of this has been reported by [Morgulis et al.], who also found that the region where the redistribution took place contained noise in the GHz range (indicating that wave-particle interactions were responsible for the redistribution process). It is natural to expect that, in space too, correspondingly fast redistribution may sometimes occur in initially collimated beams emerging from space charge sheaths. The study of the beams with a view to detecting such processes would require particle measurements with high angular resolution, and because the beams may be narrow, high time resolution may be needed as well. As it is in practice close to impossible to have good resolution in time, space and energy at the same time, compromises are necessary. However, at least in the case of upward-directed beams, much is still to be learned even from rather crude experiments. (Very high-altitude rockets may also be useful for detecting sheaths. However, if the sheaths are short-lived or localised, the probability of finding them by means of rockets may be small.) 4. CONCLUDING REMARKS Various experiments and coordinated studies that may help clarify the complicated electro dynamics of the low-density plasma above the ionosphere have been mentioned. The difficulties in obtaining the amount of resolution and of space- and time coverage are inherent in the techniques that have to be usee* in space. This is a basic difference from what is the case in the laboratory. (Consider, for example, the experiment by [Morgulis et al.] and the effort that would be needed to do anything similar in space.) Still, it appears that there may be close similarities between some pheno mena occurring in space and their counterparts in the laboratory, especially in the field of sheath formation and the wave-particle interactions associated Tith them. It should therefore be pointed out, in conclusion, that a conscious coordination of space and laboratory studies might greatly enhance the cost-efficiency of the research on these phenomena. 155 '• 'i^'Kiiin^.n.nt.lUJKIII.I.jlli.Hlhlh InjiiiMllllliill ill DISCUSSION R. Grabowski. / remember theoretical considerations concerned with the equatorial ebctrojet; they proposed current systems in the meridian plane, these current systems producing an additional magnetic field component, a small magnetic field component; but experimenters have estimated that this additional magnetic field due to the current systems has measurable size. Do you think that such components due to the longitudinal currents may be of such a size as to be detectable by magnetometers or similar devices? L.P. Block. In the polar ionosphere, they have been detected by Zmuda and his collaborators. How it is in the equatorial region, I do not really know. They are easily measurable in the polar region. The field-aligned currents produce East-West magnetic field variations as large as 1000 gammas, according to the observations. A. Eviatar. / wonder if you could comment on recent work by Kennel andKindell in which they considered the possibility that field-aligned currents, as predicted or as observed, will excite ion acoustic instability, i.e. that the Fried and Gould criterion threshold for ion acoustic wave instability would be exceeded by the current densities that one expects to find in the magnetosphere. I believe that they calculated or estimated that this would take place. This should work also as an auroral particle accelerator, dissipating, as it were, by means of ion acoustic waves. You have generated a dissipation mechanism which would feed energy into some preferred portion of the particle distribution. I think you should comment on this. LP. Block. This is one possible way of obtaining anomalous resistivity that I mentioned here and I think it could very well operate since the current densities observed are quite sufficient to cause this. It is also possible that stable electrostatic potential double layers may be created as I mentioned. This has been observed frequently in the laboratory whenever currents flow between regions with plasmas of different properties, i.e. temperature and/or density. The experiment that we design should be aimed at clarifying this question, whether the one mechanism or the other operates, or both. 156 MAGNETOSPHERIC STRUCTURE DEDUCED FROM WHISTLER OBSERVATIONS AT HALLEY BAY J.L. Sagredo and K. Bullough Department of Physics, University of Sheffield (Great Britain) ABSTRACT Whistlers observed at Halley Bay (333.4° E; 75.5° S; 60.7° invariant latitude) on 1967 July 26, extending through the period 0509 to 2305 U.T., were found to have exit points situated along a strip about 100 km wide, passing through Halley Bay in an azimuthal direction 30° E of N between 57 and 62° invariant latitude. A mechanism which can give rise to such a well-defined locus which co-rotates with the Earth is not clear. Nevertheless, it does appear that the locus coincides with the contour of solar zenith angle 102° at 1800 U.T. July 25. This was also the time of occurrence of a substorm and it is suggested that the magneto- spheric structure was initiated by proton precipitation along the solar zenith angle 102° contour. 1. INTRODUCTION The British Antarctic Survey base at Halley Bay (333.4° E; 75.5° S; 60.7° invariant latitude), like other Antarctic bases such as Eights and Byrd [Helliwell, a] is ideally situated for the study of VLF phenomena. For example, the very high whistler rates obtained over extended periods during the Austral winter have made possible extensive studies oftheplasmapause [Carpenter, b\. In 1967, aVLF goniometer (0.5 to 11 kHz) was installed at Halley Bay in order to study the distribution of whistler and emission exit points. Similar studies had been initiated by Ellis [Ellis and Cartwright] in Australia and [Watts; Crary] in the U.S.A. On July 26 1967 an extremely high whistler rate in Halley Bay made it possible to delineate, in some detail, the associated magnetospheric structure. A study of knee- whistlers observed in the late morning of this day has been published elsewhere [Bullough and Sagredo]. 157 2. EQUIPMENT The VLF goniometer consists of two vertical loops (30' x 30') mounted at right angles to each other. From these two loops a single loop, rotating about a vertical axis at 25 s~l, is synthesised electronically. The equipment has a sensitivity of about 10"18 watt m~2 Hz-1 at 5 kHz. If the electromagnetic wave detected by the equipment has travelled some distance in the Earth/ionosphere waveguide, so that the transverse magnetic mode is dominant, then the modulation of the signal amplitude by the rotating loop may be used to determine the azimuth of the source. While the crossed- Ioop technique of determining the azimuth of a whistler exit point is imprecise [Crary], the high whistler rate observed on July 26 made it possible to obtain many measurements of bearing, over a range of frequencies, for each exit point, since the duct structure changed only slowly during each period of observation. 3. OBSERVATIONS On July 26 1967, whistlers were recorded during the periods 0509 - 0534, 1206 - 1296 and 2201 - 2305 U.T. (these periods were chosen to coincide with overhead passes of the satellite Ariel III at Halley Bay and its conjugate point) at the rate of about 30, 10 and 30 per minute respectively. In the early morning and late evening periods, one minute in every ten of the tape-recorded data was selected for reproduction on a sonagram and analysed. All the data in the late morning period were analysed. For each rotation of the loop a mean azimuthal bearing was determined from the two maxima and minima of the modulation pattern. An internally-generated calibration pulse provided a bearing reference (due North). The period of rotation (0.04 s) was such that the apparent bearing could be determined as a function of frequency for individual whistlers. The r.m.s. deviation in bearing azimuth for a single whistler was typically + 20°. Whistlers, originating in different lightning strokes but clearly propagating along the same magnetospheric path and emanating from the same exit point, were grouped together. The L-shell, along which an individual whistler propagated, was calculated from its frequency/ time characteristic. The magnetospheric model adopted was similar to that of [Angerami], which assumes diffusive equilibrium inside the plasmapause and a collisionless plasma outside. Values of ion abundance and temperature at 900 km altitude were obtained from Alouette 2 and Injun 3 data [Rycroft and Alexander]. Since it was usually difficult or impossible to identify the originating sferic on the sonagram, values of the nose travel time (r„) and nose frequency (_/"„) were obtained by a method due to [Dowden and Allcock]. The estimated error (|4f„[) in t„ and \Af,\ in/„ are < 2 % and < 1 % respectively for/, > 4 kHz. The invariant latitude (A = cos-1 L~"2) of a whistler exit point is then determined with an error probably not exceeding + 0.1°. Having obtained the azimuth and invariant latitude of a whistler exit point it is possible to locate the latter on a map. Whistler exit points deter mined from measurements on two or more whistlers are shown in Figure 1. The analysis revealed the following features : a) Most of the exit points of whistlers inside the plasmasphere were situated along a strip about 100 km wide passing through Halley Bay in an azimuthal direction 30° E of N between 57 and 62° invariant latitude. The edge of this strip was relatively sharp and well-defined to the West with a few exit points located outside and to the East of the strip. b) At mid-day, knee-whistlers observed outside the plasmapause had exit points which were closely aligned along an L-shell at an invariant latitude of 62.5°. They exhibited a marked variation 158 Figure 1. — Distribution of whistler exit points associated with 2 or more whistlers (Halley Bay, 1967 July 26). In parentheses, No. of whistlers in the group for which both L and azimuth were determined. | 1 : R.M.S. deviation in the measurement of azimuth. (s: 3 : 1) in electron tube content over about 10° of invariant longitude and a drift of about 50 ms-1 to lower L-shells [Bullough and Sagredo]. The exit points of normal whistlers, within the plasma- sphere, did not exhibit a measureable drift. c) The plasmapause, during each of the three periods on this magnetically quiet day (SKP = 12—), lay about 2° polewards of the mean position found by [Carpenter] for moderately disturbed days. 4. DISCUSSION Apart from the longitudinal structure close to the plasmapause [Bullough and Sagredo], the outstanding feature of these observations was the clearly-defined locus of whistler exit points within the plasmasphere which persisted throughout a period of 16 h. The position (local time/latitude) of this locus and its conjugate in the northern hemisphere relative to solar zenith angle contours 90 and 100° and two substorms at 1800 and 2300 U.T. on the previous day is ,uO\vn in Figure 2. It appears that the only significant alignment of this locus, at Halley Bay or its conjugate, was that at 1800 U.T. with the solar zenith angle contour of 102° in the southern hemisphere. 159 1200 LT Figure 2. — Location (local lime/latitude coords.) of the mean locus of whistler exit points and its conju gate in the northern hemisphere relative to contours of solar zenith angle. Halley Bay : 1967 July 25, 1600 U.T. to July 26, 0100 U.T.; S,, S2 are substorms on July 25, at 1800 and2300 U.T. respectively. The creation of the whistler duct structure and associated exit points may be due to the scattering of energetic protons into the atmospheric loss cone by resonance interactions with ion cyclotron tur bulence. [Cornwall, Coroniti and Thorne] have discussed this mechanism in connection with ihe turbulent loss of ring-current protons. Thus energetic protons injected during a substorm in the evening sector may undergo rather rapid radial diffusion to L=; 3 to 5 [Frank, b]. Those not precipi tated on crossing the plasmapause boundary will drift westward until they encounter field lines at the magnetic equator which map down to the dusk boundary in the ionosphere. Precipitation could occur along this locus if there was an increase in the local plasma density and hence a decrease in the magnetic energy/particle at the equator [Kennel and Petschek; Brice and Lucas]. Another possibility is a change in the wave reflection condition for the sunlit ionosphere [Brice and Lucas]. Once created, such a region will tend to be self-sustaining since it will remain a preferred location for energetic proton (or electron) precipitation, and will co-rotate with the Earth. 160 Evidence for the existence of persistent magnetospheric structure (' magnetospheric fingers') , localised in invariant longitude, which co-rotates with the Earth has also been found in the study of VLF emissions at medium latitude observed on Ariel m [Bullough, 6; Kaiser, Bullough and Hughes]. Emissions of moderate intensity at 3.2 and 9.6 kHz have a maximum in occurrence on fieldUne s which map down to the sunlit side of the dawn boundary in the topside ionosphere. This magnetospheric structure is also probably related to the ionospheric fingers of enhanced electron density found by [Piggott]. [Heacock] has shown, in agreement with our proton precipitation model, that PC 1 micro- pulsations, which may last typically an hour, have a magnetospheric source which co-rotates with the Earth. It is interesting to note that the typical size of the spread F irregularities associated with whistler occurrence [Sagredo and Bullough] is about 1 km, which is twice the gyroradius of a 30 keV proton at F-region heights [Herman]. In conclusion, it is clear that persistent longitudinally localised enhancements in plasma density are an important feature of the magnetosphere. A more detailed presentation and discussion of this work will be made elsewhere. 161 DAWN-DUSK ELECTRIC FIELDS ACROSS THE MAGNETOSPHERE DERIVED FROM PLASMAPAUSE OBSERVATIONS M.J. Rycroft Department of Physics, University of Southampton, Great Britain ABSTRACT Whistler observations of the position of the plasmapause presented by [Carpenter, a] have been analysed statistically by [Rycroft and Thomas]. The inward motion of the plasmapause, associated with increased magnetic activity and with increasing local lime during the night, is interpreted quantitatively using a theory developed by [Scliield]. It is shown that the average dawn-dusk electric field across the tail of the magnetosphere, due to the interaction of the solar wind with the geomagnetic field, increases linearly from 0.7 kV/Re at Kp = 0o to twice that value, namely 1.4 kV/RE, at Kp = 5—. 1. INTRODUCTION From the propagation times of multi-path nose whistlers generated by a specific lightning discharge, the electron density profile in the equatorial plane of the magnetosphere can be derived. A knee in this profile, where the electron density — the density of thermal plasma — decreases by an order of magnitude or more within a fraction of an Earth's radius, is often apparent; this feature is now known as the plasmapause. In the much-referenced paper of [Carpenter, a], a series of whistler observations exhibiting the plasmapause, made at Eights and Byrd stations, Antarctica, in July 1963, are discussed. The radial distances from the centre of the Earth to the inner and outer edges of the plasmapause, measured every hour for twelve days, are presented in figures 4, 8 and 9 of the paper by [Carpenter, a]. These data have been used to define, on 102 occasions, the geocentric distances to the centre of the plasmapause, that is the point of inflexion of the electron density profile, as discussed in Section 3 of the paper by [Rycroft and Thomas]. 163 2. STATISTICAL ANALYSIS OF OBSERVATIONS In this paper, these 102 values of the plasmapause position are analysed statistically. Obtained by calculating the average value of the plasmapause position, L„ together with the standard deviation of the mean, at each hour of local time is the diurnal variation of the plasmapause position plotted in Figure 1. The inward movement of the plasmapause during the local night has been discussed by [Carpenter, a] ; from Figure 1 it is apparent that the plasmapause lies on a field line whose average L value oo LOCAL TIME, tir Figure 1. — Diurnal variation of the hourly average plasmapause position, Lp, obtained using the observations of [Carpenter], is 4.9 at 22.00 L.T., decreasing to 3.9 at 06.00 L.T. During the day the average L value of the plasma pause increases to 4.3 at 17.00 L.T. The outward motion of the plasmapause between 17.00 and 22.00 L.T., obtained from the data averaged at hourly intervals irrespective of the particular magnetic contributions occurring on each of the twelve days, is not as rapid as it is on any individual day, when it may reach 1 Earth radius per hour. The reason for this effect is that the time at which the outward movement of the plasmapause, to its " bulge "' position, starts depends upon geomagnetic activity. It is earlier when magnetic agitation, for example as measured by the Kp index, is large and later when Kp is small. This effect has been studied in depth by [Carpenter, c\. Now [Rycroft and Burnell] have shown that, since the 102 values of the plasmapause position are distributed randomly in K, index—local time space (their Figure 2), statistical methods of analysis can validly be used. For example, Figure 2 shows the variation of the radial distance to the plasma pause, RP, during the local night (21.00 to 05.00 L.T. inclusive) as a function of the K, index of magne tic activity ([Rycroft and Thomas], their Figure 3). The plasmapause lies on a field line closer to the Figure 2. — Variation of plasmapause position during the local night, Rp, with changing Kr index of F geomagnetic activity. Figure 3. — The difference, ARP, between the observed equatorial plane radial distance to the plasma- • pause and that computed from the parabolic regression line shown in Figure 2. Hourly average values are shown as crosses. 164 6or 2 3 4 5 6 EQUATORIAL RADIAI. DISTANCE. Rp . earth radii 21.CO 00.00 03.00 06.00 LOCAL TIME 165 Earth when magnetic activity is enhanced; typical values are Rp = 5.6 for Kp = 0, and R„ = 4.1 for K,, = 40. The computed parabolic least-squares fit to the data that is shown is a better fit than the also-computed linear regression. Figure 4. — Variation with local time, of the geocentric distance to the plasmapause in the equatorial plane. The different curves are explained and discussed in the text. 08 06 04 There is, however, considerable scatter in the points, some of which is explained by the diurnal variation of the plasmapause position during the local night shown in Figure 1. This effect is also shown in Figure 3 ([Rycroft and Thomas], their Figure 8), where the difference between the observed and computed radial distances to the plasmapause, ARe, is plotted against local time. AKP is positive before midnight and negative at dawn, showing that the plasmapause moves closer to the Earth, at a rate =* 0.1 earth radius per hour, as local time progresses through the night. The local time variations of the plasmapause position in the equatorial plane that have been discussed are summarized and plotted in Figure 4, the view being that from above the geographic North pole of the Earth. The data presented in Figure 1 are shown with their standard deviations as a solid curve, and the line of Figure 3 is shown as a dashed curve. Another solid curve represents the average behaviour of the plasmapause during periods of steady and moderate geomagnetic activity, Kp = 2 to 4 ([Carpenter, a], his Figure 6). The dot-dash curve shows a theoretically predicted plasmapause posi tion, using the theory developed by [Schield] which is discussed in the next section, and normalizing the curve to the observed average plasmapause position at midnight, Lp (00.00 L.T.) = 4.6. The inward motion of the plasmapause during the local night is clearly evident in all four curves, and the agreement between them is good between 21.00 and 06.00 L.T. 3. THEORETICAL CONSIDERATIONS Both [Nishida] and [Brice, b] have discussed the formation of the plasmapause as the boundary between plasma within the plasmapause which corotates with the Earth and plasma converted earth wards from the tail of the magnetosphere. This convection of magnetospheric plasma, a subject recently reviewed by [Axford, b], is driven by the electric field E across the magnetosphere, which arises because of the interaction of the solar wind with the geomagnetic field B. The velocity of convection is given by Since the plasma polewards of the plasmapause does not corotate with the Earth, whereas that inside the plasmapause does, the high-latitude ionosphere must slip with respect to the low-latitude ionosphere. It is proposed that this slippage, which can occur only in a region of low ionosphere conductivity, takes place at the trough in the topside ionospheric plasma studied by [Muldrew], [Jelly and Pétrie] and others. This, therefore, is the significance of the result of [Rycroft and Thomas] that, on average, there is one line of force of the geomagnetic field passing through the centres of both the plasmapause and the trough. The behaviour of charged particles moving only in the equatorial plane of a rotating dipole magnetic field, across which is superimposed a uniform electric field, is considered analytically by [Schield]. On a certain L shell the equatorial corotation potential of the rotating geomagnetic field, approximated by a dipole field of 3.1 x 10"s Tesla at the Earth's surface in equatorial regions, and surrounded by a tenuous plasma, is : 3.1 x 10~5QRE L 167 Inserting appropriate values for Q, the angular velocity of the Earth, and RE, its radius, and measuring L in units of Earth radius, this becomes numerically : L The potential of the dawn-dusk electric field across the magnetosphere, E„, producing convec tion of plasma from the magnetospheric tail is : — E„L sin £ where —- E„L sin Since thermal electrons and ions whose magnetic moments are very small can move only along an equipotential, the drift paths of charged particles — the equipotentials — are closed for those parti cles corotating with the Earth, whereas they aie open to infinity for those converting earthwards from the magnetospheric tail. Thus the plasmapause, the boundary between corotating and non-corotating plasma, is the last closed equipotential surface. The plasmapause position at time t, Lp(r), is thus : E L ( w 9 fmkV) (3) g)- ° ' ' = Moo W and r — 1+ + J\ + + sin i*l L,(,) = 2M00.00L.T.)[ ^ *] (4) The average value of Lp (00.00 L.T.) is observed to be 4.60, as mentioned in Section 2. Inserting the value of sin 0 = — 1 at 18.00 L.T., L„ (18.00 L.T.) = 2 L„ (00.00 L.T.) = 9.20 (5) Thus using equation (3), Eo = 4[L,(M.00L.T.)]jkV/RE (6) Inserting the value of sin 0 = + 1 at 06.00 L.T., L, (06.00 L.T.) = 9.20 [J2— 1] = 3.81 (7) which is in good agreement with the observed average position at 06.00 L.T. (Figure 1). 4. INTERPRETATION OF OBSERVATIONS Using equations (3) and (6), observations of L, (f) can be used in two different ways to obtain information on E„, the dawn-dusk electric field across the magnetosphere, which drives the convection of magnetospheric plasma. 168 4.! Firstly, considering all the data together without regard to the conditions of magnetic activity existing when the observations were made, equation (3) is used to study quantitatively the temporal variation of the average plasmapause position. Dividing throughout by 91.5 and replacing Lp(r) by simply L, equation (3) is rearranged to become : E —' = o ,L si•n am. -,, ! ig) r l L 91.5 Lp (00.00 L.T.) ' Equation (8) is of the form y = mx + c, which is the equation of a straight line of gradient m and intercept c. Showing the average values of L at hourly intervals, given in Figure 1, the graph of j- against L sin 4.2 Secondly, using observations divided into two groups according to whether or not Kp > 3— at the time of observations, equation (6) is used to interpret quantitatively the average local midnight position of the plasmapause. The results of following both procedures are presented in Figure 6. Average hourly values between 21.00 and 05.00 L.T., when the agreement between theory and observations L good (see Figure 4), are plotted together with error bars representing the standard deviations of the means. Best-fit straight lines are shown. It is clear that the gradient of the graph is larger for observations made when geomagnetic activity is higher. Using basically the first method, for the condition 3 2 Kp > 3— the gradient of (7.3 ± 0.6)10" RE~ leads to a value of E„ of (0.67 + 0.06) kV/RE. For Kp < 2+, E0 is found by this method to be (0.30 ± 0.03) kV/RE. These fields are plotted at values of Kp corresponding to the average Kp value in each group in Figure 7. The variation of E with 14,, derived in this v»„y from the temporal variation of the plasmapause position, is shown as a daihed line. Using basically the second method, for Kp > 3— the intercept of (0.234 ± 0.001) RE^\ giving Lp (00.00 L.T.) = 4.27, leads to a value of E„ of (1.26 ± 0.01) kV/RE. For Kp < 2 +, L, (00.00 L.T.) = 4.78 and hence Eo is (1.00 + 0.01) kV/R£. The variation of E» with Kp derived from the average midnight ptasmapause position is shown as the upper solid line in Figure 7. A variant of the second method is also used to derive the variation of Eg with Kp using the rela tion : Lp = 5.64 — (0.78 ± 0.12) ,fKp (9) given by [Rycroft and Thomas]. This pertains to the average plasmapause position during the local night. As may be seen from Figure 3, the mid-time of the observations is 01.00 L.T.; the time at which JR„ is zero is soon after 01.00 L.T. Using, for this local time, a value of the quantity in square brackets in equation (4) equal to 0.48, 169 0-30 0-28 06 0-26 LOCAL TIME 05 to 08 15 07 0-24 I «J 12 I03 I f 0-22 00 210 020 0I8 -3 -2 -1 0 Lsin <#> Figure 5. — Variation of hourly average Lvalue of plasmapause with local time (with v = 0° at 00.00 L.T. and with a difference of one hour ofL.T. corresponding to d& = 15°) in (y, L sinV\ space. It is clear that -j is directly proportional to L sin 9 between 22.00 and 04.00 L.T., enabling EQ to be calculated using equation (3). 170 ;"»< -,0-30 L*in$ Figure 6. — Plot of— vs. L sin0, the observations being divided into two groups according to whether or not Kf > 3—. 3 Kp >3—; j= (7.3 ± 0.6) 10~ L sin0 + (0.234 + 0.001); K„<2+; — = (3:3 ± 0.3) 10~3 L sin0 + (0.209 + 0.001). In the first method discussed in the text, the gradient of each least-squares linear relationship between the variables, the equation of which is shown, is interpreted to find E0 using equations (3) and (8). In the second method, the intercept of each best-fit straight line is used, with equation (6), to estimate En. 171 I-6-1-025 USING RYCROFT AND THOMAS (1970) 1-2- 0-8- FROM TEMPORAL VARIATION OF LP 0-4- KP INDEX Figure 7. — Derived variation of Ea with Kr ^.tdex. The dashed line is calculated by the first method of finding Eg from the temporal variation of the L-value of the plasmapause. The solid lines are calcul ated, as discussed in the text, by the second method of finding Ea from the average value of the Lrvalue of the plasmapause at a certain local time, for example — most simply — at midnight. which is a relation of the same form as equation (6). The points are plotted in Figure 7, with error bars corresponding to the standard error of the coefficient multiplying V~K? 'n equation (9). A best-fit linear relation to these points, and the hyperbolae representing the standard errors in this relationship, are shown. The results obtained using the second method and the variant on it agree within expérimental error. However, the magnitudes of the electric field Eo are not in agreement with those deduced by following the first method. Nevertheless, the gradients of the lines shown in Figure 7 obtained by the two different methods are approximately equal, giving similar values for the rate of increase of Eo with Kp, namely 0.14 kV/R£ per unit K,. It is concluded that the second method is the more reliable way of estimating Eo, since the distance to the plasmapause at local midnight is directly interpreted. Using equations (3) and (4) together, the method can be extended to find the electric field Eo from observations of Lp (r) at any time f during the local night when the theory given is valid. The reason that the first method is less reliable is that Eo is calculated from the difference in the positions of the plasmapause at two different times, and not from the absolute value of the radial distance to the plasmapause at any one time. 172 5. CONCLUSIONS AND DISCUSSION It is concluded from this study that the dawn-dusk electric field E» across the magnetosphere increases linearly with increasing K, index, from a value of 0.7 kV/R£ (0.11 mV/m) at Kp = 0„ to twice that value, namely 1.4 kV/RE (0.22 mV/m) at Kp = 5—. This has been done by considering the plasmapause to be, on average, an equipotential, and by studying its position at local times between 21.00 and 05.00. It is clear from Figures 4 and 5 that, between 12.00 and 21.00 L.T., there is a considerable discre pancy between the observed plasmapause position and that expected on the basis of the theory deve loped by [Schield]. Possible reasons for this difference are considered briefly. The plasmapause is prevented from receding from the Earth between 12.00 and 18.00 L.T. by virtue of the large conducti vity of the daytime ionosphere; in descriptive terms, the geomagnetic field lines through the plasma pause are firmlytie d to the Earth. At sunset, the ionospheric conductivity is much reduced, enabling the plasmapause to move outwards. The finite response time of the system prevents, however, the achievement of the theoretically expected value of hp (18.00 L.T.) = 9.2 — see equation (5). Since the observed values of Lp (18.00 L.T.) are less than those found using the theoretical arguments outlined here, direct substitution of these observed values into equation (3) leads to an unrealistically large estimate of ED being made. The discrepancy between the values of Eg found from this work and values larger than these derived by [Vasyliunas] and [Carpenter, c] is explained by this effect. A typical value of the dawn-dusk electric field across the magnetosphere — 1.1 kV/R£ or 0.18 mV/m for K,, =; 3 — as shown in Figure 7 — is believed to be correct. On the other hand, typical values of the electric fields presented by [Vasyliunas] and [Carpenter, c] seem to be too large, typically by a factor of four, namely the square of the ratio of the theoretical to the observed values of LF (a 18.00 L.T.). 