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Electrodynamics of the Auroral E region

Sheila Kirkwood

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KIRUfMA ELECTRODYNAMICS OF THE AURORAL E REGION

Akademisk avhandling som med vederbörligt tillstånd av rektorsämbetet vid Umeå universitet för avläggande av filosofie doktorsexamen kommer att offentligen försvaras vid Institutet för rymdfysik i , konferensrummet Aniara, fredagen den 19 oktober 1990, kl 1015. av

Sheila Kirkwood BSc, PhD

The thesis includes the following papers:

I. Kirkwood, S., Coliis, P.N., Schmidt, W., Calibration of electron densities for the EISCAT UHF , J. Atmos. Terr. Phys. 48, 773-775, 1986

II. Kirkwood, S., Seasonal and tidal observations of neutral temperatures and densities in the high-latitude lower thermosphcre, J. Atmos. Terr. Phys. 48,817-826,1986

III. Kirkwood, S., Opgenoorth, H., Murphree, J.S., Ionospheric conductivities, electric fields and currents associated with auroral substorms measured by the EISCAT radar, Planet. Space Sci. 36, 1359-1380,1988

IV. Kirkwood, S., Eliasson, L., Energetic particle precipitation in the substorm growth phase measured by EISCAT and Viking, J. Geophys. Res. 95,6025-6037, 1990

V. Kirkwood, S., Co'lis, P.N., Gravity-wave generation of simultaneous sporadic-E layers and sudden neutral sodium layers, J. Atmos. Terr. Phys. 51, 259-269, 1989

VI. Kirkwood, S., von Zahn, U., On the role of auroral electric fields in the formation of low-altitude sporadic-E and sudden sodium layers, J. Atmos. Terr. Phys., submitted May 1990

Kiruna 1990 Electrodynamics of the Auroral E region

by

Sheila Kirkwood

Swedish Institute of Space Physics Box 812, S-981 28 Kiruna, Sweden

IRF Scientific Report 205 October 1990

Printed in Sweden Swedish Institute of Space Physics Kiruna 1990 ISSN 0284-1703 ISBN 91-7174-530-0 Abstract

The is the visible signature of an electrical current system which stretches from close to the 's surface far out into space. That current system has its ultimate source in the , through the magnetised plasma of the solar which spreads outwards from the Sun and distorts the Earth's magnetosph<»re as it travels past. The details of the interaction between the and the Earth's and atmosphere are incompletely understood and studying the aurora is one way in which we may be able to increase our understanding.

This study concentrates on the signatures of the interaction process seen closest to the Earth • i.e. in the region where the visible aurora is produced. A number of experimental investigations are presented which look at details of the dynamics and electrodynamics of auroral ionisation features in the ionospheric E region. The studies are based primarily on measurements with the EISCAT UHF incoherent scatter radar which is located in northern .

Initial calibration of the radar, and some measurements of the properties of the background atmosphere are described first. These are a neccessary basis for the detailed studies which follow, which are of two aspects of auroral electrodynamics - substorms and aurorally-associated sporadic E layers.

For the substorm studies, all-sky camera observations of the aurora over Scandinavia and ultra-violet images from the Viking satellite are used to identify the auroral forms corresponding to EISCAT measurements. This allows the determination of representative conductivities for the different auroral features which are characteristic of the substorm development. These conductivities are an important input for modelling studies of the electric current systems and have not previously been measured directly. Particle measurements from the Viking satellite are used together with EISCAT to determine the origin of the particles precipitated into the during the energy-storage phase prior to the substorm. It is found that high-energy particles are precipitated from the outer edge of the trapped-particle belts and that pre-onset auroral arcs occur very close to the trapping boundary. This suggests that the process which triggers the onset, often seen as a break-up of a pre- onset arc, also occurs close to the trapping boundary. The sporadic E studies address the question of how ion layers and associated neutral sodium layers can be produced by some process which is common in association with auroral activity. Two candidates are considered - gravity waves and electric fields. One case, of very weak ion and neutral layers, seems to be explicable by gravity wave action. Several more cases, where the layers are more intense, seem to be due primarily to electric field action. The layers are seen when an electric field directed between westward and south-eastward drives ions downward through the E region. In some cases the observed layers can be explained by the electric field alone. In others, some extra compressive effect is needed, such as a small upward wind, to explain the narrowness of the layers. Since neutral atoms cannot be layered directly by electric fields, the neutral sodium layers must be a secondary product of the ion layers.