173 GYRORESONANT WAVE-PARTICLE INTERACTIONS IN A SPATIALLY VARYING MAGNETIC FIELD AND PLASMA DENSITY* J. Troughton and G. Martelli Plasma Physics Group, School of Mathematical and Physical Sciences, University of Sussex (Great Britain) ABSTRACT We consider solutions of the linearized non-relativistic equations of motion of an electron in the fields of a right-hand circularly-polarized electromagnetic (whistler mode) wave propagating in a direction parallel to a magnetic field in a magneto-active plasma. The magnetic field and plasma density are assumed to vary in space along the direction of propagation, and are represented by functions of the type 2 2 B = B0î (I + Pz + ...) and n = n„ (I + az + ...). The gyroresonance condition for the wave- particle interaction is thus satisfied only at one point in space, i comparison of the exact trajectories of the panicles (obtained by integrating numerically the equatio is of motion) with the solutions of the linearized equations shows that the latter give a good representation of the motion as long as the initial pitch angle of the particle < 10°, and the magnetic field and plasma density show a spatial variation which is greater than a certain minimum variation, (i.e. as long as the parameters fi and a exceed certain minimum values). When these conditions are satisfied, as they are in fact in most regions of the Earth's magnetosphere, the linearized equations yield simple expressions for the change of the pitch angle of the particle. These results are used to illustrate pitch-angle scattering of electrons interacting with VLF radiation in the Earth's magnetosphere. 1. INTRODUCTION Solutions of the equations of motion of electrons in a whistler-mode wave propagating in a uniform plasma in a uniform magnetic field have been considered by a number of authors (see, for instance [Kolomenskii and Lebedev; Roberts and Buchsbaum; Dungey, c; Laird; Woolley]). Exact solutions can be obtained and the pitch-angle oscillation period can be written in terms of elliptic functions. When the strength of the wave field is much less than the unifonn magnetic field the use of perturbation techniques allows solutions to be obtained which have the form of regular pitch-angle oscillations, the amplitude and phase of which diminish as conditions further away from gyroresonance are considered. However, most situations of physical interest, such as resonant wave-particle interactions in the magnetosphere and in the solar wind, confinement of plasma in laboratory devices, etc., involve the presence of a non-uniform magnetic field. Moreover, the plasma density along the field line may also vary, as is indeed the case in the magnetosphere. 'Presented by C. Martelli. 175 In the present paper we have investigated how the presence of a non-uniform magnetic field and a plasma density variation modify the solutions obtained for the uniform case. These results are applied to the case of electrons interacting with VLF radiation in the Earth's magnetosphere. 2. EQUATIONS OF MOTION The non-relativistic equations of motion for a particle of charge e = — |e|, mass m, in an electromagnetic field described by the vectors E, B + Bo, can be written as : th m — = e(E + v X B + v x B ) (1) at 0 If the oscillating fields are those of a circularly-polarised wave propagating in a direction anti- parallel to a uniform magnetic field, we have, in rectangular coordinates : B„= B0 (0,0,1) =B2 B = (B„ cos [wt + kz], B„ sin [lot + kz}, 0) E = (— E„ sin [at + kz], E„ cos [cat + kz], 0). We also have E„ = |E[ = »,t B„ = vfh |B|, where v^ is the phase velocity of the wave. In this case we obtain, from Eq. (1) : dv± = Q,„ (v. + v#) sin ( 4 = -Q„^i cos (*-,*) at v± where tj> = (at + kz »x and », are the velocity components perpendicular and parallel to B0, i/( = 0 — Q7t, 0 being the angular coordinate of vL in the cylindrical system of coordinates v., »x, 0 in velocity space, fi, = \eBJm\, Q„ = |eB„/m|, and we have assumed the wave to propagate in the r direction. 2 We now require the static field B, to have the form Bs = B0§ (1 + fiz + ...), where p is a small expansion parameter and £ the unit vector in the z-direction. To satisfy the condition div B = 0, there must necessarily exist a radial component Br of the static magnetic field. The resulting equations of motion are then : dVi —- = — Qjoz sin (a — 0) + «„(»- + o^sin^ — do, —f- = Qj> sin (a — 0) — fi„t> sin <$ — $) (4) dt x + dto p« vr + »-» —f- = Or — cos (a — 0) — fl„ -U—E". cos (# — ifi) dk »x »j. where a is the angular coordinate of the particle, in the cylindrical coordinate system, z, r, a, and Q, = |eB>|. 176 The effect of the wave, for Q, P Qw, can now be considered as a perturbation, and the linearised solutions can be obtained by first finding the unperturbed orbits, i.e. by finding solutions with Qw = 0, and then using these solutions to integrate the complete equations of motion. Thus, with 0„ = 0, and assuming the gyroradius of the particle not to change over times of the order of a gyroperiod, we obtain, after neglecting terras of order higher than z2 in the expression for the magnetic field : dvx Pz dt 1 + pz2 »l»r du, pz dt 1 + Pz2 »i (5) di/r dt leading to solutions for particles with small pitch angles 2 2 1 2 1 v, = vn (1 - Pz m 0,,) ' * vI0 (l - j pz tr? 0„) (6) where 60, oIO and clo are the pitch angle, and the parallel and perpendicular velocities at z = 0 respec tively, and i/'o is a constant. Thus the equation for vx, under the same assumption that the variation of gyroradius during a gyroperiod is negligible, is I using -^ = vt -jM +, £~î|fc+Mï )*<'-'> The linearised solution for vx can now be found by integrating this equation over the unper turbed trajectory of the particle, i.e by using the expressions given in Eq. (6), together with : 2 °. = O«0(l + /b + "•) where Q^ is the value of Q, at z = 0. (8) The variation of wave number with z can be taken into account by writing 2 A = fc0(l + EZ + •••) (9) where Aj, is the wave number at z = 0, and s is a parameter containing the information related to the variation of the magnetic field and plasma density along the z-coordinate. We also assume that the wavelength is much shorter than the distance over which significant changes of magnetic field and plas ma density occur. If we neglect terms of order higher than z2 in the expansions of the various quan tities, the change in vx, i.e. Avx, can be written as 3 Avx = f t ^ vxdz + J awfê-+l\ sin (or + iz — ^0) where fl = — + *«, ^ b^JLltfe^ + k^^U + lnteu 177 We are interested in the change produced in vL when the particle passes through a region where the gyroresonance condition is satisfied. If we assume that this region coincides with the plane z = 0, then °>o + k0vn — QJo = 0, which is the same as a = 0. Using for D^ an expression of the type v# = v^ (1 -f- ez2), where v^ is the value of o^ at z = 0, we find the change in o^ produced when the particle moves from —z, to + z, in the form 3 Av± = - f Q„ l^S- + \\ sin fc,co s [bz ] dz + ^^- O. sin *o sin [bz\] (12) J-i, \ »=„ / 3 6ul0 where v = 8 -I- — fi ti^B . Using the substitution y = 6"2z, Eq. (12) reduces to o a M = - O. (H*L + l) i^ £' cos / * + l^L o. sin *0 sin fetf] (13) In this equation, the second term is due to the variation of the phase velocity along the trajec tory, and is usually small compared with the first term. The behaviour of the first term of Eq. (13) is illustrated in Figure 1, for iji0 = 90°. It can be seen that, as a consequence of the interaction, the value of v± not only oscillates, but also undergoes an irreversible change when passing through the region of resonance at z = 0. In the case of a mirror Figure 1. 178 configuration of the magnetic field, this results in an irreversible change of the mirror point. The maximum change of v can be estimated recalling that cosj»3 dy ~ 1.548, so that x r N-» K548^-(v + 1) (14) This change occurs mainly over a distance L a 2 b'"3, centred at z = 0. A case of particular interest occurs when both a = 0 and 6 = 0. The condition 6 = 0 requires the particle to have, at z = 0, a parallel velocity such that where mK is the plasma frequency at z = 0. The quantity i'f„ is the velocity necessary to preserve the condition of gyroresonance along the trajectory of the particle, assuming that the effect of the wave could be neglected. In fact, the interaction will produce changes in \ji and after a certain distance (depending on the strength of the wave) the linearised solution for this case becomes invalid. However, from the behaviour of the solution as b -> 0, we can expect a maximum perturbation for this case. In the following Section we discuss a criterion for establishing the limits of applicability of the above theory. 3. VALIDITY OF THE PERTURBATION TECHNIQUE The perturbation technique can be used to solve the equations of motion in a non-uniform magnetic field,onl y if some restrictions are imposed on the amplitude of the wave field. In particular, the method ussd in the present paper is valid only if the variation of the phase between the particle and the wave, produced by the wave fields themselves acting on the particle, is small compared with the phase variation produced by the non-uniformity of the main magnetic field. We can establish a criterion for the validity of the perturbation technique by comparing the relative importance of the forces acting on the particle due to the wave with that of the forces due to the non-uniform magnetic field. The longitudinal forces are nxB, («) CTi x B, (6) and the perpendicular forces are evJB, (c) ev&iz) (<0 eE„ = eo^B» (e) evfiw (J) Under uniform conditions, the combined effects of the forces (a), (e), (/) and ev±B, (0) result in an oscillation of the parameters of the particle motion, with a period of the order of T = (nA/8 t^fi,,)"2 over a typical distance (bunching distance) D » »rT. If the additional forces (b), (c) and evxdBx(z) 179 (where ABJ?) = BJz) — B^O) ), which are introduced by the non-uniformity of the field, are suffi cient to produce significant phase changes over times much shorter than T or distances much smaller than D, then we may neglect the phase change caused by the wave field acting on the particle, and use the adiabatic motion of the particle as a first-ordersolutio n to the equations of motion. For the range of parameters of interest in the case of electrons interacting with circularly- polarised electromagnetic waves in the Earth's magnetosphere, the most effective force in producing an additional phase effect is the evx ABJz) force. Hence the present theory is applicable, if the ine quality . . B j \vxàS,(zX=D\ p \(p, + P]A)B„| is satisfied. Substituting for D we obtain Q2 ^ . itin. 8 («, + »,*):°«fi Using the gyroresonant condition o> + kot = Qn to eliminate I and DP,, we obtain (15) 4 This inequality will be used later to define the upper limiting values of the amplitude of waves interacting with electrons in the Earth's magnetosphere (Fig. 2). Figure 2. 6 7 L value 180 4. APPLICATION TO THE GEOMAGNETIC CASE We consider here the case of electrons interacting with VLF radiation in the magnetosphere between L = 3 and L = 7, and assume the dipole approximation of the geomagnetic field to be valid. The variation of the fieldstrengt h and of the plasma density along a fieldlin e can be expressed through the parameters p and e. For the geomagnetic dipole field we can use the expansion A/ 9J2+---\ B-B°S(1 + 2(R^) where R„ is the Earth's radius, L is the Mcllwain parameter, and s is the curvilinear coordinate, with origin at the equatorial plane, of a point on a field line of the L-shell. By expressing the plasma density 2 n as n = n0 (1 + cS + ...), where «o is the value of n at s — 0, and using Equation (8) for Q„ we obtain a = L (£ZLL\ (" " \ B 2 \ tf ) [fi Q!0J where /% is the value of the refractive index for the VLF waves in the equatorial plane (^1+^£=^-Û)' = ',e2/e°m)- We have assumed that for a range of L-values in the neighbourhood of the plasmapause, the plasma density varies as n oc R~™, where R is the geocentric distance of a point of coordinates, and m is an index varying between 3 and 4 (see, e.g., [Angerami and Carpenter]). The actual model of the den sity variation used here has the form nocR"3 for 3R„ n oc R-" for 4 R„ < R < 7 R,. where the plasmapause, represented by a change of number density from 10zcm~3 to 10 cm"3, occurs at R = 4 R.. Under these assumptions, and recalling that the change in pitch angle is related to the change in »± by 2 1 -) 2 AV.„ = 4»! "»("« + «pli "* 1+4- v, (where we have made use of the fact that the energy of the particle remains constant in the coordinate frame moving with the phase velocity of the wave) we have calculated the maximum changes in pitch angle for electrons in the energy range from 2 to 80 keV at various L-values and for a number of wave amplitudes. These results are illustrated in Figures 3 to 7, for the case 80 = 2°, for electron energies 2, 4, 10, 40 and 80 keV, and for amplitudes of the wave magnetic vector in the range 2 to 60 my. The L-vatues, the resonant frequency 181 0.7 0.6 0.5 M 0.3 0.6 0.5 OX 0.3 0.2 "'"'. - 12mJ>^\,. - ' --•''10 m V ••s. , 5 m 8" - -- --""""" - . " - Initial pitch ongle - ^7h Ï^L^-__ Y/Z^* Snir- ^^ - "•^ttmï i - 12mï \^ i- - - 1 c 2—ÎOî 5 3' ? 10" Si 10' 1 5 - • i i • 5 E 7 1 0.G ! 0.» ÏO.2 0.15 0.1 °'°i. 0.312 0.1 e. £=10teï e.=2* 15 m*,.-' G -••'' lOnvy, 5 h 3 - Initial pilch angle 2 1 -1 -2 15 mT "-> -3 -l 3 1 ! 10' 5 3 10 5 3ï V 5il0 1 ,-5 M 5 3 2 -»'" 5 3 2>IOt" — ' £ : ! . • • ' ' ? X 3 4 5 5 7 1 182 0.4 03 0.1 0.05 0X3 Q.D2 .Jô5 5 101 5110* 3 2 lÔ1 5xï5 T S 6 Figure 7. i Figures 3, 4, 5, 6. the boundaries of the equatorial loss cone, i.e. the equatorial pitch angle of a particle which mirrors ~ 100 km above the Earth's surface. The pairs of curves symmetric with respect to 2°, represent the maximum excursions of pitch angle produced by the interaction with waves having the amplitude indicated. It can be seen that under certain conditions particles are scattered into the loss-cone and thus precipitated into the atmosphere. The effect of changing the initial equatorial pitch angle by a given amount shifts, to a first approximation, the position of the curves by the same amount. It should be noted, however, that in this case the ratio axQ^ varies with 0O, since the gyroresonance frequency depends on vn. For changes of 60 of a few degrees, this variation is, however, not very significant. One can roughly estimate the fraction of particles which are precipitated through a single wave- particle interaction, by assuming the relative phase ip0 between the wave vector and the vL vector of the electron to be a random variable when an ensemble of electrons is considered. Then, since the rela tion between the initial relative phase and pitch angle after an interaction is given by : Bp = eK+ l/ieUsin^o (16) where from Eq. (13) we have : "i i + M0U M»il« »,(.«• + »pJ i + the number n12 of particles having a pitch angle, after interaction, lying between two values 0PI and 0Pj is just the number of particles with relative phases lying between ^01 and 183 Since we assume that all phase angles are equally probable, this is given by "loi * i i \ where n,ot is the number of particles taking part in the interaction or, in terms of 0PI and Bp, If we now let flpi and 0p represent the values of pitch angle between which precipitation occurs, then we can find the fraction of particles precipitated as a function of L value. Such results are illus trated in Figures 8 and 9. It must be noted, however, that in deriving such a curve it has been assumed that the spectrum of wave amplitudes is uniform over the frequency range and L value range indicated. Initial pilch-angfe 2? electron energy 40 keV 7% 6% n 4 5 6 7 L value. Figure 8. 5. CONCLUSIONS The inclusion of spatially-varying magnetic field and number density in the theory of gyro- resonance has been treated using the linearized equations of motion. The resulting solutions have been shown to give a good representation of the motion as well as leading to simple expressions for the change of pitch angle produced by the wave-particle interaction. The results have been used to find the proportion of the total number, of particles with à given energy and initial pitch angle which are scattered into the loss cone, and thus-precipitated, through an interaction with a whistler-mode wave. Most theories of resonant wave-particle interactions in the magnetosphere have been based on uniform field models. ) The inclusion of a non-uniform field, using the method outlined in the present paper, should allow more realistic theories to be constructed. 184 3.5 4 4.5 5 5.5 6 6.5 L value Figure 9. 185 DISCUSSION A. Roux. Did you use a perturbation technique to solve the equation of motion of the particles in the conjugate static magnetic field and field of the waves? G. MarteUi. Yes. We find the zero*>rder approximation solution first and then we integrate the equation of motion over the perturbed orbit. A. Sons. In fact, you could integrate analytically the particle trajectories using adiabatic invariant techniques. I mean that it is possible to find an adiabatic invariant for particles which are trapped inside the wave; then, avoiding secular terms which probably appear in a perturbation method and lead to time- divergent solutions, you can compute the effect of the wave on particles and especially the variation of the electron or ion parallel velocity. 186 WAVE AND BEAM LABORATORY EXPERIMENTS IN A MAGNETO-ACTIVE PLASMA P.J. Christiansen, C. Christopoulos and G. Martelli * Plasma Physics Group, University of Sussex (Great Britain) ABSTRACT Experiments are described which examine : (a) the non-linear interaction of fast electron beams with whistler (helicon wanes) at the Doppler shifted cyclotron frequency; the results are compared with some theoretical predictions; (b) the natural noise spectra near the electron cyclotron frequency of an RF excited plasma; (c) the propagation of Bernstein waves at ambient plasma densities one order of magnitude higher than hitherto employed by other authors. This paper is devoted to a description of three experiments started recently in our laboratory. The experiments are concerned with the laboratory simulation of some effects relevant to VLF pheno mena in the ionosphere and in the magnetosphere. The results and their interpretation are only preliminary. • A) The first set of measurements is concerned with the non-linear resonant interaction of fast electron beams with whistler-type (helicon) waves at the Doppler Shifted Cyclotron Resonant (DSCR) frequency. DSCR phenomena have been investigated theoretically in two main ways : a) by using -recently developed quasi-linear theories and b) by examining the velocity space trajectories of single electrons satisfying the DSCR condi tion [Dungey, a, 6]. These are described by the non-linear equation of motion of a charged particle moving in a steady magnetic field and the e.m. field of a wave, with the wave vector antiparaliel to the velocity of the gyrocentre of the particle. Some recent laboratory measurements which involve DSCR effects have been carried out by [Ermakov and Nazarov, Zalesskii and Nazarov]. These consist essentially in the pulsed injection of a high-current (~ 10 A) electron beam into plasma but since the experiments *Who presented the Paper at the Colloquium. 187 -• , --I ••=:• "• !Z~\ /-•: Figure I. — Experimental device, showing discharge tube, R.F. fields, wave interferometer, electron gun, etc. are mainly concerned with electron heating, the effects measured are the diamagnetic signal, X ray emission, beam energy, etc., and as would be expected, significant effects have been detected in the region of the DSCR frequency. The experiments of [Ivanov et al.] examine similar parameters when a beam is injected into an overmoded /x -wave cavity. Figure 2.—Experimental device. Schematic diagram. 1'. Magnetic field coils; 2. Discharge tube. 3. Exciting coil; 4. Electron gun; 5. Phosphor plate; 6. Pumps; 7. Camera; 8. Microwave interfe rometer; 9. Magnetic probe; 10. Oscillator. ji u il y il innnnnrnrnnnir u 188 Our experiment has been designed to permit observation of the non-linear pitch-angle modu lation predicted by the single-particle theories. Setting aside the obvious problems of scaling from the magnetosphere to the laboratory, we have tried to avoid significant coupling of the injected beam to other modes of interaction (this point will be discussed later). The experimental plasma machine (Fig. 1, 2) consists of a 1.2 m long, 10 cm diameter pyrex tube immersed in an axial magnetic field which is variable from 0 to 700 gauss. A plasma is form;d in argon gas at pressures of =: I mtorr by RF excitation at 8 MHz of a double helical copper coil, six 16 cm periods of which are wound along the tube length. The method of plasma excitation is an extension of that of [Boswell] and most importantly for this experiment, the plasma so formed contains a standing whistler of significant amplitude at the exciting frequency. Magnetic probe measurements show it to be an m = 1 mode, the magnitude of the perpendicular wave field b, being =; I gauss (maxi mum at r = 0) and with an axial periodicity of 16 cm. A low current (1 A) of fast electrons, with energy variable between 5 and 25 keV, is injected at a variable angle (0-15°) to the steady field B0 from one end of the tube. The electrons are detected on an earthed phosphor screen at the other end. Figure 3. — Typical image formed by electron beam near DSCR. Parameters Ba = 142 G, E = 12 keV, 0 = 5°. Figure 3 shows a typical pattern traced out as the injected electrons hit the screen, recorded under CW conditions (beam energy = 12 keV, B0 = 142 gauss, injection angle = 5.5°). The pattern is detec ted near to resonance, defined by the well-known relation : io + kvz = Be where at — 8.1 MHz, k = 2ir/16 cm. At energies far above or below resonance, or when the wave is suppressed, the beam merely forms a single spot which, as resonance is approached, evolves into closed loop like that in Figure 3, with maximum dimensions at resonance. The theoretical resonance condition above is obeyed for experimental resonant energies in the range 7-16 keV to better than 4 %. We can make some general comments on the appearance of such near-resonance loops. The injected electrons move in a plasma containing several periods of standing wave. They interact only with that component of the wave which travels towards them (" magnetic Landau " effects with the other component can be ignored since vt P 189 Over one wave period the electrons, emerging from the gun in a fixed direction, see the b, of the wave at all angles, and the resulting v x Si interaction gives rise to a non-linear modulation of their initial pitch (injection) angle fl. This modulation strongly depends on the initial phase # = cos"1 v. b. Crudely put, the initial v x b force accelerates or decelerates the electrons depending on the value of (f>. Because of such a dependence, the beam maps out some pattern in real space, i.e. in the r. 0 plane, when intersecting at some fixed axial distance z of a cylinder. This pattern is related to the variation of the beam pitch angle with i i 5 lam Figure 4. — Theoretical patterns at different energies formed by beam after 1 metre travel in r, 9 plane. Cross marks injection point in r, 8 plane. Parameters B0 = 134 G, bjBa = I %. ^resonant = 10.7 keV. which the position of the electron is plotted in the r, 6 plane as a function of ij> for several beam ener gies, after one metre of travel in the axial direction. The initial pitch angle is 5°, Era = 10.7 keV, X wave =16 cm, and 6/B0 = 1 % (rather higher than the experimental 0.5 %). The qualitative agree ment between such curves and experiment is good — in particular the basic shape of the patterns, their " rotation " in space with energy, and the fact that parts of a loop are visibly brighter than others (i.e. the number An of electrons having a phase between tj> and function of energy (shown in Fig. 5) for two values of B0, all other parameters being held fixed. The resonance can be clearly seen. 190 Figure 5. — Theoretical resonance curves as determined by preliminary measurement technique. Dmaj, Dmin : major and minor dimensions of interaction loop. Figure 6. — Comparison of theory and experiment, showing resonant effect at DSCR. B0 = 142 G; «o = 5°: blB0 a 0.5 %. ? 5 -V*- 11 BEAM EHEBOVkeV In Figure 6 we compare the results of an experimental run analyzed in this way with theoretical calculation using the experimental parameters sp inputs for the calculations. There is satisfactory agreement between these preliminary results. However, we should consider another effect which can obscure the results of experiments of this kind — that of degradation or " slowing down " and scattering of the beam due to beam-plasma 191 interaction and the resulting emission of Langmuir waves. Quasi-linear theories (e.g. [Tsytovich] show that the degradation rate caused by this process is : where nb = beam density, np = plasma density, I2 plasma (np 2; 10 /cc) the distance, according to the above, that the beam must travel to be degraded by l/i? is many times the experimental interaction length. • B) Natural noise spectra In certain situations, the plasma described previously exhibits a natural noise band just below the electron cyclotron frequency. Figure 7 shows the frequency spectra of the noise received by a single probe aerial in the plasma and detected by a VHF receiver. For each value of B0, the axial field, the band terminates at about 0.7 Qe, and this fact, together with our current supposition that the noise is primarily electromagnetic in character, leads us to believe it to be associated with a velocity space instability involving the emission of whistler waves. [Vedenov el al., a] and many others [Gruber el al., Sharer and Trivelpiece, Morse, b] including a recent theoretical contribution by [Crawford et al., b] have shown that such instabilities can arise in situations in which there exists an anisotropic temperature of (ring distribution) when the perpendicular electron temperature : Tx > T, in which case an instability band exists with an upper frequency cut-off : 0 — 1 coe=!—— Oe , 0 = TJ/rl, If, as [Kennel and Petschek] and others argue, weak turbulence of this kind is associated with the diffusion of resonant electrons into regions of velocity space with high values of »n, the effect could be tested in the laboratory by injecting an additional signal into a noise band of the kind shown. The growth and saturation of such a signal should lead to an enhancement of the flux of particles in the direction of the steady field. In fact we have recorded a few percent flux increase to a double Langmuir probe designed to detect axially-directed particles when about 1 watt of 500 MHz signal is applied to a loop launcher in the plasma. A positive identification of the process involved is awaiting more rigorous analysis of the electron velocity distribution. • C) Propagation of Bernstein waves Our final remaries concern some [Bernstein] wave propagation experiments recently begun in a low density (= 10"/cc) dc plasma machine in our laboratory. The plasma is created in argon gas by injection of a slow (200 eV) electron beam from a hot cathode. Éy"now a number of laboratory experiments (Crawford et al., a; Harp; Leuterer] have been performed to study the propagation of the electrostatic modes, and particularly those using the. moving probe technique [Clinlremaille; Thomas et o/.] show that theory and experiment agree well at low ambient densities. The moving probe technique and results are'described in detail by the latter elsewhere. 192 B„ 650 G Mf|i VMM Jb ^A 400 G 260 G -a, _Jjb 170 G iMh, MHz 900 600 300 Figure 7. — Frequency spectrum of noise band near Qe for several values of B0. 193 Bernstein waves, which propagate undamped perpendicular to a magnetic field, were launched from a 1 cm long aerial oriented parallel to the static B field (~ 200 G) at frequencies in the range 400-1000 MHz in a plasma with ambient densities of 1010, 10" cm"3. The waves were detected by a similar aerial which could be moved with respect to the launcher, coupled to a VHF receiver. The launched signal couples to the plasma in a capacitative quasi-static mode as well as the Bernstein mode, giving a resultant signal, as detected by the moving receiver probe, which is modulated spatially at the Bernstein wavelength (Figure 8). The dispersion of Bernstein waves is described by the relation e->l„{X) nQe I-—- y = 0 a> — nQe ( k v \2 where X — ( -±p ) , I„ = modified Bessel of firstkind . Computation of this relation at high plasma densities coj, = toj + Qe1 P Qe, shows that the lower-frequency branches-become extremely insen sitive to density variations, and propagation experiments with single-parameter fitting of the results can be used as a means of «ieterming T± in plasmas. Our exploratory experiments have been performed using the moving-probe method with this fact in mind. Whereas previous experimenters have concentrated on dispersion measurements at low densities (~ 1010/cc, Û),» ~ ^.3 fie), the results shown in Figures 8, 9 demonstrate that this technique can be applied to plasmas at least one order of magnitude more dense without trouble, and that the results accord with theory that region of kr( where the waves can be considered electrostatic. Figure 8. — Moving probe recordings of Bernstein wave propagation at several frequencies, li B0 = 175 gauss, N, ~ I0 /cc. proba a«paratlon 194 20 1-6 tO' 1 i • • • . • 02 l-O 1-8 Figure 9. — Comparison of theory \-?f- — -251 and experiment for Bernstein wave propagation at n elevated densities. Ba ~ 175 gauss, JV, =: I0 jcc, Ttl ~ 0.8 eV. ACKNOWLEDGEMENTS It is a pleasure to thank M.L. Wooleyfor his help with the numerical calculations carried out in section (A), and to acknowledge a valuable conversation with T.A. Hall in connection with the Bernstein-wave experi ments. The invaluable technical assistance ofB.R. Biackmann is gratefully acknowledged. The research is supported by the U.K. Science Research Council and the U.K. Atomic Energy Authority. One of us (P.I. Christiansen) is grateful to the former for a fellowship. 195 PARALLEL ELECTRIC FIELD, NEAR THE AURORAL IONOSPHERE, DEDUCED FROM ENERGY SPECTRA, ANGULAR DISTRIBUTIONS AND TIME VARIATIONS OF LOW ENERGY AURORAL ELECTRONS AND PROTONS H. Rème and J.M. Bosqued, Centre d'Etude Spatiale des Rayonnements, Faculté des Sciences, Toulouse, France ABSTRACT For about 115 seconds of a French Dragon rocket experiment fired into a diffuse aurora from Andenes, Norway, at about 0428 geomagnetic local time, on November 3,1968, a correlation was observed between 5-30 keV electron flux variations and small pitch angle 0.5 - 5 keV proton flux variations. All the features of particles during this event (energy spectra, angular distributions, time variations) can be interpreted with the presence along the geomagnetic field lines, for about 115 seconds, of a 1 to 2 kV potential difference situated below an altitude of about 1500 km and accelerating positively charged preci pitated particles. The origin of such a parallel electric field, while not completely known, has been theoretically predicted recently by Kindel and Kennel. The source of the electric field is plasma turbulence, linked to 5-30 keV electron precipitation, making the parallel resistance increase due to ion cyclotron wares. 1. INTRODUCTION It is of fundamental interest to establish the presence of electric fields in space, in view of their implications in plasma instabilities, particle motions and acceleration mechanisms. In particular, the electric field influence in the aurora must be determined, since some theories on the origin of particle precipitations are founded on the presence of electric fields in the magnetosphere [Taylor and Hones; Block, b; Chamberlain; Speiser; Haerendel]. Until recently, however, the studies of electric fields have been limited because of the experi mental difficulties involved in measurements. At present, the techniques include ionospheric drifts of artificial ion clouds [Haerendel and Lust; Wescott et al,] probes on balloons [Mozer and Serlin], rockets [Mozer and Bruston] and satellites [Aggson; Gurnett, b]. If the ion cloud method is limited to 197 twilight periods, the probe method is difficult to interpret since a lot a practical difficulties arise (for example, sheath electric fields, V x B term associated with rocket or satellite motion). However, the presence of dc electric fields can be conveniently ascertained by studying and identifying acceleration and modulation mechanisms affecting particles in space. An appropriate method is to measure simultaneously angular and energy distributions of electrons and protons, since electric fields affect the physical dynamics of particles. The auroral particles with energies smaller than a few keV are well suited for this study because they are greatly influenced by these fields and also because they are most abundant [Mcllwain, a; Chase; Evans; Reasoner et o'.; Sharp and Johnson; Bernstein et al.; Westerlund]. A considerable amount of information on auroral particles has been obtained from a French Dragon rocket fired from Andenes, Norway (L 2/ 6.2) into a diffuse aurora [Rème, 1969 a, b]. Throughout the flight, the features of particles fluxes (temporal fluctuations, energy and angular distri butions) show the existence of two electron components (from 0.5 to 2; 5 keV; from =; 5 to 30 keV) and two proton components (from 0.5 to ^ 5 keV; from £ 5 to 30 keV). The temporal fluctuations of the different components are not well correlated. However, in the flight time interval 345-460 seconds, a burst appears at the same time both in 5-30 keV electron fluxes and in 0.5-5 keV proton fluxes. These proton fluxes are aligned along the geomagnetic field lines. This result was the first experimental evidence of the alignment of low-energy proton fluxes [Rème, 1969 a, b- Rème and Bosqued]. The observations obtained with the ESRO 1 satellite [Hultqvist et al.] show that this pheno menon is fairly frequent. This paper gives detailed results obtained during the 345-460 seconds flight time. Angular distributions, energy spectra and temporal fluctuations of particles support the existence of an electric field parallel to the geomagnetic field lines during this time interval and, in this context, data are presen ted to that effect. 2. INSTRUMENTATION The experiment on low-energy auroral particles mounted in the Dragon rocket payload consisted of 24 channeltron spectrometers for detection of electrons and protons in the energy range 0.5-30 keV. The energy analysis of particles was performed by a magnetic analyser for the electrons [Bosqued and Rème] and by an electrostatic analyser for the protons [Tatry et al.]. To allow the study of fast time variations, the -entrai energy was fixed for every detector. The angular distribution was obtained by combining the data supplied by 6 axial detectors looking upwards (pitch-angles analysed between 26 and 46° during a precession period of ^ 30 seconds), 6 axial detectors looking downwards (pitch-angles analysed between 134 and 154° during a precession period) and 12 radial detectors, the analysed pitch-angles of which vary from 50 to 130° according to the rotation period (0.775 second) and to the precession period; thus, the pitch-angle range analysed was from 26 to 154°. A shielded detector is used to estimate the contribution of very high energy particles (y rays, protons, cosmic rays) and a detector without magnetic analyser makes it possible to evaluate the contamination due to ultraviolet rays, X rays, ... Throughout the flight, both detectors revealed a counting rate of less than 0.2 count per second, proving that they were not affected by parasite rays or particles. The main characteristics (central energy, energy resolution, absolute efficiency, geometrical factor) of all these spectrometers are listed in Table 1. The coefficient X of this Table, multiplied by the count rate of a detector, gives the flux.(cm2 s ster)-1 keV. Electron spectrometers have a conic aperture of 1.5° half-angle and proton detectors have a rectangular aperture of 2.5 x 6° half-angles. 198 Table 1 CHARACTERISTICS OF DETECTORS Analysed Direction Analysed Central Energy particles Absolute Geometrical Detector E : electrons A : axial pitch-angle energy band efficiency factor X P : protons R : radial range O E„(keV) JE £ G (cm* ster) 1 E A 26-46 0.65 0.43 0.7 2.2 10-3 1.5 10s 2 E A » 2.4 1.6 0.45 » 0.64 105 3 E A » 20 13.3 0.15 » 2.3 10* 4 E R 50-130 0.75 0.5 0.7 » 1.3 105 5 E R » 1.0 0.69 0.6 » 1.1 10s 6 E R » 2.2 1.47 0.45 » 0.7 105 7 E R » ?.7 6.47 0.20 » 3.5 10* 8 E R » 22 14.7 0.15 » 2.1 10* 10 E A 134-154 0.63 0.42 0.7 » 1.6 105 11 E A » 2.3 1.53 0.45 » 0.66 105 12 E A » 21 14 0.15 » 2.2 104 13 P A 26-46 0.83 0.23 0.85 1.4 10"* 3.7 10* 14 P A » 3.9 1.1 » » 7.7 103 15 P A » 27 7.6 » 9.6 10"5 1.6 103 16 P R 50-130 0.81 0.23 » 1.4 10-* 3.7 10* 17 P R » 1.6 0.45 » » 1.9 10* 18 P R » 3.9 1.1 » » 7.7 103 19 P R » 9.2 2.6 » 9.6 10"5 4.8 103 20 P R » 27 7.6 » » 1.6 103 22 P A 134-154 0.82 0.23 » 1.4 10"* 3.7 10* 23 P A » 3.9 1.1 » » 7.7 103 24 P A » 27 7.6 » 9.6 10" 5 1.6 103 Detector 9 : withou t magnet (ajtial ; analysed pitch angle 50-130°). Detector 21 : shielded detector (sixial ; analysed pitch-angle , 50-130°). 3. FLIGHT CONDITIONS The Dragon rocket was fired to an altitude of 420 km from Andenes into a diffuse aurora, on November 3, 1968 at 0142 : 25 UT (=; 0428 geomagnetic local time). Launching time took place during a geomagnetically very disturbed period due to an enhancement of solar activity involving PCA, beginning on October 31, at about 0900 UT and prolonging its effect until the morning of November 4. The value of K, for the first three hours of November 3 was 7". During the flight, however, there was only a very slight indication of the PCA and it is felt that the data reported below were not influenced by any solar cosmic rays. The launching time coincided with the recovery phase of a negative magnetic bay which reached — 650 y before remaining at the steady 199 value of — 500 y for the rest of the Sight. The riometric absorption at 27.6 MHz reached 7 dB and the luminous intensity in the 4278 A band varied between 15 and S kilorayleighs. The Mcllwain para meter L varied between 6.2 and 3 during the 620 seconds of the flight. 4. EXPERIMENTAL RESULTS Throughout the flight, two electron components (0.5 to =: 5 keV and =: 5 to 30 keV) and two proton components (0.5 to œ 5 keV and = 5 to 30 keV) are observed, with different angular distribu tions, temporal fluctuations and energies (Rème, 1969 a, b; Rème et al.]. The general shape of elec tron spectra is similar to the one previously observed outside auroral arcs [Westerlund]. The existence of two proton components was recently confirmed by Soviet results obtained with Cosmos 261 [Galperin el al]. Figure I, showing count rates from 7 of the 24 detectors, averaged over 5-second intervals, summarises the main observations of interest for this Paper. Central energies and pitch-angle ranges are indicated for each curve. We note that in general the electron and proton count rates are not well correlated. However, during the time interval 345-460 seconds, a burst appears and disappears, at the same time in the fluxes of 5 to 30 keV electrons and of 0.5 to 5 keV protons with pitch-angles in the range 26-46°. These variations in the count rate of 20 keV electrons arid of 3.9 and 0.83 keV protons with 26-46° pitch-angles are shown in Figure 1 a, b, d. This Paper will be devoted to the discussion of this correlated burst. 4.1 Angular distributions i During the burst, the pitch-angle distribution is different for the 5-30 keV electrons and for the 0.5-5 keV protons. The angular distribution of the electrons remains unchanged and isotropic as it was before and after the event. On the other hand, although it is impossible to get a quantitative angu lar distribution for the protons, because of their very low count rates, it is easily seen qualitatively that their distribution tends to become aligned with the geomagnetic field lines : this can be inferred from the fact that the event is seen only by detectors analyzing small pitch-angles (Figure 1 b, c, d, e). At the end of the event (=: 460 second flight time), this angular distribution becomes nearly isotropic again as it was before the event. The 5-30 keV proton component does not undergo any variation of angular distribution during the time interval analysed here.- Both at the beginning and at the end of the correlated burst, a variation of the angular distri bution of very low energy electrons (0.5-5 ke V) is observed. Figure 2 shows that the ratio of J (650 eV) for 26-46° pitch-angle:, over J (750 eV) for 50-130° pitch-angles is smaller during the correlation than during the rest of the flight. A sudden change occurs at 460 second flight time, which corresponds to the end of the burst ; the same sudden change also takes place at the beginning of the burst (345 second flight time). Figure 1. — Count rate of various detectors during the rocket flight, averaged over 5 seconds. • 200 ELECTRONS 20KeV 26-<6* pile- angles PROTONS 10 3.9 KcV ® 26-<6*pilch onglet Ml 1 J >A^r^irV^JHJlfP^AJ PROTONS 3-9 KcV 50-130* pilch onglet © PROTONS 030 eV nJl © 26.46* pilch angles < o: PROTONS i- 010 eV 50-130* pilch angles © 2 8 VJ1* 2000 - 4000 • 2000 300 345 460 500 FLIGHT TIME ( sec.) 201 «55 460 465 470 FUIQHT TIME (sec.) c- , v • .- r J (6S0 eV) (26-46° pitch-angles) ,,, . , , , ., ,,„ Figure 2. — Variation of .'„ ... ' ,-_-., , at the end of the correlated burst (460 se- J (750 eV) (50-130° pitch-angles conds flight time). J is the particle flux for one energy and one pitch-angle range in cm~2s~' ster~l,keV. Figure 3. —Energy spectra of protons just before et just after the end of the correlated burst (460 seconds flight time). — •— radial detector data just before and just after 460 seconds flight time — •— axial detector data just before 460 seconds flight time —•— axial detector data just after 460 seconds flight time ... O... 35° pitch angle extrapoled value from radial detector data for 9,2 keV protons just before and just after 460 seconds flight time. Proton results are corrected from charge exchange and interactions in the atmosphere by using a Monte Carlo simulation technique. "1 I I i I llTf J ' i I m I i i 1À 1111 PSOTON ENERGY 202 4.2 Energy spectra Before and after the burst, the angular dif tributions of the 0.5-5 keV protons are nearly isotropic; loss cone or trapped (pitch-angles close to 90°) particles thus have similar energy distributions as measured by the 5 radial detectors and by the 3 axial detectors analyzing the small pitch-angles. The burst correlated with the electrons is detected only by low energy axial spectrometers (0.83 and 3.9 keV central energies), the higher energy axial detector (27 keV central energy) and the radial detectors not being affected. Figure 3 shows the proton energy distributions just before (=; 457 second flighttime ) and just after (=* 463 second flight time) the correlated burst. For the 50-130° pitch-angle detectors the spectrum remains almost unchanged; on the other hand, there are only 2 points available (0.83 and 3.9 keV) below 5 keV with the axial detectors; these points do not enable any accurate spectrum to be determined; but they allow an increase of the average energy of the 0.5-5 keV proton component to be deduced. The 0.5-5 keV proton flux alignment along the lines of force is thus associated with a har dening of the energy spectrum. The fluxeso f electrons with energies < 5 keV are essentially unaffected during the major part of the correlated event (Figure 1 f and g). However, at =: 445 second flight time, an increase of the count rate of < 5-keV electrons is observed. This variation does not appear to be directly linked to the burst discussed in this Paper. Moreover, throughout the flight, the variations of 0.5-5 keV elec tron fluxesd o not correspond to those of 5-30 keV electron fluxes. At 460 second flight time there is an increase of 650 eV electron fluxes and a decrease of 2.5 keV electron fluxes (Figure 4). This anti- figure 4. — Count rate of '650 eV and 2.5 keV electrons in one pitch-angle range around the end of the correlated burst. IL 26.46* pitch ancles m \h rvi 26_*6* pilch angles sw™ <60 FLIGHT TIXE 1 sec) 203 . r i • i 10 • - _ • • _ 8 • • 6 • • 4 1 ) T l I .- 2 H^vW -I— I 45S «60 465 470 FLIGHT TIME (sec.) • Variations of ,,,,-••/, 'n 26-46° pitch-angles at the end of the correlated burst Figure 5. J (2.S keV) (460 second? flight time). J is the particle flux for one energy and one pitch-angle range in cm'2 s~* ster'1, keV. correlation indicates a drastic softening in the spectrum of precipitated electrons. Figure 5 clearly shows how the spectral ratio -j-L-y-jr^4 varied in time for one range of pitch-angles sampled. The increase of the ratio at =: 460 seconds clearly confirms the large spectral softening. Figure 6 shows two energy spectra, averaged over 4 seconds just before and just after 460 seconds flight time. The end of the correlation between the higher energy electrons and the lower energy protons is thus cha racterized not only by a decrease of the high energy electron contribution but also by an increase of low energy (1 keV) contribution, which explains the softening occurring at 460 seconds. Figure 6. — Electron energy spectra averaged oner 4 seconds just before (a) and jvst after iV :he end of the correlated burst (460 seconds flight time). 111 ii| 1—I I I M!l| i—r i i i i ml i i i i i i n i i i ELECTRON ENERGYl.v 204 The main features of particle components during the 345-460 seconds flight time interval are summarized in Table 2. Table 2 MAIN FEATURES OF PARTICLE FLUXES DURING THE 345-460 SECONDS FLIGHT TIME INTERVAL ELECTRONS PROTONS energy interval from =; (component) from 0.5 to =s 5 fceV 5 to 30 keV from 0.5 to = 5 keV from a 5 to 30 keV time variations flux increase only simultaneous flux no correlation of at 445 seconds increase flux variations with (flight time) other components angular drastic change at isotropic modification in the no variation of the distribution 345 and 460 seconds throughout angular distribu angular distribu (0-90° pitch- (flight time); the the flight tion which becomes tion linked to this angles) distribution is more anisotropic; very no time interval isotropic in this ticeable alignment time interval of proton fluxes with the magnetic field energy spectrum drastic softening at hardening of 1 to indications 460 seconds — 2keV — (flight time) 5. DISCUSSION It is possible to give an interpretation of the results observed during the correlated burst because the particle characteristics can be interpreted in terms of an electric fieldparalle l to geomagnetic field lines of force and existing above the measurement height for about 115 seconds. This electric field connected to the afflux of the high energy electrons is not strong enough to affect these electrons but, on the other hand, it accelerates the low energy protons, thereby explaining their simultaneous arrival. Indeed, if an electric field is applied along the geomagnetic lines of force, the motion is described by 2 equations, provided that there are no other disturbances, such as a wave-particle interactions for example [Northrop]. a) Energy conservation : W, = W„ + qV, where W0 is the kinetic energy of the particle at the input of the zone where the electric field is present; V/t is the kinetic energy of the particle after it has crossed the zone where the V potential difference is applied; and q is the charge of the particle. 2 b) Invariance of the magnetic moment : (Wt sin o,)/B, = (W0 sin* Oo/B0), where a and B are respectively the particle pitch-angle and the magnetic field strength, at the input (index 0) and at the output (index 1) of the zone where the electric field is present. 205 From these two equations, one can deduce, in the case of a potential difference accelerating the prec';v!ated protons, — an energy increase (qV) with a pitch-angle decrease (a, < a0) for the protons; — an energy decrease (— qV) with a pitch-angle increase (xl > a0) for the electrons. All the results given in Table 2 can thus be interpreted by assuming a potential diff: r^nce of the order of 1 kV applied along the lines of force of the magnetic fieldan d accelerating the protons in the 345-460 seconds flight time interval. Indeed, the direction of the electric field must be such as to accelerate positively charged preci pitated particles, in order to account for the proton pitch-angle distribution, that is aligned along the magnetic fielddirection , and for the repelling or slowing down of the electrons, which explains the arri val of very low energy electrons seen by the anticoincidence of 650 eV and 2.5 keV electrons when the field disappears. This field also increases the electron pitch-angles, which may explain the variation recorded in the ratio J (650 eV) for 26-46° pitch-angles over J (750 eV) for 50-130° pitch-angles (Figure 2). The estimation of the 1 kV value is deduced from the analysis of the rough hardening of the proton spectrum during the event and of the softening of the electron spectrum at the end of the event. This is confirmed by the fact that the electric field does not greatly modify the energetic and angular features of the higher energy components. Source localisation In this Section, we would attempt a localisation of the electric field source using information obtained during the rocket flight. It is difficult to decide whether the correlation between 5-30 keV electron and 0.5-5 keV proton fluxes is temporal or spatial. If it is a time correlation, i.e. in the case of a disappearance or a motion of the electric field region, as the speed of the protons of 830 eV (the lowest central energy of protons measured during the flight) is about 400 km/s and as the end of the event occurs in less than 3 seconds at this energy and in less than 1 second at 3.9 keV (a better time reso lution is not achieved because the proton counting rates are very small) on the proton fluxes, such a correlation implies that the proton acceleration or modulation source must be located at an altitude lower than 1500 km. If, on the other hand, the event is space correlated, the charge exchange pheno mena should normally enlarge the dimensions of the proton precipitation area [Davidson; Rème, 1969 b]. Indeed, in the case of an isotropic precipitation of low energy protons, the spreading at the rocket altitude (350 km) is significant [Rème, 1969 b]. Since the burst ends suddenly, in less than some seconds (which corresponds to less than 2 km in view of the horizontal speed of the rocket), in the case of a space correlation, the angular distribution of protons would have to be strongly aligned along the magnetic field lines so that the hydrogen atoms created by charge exchange could not enlarge the proton precipitation region by diffusion through the lines of force. In other words, a strongly aligned angular distribution of protons shows that the acceleration or modulation source must be close to the neasurement altitude. Therefore, we concluded that, whether the correlation is spatial or temporal, low energy pro tons observed in association with 5 to 30 keV electrons must have been accelerated at low altitude. The source region, as deduced from the abrupt ending of the correlation at about 460 seconds (flight time), is located at less than 1000 km fro-.- the rocket. The main objection to the i -tence of parallel electric field is the rather paradoxical persistence of the fields in a situation where the conductivity along the magnetic field is generally considered 206 nearly infinite. During the event under study, the precipitation rate of the electrons is much greater than that of protons (Figures 3 and 6), thus leading a net deposit of negative charges in the ionosphere. In order to maintain the ionosphere neutrality, thermal electrons must escape. These electrons form a current which, under certain conditions, triggers plasma instabiUties and creates abnormal conductivi ties [Swift; Coroniti; Fàlthammar, b; Ossakov; Kindel and Kennel]. These conductivities are of the form [Sagdeev and Galeev, 6] : — e is the electron charge; mc its mass, — v is the effective collision frequency between the particles and the waves. In normal conditions, v is extremely small in the upper ionosphere. Recently [Kindel and Kennel] have shown that ion cyclotron waves are unstable when affected by parallel electron currents exceeding a critical value. Such currents can, then, reduce conductivity and supply a turbulent resist ance. The critical currents calculated by Kindel and Kennel are ten times smaller than those needed for producing the instability of ion acoustic waves formerly discussed by Swift. These critical fluxes are of the order of 1011 electrons cm"2 s"1 at an altitude of 300 km and 10s electrons cm"2 s"1 at an altitude of 1000 km. In our flight, the order of magnitude of electron fluxes at the time of correlation with low energy protons is 10' cm"2 s"1. Therefore, these fluxesar e capable of generating the proposed instability above 1000 km altitude. This instability can increase the parallel resistivity and enable a potential difference of the order of 1 kV to be established along the lines of force of the geomagnetic field. Another possibility supporting the presence of an electric field along the lines of force is that the temperature gradient between the plasma sheet (107 to 10B °K) and the ionosphere (1200°K at the time of the flight [Donat et al.]), when considered together with an electron density model, leads to potential differences of a few kV [Hultqvist]. In order to estimate this effect, it is therefore necessary to know the temperature and density distributions along an auroral field line. 6. CONCLUSION A correlated precipitation of 5-30 keV electron fluxes and of 0.5-5 keV proton fluxes aligned with the magnetic field lines of force, was found during a rocket flight. This result, when associated with measurements of very low energy electrons, constitutes evidence for the existence of a 1-2 kV potential difference along the geomagnetic field lines. The source is located below 2000 km altitude, exerts an acceleration on positively charged precipitated particles and exists for at least 115 seconds. The origin of this electric field can be related to instabiUties due to the enhanced precipitation of 5-30 keV electrons. DISCUSSION A. Bahnsen. You say the time variations in the spectrum shapes and the counting rates indicate a close position of the source — less than 2000 km. Could not such variations be explained by a fixed pattern of precipitation moving at high speeds across the rocket trajectory? H. Rème. No. If it is a space variation, the charge exchange phenomena exceed by far the extent of the precipitation of protons if their distribution is not strongly aligned; it is very difficult to speak of 207 a strongly aligned distribution here because I have no measurements at zero degree pitch-angle; but if there is a strongly aligned distribution, it must be close to the ionosphere. I cannot tell how many kilometres but not very far from the ionosphere. A. Bahnsen. / was thinking of some observations by L.M. Chase, who also observes lime-varying flux. He claims that auroral features moving across can have speeds of 100 km/s. Thii would give the picture you see even with a rather wide spread of the precipitated protons. H. Rème. Low-energy proton precipitation is linked to the 20 keV electron fluxes. If the disturbance shifts quickly but is far off, the protons coming from the distant source and moving not as fast as the electrons would keep on arriving after the end of the electron burst. As the proton and electron fluxes diminish at the same time, even for a fast-shifting precipitation, the source must be near the rocket. L.P. Block. / wonder what is your pitch-angle resolution. H. Rème. For electrons, it is a very good resolution but for protons it is not so good because proton counting rates are very low. L.P. Block. What do you mean by " it is very good for the electrons "? One degree? H. Rime. The aperture of the electron detector is 1.5 degree half-angle and the precision in the pitch- angle resolution is some degrees. L.P. Block. Did you see any detailed structure in the pitch-angle distribution ? Are there any variations ? H. Rime. They change at the beginning and at the end the correlation event. It is quite clear that the low-energy electrons are more aligned outside the event than in the event, because of the repulsion effect of the field for electrons during the correlation. L J*. Block. Some experiments reported by Albert and Lindstrom had a very good pitch-angle resolution — about 0.5 degree. They observed step-like distributions which can be interpreted in terms of double layers at three different altitudes. By analyzing these structures they found that electrons were trapped between the magnetic mirror below the rocket and the sheath above. H. Rime. Above the rocket? L.P. Block. Yes. By analyzing in detail the pitch-angle distribution, they can compute the voltage across each of the sheaths and also the altitude. The potential drops were approximately 100 volts for each sheath and the altitudes about 300 km. The results are reported in " Science", 1970 , vol. 170, p. 1398. I strongly recommend such experiments for the future because they are perhaps the most direct and comparatively the easiest way to observe effects of electrostatic double layers. 