Keywords : incoherent scatter, ionosphere, aurora, substorm, conductivity, electric field, neutral wind, tides, sporadic-E, sodium layer Contents

Introduction and summary of the

1. Introduction page 4 2. Summary of papers I-VI page 7 3. Acknowledgements page 12 4. References page 13

Papers

I. Kirkwood, S., Collis, P.N., Schmidt, W., Calibration of electron densities for the EISCAT UHF radar, J. Atmos. Terr. Phys. 48, 773-775. 1986

II. Kirkwood, S., Seasonal and tidal observations of neutral temperatures and densities in the high-latitude lower thermosphere, J. Atmos. Terr. Phys. 48, 817-826, 1986

III. Kirkwood, S., Opgenoorth, H., Murphree, J.S., Ionospheric conductivities, electric fields and currents associated with auroral substorms measured by the EISCAT radar, Planet. Space Sci. 36, 1359-1380, 1988

IV. Kirkwood, S., Eliasson, L, Energetic particle precipitation in the substorm growth phase measured by EISCAT and Viking, J. Geophys. Res. 95, 6025-6037, 1990

V. Kirkwood, S., Collis, P.N., Gravity-wave generation of simultaneous sporadic-E layers and sudden neutral sodium layers, J. Atmos. Terr. Phys. 51, 259-269, 1989

VI. Kirkwood, S., von Zahn, U., On the role of auroral electric fields in the formation of low-altitude sporadic-E and sudden sodium layers, J. Atmos. Terr. Phys., submitted May 1990 1. Introduction

The scientific study of the electrodynamics of the aurora began in the 18th century when the first observations were made of a correlation between deflections of a compass needle and the appearance of aurora (Hiorter, 1747), although the reason for the correlation was not then understood. It was not until the next century that Örsted discovered that electric currents had magnetic fields associated with them (örsted, 1820) and made the suggestion that such currents might be responsible for the magnetic fluctuations associated with the aurora . Seventy years later an "electrodynamic" theory of the aurora was proposed by Birkeland, which included basic concepts which have been found to be largely correct (Birkeland, 1908). Birkeland proposed that charged particles streaming out from the sun were caught by the Earth's magnetic field and directed towards the regions, flowing down the magnetic field lines until they were stopped by the atmosphere. He thought that the particles must heat the air as they were slowed down, causing the air to glow. After careful study of the magnetic variations associated with the aurora, Birkeland further proposed that the particles ceased their field-aligned flow and moved alor.j the auroral arcs in the atmosphere.

It was not until the experimental evidence that the upper atmosphere was ionized became available some years later (Appleton and Barnett, 1925) that it became clear that the horizontal currents could be carried by the ionized atmosphere rather than by the same particles as produced the aurora. Much more recently, since the advent of the space age, rocket measurements of the energies of the particles responsible for producing the aurora (e.g. Mcllwain, 1960) and spacecraft measurements of particles in the solar wind (i.e. the particles coming from the sun)(e.g. Hundhausen, 1968) have become available. These have shewn that the particles causing the aurora could not come directly from the sun. Instead, they are accelerated to high energies within the Earth's magnetosphere by forces which result from the interaction of the solar wind with the Earth's magnetosphere (e.g. Akasofu, 1981 and other papers in the same volume). However, Birkelands basic concept of linked field-aligned and horizontal currents has been proved correct. Although the auroral generation mechanism is now understood in outline, there are many aspects which as yet have no satisfactory explanation. These include the mechanism(s) for field-aligned acceleration of the particles, the details of auroral dynamics (the form and motion of auroral displays) and the triggering mechanism(s) for the onset of substorms. In each of these areas it should be possible to make some contribution towards reaching an understanding by making detailed measurements of the conditions in and around the auroral forms in the atmosphere.