208 GENERAL DISCUSSION (I) Chairman : Dr. B. Hultqvist B. Hultqvist. Firstly, I should like to emphasize that there is really a purpose in this Colloquium from ESRO's point of view. You know that it is necessary to gain support for the development of small scientific satellites, if only because the large Organisations prefer large undertakings for political and other reasons. In order to have the small satellites approved in the future ESRO programme, especially for magneto- spheric studies, we really have to submit very serious proposals to prove that they are going to provide many important results. In fact, you will help yourselves and all of us if you are now able to put forward important problems to be solved in this field during the next few years. Today, we should draw up an elaborated list of those problems, theoretical as well as experimental, which we think are the most important to be solved in magnetospheric studies during the seventies. We have already heard a number of such proposals during the lectures given at this meeting; so I think we could begin with summarizing those explicit considerations that have been mentioned before. Personally, I should like to remind you of one point which I had already mentioned in my talk, namely our complete lack of information about the distribution of plasma density and temperature along the polar-cap field lines. I am thinking of the open field lines which go to the distant magnetosphere and along which we expect strong electrostatic fields. Therefore, there is a great need to try to find out what the distribution of the plasma parameters is along the open field Unes. As far as I can see, one of the obvious ways of doing that is by means of an eccentric polar orbiting satellite. A theoretical point which presents itself when you are interested in the polar-cap phenomena is the transport coefficient for this type of plasma. Quite different types of diffusion mechanisms may be operating, but we must admit we do not know very weU how they work. Anyhow, we should really need to understand the production of the electrostatic fields along the field lines. 209 L.P. Block. I should like to call your attention to the list of proposed experiments, drawn up to sum marize the experiments I mentioned in my talk (see p. 147). I would particularly emphasize a few points; one is that one should measure up-going fluxes of particles as well as down-going fluxes, because if there are electric fields along the magnetic field lines, then they should also accelerate particles upwards. I should also like to underline the fact that different kinds of experiments should be onboard the same satellite, coordinated so as to measure different parameters such as magnetic fields, in order to locate the field-aligned currents, particle measurements of up-going and down-going fluxes, high-frequency waves, to look for those instabilities that could cause anomalous resistivity. At the same time density and temperature should be observed as far as these parameters are of importance in the creation of the sheet and of instabilities. B. Hultqvist. You emphasize the study of the sheets, the possible existence of sheaths and their pro perties in the upper ionosphere. L.P. Block. Yes, but that is only one thing. I should also like to investigate any kind of field-aligned currents and related field-aligned electric fields which would cause, for example, decoupling of the magnetospheric plasma from the ionospheric plasma. K. Schindler. If you want to draw up a list of the various kinds of phenomena that are still to be explained, you have also to ascertain that the curl of those parallel electric fields is different from zero in order to have decoupling. One must, therefore, also measure the perpendicular electric fields at various altitudes. G. Haskell. I would suggest that we have to look at the problem of the large scale dynamics of the magnetosphere, especially during substorms. In particular, we have to answer the question whether substorms are triggered by a change in the solar wind or by internal instability of the magnetosphere. I would propose that the actual real justification for studying wave-particle interactions is to deter mine to what extent they control the large scale dynamics of the magnetosphere. B. Hultqvist. We should not forget to deal with the acceleration of auroral particles which is one of the fundamental problems still unsolved. It is obvious that one way of tackling the acceleration pro blem is to have GEOS observations plus complementary measurements at the end of the field lines reaching the geostationary orbit in order to have complete extensive measurements of the particle populations at both places. K. Schindler. I should like to put forward the general proposal of the study of the plasma sheet. I already mentioned that what we most urgently need would be a detailed magnetic structure of the plasma sheet because this governs a great number of interesting phenomena. I should like to remind you that in this year's first issue of J. Geophys. Res. (76, p. 63, Energy spectra and angular distributions of particles in the plasma sheet and their comparison with rocket measure ments over the auroral zone, E.W. Hones Jr., J.R. Asbridge, S.J. Bame, Sidney Singer, Univ. of California, Los Alamos Scient. Lab.), there is a paper which shows that there is a very sharp electron beam in the plasma sheet and that the parallel flux is about more than 20 times the perpendicular flux. I think this is a very important result and we must see whether there is a similar situation for the ions. I think it would be of primary importance to observe the ions in the plasma sheet with a very high spa tial resolution as it might give a clue to the possible acceleration mechanisms in the plasma sheet. 210 L.P. Block. I should like to mention also the build-up of the substorm current system. G. Haerendel. Could you indicate roughly what kind of system you think would detect the build-up of the world-wide current system responsible for the substorm ? L.P. Block. By three-component magnetometers onboard a polar orbiting satellite or preferably onboard a few such satellites, so that you could make frequent measurements. R. Grabowski. I should like to suggest investigations of the global convection outside the plasma- pause. The important measurements would be the bulk velocity and, if possible, the electric field together with the magnetic field. L.R.O. Storey. Of course, a lot of these proposals have already been examined in ESRO's Mission Definition Group that gave rise to the projects elaborated by industrial firms in feasibility studies. Therefore, I should like to emphasize one point which is definitely summed up in the discussions for this mission definition and explain why it has been so. This is the basic problem of the understanding of plasma turbulence. Supposing we could have a field of plasma turbulence which is statistically homogeneous and we could measure all the wave and particle properties and supposing, in addition, we could measure the field properties at a given point (that is the mean static field, fluctuating fields, with all their components, altogether with the correla tion between these different components at the same point), and supposing we could also make the same measurements at spaced points as a function of spacing, it would be important to show that these measurements are entirely consistent. An adequate theory does not exist, yet data of this type could be stimulating for the development of such a theory. Concerning the electromagnetic turbulence, the spatial attenuation rate of electromagnetic waves is especially low, so that one could never hope to get an homogeneous field of turbulence in the magneto- sphere; so this possibility must be ruled out and electrostatic phenomena be considered where effect ively there is much more hope to get what you are looking for, since electrostatic waves are very strongly absorbed, except in the presence of some stabilizing mechanisms; so you have what you do not have in the case of electromagnetic waves : an almost local relationship between the particle population and the wave population. Below the threshold of instability the medium is stable but if you go beyond this threshold, you cer tainly find fully developed plasma turbulence and local properties are, I think, all you can measure and check with the theory. Where could we make those intended measurements ? When we considered this at the time of Mission Definition, the only place we could think of for doing this from a satellite was in the field lines going up from the auroral zone. But there, as you know, the horizontal structure is changing so rapidly, the horizontal scale is so small that you just whip through the structure without having time enough to make all the interesting measurements. But now the situation seems to have changed after the findings of Banks and his co-workers on the instability in the polar wind. Now we are aware that there is really a field of plasma turbulence which is sufficiently homogeneous both on a small and on a large scale for it to be possible to make the sort of measurement we need to check the theory. M. Feix. I should like to suggest that one of our most difficult tasks today is to select, among all these unsolved problems that have been registered, those that can really be solved and to what extent. One has, tor instance, mentioned the problem of transport coefficients, a problem that plasma physi cists have tried to solve for more than 10 years now without final results. They have just found that the transport coefficient lies between classical diffusion rate and the so-called Bohm diffusion, there 211 being a tremendous factor — say maybe 1000 or 10 000 — between the two solutions. Dr. Storey just mentioned the field of plasma turbulence. I think as long as theoreticians do not even know what are the questions to ask, it will be very difficult to design the right experiments. However, let me men tion one species of problems which could be solved now : all the problems concerned with the kinetic theory of quiet plasma, the theory of what happens within the Debye sphere. These problems have already been solved theoretically but they need experimental confirmation in space, since it is very difficult to produce plasmas with a very large Debye length in the laboratory. A. Eviatar. I am definitely more optimistic not only about the future in this fieldbu t also as for the present; the state of knowledge in plasma turbulence theory is bad but not really that bad ! Thinking with respect to the very general heading " Acceleration ", I should like to specify certain aspects of this problem. All the energy must ultimately come from the Sun, from the solar wind. Waves injected into the magnetosphere are subject to various states of damping and this, we know, is precisely an acceleration mechanism since, when a wave is damped, it means that the released energy is trans mitted to particles. The important thing is to have more fast time resolution magnetometry coupled with good time resolution particle experiments so that one could observe a damped wave at the same time that particles are being accelerated and this in various frequency ranges. Perhaps higher fre quencies are important. A phenomenon, for example, that we might try to look for is transit time damping, as a means of heating electrons. B. Hultqvist. Can you give me any figure for the time resolution you need, 10, 50 or 100 msec ? A. Eviatar. It depends of course on the waves. If you are looking for acceleration phenomena, I would like to suggest a time resolution below the proton gyrofrequency, but faster than you can measure with a standard fluxgate magnetometer. L.R.O. Storey. May I add something to these contributions as a compromise proposal. Dr. Feix's suggestion is simply, as I understand, to achieve experiments for the confirmation of linear homo genous warm plasma theory. A compromise may be to study electrostatic waves on a moving space craft at the moment when the plasma system is just below the threshold of instability. Under these circumstances when the medium is almost unstable, then you can do interesting plasma experiments to confirm the theory; for example, study of the fluctuating plasma microfield and its correlation pro perties; or you can also do electrostatic wave propagation experiment to observe the way the waves that are just going to be unstable will be amplified. R. Pellat. In my opinion, the main phenomena you can observe in plasma physics are easier to study in laboratories. On the other hand, as the magnetosphere is a very big machine, it is therefore very difficult to understand anything in this field only by point measurements. B. Hultqvist. In fact, we are aiming at having several satellites in orbit at the same time; but quite obviously we are short of satellites. I think magnetospheric studies require synoptic observations with many measuring points and one important matter for the future is not only to coordinate satellites between themselves but also to coordinate the satellites with rockets and ground-based observations. We have already pointed out the connection with the GEOS satellite as something which will certainly play an important part. Of course, one can have many different views on the importance and value of discussing very general problems but, as I said, this discussion was mainly meant to be a preparation for the next one which will be devoted to a much more specific subject, namely what should we plan for the ESRO small magnetospheric satellites. 212 1. Distribution of plasma parameters along open field lines 2. Transport coefficients 3. Sheaths and sheets 4. Field-aligned currents 5. Electric fields and curl of electric fields Decoupling of magnetospheric from ionospheric plasma 6. Large-scale dynamics of magnetosphere 7. Acceleration mechanisms 8. Detailed magnetic structure of plasma sheet 9. Detailed pitch-angle data for ions 10. Build-up of substorm current system 11. Convection parameters 12. Polar wind plasma turbulence 13. Plasma inside the Debye sphere 14. Experiments on almost unstable parameters 15. Synoptic measurements 213 ONBOARD COMPUTERS FOR SATELLITES Dr Durney and Mr Fokine, European Space Research and Technology Center, Noordwijk, Holland ABSTRACT The problems of onboard computers are analysed with particular regard to data suppression, reliability and availability. For a simple particle experiment, a comparison in made between the coupling to a conventional telemetry system and the interface with an onboard computer. The flexibility of the loner system is shown and a flow diagram is used to illustrate how such an experiment can be controlled. A method of processing data is demonstrated for a case when the phenomenon is well known and it is desi red to monitor the overall shape with the minimum of telemetry space. The difficulties of organising a spacecraft programme which includes an onboard computer are discussed and some suggestions are made for easing design problems that the experimenter may encounter. This paper is not intended as a deep technical discussion of onboard computers, but rather as an illustration of how experimenters can use them for space experiments. The limitations of computers will be outlined, the general approach to connecting an experiment and a computer will be demon strated, and a few of the technical details mentioned. It seems that a great number of space physicists who have not yet used onboard computers are suspicious of them. If any readers find themselves in this position, we hope to be able to remove some of their prejudices. Onboard computers are machines for compressing data. Given a limited amount of telemetry, the idea is to use it efficiently and squeeze as much information into it as possible. The usual rejoinder of the sceptical scientist is that this is a process which loses information and that the telemetry should more conveniently be expanded, by using a large dish or an increased bandwidth, rather than compressed. At this point it is necessary to be clear about the limitations of onboard computers. Computers are not intended for use with experiments on exploratory missions to new regions of space where unpredictable results may be expected. More exactly they are used on such missions, but more for navigation and spacecraft system control. The main usefulness of computers when applied 215 to experiments is when the preliminary exploration has already been done and the more routine work of verifying, refining and cataloguing the data becomes necessary. Computers have to be programmed and to program them it is necessary to know roughly what one is looking for. The best solution would then be to combine an onboard computer with a large dish. The main difficulty is that an onboard computer reduces the possibility of finding new, unexpected events, and it is very hard for an experimenter to accept this restriction. A further mistrust arises from a misconception. Computers are not put onboard spacecraft primarily to perform calculations. Of course, they can do calculations, but having a limited memory capacity, they have to carry out their tasks in serial which places an upper limit on the amount and complexity of the mathematics they can do. Thus the experimenter will not receive his data in a ' digested form ' unless he specifically wants this. The real efficiency of an onboard computer lies not in the calculations it can do but in its ability to control an instrument so that this equipment examines only those effects that are of interest, detecting and rejecting all irrelevant data. The telemetry space is reserved for meaningful measurements, and this is where the data compression lies. Also, if it is found that the observation limits are too wide or too narrow, if the gain is wrong or if the sampling rate is too low, then the computer can bs reprogrammed from the ground to correct this. If a whole range of effects is being observed, a list of priorities can be drawn up, so that the rarest ones are given preference for investigation; if sufficient statistics on one particular type of event are accumulated measurements of this type can then be suppressed by reprogramming, allowing more time for exa mining other effects. The system has great flexibility, and these are just a few of the many possibi lities. There are several fringe benefits involved as well, for instance the telemetry data format can be varied, such that if an event occurs which is particularly interesting for one experinent, the computer could enlarge the section of the data format previously devoted to that experiment. Binary numbers can easily be transformed to a floating point system, thus achieving a limited amount of extra data compression. If time sharing is necessary this CÎ n also be done easily. One could also consider controlling the power supply system if the computer was thought to be reliable enough. This brings us to the question of reliability. At first sight, this seems to be a problem area because of the complexity of the system. A back-up arrangement would be used as a matter of course so that not all the data would be lost if there were a catastrophic failure of the computer; however, the reliability figures for a computer of this type are surprisingly high. The mean time between failures (MTBF) of a typical computer is about 800 days, which is comparable with the usual corresponding figure for the battery system. The mean time between catastrophic failures is very much higher than this and the probability of such a failure occurring in one year is approximately zero. The reason for this is that these computers are not an innovation, they have been used over a number of years for military and navigation purposes, and so have reached a high state of development. Moreover, they can add to the reliability of experiments. If a vital detector in a multi-detector experiment fails, this need not have catastrophic results. The computer can be reprogrammed to reorganise the measure ments so that the maximum amount of scientific results can be obtained with the remaining detectors. As the sensors are usually the ' Achilles heel ' of an experiment, this is an important point. At least one space-qualified computer completely suitable for a magnetospheric satellite is available off - the - shelf in America today. For a hypothetical spacecraft programme starting imme diately however, a more advanced operational computer would probably be chosen and space-quali fied during the programme. Availability is not a problem if one is prepared to buy American equip ment. The European situation is more uncertain; designs exist on paper only. European firms may in the near future manufacture American designed computers under licence. A survey of available computers has been made and the following figureswil l give some feeling for the quantities involved in the central processing unit, which is the heart of the computer : Mass 140-700 g; Power cons. 2-10 W; Volume 130-3,300 cm3. 216 The price of these units varies over a wide range, but is unlikely to be more than 2 % of the price of a cheap spacecraft excluding the launcher and experiment costs. It is interesting to note that more miniaturised computers tend to cost less because of different manufacturing techniques. We now come to the actual problem of connecting an experiment to a computer, which is done through an interface box, sometimes called the I.O unit. The design of this box, crucial to ensure the flexibility and success of the experiment, presents special problems. It needs detailed knowledge of how both the computer and the experiment operate. As neither the computer engineer nor the experimenter are likely to possess this knowledge for both systems, extremely close cooperation between the specialists is necessary. Moreover, as each experiment has its proper interface box and the control sequences are interwoven, all the boxes must be designed in conjunction. First of all, the scien tists must be very clear about what they want to do with their experiments and they should preferably provide detailed block diagrams; then, they must all be prepared to work in close cooperation with each other and with the computer engineers until the design of the interface boxes is finalised. The most important point to realise here is that any communication difficulty between the experimenters and the computer experts at this stage will at best result in a waste of time and at worst could ruin the mission. At this stage let us consider the interface box for a simple particle experiment (Figure 1). Two things are worth noticing in this demonstration. First, an interface box for any particle experiment would use similar circuits. Second, there are hidden advantages in these boxes because they contain a number of circuits that would normally be built and supplied by the experimenter. As they are now built and supplied by someone else, the experimenter has more time to concentrate on his detectors. Figure 1. — Particle experiment. -TELEMETRY- -jshaptrj • I And I p^Rggis'.gr 1 IF -JçK,f^l '—I Ann I T^3negiatcr 2 -|shaper[ —JAnd [— ^Regisl -jShaperf- 217 This first Figure shows a block diagram of a channeltron experiment connected to a conven tional telemetry system. To the left is a bank of ten channeltron detectors. Each particle which erters a channeltron produces at the output a pulse which passes through a shaper and a gate into a register. At fixed intervals the telemetry closes the gates and samples J,i contents of the registers. In this form there are two important restrictions to the experiment. First, the telemetry samples the registers at fixed intervals which are determined before the spacecraft is put into orbit. For some particle events, this interval is likely to be too long, with a resulting loss of information; at other times the interval will be short compared with the particle fluctuations, thus making inefficient use of the telemetry. The second restriction applies to the mode of operation of the experiment. The experi ment can count either protons or electrons by the application of a negative or a positive voltage to the deflection plates of the channeltrons. For simplicity and reliability an alternating system switched by the telemetry gating pulse has been chosen here. This choice is also influenced by the fact that although it is possible to think of more sophisticated systems, it would be very difficult to decide at which counting rate levels these systems should be pre-set. The alternating system used here has the dis advantage of resulting in a 50 % loss of any event where only protons or electrons are concerned. Mr. Fokine will now present a block diagram of the same experiment when connected to an onboard computer. PARTICLE EXPERIMENT APPLIED TO A COMPUTER When using a computer, the basic scientific objectives of the particle experiments will remain unchanged; electron and proton particles will be detected, accumulated in binary counters and the results transmitted to the ground after any data reduction and compression. Identical (or improved) sensors can be used with some modifications to the associated electronics to provide interfacing with the computer. Since particle experiments are basically a process of detecting and accumulating pulses over a fixed time interval, most interfaces can be identical, leading to a normalization of the interface electronics. This is a great advantage to the particle experimenters, because this counting and control function can be assumed in the interface unit, thus relieving the experimenters of the major part of the electronic design tasks which can easily be done by the computer system designer. The main differences between particle experiments from the computer system designer's point of view are : the sample rates, the detection threshold levels, the calibration periods and associated control functions. Emphasis is directed to the following points : — One does not have to have a fixed mode pattern when using a computer; e.g. Figure 1 shows the experiment, normally in the electron made, being altered to the proton mode when detector 10 detects more than a predetermined rate. This rate can be changed by repro- gramming the computer memory by telecommand. — Sampling rates are no longer telemetered but instructions are stored in program modules in the computer memory. These rates can be variable. The use of a computer rather than an encoder-decoder cannot lead to a degradation of the particle experiment. On the contrary, it will enhance its value and make it more effective and flexible by having the parametric variables stored in a non-permanent, reprogrammable computer memory (i.e. it will not be " hardwired " as in the classical encoder-decoder design). 218 COMPUTER REQUIREMENTS FOR LOW-ENERGY PARTICLE EXPERIMENT This model experiment will include twelve detectors, each capable of a maximum pulse rate of 106 per second. Each pulse, after being conditioned, will be a square wave and will represent a detected particle (Figure 2). Two of the detectors will have variable energies applied to a pair of deflection plates and will be driven by a staircase voltage generator under control of the computer. The staircase will be divided into 64 steps with two different sampling intervals representing Fast Mode (10 msec sampling interval) and Slow Mode (100 msec sampling interval). During the sampling intervals, pulses from the two detectors will be accumulated. The energy level at the time of sampling must be known for processing the data. The sweeps applied to these two detectors will be synchronized. The outputs from the other 10 detectors will be accumulated during the same sampling periods and will be identified as either electrons or protons. The accumulated data must be stored and transmitted to the ground station (when in view) with an accuracy of 5 %. Since the data acquisition will occur about once per orbit, the data storage must be capable of storing at least one orbit's worth of data. No measurements are expected at latitudes less than 60°. One of the data reduction tasks will be to reject all data if the accumulated count per sampling interval of the lowest energy channel is less than a predetermined initial value X. This value will be calculated after launch, modified to X' and programmed into the computer via the telemetry link from the ground station. This modification of X will be repeated as often as required. Figure 2. — Particle experiment with an onboard computer. -EXPERIMENT •INPUT -0UTPUT- 219 As an exercise for the magnetospheric satellite study, two conditions were imposed, as described in Figure 3 : Figure 3. — Particle detector outputs (conditions 1 and 2). N = counting rate from the counter measuring E MeV EQ = slope of energy spectrum N„ = constant CONDITION 1 N h 220 — the output of the detectors would assume a characteristic curve of a decreasing exponential (condition 1); — this exponential curve will have perturbations consisting of randomly placed peaks (condi tion 2). For certain periods, the accumulated data will be reduced to two parameters for condition 1 (No and Eo) prior to transmission to the ground. For condition 2, the parameters N0, E„, P„ E,, W„ P2, E2, W2 will be transmitted to the ground for decoding and reconstitution into the original information. A secondary task will be to calibrate the detectors once per week. This calibration mode will last for about 5 minutes and will accumulate about 300 kbits of calibration data in the bulk 1 Mbit memory storage. The calibration mode will be inhibited at latitudes above 60°. These calibration data will be available to the experimenter when transmitted on command to the ground station. Prior to final integration of the spacecraft, the experiment can be easily modified by adding or substracting developed standard counting and control function modules. The allocation of control functions is done by designating discrete bit positions in input words (for status) or output words (for control functions) assigned to the particle experiment. These I/O words are stored in the computer memory as corresponding coded words in the particle experiment programme module. The simpli fied flowdiagra m (Figure 4) of the model low-energy particle experiment is an example of how the computer control functions are performed in real time. Basically four loops are included, as follows : — activity detection loop, — slow mode loop, — fast mode loop, — calibration mode lcop. The activity detection loop is used to automatically reject data below a fixed(bu t reprogramma ble) lower threshold level. This level will be adjusted according to the result of the analysis of data received on the ground. Background noise, spurious signals, etc. are rejected until a consistent acti vity builds up to X counts/100 msec, at which time all detector outputs are recorded. In the slow mode loop, all counter outputs are recorded until activity subsides to below X counts/ 100 msec or exceeds Y counts/100 msec, at which time the computer will automatically enter the fast mode. In the fast mode loop, increased resolution of the activity is achieved by sampling each counter every IS msec instead of 100 msec. The fast mode will be sustained as long as the counters record more than Y particles per 15 msec. In the calibration mode loop, all built-in calibration sources are used and the detectors are cali brated according to the experimenter's requirements, as often or as infrequently as he wishes, once a year if so desired, there being no limit on timing. CURVE FITTING TECHNIQUES This is an example of what can be done by calculation by the onboard computer. This sort of data reduction technique can be applied if there is not too much interest in fine structure and if the basic shape of events has already been determined either from previous satellite programmes or from initial data from the MagSat project. This program module could be programmed prior to launch or n months after it if the experimenter had sufficient confidence in the initial raw data received. 221 1 ' ' I ill! I< Il i iii l.Litt,!il i,!,!,!,!,!,!;!,!!,!!!,! ,,;;;,; From previous ( ENTRY J measurements Reset experiment to zero state INITIAL IZATION Bring up power supplies, etc. Start 100 ms clock Set up electron/proton mode Detect lower threshold iavel X . lower level Data to be processed by another module NO ,COUHT> y Y I upper level YES CALIBRATE Start 15 ms clock ALL FAST MODE Count for 1 min DETECTORS Test for activity NO / TIME TO EXIT { EXIT J To next experiment Figure 4. — Simplified flow diagram. 222 Reference is made to Figure 2 for the following discussion. A program which fits a curve of the type N = N„"£/Eo had been written and tested (conditions 1 and 2 of the particle experiment. See Appendix 1). It must be stressed that the characteristic curve investigated was only a hypothesis made up for these studies. A much more complex and time-consuming method may be required for the actual selected experiments. The curve-fit program has been tried in FORTRAN on a SDS 930 computer with a 24-bit word and floatingpoin t routines; the sizes of each program part is as follows : Main program 113 words Logarithm 139 words Exponent 151 words Total 403 words 02 KR The equation v = 40 e'°- "* was used for the trials (K is a constant and R is a random variable, flat in distribution in the range of 0.05). The curve-fit programme obviously worked better with more sampling points, when X was increased from 10 to 50 sampling points. An extension of the basic program was tried. This extension was to look for exceptions to the exponential law and to report on these separately (Condition 2). The basic program can be easily adapted to look for upward discrepancies, downward discrepancies or both. The threshold can be set by telecommand for added flexibility. The extra storage requirement for this exception-finding process was (70) — 24 bit words on the SDS 930. This example proved to be quite encouraging for the idealized case but may not be applicable to expected outputs of the particle detectors since the plot of particles versus energy level can be expected to be more complex. This particular example of a curve-fitting programme requires approximately 500 words. The advantage is that only two parameters would be transmitted instead of 64 in the model experiment thus leading to a 32 : 1 reduction per detector. DATA COMPRESSION TECHNIQUES Some acceptable methods of data compression and reduction have been investigated for possi ble inclusion in the tasks to be performed by the onboard computer. Unfortunately not all of the methods can be used because of the limited memory available in small spacecraft-computers as presently envisioned (8 k 16 bit words). A compression ratio of S : 1 (1 % tolerance) is likely when using polynomial predictors and interpolators with the corresponding penalty of increased software complexity. Regrettably this type of technique canne* be applied to some of the expected detector outputs and other methods should be investigated, e.g. : — adaptive tolerance techniques, — selective monitoring, — parameter extraction, — logarithmic counters, — floatingpoui t conversion, — difference transmission (Delta). 223 The usefulness of cross-correlation and/or Fourier transform routines have not been fully investigated for the wave experiments. A timing and memory storage estimate has been made for a FFT of 64 points, with the following results : — 2 k of memory for a program of temporary storage, — 2 sec processing time. Obviously such a method is prohibitive because of the large memory storage requirements and long processing time. If it is imperative to implement FFT's for a particular wave experiment, it is recommended that a dedicated parallel FFP (Fast Fourier Processor) be included in the system as a pre-processor and packaged as part of the experiment. CPU SUMMARY Since most of the candidate computers were originally designed and packaged primarily for military navigation applications in advanced air-breathing aircraft, one has to exclude this non-essen tial navigation function from the individual packaging schemes and to consider only the true charac teristics of the CPU's. An attempt r"»s thus been made to " surgically remove " the CPU as a stand alone item. In the ESRO MagSat tuucept, the proposed system will be designed around a basic off- the-shelf CPU (with memory) with the I/O functions specifically dedicated to particle and wave sensors rather than navigation sensors. A quick review of the representative computer systems reveals that the basic CPU will be minuscule compared to last-decade military CPU's or today's commercial rjini- computer CPU's. The CPU characteristics tentatively established by Dr. Durney are repeated here for convenience : — mass 140-700 g — power 2-10 watts — volume 130-3300 cm3 — MTBF > 20 000 h (calculated). The wide range of the parameters is attributed to the different technologies used in the cons truction of the different equipments. In fact, the technology can vary from the low power T2L or Cosmos logic to the numerous acceptable design/ fabrication techniques presendy used in producing high-yield LSI arrays (e.g. Texas Instrument's Large Scale Integration, " k " slice or discretionary wiring techniques). The main point to notice is the availability of powerful microminiaturized CPU's meeting the MagSat requirements of off-the-shelf availability. The feasibility of such devices is now past history with the successful introduction and imple mentation of LSI/MSI technology in military and aerospace CPU's. An example of such a computer is the OBP (On Board Processor) built by Westinghouse Electric Co.-p. under contract from NASA Goddard Space Flight Center for the OAO (Orbiting Astronomical Observatory) programme. A follow-up computer is expected to be available in 1971 which will surpass present ESRO requirements. A summary of the characteristics of a typical MagSat computer system is described in Table 1. Representative commercial and present operational military avionic computer systems are included for a quick comparison. The following partial list represents candidate computers that meet most or all of the prime ESRO requirements (e.g. weight, power, availability, etc.). 224 Designation Status 1. Westinghouse* AOP hardware stage 2. CDC* 469 hardware stage 3. SAAB* D6-27 design stage (proposed for the Swe dish satellite programme) 4. GFW* TR-16 study phase 5. Litton** LI-1416 S hardware stage 6. Ferranti** FM-I200 hardware stage 7. ESRO/Selenia* study phase * space designed or qualified oamputer » ** repackaging and/or partial redesign required to meet all ESRO requirements [e.g. space qualification!- COMPUTER SIZING For brevity, a computer (CPU) was properly selected from the available candidate computers as described in the responses to the RPQ. A trade-off analysif was performed to " best St " a compu ter to the given specifications. As related to the data handling system design, the computer sizing task is a small but important part of the overall problem of system configuration and the selection process is not elaborated here. The important point is that the selected CPU will be a fully developed off-the-shelf item with a comple tely debugged software support package. This implies there will be no non-recurring CPU develop ment costs. The present computational throughput requirements for the selected mission do not warrant the development of a " tailor made " computer. In fact, most applicable computers were developed for sequentially organized problems such as navigation and therefore can be considered too powerful for our application in terms of instruction repertoire. EXPERIMENTERS DESIGN RESTRICTIONS/FREEDOM Each experimenter will have complete design freedom up to the interface circuitry (within certain system limitations). The choice of the technology to be used will be left to each individual experimenter as long as system voltage compatibility exists (e.g. RTL, DTL, T2L, P-MOS, COS-MOS, etc. [L.S. Garrett]). Strict adherence to the Interface Specification will be a mandatory requirement for a smooth and timely development and integration phase. Hopefully, small and large design incompatibility problems wiB be detected early in the definition phase and corrective actions taken prior to tne design phase. Since a large number of bugs can be expected in the first spacecraft, due to the early stage of the learning curve, there mast be a strong team effort to reduce the tendency to wait for the integration phase for detecting all possible errors due to incompatibilities and interferences. The only presently foreseen restrictions to be imposed upon the experimenters will be in consi deration of :' — memory core allocation, • - — sampling interval limitations — weight, power, volume. 225 AIDS TO EXPERIMENTERS It is the responsibility of ESRO to issue proper Systems Specifications and correspondingly it is up to the experimenter and subsystem supplier to issue equivalent specifications. To ease the tran sition from present classical satellite design concepts to the integrated computerized design concept, it is proposed that the following ideas be implemented prior to the experiment selection and Project Definition Phase : — Preparation of a User's Guide similar to NASA's „ Tips To Experimenters ". This document will describe in sufficient technical detail the following : • electrical interface characteristics (voltage levels, rise time, fall time, noise immunity, capacitive loading, maximum length of wire, fan-out capabilities, etc.); • flow charting techniques; • generation of standard timing charts; • definition of standard terms, symbols, terminology, abbreviations, graphical descriptions of all logic gates (NAND, NOR, etc); • test point allocation; • self-test or calibration capabilities; • generation of logic equations. — Distribution of the User's Guide to all potential users for extensive utilization in preparing experi ment proposals. — Initial establishment of a centralized source of technical information exchange and dissemination concerning : • availability of technology and, at a later date, availability of an installation for program module debug and verification on a computer simulator or on a non-qualified computer system; • hardware-software trade-off analysis; • data reduction techniques; • testing concepts; • techniques of fault isolation. CONCLUSIONS The conclusions of the Feasibility Study on whether and to what extend to use an onboard computer in an integrated data handling system can be briefly summarized as follows : — onboard computers present many applications and advantages for use on future ESRO scientific satellites; — they are ideally suited for complex wave-particle interaction types of mission (e.g. real-time control); — if sufficient scientific interest is expressed, one could have such a satellite operating by 1975. Taking into account the previously mentioned " suspicion " some experimenters have against onboard computers, we hope that these brief remarks will convince them of the usefulness and relia bility of present state-of-the-art computers. 226 It cannot be over-emphasised that, scientific investigators and experimenters being the ultimate customers of such a programme, it is up to them to express sufficient scientific interest for this appli cation. I am confident that the engineers and technicians of the European Aerospace Industry can have this advanced concept of a wave-particle interaction mission flying by 1975. There is no question as to the feasibility of such a project in the light of the available hardware and expertise in Europe. Table 1 Model Commercial/industrial Military (MIL-SPEC) Aerospace (space standards qualified) Application Data acquisition and Avionics (e.g. inertial Satellite Data acquisi- control navigation) and control Data word size 16 8-32 16-18 Memory (type) core core plated wire/ solid state • Basic size (words) 4k 4-8 k 2-4 k • Max. size 32 k 32 k 8 k (64 available) Execution speed • Add (/isec) < 2 < 5 3-5 • Multiply (jisec) (S)* < 100 < 20 20-35 (H)** < 20 (S) < 200 < 30 30-60 • Divide (ji sec) (H) < 30 Weight (kg) heavy 25-30 3 max. Volume (in3) large small < 150 Power (watts) 300 40-50 < 10 Status production production production MTBF (calculated) not available IC : 3000 hr min : 20000 hr LSI : 10000-20000 hr Simulator yes yes required Assembler yes yes yes Compiler FORTRAN IV yes FORTRAN minimum not required Power failure protection yes yes yes Input transfer rate 500 kHz to 500 kHz to 500 kHz (words) direct access 1MHz 1MHz Interface options • Digital input/ digital output yes yes yes • A/D, D/A, multiplex yes yes yes Priority interrupts yes yes yes •Software •"Hardware 227 ANNEX 1 CËXPONENTIÀL CURVE-FIT CTHIS PROGRAM FITS A CURVE OF THE FORM CY=A*EXPt-3*x;i TO A SET OF SAMPLE PAIRS Y[M],X[H] , CTHÉRE BEING N SUCH PAIRS. CIF A PARTICULAR PAIR FAILS TO LIE WITHIN A PRESET CTHRESHOLD OF THE FITTED CURVE IT IS REJECTED AND CTHE CURVE-FIT IS REPEATED WITHOUT IT. CTHE TEST PROGRAM BELOW CHECKS THE ROUTINE ON CSETS OF 10 POINTS IN WHICH POINT 5 IS SCALED BY CA FACTOR ENTERED FROM THE KEYBOARD. CALL THE POINTS ARE SCATTERED BY A RANDOM AMOUNT CTO SIMULATE EXPERIMENTAL UNCERTAINTY. CTHE RESULTS ARE PLOTTED USING A SEPARATE ROUTINE CCALLED «PLOT* WHICH IS NOT PART OF THIS PACKAGE. C C C DIMENSION Xfio] ,Y [10] ,YDUMP [10J CINITIALISE RANDOM SEQUENCE Z=RAND[-0.62j CINPUT PEAK SCATTER RATIO is3 CALL INR [8,11, SCAT] SCAT1 =2 .0» ALOG [SCAT] CINPUT EXCEPTION SCALING RATIO CALL INR [8, 11,EXCEPT] CGENERATE POINT-PAIRS N=10 D81 J=1,N X[JJ=J*10 Y [JJ=40.0*EXP[-0,02*X[JJ+SCAT1* [RANDtO.O]-0,53^ 1 YDUMPGD=Y[JJ Y[5]=Y £]*EXCEPT YDUMPf5]=Yf5j CINPUT THRESHOLD CALL INR[8,11 .THRESH] C C PRINT100.SCAT,EXCEPT,THRESH 100 FORMAT [^EXPONENTIAL CURVE FTT.PEAK SCATTER RATIO =i 1F9.4,$ SAMPLE 5 SCALED BYi, F9.^, à THRESHeLD=i,F9.4] THR£SH=ALOS [THRESH] C C CCALL THRESHOLD PROGRAM [FIG.5.5.5=20] FLAG=0 CCALL CURVE-FIT [FIG .5 .5 .5.19] 22 SUMX=0.0 SUMXSQ=0.0 SUMLOG=0.0 * M=0 RECIPN=1.0/FLOAT [N] k M=M+1 IF[H-N]2,2,3 , 2 SUMX=SUMX+X[M] SUMXSQ=SUMXSQ+X [M J «X [Mj G0T04 228 3 XMEAK=SUMX»HECIPN H=0 9 M=M+1 IFrH-Hj5,5,6 5 IF[FLAG] 7,8,7 8 Y [M] =ALOG fY fM]J 7 STIMLeG=SDHLOQ+Y IM] SUMTOP=StfMTep+Y [M] * [X [M] =XMEAN] G0T09 6 B=SUMTOP/tSUMX»XKEAN-SUMXSQ] A1=B*XMEAN+SUML&G*RECIPN A=EXP[A1] FLAG=1 .0 CEXIT CURVE-FIT C C CPLOT CURVE PRINT101,A,B 101 FeHMATt^ PREDICTED C6EFFICIENTS= ^,2F9."*] CALL PLOT[120,50,RESIZE] CALL PL0T[0,0,4HBRIGj DQ10 J=1,N 10 CALL PLÔT[IFIX[X[J]+O.5J,IFIX£ÏDUMP[JJ+0.5],1HX3 D011 J=1,120 11 CALL PL0T[J,IFIXCA*EXPC-3*FL6ATCJ]J+0.5],1H*3 CALL PLOT[0,0,^HPLeT] C C CC6NTINUE WITH THRESHOLD PROGRAM AMAX=0.0 H=0 12 M=M+1 IF[M-N]13,13,1'* 13 ERRL0G=A1-B*X[HJ -Y[M] IF[ERKL6G]15,15,16 15 ERRLOG=EHRLOG 16 IF [ERRLOG-AMAX]12,12,18 18 AMAX=ERRL6G LOC-M G0T012 11* IF [AMAX-THRESH]19,19,20 19 PRIST102 102 FORMAT[$CURVE-FIT COMPLETE*] GeT623 20 PRINT103,LeC,N,L0C 103 ' FORMAT ftSÏÏBSEÇDENTLY DELETE S AMPLE*, 16/ 14SAMPLE$,16,£ NOW CALLED SAMPLER,[6] PRINTIO'f 10»» FeRMATftl£J Y LCC «YM YDDMP Ileal =YDUMPfN] X[L0C]=X[NJ N=N-1 G0T022 END THE PHYSICS OF THE CHANNEL ELECTRON MULTIPLIER C. Barat Centre d'Étude Spatiale des Rayonnements, Toulouse, France ABSTRACT Since 1966, the Centre for Study of Radiations in Space has been using the \/indowless tubular electron multiplier for the detection of low-energy charged particles in rocket and satellite experiments. The principal characteristics and the working conditions of the detector are given in the first part of the lecture. In the second part, the author discusses the stability of these characteristics under the conditions of the space environment, and presents the latest results obtained from a study of the aging of the tube, the object of which is to minimise the sensitivity of the emissive layer to storage conditions. The detection of low energy particles is generally difficult because of the presence of an envelope which surrounds the sensitive volume of detectors. This envelope absorbs part of (or even all) the incident particle energy. The channel electron multiplier is a windowless detector, having thus a very low energy threshold since it detects 50 eV electrons and 300 eV protons. Besides its easy use, its reduced dimensions and its low power consumption, it is a particularly suitable space detector. On the contrary, the principle of secondary emission detectioa does not permit particle spectro metry. The selection of charged particles according to their nature and energy is performed by an electrostatic or magnetic analyser placed in front of the channel multiplier input. In this case, the channel multiplier acts as a particle count meter. But the main physical problems caused by the utilisation of these detectors, particularly on satellites, arise from the direct contact of their emissive layer with the ambient environment. 1. DETECTOR CHARACTERISTICS Before studying these problems, we intend to define the principal characteristics of the detector, namely its gain, its efficiency and its resolution. 1.1 Gain The electron multiplier presents itself as a hollow glass tube which is generally bent. When an incident particle strikes the emissive layer, at its input, it may release an electronic multiplication process along the tube. By definition, the multiplier gain is the quotient of the output charge Q by the elementary charge : G = Qlq. Above all, it is a function of the supply voltage. Below a value of about V, = 2 500 volts, called saturation voltage, the multiplier gain is given by : G = 6", where 6 is the secondary emission yield of the emissive layer and n the average number of collisions in the tube. 231 I I I ,, , II Ml II llu.l .1.1 .'-•' For a voltage higher than 2 500 volts, the space charge of secondary electrons limits the outptu charge and nonsequently the gain value. In this case, one can use the electron multiplier as a count meter for particles. The function G = f(V) for V > V, is different for each multiplier. The gain is a linear func tion of the channel voltage for an aged 310 AX. Mullard multiplier but it is an exponential function of the voltage for the aged 4010 Bendix multiplier (Figure 1). The electron multiplier can be used for pressures less than 10"* Torr. But the ionisation of residual atmospheric atoms by secondary electrons causes an ionic feedback which can induce a para sitic cascade. This phenomenon, observed between 10"* and 10"3 Torr, causes a low gain increase. It is attenuated by bending the tube in the charge-space region so as to let positive ions be rapidly absorbed in the tubewall, their energy being no longer sufficient for emission of secondary electronss Below 10"5 Torr, the gain is practically independent of pressure. However, this result wa- obtained over a relatively short period. In fact the latest results show that residual pressure plays ail important part on the surface state of the emissive layer and consequently determines the detector characteristics. The average gain of the multiplier is indépendant of the counting rate for a «alue of less than 103 cp.s., which corresponds to a flux of 106 particles cmJ/s for an efficiency of 10 % and an input surface of 1 mm2. The figure 2 shows that the gain decreases when the counting rate increases. The dimi nution is caused by the dead time of the multiplier, the resistance of which is about 10' ohms. 1.2 Efficiency The absolute multiplier efficiency is defined as the quotient of the output pulse number by the input particle number. It is the product of collection efficiency in the tube — the value of which is about 90 % — by the detection efficiency. The detection efficiency varies according to the nature and energy of the incident particle, but it also depends or the layer composition and on the angle that the particle direction makes with the detector input axis. Figure I. — Electronic gain as a function of channel *Utage. 2.5 3 3.5 4 CHANNEL VOLTAGE i kV i 232 Detection efficiency for electrons has an energy function in agreement with the universal law of secondary emissions for solids. The absolute efficiency is 90 % for 400 eV and about 10 % for the electrons of energy greater than 1 keV. The energy threshold is about 50 eV (Figure 3). Protons of energy greater than 300 eV are detected by the electron multiplier. The detection efficiency exceeds 80 % for over 2 keV. Different types of positive and negative ions are detected with a similar efficiency (Figure 4). The electron multiplier is net sensitive to visible light. On the contrary, detection efficiency is important for photons whose wavelength is less than 1 600 A; it rises to 20 % at 700 A. The effi ciency value is appreciable for X rays then decreases progressively when the photon energy increases (Figure 5). Detection efficiency is a function of the y> angle of the particle direction with the perpendicular axis of the input plane. For multipliers bent to 270°, the efficiency, proportional to b, is given by : à (cos fl)"2 = est COUNT RATE Figure 3. — Multiplier absolute detection efficiency for electrons. —I T T- T T r -\ r i p BENOIXC.E.M. «010 100 I 10 ui a —a : EVANS(tS0ty CALCULATED FROM W -•« :ntMIK(neS)EXPERUIENTAL DATA .-* : BOSO.UED0967J CALCULATED FROM GLASS o _Q :BOSQUED(l»7) EXPERIMENTAL DATA (A 233 Figure 4. — Multiplier absolute detection efficiency for protons and He* ions. 100 5z ui D E BENDIX C.E.M. A01D Z o 10 •0 : FRANK U9BS) Ll+ IONS sI- aUJ -* : SHARBER (19SB) -• : BURROUS (196B) PROTONS (RELATIVE EFFICIENCY) 3 -G : TATRY 0969) PROTONS - HE* 8 m 1 10 INCIDENT ION ENERGY CkeV) Figure S. — Absolute V. V. V. detection efficiency of nine Bendix multipliers [M.C. Johnson]. 400 600 800 a 1000 1200 1400 1600 WAVELENGTH (Â) where 6, a function of y>, represents the angle of the particle direction with the perpendicular at the point of impact on the layer. The efficiency value is maximum when 6 is close to 0°. On the contrary, the straight part of the 310 A.L. Milliard tube causes an efficiency diminution for y = 0° (Figure 6). 1:3 Resolution The-space charge of secondary electrons limits the value of the output charge for a channe voltage greater than the saturation voltage. In this case, the pulse height distribution shows a peak. The saturation is defined as the quotient of the F.W.H.M. distribution by the maximum abscissal 234 Its value is about 20-50 % for a counting rate of less than 103 ç.p.s., then increasing for greater counting rates. The pulse height distribution is exponential without a saturation phenomenon. In this case, it is no longer possible to count the output pulses accurately and to define a multiplier resolution (Figure 7). Figure 6. — Relative detection efficiency as a function of incidence angle. 6-1 1 1 " |c.S.F. | _ 1 - i i i 1 1 1 1 i —i • i i i 'v\ 1 BENDIX - z o - - a 2 u - t- Ul - Q i i i 1 1 1 UJ 30 20 10 0 10 20 30 > 6 1 1 1 V- 2« IMULLARD _ UJ :@^ a. A < ~-±. 1 / ' i i i t 1 % ANGLE OF INCIDENCE (degrees) ~i i i i r -—\"T—i—i—i—i—i—i—!—r 3KV END1X C E. H. 4010 \ J l 1 >i»f I 2CaJ^-l-.-^ ' Jt' I—l—I—I V I—I—L IS 30 46 0 120 240 J60 CHANNEL NUMBER Figure 7. — Pulse height distribution of a channel multiplier. 235 2. CHARACTERISTIC STABILITY The multiplier lifetime is determined by the number of accumulated counts. Three phases characterise the gain variation (Figure S) : — from 0 to 5.107 counts, the gain decreases by a factor of about 2 or 3. This phenomenon may be explained by the desorption of atoms or molecules of residual atmosphere. These atoms or molecules which are adsorbed in the emissive layer contribute to the secondary emission. This phase is called the « clean-up phase ». — From 5.107 to approximately 10'° counts, the gain is stable. This phase, called « plateau », corresponds to the intrinsic characteristics of the multiplier. — The region of gain fatigue begins before 10'" accumulated counts. This irreversible phase leads to the multiplier destruction. For 2.10" counts, the gain drops by about 50 %. Figure 8. — Gain variation as a function of total counts [B.D. rJettke], T" 1 r 2.8- REG.ION OF GAIN FATIGUE BENDIX C.E.M. 4010 ./ ./ 0.4 O .10 1x10' 1x10° 1x10= 1x10' 1x10" ACCUMULATED COUNTS In fact, the gain is exactly constant in the « plateau » region only for pressures of about 10"' Torr. For greater pressures, some unknown and complex exchange phenomena seem to occur on the surface of the emissive layer and the gain can be changed versus the pressure. Moreover, the resolution is constant during the « plateau » period and it progressively increases during the gain fati gue period. The Figure 9 represents the variation of pulse height distribution during the « clean-up phase ». These tests were made on CEM 4010 Bendix multipliers stored without any special precautions; they show that two desorption time constants exist. The short first time constant corresponds to an important gain drop during the first 10s counts. The second time constant ends for 5-8.107 counts, which correspond to the end of the « clean-up phase ». These two constants may correspond to two different gas desorptions. The gain drop may be also explained in two different ways : — Firstly, one can consider that the yield increase is due to absorbed gas ionisation. — On the other hand, one can suggest that the atoms included in the crystal lattice of the emissive layer play a role comparable with that of some donor levels which contribute to the secondary emission. 236 FOR 3 S 10 ACCUMULATED COUNTS 5 10 15 20 25 FOR 2 10 ACCUMULATED COUNTS 15 20 25 FOR T - 10 ACCUMULATED COUNTS 10 15 20 25 OUTPUT CHARGE HO.--11 c- ) Figure 9. — Variation of the pulse height distribution in the « clean-up » phase. When one examines the curves of Figure 9, one notes that the resolution, which is propor tional to the F.W.H.M. of the distribution, rapidly decreases during the « clean-up phase ». One sees that the distribution leads to a Gaussian curve which generally characterises the « plateau » period for 4010 and 4013 Bendix multipliers. Figure 10. — Relative efficiency as a function of temperature in the « plateau » phase. TE*PEHATUSE<*C) 237 Figure 10 shows that the efficiency is stable in function of temperature. This result may prove that the secondary emission yield does not depend on the temperature. 