Until the 1970s the only method available to make such measurements was by sounding rocket. The sporadic nature of such measurements, and the difficulties of timing a launch to catch a particular auroral feature were a severe "limitation. In the 1970s and 1980s two types of radar became available which offered the possibility of continuous monitoring of conditions in the ionosphere in the auroral region. The first type of radar, HF backscatter, uses coherent echoes scattered from electron density irregularities in the 100-120 km height region to map the electric field (Greenwald, 1978). Considerable progress was made using such radar measurements together with ground-based magnetometer arrays in making realistic models of the 3- dimensional current systems associated with some large-scale auroral features (e.g. Opgenoorth et al., 1983). The method, however, was limited by a lack of knowledge of the conductivities and neutral winds and the failure of the coherent radar to detect low electric fields (below 15 mV/m).

In 1971 the first incoherent scatter radar in the auroral zone came into operation, at Chatanika in Alaska. In principle, an incoherent scatter radar can measure height profiles of electron densities (and hence conductivities), and electron and ion temperatures continuously. By scanning the direction of the beam or by using multiple receivers, it can also measure ion drifts and electric fields. In some cases neutral densities (height region 90 - 120 km) and ion composition (e.g. proportion of Fe+ ions in sporadic E layers, ratio of O+/ (NO+,O2+), ratio of H+/O+) can also be estimated. The Chatanika radar was used to make initial studies of the neutral winds, electric fields and conductivities in the auroral region (Brekke et a!., 1973, 1974). However, the rather coarse altitude resolution available (several 10s of km) and the long time-scales needed to make the measurements (several minutes) limited their usefulness as regards studies of auroral electrodynamics. The early studies from Chatanika have been superseded by results from the EISCAT radar, which is situated in northern Scandinavia and started operation in 1981. Whereas the Chatanika radar was monostatic (requiring scanning of the beam to measure electric fields and winds), the EISCAT UHF radar is tri-static, allowing continuous electric field measurements. Further, the altitude resolution available with the EISCAT radar is much better - 2-3 km for typical auroral measurements and as little as 300 m in special cases. The more sophisticated signal-processing system of the EISCAT system has also allowed much more flexibility in the measurements and a greatly improved statistical accuracy.

A number of papers have been published using EISCAT measurements to catalogue the general features of the electric field (e.g. Senior ot al., 1990), neutral winds, (Kirkwood ,1986, Virdi et al., 1986) and conductivities (Brekke and Hall, 1988) in the auroral zone. These provide valuable background information for more detailed studies of aurora-related electrodynamic effects.

The papers summarized below represent studies gathering first some important background information and then some more detailed measurements of the dynamics and electrodynamics of substorms as seen in the ionospheric E region and of aurorally-associated sporadic-E layers. The papers are primarily concerned with measurements in the region between 80 - 140 km altitude, where the auroral particles typically deposit most of their energy. The measurements are of plasma densities and conductances, neutral winds and electric fields and have been made using the EISCAT UHF radar. They are complemented by other ground-based observations (from all-sky cameras, magnetometers and riometers) and by observations from space (auroral images and energetic particle spectra from the Viking satellite), when appropriate. 2. Summary of papers.

Paper I describes the calibration of the EISCAT UHF radar. Since electrical conductivities are directly proportional to electron densities it is important that these be measured accurately, and that we know how large any experimental uncertainties might be. The paper is very short, but describes only the final result of a long process of technical adjustments and corrections made in cooperation with the programming and technical staff at the radar site.