3. THE TEMPERATURE EFFECT The temperature effect on the gain (proportional to the output current) is important for multi pliers (Bendix and Milliard) in the « clean-up phase ». On the contrary, we see (Figure 11) that up to 50 °C, the C.EM. 4010 Bendix multiplier gain is relatively weak in the « plateau » phase but undergoes a sudden rise around 60 °C. The variation of the 310 Milliard A.L. gain is similar. These results may be explained by comparing the emissive layer to an n-type semiconductor. Moreover, we may assume that the secondary electron yield is proportional to the electron density in the conduction band. For this reason, we compare the pulse current of the aged Milliard 310 A.L. multipliers with the theoretical data of conduction current for different values of incident flux. On this curve, the — 30 °C value of f. e conduction current is normalized to the corresponding data of the output pulse current. Up to about + 20 °C, the pulse current is proportional to the donors of the emissive layer. The b) curve slope leads to the binding energy of these donor atoms. Over + 20 °C, the pulse current increases ir ore rapidly. We suggest that it derives from the following two contributions (Figure 12) : — Firstly, a current proportional to the donor current of the emissive layer. — Secondly a current proportional to the semiconductor intrinsic current characterized by the a) curve. This curve slope leads to the calculation of the width of the forbidden band. We find a value of zlE = 1.32 eV and we notice that it is close to the silicon value (the channel multiplier is above all a glass tube). Likewise the gaseous atoms act as donor levels for a multiplier in the clean-up phase. Detailed reports on characteristics of channel multipliers are available in the literature [J. Adams and B.W. Manley; K.C. Schmitt and CF. Hendee; J.-M. Bosqued and H. Rème; B. Tatty et al.; C. Barat; M.C. Johnson; B.D. Klettke et al.]. We hope to publish data on the characteristic stability and the temperature effect in the very near future. 10 20 30 40 50 60 TEMPERATURE ("C) Figure 11. — Average gain as a function of temperature in the « plateau » phase. 238 TEMPERATURE (°C ) 50 30 10 -10 i r T—r .10 10 _ \ \3 \ * MULLARD 310 A.L. \ < \ g-, 10.1 1 v, . a. ce v-.. D a \ v. * w —-\ (0 _i * 3 \ 9 a -12 \ a. 10 * 2.6 10° C.P. S. -J H 3 1.2 10 C.P. S. o \ * 4 3 1C C.P.S. 7 10' C.P. S. _ \ \ -13 10 \. 3.5 1/T CK*1x10"3) Figure 12. — Equivalence n-type semiconductor current. Experimental data for a Mullard 310 A.L. multiplier as a function of temperature. 239 FAST ANALYSIS OF PITCH ANGLE AND ENERGY DISTRIBUTION OF ENERGETIC PROTONS Mrs J. Etcheto and B. de la Porte des Vaux Groupe de Recherches Ionosphériques, Saint-Maur-des-Fossés, France ABSTRACT We describe the principle of a new method of measurement of the pitch-angle distribution of protons. We use a position-sensitive solid-state detector to determine the angle of arrival of the protons with respect to its axis. This device is able to measure the energy and angle of arrival of 10* particles per second. Two ways of using it, depending on the telemetry bandwidth available, will be presented. This device can measure the pitch-angle distribution of medium-energy protons very quickly and precisely. Some applications to the study of wave-particle interactions will be suggested. 1. INTRODUCTION It is rather difficult to measure simultaneously the pitch angle and energy distributions of particles in the magnetosphere. Two ways are usually used. Either to set up many detectors looking in different directions; this kind of device occupies much volume and is heavy. Or to use only one detector and to wait for one complete spinning period of the satellite, so as to reconstitute at least part of the whole pitch-angle distribution. Often, in view of the limited telemetry bandwidth available, experimenters are obliged to scan in energy or in pitch-angle the telemetered measurements. We have considered another method which allows us to measure simultaneously the energy and pitch-angle distribution in a wide range of pitch angles, using only one detector. This detector is a position-sensitive device of the surface barrier type. This method has been described in two pro posals to ESRO, one for a satellite experiment [Etcheto and de la Porte des Vaux, 1970 a], the other for a rocket experiment [Etcheto and de la Porte des Vaux, 1970 6]. More detailed information can be found in these two Proposals. 241 We will describe here the operating principle of this device and give the theoretical limiting accuracy that we can achieve with this kind of detector. We shall indicate two possible methods to transmit the measurements of the distribution function. One of them takes into account the spinning movement of the vehicle and thus enables us, in a very simple way, to content ourselves with a small telemetry bandwidth. Numerical results that we have already obtained with a preliminary version of this device will be also reported. 2. MEASUREMENT OF THE ENERGY AND PITCH-ANGLE DISTRIBUTION 2.1 Position-sensitive detector The position-sensitive detector is a rectangular surface barrier detector, in the back of which a resistive layer, very homogeneous, has been created. Any particle entering this detector generates two pulses. The first, which is received on the front (Au) surface, is proportional to the energy loss. The second pulse appears at the back, i.e. on the resistive layer, over a very small area, and is proportional both to the energy loss and to the distance x between the impact point and the grounded end (Figure 1). -W- O1-^ Si- Au SURFACE BARRIER DETECTOR imm>mmw»»i»M/M»JMi»i»»ii RESISTIVE LAYER >L CHARGE PREAMPLIFIER *y x+y Figure 1. — Position sensitive detector. By dividing the amplitude of one pulse by that of the other, it is thus possible to obtain the value of x. It is necessary to divide the impulses on board in order to keep all the accuracy of the energy measurement to perform the division (Figure 2). Figure 2. — Schematic block diagram of the experiment in the case of a large telemetry bandwidth. E and x are transmitted to the ground for each particle. ^ Figure 3. — Geometrical arrangement of the detector. 242 CHARGE PREAMPLIFIERS £, ENERGY ^ POSITION-JANGLE /loo" detector L = 30 mm H = 20 C s 3 A j2^> : 3 V£X-. 1 e s 1 •«- > 243 If the detector is placed behind a small slit as shown in Figure 3, the position signal depends upon the angle of arrival of the particle. Usually, the relationship between the angle a and the position x is not a linear one. But for a limited range in the values of a, and for a given geometrical position of the detector with respect to the satellite, a linear relationship can be achieved with an accuracy of ± 1.5°. Only two thirds of the detector area are used because, for small values of*, the accuracy becomes very poor. Typical dimensions of the device are given on Figure 3. At the moment we intend to use this detector for measuring only protons because of difficulties which would arise from the elimination of protons inside an electron detector. Moreover, this elimi nation would result in the diffusion of the electrons onto the slit edges, which would probably add to he tinaccuracy on the anpular measurement. On the contrary, eliminating electrons in a proton detec tor is very easy if one us .a a broom magnet in front of the detector. 2.2 Accuracy on the position measurements The accuracy of the angular measurements depends on the position measurement which is obtained by dividing one of the pulses (xE) by the other (E). The accuracy of the position measure ment is then given by : Ax _ A (*E) AE AV x xE + E + V where AV/V is the inaccuracy coming from the electronic processing, that is to say the non-linearity and nofse of the dividing system. AV/V is, for the smallest signal that we are using, of the order of 3%. Because of the large capacity of the detector (~ 50 pF), we do not have, for the time being, an energy resolution better than 10 keV. It seems difficult to reduce this capacity since we need a large surface in order to cover a wide pitch-angle range. Moreover, the depleted depth shall not be greater than 300 n if we want to prevent high energy electrons, which cannot be swept avay by the broom magnet, from spoiling the proton measurements. Finally, due to the large surface of the detector, the polarization current is rather important; so is the noise which is associated with such a current. But this effect can be reduced by cooling the detector. The resolution on the position output is worse because, in addition to the current noise just mentioned, there is a noise which is produced by the resistive layer, at the back of the detector. Such a noise can be reduced by improving the technique for depositing this resistive layer and by cooling the detector. In Table 1, we give the computed accuracy of the angular measurement for different resolutions in both E and (xE). One sees that the device is really interesting above 500 keV if A (xE) = 30 keV and above 200 keV if A (xE) = 15 keV. A preliminary version, now under test in our laboratory, has the following accuracy : AE = 10 keV; A (xE) = 30 keV. A new detector is being built in industry, which will give a better accuracy. 244 Table 1 Angle Energy (MeV) 0.2 0.4 0.6 1.0 30 4° 2.5° 2° 1.6° JE = 5 keV 50 5 3.5 2.8 2.3 J (xE) = 5 keV 75 7 4.5 3.8 3.1 100 8 5.5 4.7 4 30 10° 5.5° 4° 2.7° JE = 10 keV 50 11.5 6.5 5 3.5 J (xE) = 15 keV 75 13.5 7.5 6 4.5 100 15 9 7 5.5 30 17° 9° 6.5° 4° JE = 10 keV 50 19 10 7.5 5 J (xE) = 30 keV 75 21 11 9 6 100 23 12 10 7 * This parameter is the angle of amval of a particle with respect to the spin axis: for a configuration similar to the one pictured in Figure 3. _ _ . 3. ONBOARD PROCESSING OF THE DATA 3.1 Case of a large telemetry bandwidth If we have at our disposal a large telemetry bandwidth, it is possible to transmit two informations, x and E, for each particle without onboard storage. This is the case with rocket experiments. The energy pulse goes to a pulse amplitude selector, analogic or digital. The position data is also selected into a given number of channels and both measurements are telemetered together. On the ground the position of each particle is related to its real pitch angle by a computer which takes into account the attitude restitution of the rocket: Assuming that the total energy and pitch-angle ranges are divided respectively in 8 energy channels and 16 pitch-angle channels, each particle can be symbolized by a word of 7 bits (3 + 4). The maximum counting rate which is permissible at present is of the order of 10" counts/sec. This defines .the maximum bandwidth of the telemetry required. Practical solutions for transmitting these data in the case of both a digital and an analog tele metry are described elsewhere [Etcheto and de la Porte des Vaux, 1970 b]. 245 3.2 Case of a small telemetry bandwidth Whatever the practical solution which is adopted, h is obvious that such a large amount of telemetry bandwidth is not permissible on board a satellite for one experiment alone. Therefore, we are obliged to store the results in a memory over large periods of time (of the order of one to five seconds). The memory will be a matrix of 8 columns and 16 rows for example, the content of which will be read periodically. DETECTOR APERTURE Figure 4. — Definition of the angles. If the satellite is magnetically stabilized, there will be no problem; but if it is not, the angular measurements must be transformed before being stored. As a matter of fact a is not uniquely related with the true pitch angle of the particle, because of the spinning motion of the satellite; Figure 4 shows the geometry of the problem. — a is the measured angle; — 4> is the real pitch angle; — 0 is the angle between the magnetic field and the spin axis of the satellite; generally it has a very slow variation with time; — I/I is the phase angle of the spinning motion and varies proportionally to the time. The complete relation between these angles is : cos This relation should be computed by an onboard computer. If the satellite does not carry such a device, it is possible to use an approximate formula, much simpler and also sufficiently accurate provided 9 is not too large : 246 Cf degn Figure 5. — Error on the computed pitch angle made by using the approximate formula $ — a — 0 cos tji instead of the exact one cos Figure 5 represents the maximum error on the pitch angle that one makes if one uses this approximate formula. The minimum a value has been taken to be 30°. If 6 is less than 15°, the error is smaller than 3.5°. Using this approximation, it is easy to do this calculation onboard without Figure 6. — Schematic block diagram of the experiment in the case of a non magnetically stabilized satellite with a small telemetry bandwidth. Only the number of particles in each channel of pitch angle and energy is telemetered. AHUOO . DIGITAL 5 CONVERSION H ENERGIES • kit WORDS TO TELEMETRY + MEMORY • AHAIOS . DIGITAL CHARGE COMVGRSroM PREAMPLIFIERS • DmSHffl rBHE 1. 247 l I I 1.1..!;„_.. I ill ' IllH U.ll.li J Illllllllllllllillllllllliilliilllllllllll lllllllilllil;llllill a real computer, provided 8 is supplied either by telecommand coming from a ground computer making a real-time attitude restitution or from the satellite by an onboard treatment of the magnetometer data. We also have to supply the knowledge of \ji which can be given by one axis of a magnetometer or by a solar sensor or a similar system. A schematic diagram of such a treatment is given on Figure 6. Here all the data handling of the pitch-angle correction is performed in a digital form. 4. CONCLUSION This device has the advantage of being very small. The experiment of Figure 6 has the following characteristics : volume, 31; weight, 2 kg; power consumption, 2 W. It is able to measure a pitch angle distribution very quickly, as long as enough particles are present in the medium (about 1 s for 16 energies and 16 angles for realistic values of the flux and telemetry bit rate at the geostationary orbit) and with a sufficient precision if we are not interested in pa" deles having too low an energy. It should allow us to study in detail the quasi linear wave-particle interactions, i.e. those invol ving waves with a wide frequency spectrum. Of particular interest, in this respect, is the study of the establishment of the steady state equilibrium. We could also study some purely non-linear aspects of the interactions, for instance the trapping of particles into a monochromatic wave and its consequences [Laval et al.]. As an example, the theory predicts that the pitch-angle distribution with be distorted during these interactions, this distor tion oscillating at a period which is the same that the trapping period (which is of the order of 10 sec for usual electromagnetic amplitudes). On a longer time scale, the pitch-angles of particles in a narrow energy range will decrease. These are only some examples of the phenomena that we could study with such a device. More generally, we could study all the phenomena which modify quickly the pitch-angle distribution of protons. ACKNOWLEDGEMENTS . We wish to thank Dr. R. Gendrin, who gave us the idea of studying the position-sensitive detecting device, and who helped us continuously during the course of this study. We want also to acknowledge the work of Mr J. Etcheto, who participated in the development of the electronic systems. 248 THE STUDY OF PLASMA RESONANCES WITH A SINGLE ANTENNA Michel Petit Centre National d'Etudes des Télécommunications, Issy-les-Mou'r-eaux, France ABSTRACT Plasma resonances detected with a single antenna can provide us with reliable measurements of electron density and electron gyrofrequency. The physics of the phenomenon is not yet completely explored, and more information is likely to be available in the detailed structure of the ringing signals received after transmitting a pulse at some resonance frequency (i.e. variation of amplitude and waveform versus time delay). The experimental set-up can be designed to study both resonances and natural waves without adding much complexity to the onboard system. 1. INTRODUCTION The possibility of studying resonances with a single antenna was experimentally discovered when the first attempts were made to put ionosondes onboard spacecraft. It is now well known that the topside ionograms, in addition to showing conventional traces also show resonance spikes. For some particular frequencies the receiver records a long ringing signal, lasting for several milliseconds after pulse transmission. It was soon agreed that the frequencies for which this phenomenon occurs are fixed by properties of the local phsma rather than by properties at some distant point where reflection might take place. 2. BASIC THEORY 2.1 Theory in an homogeneous plasma a) PREDICTION OF RESONANCE FREQUENCIES A plasma in a magnetic field is capable of sustaining a great variety of wave motions. Among these waves, some can be found for which the group velocity vanishes, frequency and wave number being purely real (no damping). This happens for certain discrete frequencies. Such wave packets remain at the same place and an antenna will detect them after having excited a broad spectrum of waves in a frequency band that includes one of those particular frequencies. 249 The first theoretical approach [Dougherty and Monaghan] involves searching through the solu tions of the dispersion re'"!,.. ior waves having zero group velocity. It turns out that the most important waves for this purpose are plasma oscillations and Bernstein modes. The relevant waves are mainly occurring : — at (op plasma frequency with \k\ = 0, parallel to B; — at ioT upper hybrid frequency with \k\ nearly 0, perpendicular to B; — at wb electron gyrofrequency with \k\ = 0 or oo, perpendicular to B ; — at ncob harmonics of gyrofrequency, with \k\ = 0 or small, perpendicular to B. b) EVALUATION OF THE RECEIVED SIGNAL The second step is the study of the efficiency with which the wave packets having zero group velocity are excited and detected by an antenna of a given form. The form of the current distribution within the antenna is always taken as a guess and indeed in many calculations the antenna was assumed to be an infinitesimal dipot. The problem is then solved by using a double Fourier transform in space and time E (k, a>). Values of the field for relatively large positive values of the tinu t depend mainly on residues at poles or branch cut integrals of the Fourier transform in time. The contribution of the former will result in a time dependence as e1"' for a pole at frequency to, while the branch cut integrals typically involve an additional factor which is a power of t. This is the reason why most of the resonances are predicted as having a decay law of the form r""2, t~3/2, t~sl2. The singularities of the Fourier transform in time correspond to the ringing signals. They correspond to poles of E (k, to) pinching the contour of integration in the k space and it is easily shown that the condition of pinching is equivalent to the annulation of group velocity. This second step is therefore perfectly consistent with the first and leads to the same resonance frequencies. 2.2 Effect on inhomogeneity a) MAGNETIC FIELD NON UNIFORMITY [Shkarofsky] showed that the variation in space of the Earth magnetic field was large enough to limit k\\ to finitevalues . A non zero value of k || implies then that either m or k± has to be complex near the harmonics nmk of the electron gyrofrequency, at least for n > 2. Shkarofsky concludes that the resonances at these harmonics will be damped according to an exponential decay law and computes, on the basis of qualitative arguments, the order of magnitude of the time constants. b) ELECTRON DENSITY NON UNIFORMITY [McAfee, 1968, 1969] was the first to realise the importance of a subtle effect of electron density non uniformity. This concerns plasma frequency and upper hybrid frequency. Let us illustrate the phenomenon with the first case. Close to the solution (to = tup and k = 0) of the electrostatic dispersion relation, solutions exist with very small group velocity. The frequencies of these waves lie slightly above mp and the direction of the group velocity is a very sensitive function of (to — to,) and therefore of to,; This results in sharply curved ray paths along which a wave packet moves relatively slowly. Some of these ray paths intersect the satellite orbit and if the wave packets are returned with the correct delay time, they will be observed by the spacecraft. Slightly different frequencies will therefore be received successively by the satellite, giving an effect similar to a plasma resonance, provided the frequency shift is small enough. Quite often, the satellite can come across two possible 250 paths having the same delay at the same point. The two paths relate to slightly different frequencies, which results in the appearance of beats within the envelope of the received signal, just as happens in conventional topside sounders. This phenomenon, first investigated by ray tracing techniques, can also be studied by the WKB method [Fejer and Yu]. This method leads to a fairly simple determination of the received frequency as a function of time delay. In addition, it permits an estimation of the field which varies as r""2: Fejer and Yu's work was extended by [Graff] to the upper hybrid frequency and to any relative orien tation of the magnetic field, any satellite velocity and any density gradient. 3. EXPERIMENTAL RESULTS 3.1 Resonance frequencies Experimental results on resonance frequencies are in good agreement with the above theoretical analysis and the determination of resonance frequencies by this method can be considered as a safe way of determining electron density and magnetic field intensity. This is illustrated by the results of the EIDI rocket. This experiment was mainly devoted to the study of the impedance of a dipole embedded in the ionospheric plasma. In order to compare the results with theory, the radioastro- Figure I. — Electron density profiles obtained from plasma resonances (22 oct., 1970; 08 h 23 UT). RJ 195 EIDI MV2 22oct 1970 500 - altitude Z 08(123 T.U. Fréquence de la réeonance plasma Fn en fonction de l'altitude Z (expérience NE '.sondeur à relaxation ) -a- montée -a- descente 100 " fréquence 1 2 4 5 6 7 a 9 10 3 • | | | 50 1 251 nomers of Meudon Observatory needed values of electron density. A resonance experiment was performed on the same rocket and the results are shown on Figure I. The accuracy of the method is illustrated by the smoothness of the density profiles, although the data presented are based on quick look analysis. In the final treatment, error bars will be reduced by a factor of about ten. Difference between upleg and downleg results is believed to be real and due to a horizontal gradient in electron density. This feeling is confirmed by the impedance measurements. 3.2 Decay of signal amplitude Experimental results do not appear to be in agreement with theoretical predictions, the signal being generally observed to decay more rapidly than t~", with a expected between 1/2 and 7/2. This is illustrated by Figure 2, which represents an Alouette 2 record of amplitude versus time. The dynamic range of the receiver was 40 dB; for an increase of 20 or 30 % in time delay, the field decreases by a factor of about 100, this being obviously inconsistent with a variation of the t~" type. Figure 2. — Amplitude of ringing signal versus time delay after pulse transmission, as observed by Alouette 2 satellite. time <• 232 Volts efficaces aux FU 195 EIOI MV1 06/10/70 bornes de I antenne 30mV - Hn*5 01' 453 Z = 467 km 10mV H0+5 04 674 • i 2FU = 2.068 MHz 3mV Z s 469 km ImV - o • 300uV - . o o • o o 100jiV IOJ*'- ° „ ^Hum^ms) -) «n'^'l • 05 Figure 3. — Amplitude of ringihg signal versus time delay, after pulse transmission, as observed in EIDI experiment for a resonance at 2 f„. 253 JI Volts efficaces aux FU 195 EIOI Mtfl 06/10/70 bornes de l'antenne H0+5'01"413 30mV - Z=467km o o i'04'634 o •i 3F3FHH=3=3.102MH. z Z=46f: 469l km 300jiV - o o o, o o o o o • • o 100JJV - lOjAf - Temps (m* ) i-l 0.5 15 Figure 4. — Amplitude of ringing signal versus time delay, after pulse transmission, as observed in EIDI experiment for a resonance at 3 fB. 254 Coming back to the EIDI rocket, a short time constant was used in the automatic gain control circuit, thus preventing any saturation and enabling the resonance signal to be recorded throughout its duration. Telemetered signal is roughly proportional to the logarithm of input voltage which is given on the vertical axis of Figure 3 as a function of time delay. The two curves correspond to reso nances observed at 2/H for two altitudes distant by 2 km. They are very similar but indicate a decay which is roughly exponential. Figure 4 is a similar record for a 3f„ resonance. While [Shkarofsky] predicted that this reso nance could be damped more rapidly than the 2f„ resonance, the opposite is actually observed. As a conclusion, it does not seem that current theory is suitable for interpreting resonance amplitude decay. 3.3 Fine structure of resonance signals McAfee's theory gives way to a new possibility of using resonance techniques in so far as it predicts that two waves will be received simultaneously. The frequency of these two waves varies slightly with time delay; so does their différence, which is the frequency of the beats envelope observed on some ionograms. Figure 5 [Warnock, McAfee and Thompson] is a comparison between experi mental data and theoretical curves corresponding to various electron temperatures. This comparison obviously leads to electron temperature determination. Such a determination is not very accurate but may still be very useful in magnetospheric studies. Figure S. — Comparison between experimental data (open circles) and theoretical curves (solid lines) for the beat period versus time delay IWarnock, McAfee and Thompson]. log Delay (msec) 255 i 15 500 1500 lB (Hz) Figure 6. — Comparison between experimental data (black circles are obtained by averaging open circles) and theoretical curves (solid lines) for the beat frequency versus time delay [R. Feldstein, to be published]. Figure 6 represents a similar study made by R. Feldstein (CNET). In addition to the previous results, a more or less systematic oscillation appears, the frequency of which is significantly different from the proton gyrofrequency, although it is of the same order of magnitude. The origin of this oscillation is at present not well understood but its existence is for the time being the most severe cause of inaccuracy in temperature determination. 256 4. EXPERIMENTAL SET-UP The experimental set-up necessary for this kind of diagnostic method is not very different, from the one which can be used for the study of natural waves : the basic apparatus is a super heterodyne receiver which can be swept in frequency near the electron gytofrequency and near the plasma fre quency. For resonance studies, a transmitter is also needed but the transmitted power can be much lower than in the conventional topside sounders which are mainly devoted to observation of remote echoes. The transmitter is therefore a fairly simple amplifier. 5. CONCLUSION It is possible to design an integrated wave experiment which can serve both as a tool for the study of natural waves and as a diagnostic device for plasmas by means of their resonances. Such an experi mental set-up is already planned for the Geos satellite by the joint efforts of the Space Science Depart ment of ESTEC, the Groupe de Recherches Ionosphériques and the Centre (National d'Etudes des Télécommunications. The basic concept however could be applied in any magnetospheric satellite. DISCUSSION D. Cartwright. It is almost as easy to measure the phase as well as the antenna impedance; it only takes a little more circuitry and you get a lot more information. We did this on a rocket flight but unfortunately the vehicle did not work. M. Petit. You suggest using the measurements of the antenna impedance as a diagnostic technique ? D. Cartwright. Yes. You can almost as easily, with just a small modification to your instrumentation, measure the phase of the impedance as well as the amplitude of the impedance and this gives you a lot of additional information. M. Petit. The philosophy of the EIDI rocket was to check the theory of antenna impedance. Dipole impedance was therefore measured by radioastronomers of Meudon Observatory. The resonance experiment I was referring to is a completely independent method for measuring electron density; an indépendant method for electron density determination was necessary since the basic aim was to check impedance theory. The resonance technique is based on the detection of transient signals which occur just after you have transmitted but only when the transmitted frequency is in a well known range of particular frequencies, including plasma frequency. The diagnostic technique is simply based on the existence of transient signals. 257 EXPERIMENTS WITH PLASMA WAWES J.O. Thomas, M.K. Andrews, T.A. Hall and M.C. Fang Department of Physics, Imperial College, London ABSTRACT Experimental and theoretical work on plasma wave propagation at frequencies near the plasma, upper hybrid and electron gyroharmonics are briefly discussed. Reference is made to both laboratory plasma and topside sounder satellite experiments. 