Although it is possible, in principle, to make absolute measurements of electron density using an incoherent scatter radar (by Faraday rotation or by plasma-line measurements) this is not technically practical for routine operations. The electron density must instead be calculated from the proportion of the transmitted power which is returned to the receiver from the scattering volume in question. Both the transmitted and received powers are difficult to measure directly - the one being very large (1-2 MW) and the other very small ( 1015 - 10"20 W). In practice, both are measured in relative terms. The latter is compared to an electronically produced noise signal, whose stability must be ensured. The transmitter power was initially monitored by sensors in the output waveguide but comparisons of the derived electron densities for different transmitter duty-cycles revealed problematic threshold effects. Finally, a method of calculating the relative transmitted power from instantaneous measurements of the high-voltage applied to the transmitter klystron was found to give the most consistent results - i.e. the derived electron densities were no longer dependent on the level of power transmitted nor on the duty cycle. There remained the absolute calibration of the electron densities which could only be achieved by comparison with absolute measurements. A first estimate of the calibration factor (the "system constant") was made by comparison between simultaneous ion-fine and plasma-line observations (Björnå and Kirkwood, 1986) and Paper I demonstrates further confirmation of this value by comparison with ionograms.

In practice, changes to the system (e.g. adjustments, aging or exchange of the transmitter klystron, changes to the noise injection, changes in the antenna feed system ) will result in a change in the system constant so that the value given in the 8 paper can only be considered reliable for the years 1984-1986, during which time the system remained stable. At other times the calibration must be checked by comparing with ionograms, or in critical cases, simultaneous plasma-line observations must be made.

Paper II uses a year of measurements from the radar to study the characteristics of the neutral atmosphere between 90 and 120 km altitude. There are two aspects to the paper, the first being a comparison of the average temperatures and neutral densities with model values and the second being tno demonstration of considerable variability including strong tidal effects, particularly the semidiurnal tide in the neutral wind. Global models of the neutral atmosphere have been based mainly on measurements at low and middle latitudes. Model neutral density values are used in the analysis of the incoherent scatter data and in calculating conductivities and it is therefore important to compare the models with high-latitude measurements to assess their accuracy. As the paper demonstrates, two of the most widely used models (CIRA72 , MSIS83) are fairly accurate, leading to underestimates of average collision frequencies by only 30-50 % in the 90-105 km height interval. A newer version of the MSIS model (MSIS86, Hedin 1987), which has become available since Paper II was published, gives slightly higher neutral densities (5-10% higher between 90-105 km altitude) and thus fits the observations a little better. Collision frequencies have been obtained for slightly higher altitudes by Huuskonen et al., (1989 ) (up to 110 km) and Nygren et al. (1987, 1989) { up to 120 km ) where reasonable agreement with the models has also been found. For calculating conductivities the MSIS models would therefore seem to be adequate, provided the possibility of systematic (and variable) differences from the real values is not forgotten. For use in incoherent-scatter analysis (i.e. for deriving temperatures in the lower E-region) the models are not sufficiently accurate and a more realistic, empirical model is proposed in the paper, based on the observations.

The tidal winds examined in the paper are of interest in the context of auroral electrodynamics since they are surprisingly strong, much stronger than observed at lower latitudes or as predicted by models. The meridional wind was found to reach more than 100 m/s just above 100 km altitude. It has generally been assumed in the past that winds are too small to make any significant contribution to the electric currents. However, these observations, later supported by others at EISCAT (Virdi et al..1986) and by the Chats nika radar in Alaska (Johnson et al., 1987) indicate that strong winds at just those heights where they can easily drive electrical currents are the rule, rather than the exception at high-latitudes.

Papers III and IV are concerned with auroral substorms. Although the aurora is generally very variable, a particular sequence of events involving the appearance, movement and expansion of auroral s has been observed to occur frequently and has been named the auroral substorm Akasofu, 1964). The substorm is thought to be the signature of a release of energy which has been stored in the magnetosphere by interaction with the solar wind. On the larger scale, there is still considerable controversy over where in the magnetosphere the substorm starts, and the mechanism by which it is triggered is not known. On the smaller scale, the substorm includes some of the brightest and most dynamic auroral forms observed (e.g. the westward travelling surge and omega bands ), which are also ill-understood.