259 MAGNFTOSPHERIC STUDIES AT 10 EARTH RADII G.P. Haskell Dept of Physics, Imperial College, London, Great Britain ABSTRACT It is suggested that the most fundamental problem in the physics of the magnetosphere is the problem of the substorm. In particular, it is important to ascertain whether substorms are triggered by changes in the solar wind or by an internal .;<:tab'Ut\ cf • V magnetosphere in which waie-particle interactions may play an important part. Further, it is suggested that the region of space near 10 RE in the equatorial plane is especially suitable for experimental studies of this problem. Satellite orbits with apogees close to 10 RE are needed because it is important that the satellite should spend a long time in the region of interest compared with the chaiac- teristic time periods of substorms. The central problem in the physics of the magnetosphere is that of the magnetospheric substorm. In particular, the main question to be answered is : are substorms triggered by a change in the solar wind or by an internal instability of the magnetosphere ? The study of small-scale wave-particle interactions is important because it is likely that some of these small-scale effects control the large- scale motions and the transport of energy within the magnetosphere during substorms. The purpose of this brief presentation is twofold. Firstly, it is to suggest that the region near 10 R£ (Earth radii) from the centre of the Earth in the equatorial plane is uniquely suitable for an experimental study of this problem. Secondly, it is to discuss suitable satellite orbits. The main requirement of the orbit is that the satellite should spend a long time in the region of interest compared with the characteristic time scales (hours) of substorms. This means that an eccentric orbit should have its apogee close to 10 RE. 261 magnetopause to Sun magnetosheath '/, region of Af observed intense s/. low energy electron fluxes Figure 1. — A sketch of the equatorial plane showing the approximate locations of the magnetopause and the inner edge of the plasma sheet at magnetically quiet times (from [VasyliunasJ). Figure 1 shows why measurements in this region near 10 RE would be important in a syr iptic study of the magnetosphere. On the day side there is the magnetopause, and on the night side the inner edge of the plasma sheet at magnetically quiet times. On the day side it would be valuable to monitor the following and to compare them with other simultaneous measurements during substonns : a) movements of the magnetopause, which may result from compression or erosion of the magnetosphere; b) changes in the post-shock solar wind, adjacent to the magnetopause, at times when the satellite is beyond the magnetopause. On the night side, the inner edge of the plasma sheet and the large scale configuration of the magnetic field are important features to monitor. There are indications that the ' tiue ' start of a substorm is the equatorward movement of auroral arcs which, presumably, accompanies the known earthward movement of the plasma sheet. Therefore, it is important to monitor the following during substonns : a) the tii at which the inner edge of the plasma sheet starts to move inwards; b) changes that occur in the plasma and waves, near the inner edge of the plasma sheet; 262 c) changes in the local magnetic field, which would be very sensitive to the position of the ' hinge ' between the magnetic equatorial plane and the neutral sheet; d) changes in energetic particles and their pitch angles, which would permit inferences about the large-scale fieldconfiguratio n (e.g. open or closed field lines). Figure 2 shows two suitable equatorial orbits. The first is the simplest eccentric orbit that reaches 10 RE. Its period is about 18 hours and it would spend about one-third of its time between 9 and 10 Re. It would cover all local times in one year. Period 18 h. Period 24 h. Figure 2. — Two suggested orbits, showing the time spent near apogee. A satellite in the second orbit shown would make an ideal companion for GEOS. By keeping the apogee at 10 RE and putting the perigee at about 3.2 R£ one can achieve a period of 24 hours. If this were launched onto the same average meridian as GEOS, it would circulate around GEOS as seen from the Earth. Again, it would spend about one-third of its time between 9 and 10 RE. However, it is not obvious whether or not this orbit is within the scope of the proposed ESRO pro gramme. To summarise, I suggest that wave-particle interactions should be studied in the context of the magnetospheric substorm, and that attention should be concentrated on the day side magnetopause aud the inner edge of the plasma sheet at the start of substorms. Eccentric orbiting satellites with apogees near 10 R£ in the equatorial plane would be suitable for this purpose. 263 L'ÉTUDE DES INTERACTIONS DANS LA MAGNETOSPHERE ET LE PROGRAMME DE L'ESRO F. du Castel Centre National d'Etudes des Télécommunications, France L'objet de cette dernière Séance du Colloque est d'examiner les implications que peuvent avoir sur les projets de recherche spatiale en satellite les discussions menées au cours des Séances précédentes sur les aspects théoriques et expérimentaux des problèmes d'interactions entre ondes et particules dans la magnetosphere. Ces idées ont été précédemment débattues par le Groupe scientifique ION de l'ESRO et c'est sur sa proposition que l'ESRO a engagé une étude de faisabilité d'un programme de petits satellites magnétosphériques. Les résultats de cette étude et les maquettes correspondantes de satellites sont présentés à l'occasion de ce Colloque. Mais avant de rappeler les motivations du Groupe ION et le contenu du programme pro posé, il est peut-être nécessaire de revenir sur la première Discussion générale qui semblait oppo ser certains théoriciens et certains expérimentateurs. Les premiers faisaient valoir qu'il faudrait avant tout tirer profit des résultats existants pour atteindre une compréhension globale du fonctionnement de la magnetosphere, objectif qui paraît aujourd'hui réalisable. Les seconds soulignaient combien il serait important d'entreprendre de nouvelles expériences, pour approfondir les connaissances sur des aspects fondamentaux mal connus. Il me semble utile dans cette controverse de rappeler que les résultats mentionnés par les théori ciens proviennent d'expériences conçues, parfois dix ans plus tôt, par des expérimentateurs et qu'un tel délai entre conception et utilisation paraît difficilement évitable en recherche spatiale. C'est donc à longue échéance qu'il faut penser les expériences d'aujourd'hui, dans la limite des contraintes imposées à la recherche spatiale européenne, limites qui, souvent, ne dépendent pas des scientifiques. C'est dans cet esprit que je voudrais présenter à la discussion les propositions dont l'origine se trouve dans les travaux du Groupe ION. Les idées fondamentales dont est parti le Groupe pour promouvoir l'étude d'un programme de petits satellites sont de deux sortes. Le premier intérêt d'une série de petits satellites serait de permettre, pour un coût a priori comparable à celui d'un unique gros satellite, des délais de réalisation plus courts. Le second aspect fondamental est que l'état des connaissances sur la magnetosphere nécessite désormais non plus des études à but descriptif mais la compréhension de phénomènes physiques parti culiers, nécessitant des expériences coordonnées et adaptables. 265 Pour répondre à ce double souci, on est conduit, d'un point de vue technique, à la conception d'une petite série de satellites à base d'éléments normalisés, nécessaires pour réduire le temps de réali sation à moins de deux ans, ainsi qu'à l'introduction à bord du satellite de moyens de calcul élaborés permettant une gestion scientifique souple des expériences. D'un point de vue scientifique, il devient nécessaire de définir des missions précises, avant toute sélection d'expériences, et d'accroître le rôle scientifique des équipes de recherches impliquées aux divers stades du projet (élaboration, opérations et interprétation), au détriment peut-être de leur rôle technique dans la construction des expériences. Ce dernier point devrait d'ailleurs conduire à augmen ter le nombre de scientifiques pouvant participer aux projets, alors que certains d'entre eux sont actuel lement tenus à l'écart de la recherche spatiale faute de moyens techniques adéquats et non de compé tences scientifiques. C'est sur ces bases qu'un Groupe de définition de mission a été désigné par le Groupe ION, sans attendre un accord formel des instances de l'ESRO sur un tel programme. Ce Groupe a d'abord considéré que la mission fondamentale qui devait être assignée au programme « Petits satellites » de l'ESRO relevait de la physique du plasma magnétosphérique, dans le cadre général des phénomènes d'interactions entre ondes et particules. Il a ensuite proposé quelques orbites-types, soit à basse alti tude (compatibles avec les lanceurs des pays membres), soit à apogée élevé (compatibles avec le futur lanceur européen). Ces diverses orbites sont rappelées sommairement sur le Tableau ci-dessous. Le Groupe a enfin sélectionné des expériences-types et défini les fonctions des moyens de calcul à bord. Ces expériences concernent les mesures d'ondes — magnétiques et électriques — les mesures de particules — nécessaires à l'étude des phénomènes d'interactions — et les mesures complémentaires nécessaires à la détermination des conditions d'ambiance (plasma thermique et champ magnétique). Leurs principales caractéristiques sont rappelées sur le même Tableau. Les études de faisabilité entreprises alors par des sous-traitants industriels ont défini les confi gurations possibles de satellites compatibles avec les divers lanceurs*. Elles ont montré la possibilité de répondre aux exigences proposées et ont évalué les coûts de l'opération. Tels qu'ils apparaissent à l'issue de ces études préliminaires, les petits satellites de l'ESRO sont des systèmes « à fonctions multiples », dotés d'une grande souplesse d'utilisation. Le premier terme doit être entendu au sens qu'il a dans le vocabulaire de l'informatique (general purpose); il veut dire que sont exclus a priori des équipements très spécifiques, tels que canons à électrons ou sondeurs en contre-haut. Le second terme signifie que, pour un ensemble de capteurs donnés (répartis en énergies pour les particules et en fréquences pour les ondes), il est possible de programmer (ou de reprogram mer) des expériences diverses en utilisant de façon plus ou moins complexe un nombre variable de capteurs. Il implique aussi la possibilité, pour une mission donnée du satellite, de remplacer l'un des éléments normalisés par un autre, pour mettre par exemple l'accent sur un domaine d'ondes ou un domaine de particules choisis. La souplesse d'utilisation découle enfin des possibilités offertes par les nombreux supports et les divers mâts envisagés. Quelle est actuellement la situation du projet ? Le point de vue du Groupe ION n'est pas par tagé par l'unanimité des groupes scientifiques de l'ESRO; d'autre part, certains pays-membres présen tent des objections à un programme de petits satellites; aussi la décision sur le projet dépendra-t-elle pour une part de l'intérêt que lui manifesteront les scientifiques européens. L'un des buts du Groupe ION en suscitant ce Colloque était justement de connaître le « soutien » que rencontrent ses proposi tions. Ces Journées consacrées à une revue des problèmes soulevés par les interactions ondes-particules dans la magnétosphère permettent peut-être de répondre à cette première question et de le faire dans un sens favorable. Mais il serait aussi important de chercher à déterminer, parmi les nombreux problèmes évoqués pendant la première Séance de discussion générale, quelles sont les missions précises auxquel les on devrait accorder la priorité (en vérifiant leur compatibilité avec les conclusions des études de faisabilité). Les discussions de ce Colloque devraient ainsi servir de guide aux travaux du Groupe ION pour faire progresser le projet de programme « Petits satellites » de l'ESRO. 'Pour plus de détails, an se reparlera aux Happons d'éludé disponibles auprès de la Direction de l'ESRO. 266 ORBITES BASSES ORBITES EXCENTRIQUES ORBITES quasi polaire équatoriale 7 — 15 R circulaire 500 km quasi polaire ~ 25 R elliptique ~ 2 000 km quasi polaire ~ 8 R orientation // B0 EXPÉRIENCES 0 particules e'p* 100 eV— 30keV e-p* 100 eV— 50keV e'p* 30keV — 300 keV e-p+ 50 keV — 200 keV e'p* a* 200 keV — > 1 MeV + superthermiques + spectromètre ionique 0 ondes magnétiques (3 composantes) 120 Hz — 2 kHz (barres) 10,1 Hz — 100 Hz (barres) \l kHz— 2 MHz (boucles) 1100 Hz — 100 kHz (boucles) électriques 3 composantes) |20 Hz — 2 MHz (sphères) |20 Hz — 100 kHz (6 dipôles sur 2 mâts) 9 plasma sonde à plasma résonances du plasma impédance mutuelle + champ électrique continu • champ magnétique magnétomètre triaxial CONFIGURATIONS 6 mâts orthogonaux 4 longs mais 2 mâts axiaux 1 mât axial électronique en boîtiers normalisés 12 + 6 détecteurs de particules n détecteurs de particules calculateur de bord (option) calculateur de bord LANCEURS 1. Diamant amélioré Europa II 2. Black - Arrow (Thor Delta) SATELLITES • poids, kg (total/ 1. 135/30 150/29 expériences) 2. 93/15 • puissance (W) /. 20 10 2. 10 • mémoire (kbits) 4 8 • coût, M S (1°, 2", 3°) 1. 14, 6, 6 14, 9, 9 2. 7, 3, 3 267 DISCUSSION GÉNÉRALE (II) Compte rendu par F. du Castel (CNET). Président de séance Le premier point abordé dans la Discussion concerne les orbites souhaitables. Le Dr Haerendel plaide en faveur d'une orbite polaire excentrique, d'apogée voisin de 8 R, qui présente l'intérêt de coïncider avec une même ligne de force le long d'une bonne partie de la trajectoire et pendant un temps relati vement long. Une telle orbite offre notamment d'intéressantes perspectives pour l'étude des phéno mènes associés au vent polaire. Le Dr Storey souhaite que l'absence du Dr Gurnett, à qui il avait demandé de présenter les possibilités offertes par les orbites à basse altitude, ne conduise pas à sous-estimer l'intérêt de telles orbites. Des observations récentes faites sur ce type d'orbites, à haute latitude, ont montré l'existence de rayonne ments TBF provenant de la région des points-miroirs, dont l'étude permet une approche peut-être plus simple des phénomènes d'instabilité du plasma. Cependant la suite de la Discussion semble montrer un intérêt plus marqué de l'assistance pour des orbites excentriques, ainsi qu'une certaine crainte que les performances des petits lanceurs européens actuels ne permettent pas des expériences suffisamment complexes pour une étude fine des phéno mènes. Un deuxième problème abordé est celui de la mission générale qui devrait être assignée au projet. Le Dr Schindler, reprenant une discussion précédente (cf. Discussion générale, I), insiste sur l'importance de la résolution spatio-temporelle des phénomènes; il craint que le programme ne se trouve réduit au lancement d'un unique satellite, ce qui ne permettrait pas de remplir l'objectif souhaité. C'est alors essentiellement dans une corrélation de ses observations avec celles du programme Geos que ce satellite trouverait toute son importance. Cette importance est soulignée par d'autres participants, qui convien nent que les projets proposés à l'étude de faisabilité répondent assez bien à cette orientation. Dans une troisième partie de la Discussion, on examine quelques aspects des expériences sur les ondes et les particules. Le Dr Storey souligne la différence de situation selon qu'on se trouve à haute ou à basse altitude, en raison de la dimension des antennes par rapport à la longueur de Debye du milieu, aussi bien pour l'étude des ondes électromagnétiques que pour celle des ondes électrostatiques. Il montre comment les types de capteurs proposés dans l'étude de faisabilité permettent de répondre à 269 ces exigences opposées. Il montre également les possibilités qui existent d'utiliser ces mêmes capteurs pour la mesure des mouvements propres du plasma et rappelle la nécessité d'un choix judicieux des gammes de fréquences à étudier. Le Dr Marlelli insiste pour sa part sur l'intérêt d'une étude spectrale des bruits électrostatiques. Il aborde d'autre part, ainsi que le Dr Wilhelm et le Dr Storey, le problème du choix des expériences les plus intéressantes pour les mesures relatives aux particules et notamment pour l'étude des instabilités dans le vent polaire. Enfin, le Dr Rothwell exprime les préoccupations d'un grand nombre de spécialistes devant les consé quences qu'aurait pour la recherche spatiale européenne une réduction des activités de l'ESRO et en particulier les répercussions qu'aurait pour les chercheurs européens une éventuelle suppression des bourses d'étude accordées par l'ESRO. 270 REFERENCES Abdalla, M. Nonlinear particle trajectories in a whistler mode wave packet, Plan. & Space Sc, 18 (1970), p. 1799. Adams, J. The mechanism of channel electron multiplication, IEEE Trans. Nucl. Manley, B. W. Sci., NS-13 (1966), p. 88. Aggson, T. L. Probe measurements of electric fields in space, in Atmospheric Emissions, B. M. McCormac and A. Omholt éd., Van Nostrand Reinhold Co., New York, 1969. Akasofu, S. I. Magnetic substorms as a discharge process, Nature, 221 (1969), p. 1020. Albert, R. D. Auroral particle precipitation and trapping caused by electrostatic Licdstrom, P. J. double layers in the ionosphere, Science, 170 (1970), p. 1398. Alexeff, I. Effects of electron temperature variation on ion acoustic waves, Jones, W. D. Phys. Fluids, 11 (1968), p. 167. Montgomery, D. Alexeff, I. Observations of ionic sound waves in plasma : their properties and Neidigh, R. V. applications, Phys. Rev., 129 (1963), p. 516. Alfvén, H. On the theory of magnetic storms and aurora, Tellus, 10 (1958), p. 104. Alfvén, H. Currents in the solar atmosphere and a theory of solar flares, Solar Carlqvist, P. Phys., 1 (1967), p. 220. Alfvén, H. a Cosmical Electrodynamics. Fundamental Principles, Clarendon Press, Fâlthammar, C. G. Oxford, 1963. Alfvén, H. b A new approach to the theory of the magnetosphere, in Cosmic dynamics, Fâlthammar, C. G. vol. 2, in press. van Allen, J. A. Lifetimes of geomagnetically trapped electrons of several MeV energy, Nature, 203 (1964), p. 1006. Angerami, J. J. A whistler study of the distribution of thermal electrons in the magneto- sphere, Stanford Electronics Lab., Stanford, T. Rep. n° 3412-7, Radio- science Lab., 1966. Angerami, J.J. Whistler studies of the plasmapause in the magnetosphere. 2. Electron Carpenter, D. L. density and the total tube electron content near the knee in magneto- spheric ionization, J.G.R., 71 (1966), p. 711. 271 Armstrong, J. C. Satellite-observed magnetic perturbations due to field-aligned current Zmuda, A. J. in the auroral oval. Fifty-first Annual Meeting of the Amer. Geophys. Union, Washington, 1970. Aubry, M. P. Inward motion of the magnetopau.se before a substorm, UCLA Inst, Russel, C. T. of Geophys. and Plan. Phys.. Rep. n° 846 (1970); see also J.G.R., 75 Kivelson, M. G. (1970), p. 7018. Aubry, M. P. Motion and structure of the magnetopausc, UCLA Inst, of Geophys. Russel, C. T. ami Plan. Phys., Rep. n° 865, 1970. Kivelson, M. G. Axford, W. I. a The polar wind and the terrestrial helium budget, J.G.R., 73 (1968), p. 6855. Axford, W. I. h Magnetospheric convection, Rei\ Geophys., 7 (1969), p. 421. Babic, M. The stability of a strongly ionized positive column in a low pressure Sandahl, S. mercury arc, to be presented at the Tenth Intern. Conf. on phenomena Torvén, S. in ionized gases, Oxford, Sept. 1971. Balsley, B. B. Some characteristics of non-two-stream irregularities in the equatorial electrojet, J.G.R., 74 (1969), p. 2333. Bame, S.J. Characteristics of the plasma sheet in the Earth's magnetotail,/.G.JÎ.,72 Asbridge, J. R. (1967), p. 113. Felhauser, H. E. Hones, E. W. Strong, I. B. Banks, P. M, The polar wind, J.G.R.. 73 (1968), p. 6846. Holzer, T. E. Banks, P. M. High latitude plasma transport : the polar wind, J.G.R., 74 (1969), Holzer, T. E. p. 6317. Barat, C. Mise en évidence de l'influence de la température sur le gain d'un multiplicateur tubulaire sans fenêtre, Nucl. Instr. and Meth., 87 (1970), p. 247. Barrington, R. E. A helium whistler observed in the Canadian satellite Alouette II, Bclrose, J. S. Nature, 210 (1966), p. 80. Mather, W. E. Béghin, C. Observations à bord d'une fusée de bruits TBF naturels au cours d'une aurore, Ann. Geophys., 23 (1967), p. 275. Bernstein, I. B. Phys. Rev., 10 (1958), p. 109. Bernstein, W. Measurements of precipitated 1-20 keV protons and electrons during Inouye, G. T. a breakup aurora, J.G.R., 74 (1969), p. 3601. Sanders, N. L. Wax, R. L. Bernstein, I.B. A new derivation of quasi linear theory, J. Plasma Physics, 4 (1970), Klotzenberg, J. P. p. 595. Berthomier, C. Temps de groupe c. direction de la normale d'onde de signaux TBF du type chœur de l'aube enregistrés au cours de l'expérience Fu 171, Thèse de 3e cycle, Univ. de Paris, 1970. 272 Biskamp, D. Instability of two-dimensional collisionless plasmas with neutral points, Schindler, K. subm. to Plasma Phys., 1971. Block, L.P. a On the distribution of electric fields in the magnetosphere, J.G.R., 71 (1966), p. 855. Block, L. P. b Acceleration of auroral particles by electric fieldassociate d with magneto- spheric plasma motion, I.A.G.A. Gen. Scient. Assembly, Madrid, sept. 1969. Block, L. P. c Acceleration of auroral particles by electric double layers, 1971, Royal Inst, of Technology, Stockholm. Block, L. P. Effects of field-aligned currents on the structure of the ionosphere, Fâlthammar, C. G. J.G.R., 73 (1968), p. 4807. Block, L. P. Field-aligned currents and auroral precipitations, in Atmospheric Fâlthammar, C. G. Emissions, B.M. McCormac and A. Omholt éd., van Nostrand Publ. Co., 1969. Bogolubov, N. N. Introduction to nonlinear mechanics, Princeton Univ. Press, 1947. Krylov, N. Booker, H. G. Radir studies of the aurora, in Physics of the Upper Atmosphere, J. A. Ratcliffe edit., New York, Academic Press, 1960. Bosqued, J. M. Caractéristiques des multiplicateurs d'électrons sans fenêtre; utilisation Rème, H. en fusée comme détecteurs d'électrons auroraux de faible énergie, Nucl. Instr. and Meth., 57 (1967), p. 6; see also SPARMO Bull, 2 (Dec. 1967), p. 41. Bostrôm, R. a A model of the auroral electrojet, J.G.R., 69 (1964), p. 4983. Bostrôm, R. b Currents in the ionosphere and magnetosphere, Ann. Géophys., 24 (1968), p. 681. Bostrôm, R. c Polar magnetic substorms, Adv. Study Inst, on Auroral and Airglow, Kingston, Ontario, in press, 1971. Boswell, R. W. Plasma production using a helicon wave, Phys. Lett., 33 A (1970), p. 457. Bowles, K. L. Field-aligned E-region irregularities identified with acoustic plasma Balsley, B.B. waves, J.G.R., 68 (1963), p. 2485. Cohen, R. Bowles, K. L. The association of plane-wave electron-density irregularities with the Cohen, R. equatorial electrojet, J.G.R., 68 (1963), p. 2503. Brice, N. M. a Fundamentals of very low frequency emission generation mechanisms, J.G.R., 69 (1964), p. 4515. Brice, N. M. * Bulk motion of the magnetosphere, J.G.R., 72 (1967), p. 5193. Brice, N.M. c Artificial enhancement of energetic particle precipitation through cold plasma injection, J.G.R., 75 (1970), p. 4890. Brice, N. M. Influence of magnetospheric convection and polar wind on loss of Lucas, C. electrons from the outer radiation belt, J.G.R., 76 (1971), p. 900. 273 Brown, W. L. Acceleration of trapped particles during a magnetic storm on April 18, Roberts, C. S. 1965, J.G.R., 73 (1968), p. 153. Cahill, L. J. Davis, L. R. Mcllwain, C. E. Budden, K. G. Radio waves in the ionosphere, Cambridge Univ. Press, 1961. Bullough, K. a Radio-echo observations of the aurora in Terre Adélie, Ann. Géophys., 17 (1961), p. 195. BuUough, K. b The orincipal zones of ELF/VLF emission, Mtg on storm effects in the ionosphere and magnetosphere, Royal Astron. Soc, 20th Nov. 1970, London. Bullough, K. a Satellite evidence for the generation of VLF emissions at medium Hughes, A. R. W. latitude by the transverse resonance instability. Plan. Space Sci., 17 Kaiser, T. R. (1969), p. 363. Bullough, K. b VLF observations on Ariel III, Proc. Roy. Soc, A 311 (1969), p. 563. Hughes, A. R. W. Kaiser, T. R. BuUough, K. c Space Research, XI (1971), Akademie Verlag. Sagredo, J. L. Hughes, A. R. W. Kaiser, T. R. Bullough, K. Longitudinal structure in the plasmapause; VLF goniometer obser Sagredo, J. L. vations of knee-whistlers, Nature, 225 (1970), p. 1038. Buneman, O. Excitation of field-aligned sound waves by electron streams, Phys. Rev. Lett., 10 (1963), p. 285. Calvert, W. Steep horizontal electron density gradients in the topside F-jayer, J.G.R., 71 (1966), p. 3665. Camidge, F. P. Magnetic field perturbations in the magnetotail associated with polar Rostoker, G. magnetic substorms, Can. J. Phys., 48 (1970), p. 2002. Campbell, W.H. Low attenuation of hydromagnetic waves in the ionosphere and implied characteristics in the magnetosphere for the Pc 1 events, J.G.R., 72 (1967), p. 3429. Carlqvist, P. Solar flares caused by high impedance regions in current filaments, in Mass motions in solar flares and related phenomena, Y. Ohman, Almqvist and Wiskell éd., Stockholm, 1968. Carlqvist, P. Current limitation and solar flares, Solar Phys., 7 (1969), p. 377. Carlqvist, P. Space charge regions above the aurora, J.G.R., 75 (1970), p. 7140. Bostrôm, R. Carpenter, D. L. a Whistler studies of the pli Tnapause in the magnetosphere. I. Temporal variation in the positior. A the knee and some evidence on plasma motions near the knee, J.G.R., 71 (1966), p. 693. Carpenter, D. L. b Recent research on the magnetospheric plasmapause, Radio Set., 3 (1968), p. 719. Carpenter, D. L. c Whistler evidence of the dynamic behaviour of the duskside bulge in the plasmapause, J.G.R., 75 (1970), p. 3837. 274 Carpenter, D. L. Direct detection by a whistler method of the magnetospheric electric Stone, K. field associated with a polar substorm, Plan. Space Sci., 15 (1967), p. 395. Cartwright, D.G. A controlled experiment of wave-particle interactions in the ionosphere, Kellogg, P. J. Nature, 231 (1971), p. 11. Caufmann, D. P. Double probe measurements of dc electric fields with the Injun S satelhte, Gurnett, D. A. Univ. of Iowa Rep. n° 71/4, 1971. Chamberlain, J. W. Electric acceleration of auroral particles. Rev. Geophys., 7 (1969), p. 461. Chandrasekhar, S. The stability of the pinch, Proc. Roy. Soc, 245 A (1958), p. 435. Kaufman, A. N. Watson, K. M. The electrical conductivity of the ionosphere : a review, Suppl. del Chapman, S. Nuovo Cimenta, 4 (1956), p. 1385. Spectral measurements of auroral zone particles, J.G.R., 73 (1968), Chase, L.M. p. 3469. Plasma waves in space and the laboratory (NATO advanced Study Inst., Clinkemaille, A. R^ros, Norway, April 1968), Edinburgh Univ. Press, 1970. Cloutier, P. A. Detection of geomagnetically aligned currents associated with an Anderson, H. R. auroral arc, J.G.R., 75 (1970), p. 2595. Park, R. J. Vondraek, R. R. Spiger, R.J. Sandel, B. R. Cole, G. in prep. (1971). Schindler, K. Coleman, P. J. Jr A model of the geomagnetic cavity, McDonnell Douglas, MDAC Paper WD 1385, Nov. 1970. Coleman, P. J. Jr Tangential drag on the geomagnetic cavity, in Cosmic Electrodynamics, 1 (1970), p. 145. Coleman, P.J. Jr Fluctuations in the distant geomagnetic field during substorms, in McPherron, R. L. Particles and fields in the magnetosphere, B.M. McCormac éd., Reidel Publ. Co., 1970. Cornwall, J. M. a Scattering of energetic trapped electrons by very-low-frequency waves, J.G.R., 69 (1964), p. 1251. Cornwall, J. M. b Mutually interacting instabilities in the magnetosphere, in Particles and Fields in the Magnetosphere, B. McCormac éd., D. Reidel Pub. Co., 1970, p. 266. Cornwall, J.M. c Cyclotron instabilities and electromagnetic emissions in the ultra-low- frequency and very-low-frequency ranges. J.G.R., 70 (1965), p. 61. Cornwall, J.M. d Micropulsations and the outer radiation zone, J.G.R., 71 (1966), p.2185. Cornwall, J. M. Turbulent loss of ring current protons, Plasma Physics Group, Dpt of Corbnitt, F.V. Physics, Univ. California, Los Angeles, Rep. R59, 1970; see also J.G.R., Thome, R.M. 75, (1970), p. 4699. 275 Coroniti, F. V. Turbulent conductivities in the magnetosphere, in Planetary electro dynamics, S.C. Coroniti and J. Hughes éd., Gordon and Breach, New York, 1970; Fourth Intern. Conf. on the universal aspects of atmospheric electricity, Tokyo, May 1968. Coroniti, F. V. Electron precipitation pulsations, J.G.R., 75 (1970), p. 1279. Kennel, C. F. Crary, J. H. The effect of the Earth ionosphere waveguide on whistlers, Stanford Electronics Lab., Stanford, T. Rep. n° 9, Radioscience Lab., 1961. Crawford, F. W. Excitation of cyclotron harmonic resonances in a mercury-vapor Kino, G. S. discharge, Phys. Rev. Letters, 13 (1964), p. 229 Weiss, H. H. Crawford, F. W. Plasma Waves in space and laboratory (NATO Advanced Study Inst. Lee, J. C. Rtfiros, Norway. April 1968), Edinburgh Univ. Press, 1970. Tataronis, 3. A. Cummings, W. D. Magnctospheric substorms observed at the synchronous orbit, J.G.R., 73 Barfield, J. N. (1968), p. 6687. Coleman, P. J. Davidson, G. T. Expected spatial distribution of low energy protons precipitated in the auroral zones, J.G.R., 70 (1965), p. 1061. Deforest, S. E. Pksma clouds in the magnetosphere, UCLA San Diego, Rep. UCSD- Mcllwain. CE. SP-70-04, May 1970. Sec also J.G.R., 76 (1971), p. 3587. Donat Ann. Gêophys., 27 (1971), p. 1. Dougherty, J. P. Ionospheric E-region irregularities produced by nonlinear coupling Farley, D. T. of unstable plasma waves, J.G.R., 72 (1967), p. 895. Dougherty, J. P. Theory of resonances observed in ionoyams taken above the ionosphere, Monaghan, J. J. Proc. Roy. Soc, London (1966), A 289, p. 214. Dowden, R. L. Determination of nose frequency of non-nose whistlers, CIRES Preprint AUcock, G. McK. 32, Univ. Colorado, Boulder, Col., 1970. Dragt, A. J. J.G.R., 66 (1961), p. 1641. Drummond, W. E. Non linear stability of plasma oscillations, Nucl. Fusion Suppl. (1962), Pines, D. p. 1049. Drummond, W. E. Nonlinear plasma oscillations, Ann. Phys., 28 (1964), p. 478. Pines, D. Dungey, J. W. a Resonant effect of plasma waves on charged particles in a magnetic field, /. Fluid Mech., 15 (1963), p. 74. Dungey, J. W. b Loss of van Allen elections due to whistlers, Plan. Space ScL, 11 (1963), p. 591. Dungey, J. W. c Effects of electromagnetic perturbations on particles trapped in the radiation belts, Space Sci. Rev., 4 (1965), p. 199. Dungey, J.W. Theoretical studies of protons in the outer radiation belt, in Space Hess, W.N. Research V (1965), p. 399; D.G. King-Hele et al. éd., North Holland Nokada, M.P. Pub. Co. Dupree, T. H. A perturbation theory for strong plasma turbulence, Phys. Fluids, 9 (1966), p. 1773. 276 Eather, R.H. The ring current as the source region for protons auroras. Cosmic Elec Carovillano, R.L. trodynamics, 2 (1971), p. 105. Egeland, A. Ion-reflection of downward-propagating whistlers at low latitudes. Leer, E. J. Atmosph. Terr. Phys., 32 (1970), p. 1983. Holtet, J. A. Ellis, G.R.A. Directional observations of radio noise from the outer atmosphere. Cartwright, D. G. Nature, 184 (1959), p. 1307. Ermakov, A. I. Cyclotron interaction between an electron beam and the fast magneto- Nazarov, N. I. sonic wave, Sot'. Phys. Techn. Phys., 14 (1970), p. 1180. Etcheto, J. Diffusion of particles in the presence of simultaneous VLF and ULF Gendrin, R. electromagnetic waves, J.G.R., 76 (1971), p. 1079. Lemaire, D. Etcheto, J. a Fast measurement of pitch angle and energy distribution of high energy de la Porte des Vaux, B. protons (0.2 < E < 10 MeV), Groupe de Rech. lonosph., NTP/66, 1970, Orléans. Etcheto, J. b Mesure rapide de la distribution en angle d'attaque et en énergie des de la Porte des Vaux, B. protons de moyenne énergie (0.2 < E < 5 MeV). Proposition à l'ESRO, 1970. Evans, D. S. On auroral electrons, Ann. Géophys., 24 (1968), p. 641. Eviatar, A. The role of electrostatic plasma oscillations in electron scattering in the Earth's outer rnagnetosphere, J.G.R., 71 (1966), p. 2715. Fairfield, D. H. The configuration of the geomagnetic field, Int. Symp. on Solar- Terrestrial Physics, Leningrad, May 1970, in press. Fairfield, D. H. Configuration of the geomagnetic tail during substorms, J.G.R., 75 Ness, N. F. (1970), p. 7032. Falthâmmar, C. G. a Some aspects of particles and fields in the magnetosphere, in High latitude particles and the ionosphere, B. Maehlum éd., Academic Press, London, 1965. Falthâmmar, C. G. b Fundamental electromagnetic processes in the outer magnetosphere, in Atmospheric Emissions, McCormac and A. Omholt éd., Van Nostrand Reinhold Comp., New York, 1969. Farlev, D. T. Jr A plasma instability resulting in field-alignedirregularitie s in the iono sphere, J.G.R., 68 (1963), p. 6083. Fejer, J. A. Excitation of plasma resonances by a small pulsed dipole in a weakly Yu, W. M. inhomogeneous plasma, J.G.R., 75 (1970), p. 1919. Feldstein, Y. I. Peculiarities in the auroral distribution and magnetic disturbance dis tribution in high latitudes, caused by the asymmetrical form of the magnetosphere, Plan. Space Sci., 14 (1966), p. 121. Feldstein, Y. I. Dynamics of auroral belt and polar geomagnetic disturbances. Plan. Starkov, G. V. Space ScL, 15 (1967), p. 209. Frank, L. A. a A survey of electrons E > 40 keV beyond 5 Earth radii with Explorer 14, J.G.R., 70 (1965), p. 1593. 277 Frank, L. A. h Direct detection of the asymmetric injection of extraterrestrial " ring current " protons. Univ. towa, Res. Rep., 69-39; see also Direct detection of the asymmetric increases of extraterrestrial " ring current " protons intensities in the outer radiation zone, J.G.R., 75 (1970), p. 1263. Fraser, BJ. Temporal variations in Pc ! geomagnetic micropulsations, Plan. Space Sci., 16 (1968), p. 111. Fried, B. D. Longitudinal ion oscillations in a hot plasma, Phys. Fluids, 4 (1961), Gould, R. W. p. 139. Frieman, E. Kinetic theory of weakly unstable plasma, Ann. Phys., 28 (1964), Rutherford, P. p. 134. Fritz, T.A. Initial observations of geomagoetically trapped protons and alpha Krimigris, S.M. particles with OGO 4, Univ. of Iowa, Res. Rep., 68-65, 1968. Galperin, Y. I. Auroral protons measured on Cosmos 261 and the resonant concept of Gladyshev, V. A. a substorm, Kosmicheskie Issl, 8 (1970), p. 457. Gurevich, A. V. Kuzmin, A. K. Ponomarev, Y. N. Garrett, L. S. Integrated circuit digital logic families. I. RTL, DTL, HTL devices, IEEE Spectrum (Oct. 1970), p. 46. - II. T2L devices, IEEE Spectrum (Nov. 1970), p. 63. - TJI. ECL and MOS devices, IEEE Spectrum (Dec. 1970), p. 30. Gendrin, R. Pitch angle diffusion of low energy protons due to gyroresonant inter action with hydromagnetic waves, J. Attn. Terr. Phys., 30 (1968), p. 1313. Gendrin, R. Substorm aspects of magnetic pulsations, Space Sci. Rev., II (1970), p. 54. Gendrin, R. a Very low frequency and particle rocket experiment at Kerguelen Islands, Berthomier, C. I. Very low frequency measurements, J.G.R., 75 (1970), p. 6153. Cory, H. Meyer, A. Sukhera, B. Vigneron, J. Gendrin, R. b Very low frequency and particle rocket experiment at Kerguelen Islands, Etcheto, J. II. Particle measurements, J.G.R., 75 (1970), p. 6169. de la Porte de Vaux, B. Gendrin, R. Wave packet propagation in an amplifying medium and its application Lacourly, S. to the dispersion characteristics and to the generation mechanisms of Roux, A. PC 1 events, Planet. Space Sci., 19 (1971), p. 165. Solomon, J. Fcigin, F. Z. Gokhberg, M. V. Troitskaya, V. A. Yakimenko, V. L. Gendrin R. Caractéristiques des pulsations irrégulières de période décroissante Lacourly, S. (IPDP) et leurs relations avec les variations du f ux des particules pié Troitskaya, V.A. gées dans la magnétosphère, Plan. Space Sci., 15 (1967), p. 1239. Gokhberg, M. Shepetnov, R.V. 278 Graff, Ph. Analytical study of oblique echoes at the upper hybrid resonance, J.G.R., 75 (1970), p. 7193. Graff, Ph. General expression of the oblique echoes at the plasma resonance, J.G.R., 76 (1971), p. 1060. Graff, Ph. Study of the oscillations stimulated at the upper hybrid resonance by a pulsed dipole antenna in a weakly inhomogeneous plasma, /. Plasma Phys., to be published (1971). Gruber, S. High frequency velocity space instabilities, Phys. Fluids, 8 (1965), Klein, M.W. p. 1504. Auer, P. L. a Low temperature in the ionosphere obtained from cyclotron damping Gurnett, D.A. of proton whistlers, J.G.R., 71 (1966), p. 3639. b Satellite measurements of dc electric fields in the ionosphere, in Particles Gurnett, D. A. and fields in the magnetosphere, B.M. McCormac éd., Reidel Pub. Co., Dordrecht, 1970. Gurnett, D. A. Ion temperature in the ionosphere obtainec from cyclotron damping Brice, N. M. of proton whistlers, J.G.R., 71 (1966), p. 3639. Gurnett, D. A. The low-frrequency cutoff of ELF emissions, J.G.R., 73 (1968), p. 7437. Burns, T. B. Gurnett, D. A. Ion cyclotron whistlers, J.G.R., 70 (1965), p. 1665. Shawhan, S. D. Brice, N. M. Smith, R. L. Haerendel, G. Electric fieldsan d their effects in the ionosphere, S.T.P. Symp., May 1970, Leningrad. Haerendel, G. On the balance between radial and pitch-angle diffusion, in Particles and fields in the magnetosphere, B.M. McCormac éd., D. Reidel Pub. Co., 1970. Haerendel, G. Diffusion theory of trapped particles and the observed proton distri bution, in Earth's particles and fields,B.M . McCormac éd., Reinhold Book Corp., 1968. Haerendel, G. Electric fields in the ionosphere and magnetosphere, in Particles and Lust, R. fields in the magnetosphere, B.M. McCormac éd., Reidel Pub. Co., Dordrecht, 1970. Hagège, K. Low frequency drift waves in the magnetosphere during substorms, Laval, G. ESRO SP-72, Proceedings of the Colloquium on wave-particle inter Pellat, R. actions in the magnetosphere, Orléans, March 1971. Harp, R.S. Propagation of longitudinal plasma oscillations near cyclotron har monics, Appl. Phys. Lett., 6 (1965), p. 51. Hasegawa, A. Drift mirror instability in the magnetosphere, Phys. Fluids 12 (1969), p. 2642. Hasègawa, A. Heating of the magnetospheric plasma by electromagnetic waves generated in the magnetosheath, /.G.J?., 74 (1969), p. 1763. Heacock, R. R. The relation of the PC 1 micropulsation source region to the plasma- sphere, J.G.R., 76 (1971), p. 100. 279 Hellivell, R. R. a Whistlers and related ionospheric phenomena, Stanford Univ. Press, Calif., 1965. HelliweU. R. A. b A theory of discrete VLF emissions from the magnetosphere, J.G.R., 72 (1967), p. 4773. Helliwell, R. A. c Low frequency waves in the magnetosphere, Rev. Geophys., 7 (1969), p. 281. Hendrickson, R. A. The Electron Echo Experiment : a new magnetospheric probe, Nature, McEntire, R. W. 230 (1971), p. 564. Winckler, J. R. Heppner, J.P. Magnetospheric convection patterns inferred from high-latitude acti vity, in Atmospheric emissions, B.M. McCormac and A. Omholt éd., Van Nostrand Reinhold Co., 1969. Herman, J. R. Spread F and ionospheric F-region irregularities, Rev. Geophys., 4 (1966), p. 255. Herzberg, L. Ionospheric conditions following the proton flare of 7 July 1966, as Nelms, G.L. deduced from topside soundings, Annals of the IQSY, 3 (1969), p. 426; see also The proton-flare project (the My 1966 event), A.C. Stickland éd., MIT Press, 1969. Hess, W. N. The radiation belt and magnetosphere, Blaisdell Pub. Co., 1968, Waltham, Mass. Hoh, F. C. Instability of Penning-type discharges, Phys. Fluids, 6 (1963), p. 1184. Hones, E. W. Jr Magnetotail plasma and magnetospheric substorms, in Particles and fields in the magnetosphere, B.M. McCormac éd., D. Reidel Publ. Co., 1970. Hones, E. W. Electric field generated by a rotating magnetized sphere, J.G.R., 70 Bergeron, J.E. (1965), p. 4951. Hughes, A. R. W. in Radiating atmosphere, B.M. McCormac éd., D. Reidel Pub., Dordrecht, Kaiser, T. R. 1971, p. 328. Hughes, A. R. W. a The morphology of high latitude VLF emissions, in Ionospheric fore BuIIough, K. casting, AGARD Conf. Proc. n° 49 (1970). Kaiser, T. R. Hughes, A. R. W. b Space Research Xi (1971), p. 1323, Akademie Verlag. Kaiser, T. R. BuIIough, K. Hultqvist, B. On the production of a magnetic field aligned electric field by the inter action between the hot magnetospheric plasma and the cold ionosphere over the polar caps, Kiruna Geophys. Observ., Preprint, September 1970. Hultqvist, B. Observations of magnetic field aligned anisotropy for 1 and 6 keV Borg, H. protons in the-upper atmosphere, Kiruna Geophys. Observ., Preprint, Riedler, W. May 1970. Christophersen, P. Ivanov, B. I. et al. Inter. Conf. on Physics of ionized gases, Hercegovi, Yugoslavia, p. 653. 280 Jelly, D. H. The high-latitude ionosphere, Proc. I.E.E.E., 57 (1969), p. 1005. Pétrie, L. E. Johnson, M. C. A secondary standard vacuum ultraviolet detector, Rev. ofSci. Instr., 40 (1969), p. 311. Jones, D. The theory of the effect of collisions on ion-cyclotron whistlers, in Plasma Waves in Space and in the Laboratory (NATO, advanced Study Inst., R^ros, Norway, April 1968), Edin. Univ. Press, 2, p. 471, 1970. Jones, D. Th-, effect of the latitudinal variation of the terrestrial magnetic held strength on ion-cyclotron whistlers, J. Atmasph. Terr. Phys., 31 (1969), p. 971. Jôrgensen, T. S. Interpretation of auroral hiss measured on OGO 2 and at Byrd station in terms of incoherent Cerenkov radiation, J.G.R., 73 (1968), p. 1055- Kadomtsev, B. B. Piasma Turbulence, London, Academic Press, 1965. Kaiser, T. R. Private comr-.'nication. Kaiser, T. R. Mtg for discussion on the polar ionosphere and the magnetosphere. Bullough, K. Royal Soc, 15-16 Dec. 1970, London. Hughes, A. R. W. Karlson, E. T. Streaming of a plasma through a magnetic dipole field, Phys. Fluids, 6 (1963), p. 708. Kennel, C. F. Limit on stably trapped particle fluxes, J.G.R., 71 (1966), p. 1. Petschek, H. E. Kennel, C r. VLF electric field observations in the magnetosphere, J.G.R., 75 (1970), Scarf, F.L. p. 6136. Fredricks, R.W. McGehee, J.H. Coroniti, F.V. Kenney, J.F. Micropulsations and magnetosphere, J.G.R., 73 (1968), p. 6737. Knaflich, H.B. Liemohn. H.B. Kindel, J. M. Auroral electrostatic ion cyclotron wave instability, Amer. Geophys. Kennel, C. F. Union Trans., 50 (1969), p. 291. King, J.H. Model of the trapped radiation environment. Vol. IV. Low-energy protons, NASA SP-3024 (1967). King, H. J. Knauer, W. Hughes Res. Lab. Proposal n° 67M-7521/82975, 1967. Klettke, B. D. Krym, N. D. Sixteenth Nucl. Symposium, IEEE. Wolber, W. G. Knox, F.B. Growth of a packet of finite amplitude very low frequency waves, with a special reference to the magnetosphere, Plan. Space Sci., 17 (1969), p. !3. Kolomenskii, A. A. Resonance effects associated with particle motion in a plane electro Lebedev. A.N. magnetic wave, SOD. Phys. JETP, 17 (1963), p. 179. 281 Koons, H. C. J.G.R., in press (1971). McPherson, D. A. Schulz, M. Laird, M. J. On gyroresonance, J. Plasma Phys., 2 (1967), p. 59. Landau, L. D. J. Phys. U.S.S.R., 10 (1946), p. 25. Lanzerotti, L. J. Drift mirror instability in the magnetosphere : Particle and field Hasegawa, A. oscillations and electron heating, J.G.R., 74 (1969), p. 5565. McClennan, C. G. Laval, G. Interactions between monochromatic waves and particles, ESRO-GRI Pellat, R. Col), on wave-particle interactions in the magnetosphere, Orléans, Roux, A. March 1971. Lemaire, D. Etude expérimentale des interactions ondes-particules. Dépouillement des mesures de particules faites au cours d'une expérience sur fusée tirée des îles Kerguelen, Thèse de 5e cycle, Univ. de Paris, 1971. Leuterer, F. Forward and backward Bernstein mode, Plasma Phys., Il (1969), p. 615. Lezniak, T. W. Experimental study of magnetospheric motions and the acceleration Winckler, J. R. of energetic electrons during substorms, Univ. of Minnesota, Sch. of Phys. and Astron., Cosmic Ray Group Techr.., Rep. CR-149, April 1970; see also J.U.R., 75 (1970), p. 7075. Liemohn, H. B. Cyclotron resonance amplification of VLF and ULF 'vhistlers, J.G.R., 72 (1967), p. 39. Linson, L. M. Current voltage characteristics of an electron-emitting satellite in the ionosphere, J.G.R., 74 (1969), p. 2368. Lucas, C. Irregularities in proton density deduced from cyclotron damping of Brice, N. proton whistlers, J.G.R., 76 (1971), p. 92. Lutomirski, R. F. Exact non linear electromagnetic whistler modes, Phys. Rev., 147 Sudan, R. M. (1966), p. 156. Maynard, N. C. EleCric field observations of ionospheric whistlers, Radio Science, 5 Aggson, T. L. (1970), p. 1049. Heppner. J. P. McAfee, J. R. Ray trajectories in an anisotropic plasma near plasma resonance, J.G.R., 73 (1968), p. 5577. McAfee, J. R. Topside resonances as oblique echoes, J.G.R., 74 (1969), p. 802. McAfee, J. R. Topside ray trajectories near the upper hybrid resonance, J.G.R., 74 (1969), p. 6403. McDiarmid, I. B. Local time asymmetries in the high latitude geometry of the outer Burrows, J. R. radiation zone for the different electron energies, Can. J. Phys., 46 (1968), p. 49. Mcllwain, C. E. Direct measurements of particles producing visible auroras, J.G.R., 65 (1960), p. 2727. Mcllwain, C. E. Comments and speculations concerning the radiation belts, Annals of the IQSY, 4 (1969), p. 302. 282 McPherson, D. A. Dependence of ELF emissions on the location of the plasmapause, Koons, H. C. J.G.R., 75 (1970), p. 5559. Meyer, A. Etude, réalisation et exploitation d'équipements scientifiques destinés à la réception des émissions électromagnétiques naturelles de très basse fréquence et embarqués à bord de trois fusées Dragon tirées aux îles Kerguelen en mars et avril 1968, Thèse de Doctoral, Univ. de Paris, 1969. Mihalov, J.D. Reconnection and noise in the geomagnetic tail, in Cosmic Electro Sonett, C.P. dynamics, 1 (1970), p. 178. Colburn, D.S. Mihalov, J.D. Low-energy proton radiation belts, J.G.H., 71 (1966), ^. 2207. White, R.S. Montgomery, D. Discrete spectra and damped waves in quasi linear theory, J. Plasma Vahala, G. Physics, 4 (1971), p. 677. Morgulis, M. D. Thermalization of electrons in a short arc plasma in cesium vapors, Korchevoi, Yu. P. Eight Intern. Conf. on phenomena t: ionized gases, Vienna, 1967; see Dudko, D.Ya. also Zhurnal Tekhnicheskoi Fisiki, 38 (1968), p. 1065. Morse, D. L. a Low-frequency instability of partially ionized plasma, Phys. Fluids, 8 (1965), p. 1339. Morse, D. L. b Observation of velocity space instability, Plasma Phys., 11 (1969), p. 175. Mozer, F. S. Electric field measurements in the auroral ionosphere, J.G.R., 72 Braston, P. (1967), p. 1109. Mozer, F. S. Rocket measurements of energetic particles. I. Description of the Crifo, J. F. experiment, J.G.R., 70 (1965), p. 5699. Blamont, J. E. Mozer, F. S. Magnetospheric electric field properties deduced from simultaneous Manka, R. N. balloon flights, J.G.R. (1971), in press. Mozer, F. S. Magnetospheric electric field measurements with balloons, J.G.R., 74 Serlin, R. (1969), p. 4739. Muldrew, D. B. F-layer ionization troughs deduced from Alouette data, J.G.R., 70 (1965), p. 2635. Muzzio, J. L. R. Ion cutoff whistlers, J.G.R., 73 (1968), p. 7526. Nishida, A. - Formation of plasmapause or magnetospheric plasma knee by the combined action of magnetospheric convection and plasma escape from the tail, J.G.R., 71 (1966), p. 5669. Northrop, T. G. The adiabatic motion of charged particles, Interscience Publ., New York, 1963. Nunn, D. Non linear wave/particle processes in an electrostatic wave packet, /. Plasma Physics, 5 (1971), p. 199. Nunn, D. A theory of VLF emissions, to be published in Plan. & Space Sc. (1971). O'Brien, B.J. Lifetimes of outer-zone electrons and their precipitation into the atmosphere, J.G.R., 67 (1962), p. 3687. 283 Ossakow, S. L. Anomalous resistivity along lines of force in the magnetosphere, J.G.R., 73 (1968), p. 6366. Parker, E. N. Formation of the geomagnetic storm main phase ring current, J.G.R., 66 (1961), p. 693. Persson, H. Electric field along a magnetic line of force in a low density plasma, Phys. Fluids, 9 (1963), p. 1756, Persson, H. Electric field parallel to the magnetic field in a low density plasma, Phys. Fluids, 9 (1966), p. 1090. Piggott, W. R. The use of satellite data for prediction purposes, Conf. on ionospheric forecasting, Québec, 1969, AGARD Conf. Proc, n° 49, 1970. Pizella, G. Electrons in the van Allen zone measured with a scintillator on Davis, R. L. Explorer XIV, G.S.F.C. Techn. Rep., n° X-611-112, March 1966. Williamson, T. M. Pizella, G. Energy spectrums for proton (200 eV g E S 1 MeV) intensities in the Frank, L.A. outer radiation zone, J.G.R., 76 (1971), p. 88. Pizella, G. Differential energy spectrum of geomagnetically trapped protons with Randall, B.A. the Injun 5 satellite, J.G.R., 76 (1971), p. 2306. Rawer, K. Radio-observations of the ionosphere, in Handbuch der Physik, 49J2, Suchy, K. 1967, Berlin, Springer-Verlag. Reasoner, D. L. Detection of alpha particles in auroral phenomena, J.G.R., 73 (1968), Eather, R. H. p. 4185. O'Brien, B.J. Rème, H. a Répartition angulaire et énergétique des particules de basse énergie dans une aurore diffuse, Thèse de doctorat es Sciences physiques, Univ. de Toulouse, 1969. Renie, H. b Spectral and angular distributions of low energy auroral parade?. IAGA Gen. Scient. Assembly, Madrid, September 1969. Rème, H. Observation de flux de protons de basse énergie parallèles aux lignes de Bosqued, J. M. force du champ géomagnétique dans l'ionosphère aurorale, C.R. Acad. Sciences, 1970, to be published. Rème, H. Characteristics of auroral electrons and protons measured between Cotin, F. 150 and 420 km, S.T.P. Symp., Leningrad, May 1970. Cambou, F. Roberts, C. S. a Electron loss from the van Allen zones due to pitch-angle scattering by electromagnetic disturbances, in Radiation Trapped in the Earth's Magnetic Field, Ed. B.M. McCormac, D. Reidel Pub. Co., Dordrecht, 1966. Roberts, C. S. b Pitch-angle diffusion of electrons in the magnetosphere, Rev. Geophys., (1969), p. 305. Roberts, C. S. Bounce resonant scattering of particles trapped in the Earth's magnetic Schulz, M. field, J.G.R., 73 (1968), p. 7361. Roberts, C. S. Motion of a charged particle in a constant magnetic fieldan d a transverse Buchsbaum, S.J. electromagnetic wave propagating along the field, Phys. Rev., 135 (1964), p. 1381. 284 Rodriguez, P. An experimental study of Very-Low-Frequency mode coupling and Gurnett, D. A. polarisation reversal, J.G.R., 76 (1971), p. 960. Rogister, A. Type IT irregularities in the equatorial electrojet, J.G.R., 75 (1970), d'Angelo, N. p. 3879. Rogister, A. On the kinetic theory of stable and weakly unstable plasma. Part 2, Oberman, C. J. Plasma Phys., 3 (1969), p. 119. Rosenbluth, M.N. Microinstabilities, in Plasma Physics, Vienne, IAEA. 1965. Roulands, J. Quasi linear theory of plasma cyclotron instability, J. Exper. Theor. Shapiro, V. D. Phys., 50 (1966), p. 979 (Sov. Phys. JETP, 50, p. 979). Shevchenko, V. I. Roux, A. Self-consistent solution of the quasi linear theory; application to the Solomon, J. spectral shape and intensity of VLF waves in the magnetosphere, J. Aim. Terr. Phys. (1971), to be published. Russel, C.T. Magnetic fields, in Particles and fields in the magnelosphere, B.M. Holzer, R.E. McCormac éd., D. Reidel Pub. Co., 1970. Russel, C.T. Cosmic Electrodynamics, 1 (1970), p. 67. Thome, R.M. Russel, C.T. a Magnetic fluctuations between 30 and 1 000 Hz within the magneto- Holzer, R. E. sphere (abstract), Trans. Amer. Geophys. Union, 49 (1968), p. 259. Smith, E. J. Russel, C. T. b Magnetic field variation in the near geomagnetic tail associated with McPherron, R. L. weak substorm activity, UCLA Inst, of Geophys. and Plan. Phys.. Coleman, P. I. Jr Preprint n° 886, 1970. Rycroft, M.J. Model hydrogen and helium ions concentrations in the plamasphere, Alexander, P. D. COSPAR, May 1969, Prague, Czechoslovakia. Rycroft, M. J. Statistical analysis of movement", of the ionospheric trough and the Burnell, S.J. plasmapause, J.G.R., 75 (1970), p. 5600. Rycroft, M.J. The magnetospheric plasmapause and the electron density trough at Thomas, J. O. the Alouette 1 orbit, Plan. Space Sci., 18 (1970), p. 65. Sagdeev, R. Z. Intern. Centre far Theoretical Phys., Trieste, Rep. 1C/66/64, 1966. Galeev, A. A. deev, R.Z. Nonlinear plasma theory, T.M. O'Neil and D.L. Book, éd. W.A. Ben Galeev, A. A. jamin Inc., New York, 1969. do, J. L. Longitudinal structure near the plasmapause; VLF goniometer obser Bullough, K. vations of knee-whistlers and the role of spread F in whistler obser vations, Mtg on solar-terrestrial physics, Leningrad, May 1970. Scarf, F. L. Landau damping and attenuation of whistlers, Phys. Fluids, 5 (1962), p. 6. Scarf, F. L. AC Fields and Wave-particle Interactions, in Particles and Fields in Kennel, C. F. the Magnetosphere, Dordrecht (B.M. McCormac, éd.), D. Reidel Ftedricks, R. W. Pub. Co., 1970. Green, I. M. Crook, G. M. 285 Scharer, S. C. Cyclotron wave instabilities in a plasma, Phys. Fluids, 10 (1967), Trivelpiece, A. W. p. 591. Schield, M. A. Drift of non-interacting charged particles in a simple geomagnetic field, Univ. of Iowa, Rep. 69-54, 1969. Schindler, K. Stability of plasma sheaths, Phys. Fluids, 11 (1968), p. 1192. Soop, M. Schmitt, K. C. Continuous channel electron multiplier operated in the pulse saturated Hendee, C. F. mode, IEEE Trans. Nucl. Sci., NS-13 (1966), p. 100. Shapiro, V. D. Quasi linear theory of instability of a plasma with an anisotropic ion Shevchenko, V.I. velocity distribution, J. Exper. Theor. Phys., 45 (1963), p. 1612 (Sov. Phys. JETP, 18, 1964, p. 1109). Sharp. R. D. Satellite measurements of auroral particle precipitation, in Earth's Johnson, R. G. particles and fields, McCormac éd., Reinhold Book Corp., 1968. Shkarofsky, LP. Higher order cyclotron harmonic resonances and their observation in the laboratory and in the ionosphere, J.G.R., 73 (1963), p. 4859. Simon, A. Instability of a partially ionized plasma in crossed electric and magnetic fields, Phys. Fluids, 6 (1963), p. 382. Skadron, G. Nonlinear stabilization of a two-stream plasma instability in the Weinstock, J. ionosphere, J.G.R., 74 (1969), p. 5113. . Smith, R. L. Polarisation of proton whistlers, J.G.R., 75 (1970), p. 7261. Sonnerup, B. U. O. Resonant vibration of the magnetosphere observed from Explorer 26, Cahill, L. J. Ir J.G.R., 74 (1969), p. 2276. Davis, L. R. Speiser. T. W. Some recent results using the Dungey model, in Atmospheric Emissions, B.M. McCormac and A. Omholt éd., Van Nostrand Reinhold Co., New York, 1969. Speiser, T. W. The neutral sheet in the geomagnetic tail : its motion, equivalent Ness, N. F. currents and field line connection through it, J.G.R., 72 (1967), p. 131. Stix, T. H. The theory of plasma waves, New York, McGraw Hill Book Co. (1962, 1968). Storey, L. R. O. An investigation of whistling atmospherics, Phil. Trans. Roy. Soc, 246 A (1953), p. 113. Sugiura, M. A model equatorial electrojet, J.G.R., 71 (1966), p. 1869. Cain, J. C. Sugiura, M. An improved model equatorial electrojet with a meridional current Poros, D.J. system, J.G.J?., 74 (1969), p. 4025. Sukhera, B. Etude de la propagation ionosphérique des émissions TBF (souffle et chœur de l'aube) entre 400 km et le sol. Comparaison avec les résultats obtenus par l'expérience sur fusées Fu 171 effectuée aux Ses Kerguelen, Thèse de 3e cycle, Univ. de Paris, 1970. Swift, D.W. A mechanism for energizing electrons in the magnetosphere, J.G.R., 70 (1965), p. 3061. 286 Tatry, B. Characteristics of electron multipliers used as detectors for low energy Bosqued, J. M. protons, Nucl. Instr. and Melh., 69 (1969), p. 254. Rème, H. Taylor, H. E. Adiabatic motion of auroral particles in a model of the electric and Hones, E. W. Jr magnetic fields surrounding the Earth, J.G.R., 70 (1965), p. 3605. Terry, P. D. Complex ray theory for ion cyclotron whistlers. Nature, 229 (1971), p. 200. Theodoridis, G. C. Pitch angle diffusion of relativistic outer belt electrons, Ann. Géophys., Paolini, F. R. 23 (1967), p. 375. Thomas, J. O. Imperial College, SPT 105-70 (1970). Andrews, M. K. Hall, T. A. Thome, R. M. Quasi trapped VLF propagation in the outer magnetosphere, J.G. R., 12 Kennel, C. F. (1967), p. 857. Tidman, D. A. Scattering of a test particle by enhanced plasma fluctuations, Phys. Eviatar, A. Fluids, 8 (1965), p. 2059. Tidman, D. A. Landau damping on transverse waves in the exosphere by fast particle gi, R. K. fluxes, J.G.R., 67 (1962), p. 2215. Tonks, L. Phys. Rev., 33 (1929), p. 195. Langmuir, C. Torvén, S. Current limitations and electrical gas clean-up in a low pressure mercury discharge, Arkivfar Fysik, 35 (1968), p. 513. Torvén, S. Private communication, 1971. Babic, M. Tsytovioh, V.N. Kiretic equation for elementary excitations and non linear interactions between waves in a plasma, transi, from Russian, Rept NP., 17575. Vasyliunas, V. M. A survey of low energy electrons in the evening sector of the magneto sphere with OGO 1 and OGO 3, J.G.R., 73 (1968), p. 2839. Vedenov, A. A. Quasi linear theory of plasma oscillations, Nucl. Fusion, 2 (1962), Velikhov, E. P. p. 465. Sagdeev, R. Z. Vedenov, A. A. Vspekhi, 4 (1961), p. 332. Velikov, E. P. v, R. Z. Vette, J.t. Summary of particle population in the magnetosphere, in Particles and fields in the magnetosphere, B.M. McCormac éd., D. Reidel Pub. Co., 1970. Walt, M. Radial diffusion of trapped particles and some of its consequences, Rev. Geophys. and Space Physics, 9 (1971), p. 11. Wang, T. Intennode coupling at ion whistler frequencies in a stratified collisionless ionosphere, J.G.R., 76 (1971), p. 947. 287 Warnock, J. M. Electron temperature from topside pi;-ma resonance observations, McAfee, J. R. J.G.R., 75 (1970), p. 7272. Thompson, T. L. Watts, J. M. Direction finding on whistlers, J.G.R., 64 (1959), p. 2029. Weinstock, J. Formulation of a statistical theory of strong plasma turbulence, Phys, Fluids, 12 (1969), p. 1045. Wescott, E. M. Electric fields in the vicinity of auroral forms from motions of barium Stolarik, J. D. vapor releases, J.G.R., 74 (1969), p. 3469. Heppner, J. P. Westerlund, L. H. The auroral electron energy spectrum extended to 45 eV, J.G.R., 74 (1969), p. 351. White, R.S. The time dependence of the low-energy proton belts, J.G.R., 72 (1967) p. 943. Williams, D. J. Nightside magnetosphere configuration as obtained from trapped Mead, G. D. electrons at 1100 km, J.G.R., 70 (1965), p. 3017. Woolley, M. L. Particle orbits in a constant magnetic field and transverse electro magnetic wave. Plasma Phys., 12 (1970), p. 779. Zalesskii, Ju. G. Resonant electron heating mechanism in a beam plasma discharge, Nazarov, N. I. Sou. Phys. Techn. Phys., 15 (1970), p. 715. Zmuda, A. J. Transverse magnetic disturbances at I 100 km in the auroral arc, Martin, J. N. J.G.R., 71 (1966), p. 5033. Heuring, F. T. Zmuda, A.J. Dayside magnetic disturbances at 1 100 km in the auroral oval, J.G.R., Heuring, F. T. 72(1967), p. 1115. Martin, J. H. UNION PARISIENNE D'IMPRIMERIES. 13. rue Yvei-Toudic. PARIS «•)