Paper III presents, first and foremost, detailed measurements of the conductivities which occur in the various auroral forms appearing at the substorm onset. These are a necessary input for modelling studies of the electric-current systems. The values found in the study are in some cases several times higher than previously assumed in the models. The paper also finds indications that the electric field can be very low in the most intense arcs (with the highest conductivities) so that the neutral wind might be the primary agent driving currents there. There are also indications that the strong electric fields observed prior to the substorm onset, which are a signature of the energy-storage process, disappear at varying times (2-20 minutes) before the onset. This rather supports the idea that the substorm trigger is a random event rather than an instability which is produced whenever the energy-storage rate exceeds some threshold.

Paper IV addresses the question of the origin ( within the magnetosphere * of the various particle populations which are precipitated during the energ, torage (growth) phase of the substorm and at the onset. A distinctive pattern of energetic particle precipitation during the growth phase was identified several years ago using riometers and balloon-borne X-ray detectors. The electron density profiles measured by the EISCAT radar allow the identification of the particles as a distinct, high-energy population. A comparison with simultaneous particle measurements from the Viking 10 satellite , which passed over Scandinavia at about 7000 km altitude during two of the observed growth-phases, shows that the high-energy population comes from the outer edge of the radiation belts (the zones of trapped particles). Comparison of the EISCAT observations with optical (all-sky camera) recordings of the aurora shows that pre- onset arcs occur immediately poleward of the zone of high-energy precipitation, i.e. immediately outside the trapping boundary. Since the initial brightening which signals the onset of the substorm often occurs on a pre-onset arc, it seems that the onset may also occur very close to the trapping boundary. Since this boundary is found at a distance of about 6-7 Rg towards the magnetotail, the result is rather in disagreement with many models of substorm triggering which suggest that the onset is initiated beyond 10 RE in the magnetotail (e.g. Russel and McPherron, 1973 ) or at even greater distances in the plasma-sheet boundary layer ( Rostoker and Eastman, 1987). However, the result in paper IV is supported by some other recent observations, notably those of Roux (1985) and Lopez et al. (1989), who have found evidence from measurements made by satellites that the onset is initiated closer to the Earth than 10 Re- Papers V and VI address the question of how narrow layers of ions and atoms can be formed in association with auroral events. Narrow ion layers (sporadic E) are not uncommon in the ionosphere. They have been much studied at low and mid-latitudes by ionograms and by rockets and it is generally accepted that they are there formed by the gathering of long-lived metallic ions into a thin layer by a shear in the horizontal neutral winds. Some of the thin layers observed at high latitudes seem to be able to be explained by the same mechanism - i.e. the slowly-descending layers commonly appearing on summer afternoons above 110 km altitude (e.g. Rathbone and Johnson, 1985). However, another group of sporadic E layers, which appear primarily at lower altitudes in the evening and early morning hours at auroral latitudes cannot be so easily explained.The high frequency of collisions between ions and neutrals at the lower altitudes and the high inclination of the magnetic field at high latitudes make the wind-shear mechanism extremely ineffective there. A further question has arisen recently, with the observation of thin layers of neutral sodium, apparently coincident with the ion layers ( von Zahn and Hansen, 1988 ), as to how both might be layered simultaneously.

Paper V presents observations of ion layers made with EISCAT at the same time as a 11 neutral sodium layer was observed close to the radar site. The ion layer seen during the time sodium observations were made was very weak and appeared to vary in step with a strong gravity-wave which was also observed with the radar. The horizontal winds and electric fields measured by the radar were not then in the correct direction or of sufficient strength to cause the layering. The paper uses computer simulations to examine the possibility that both neutral and ion layers could be formed by the gravity wave. It seems that this is possible, in the case of the weak layers observed on this occasion, provided that there is a source of metallic ions and atoms above the altitude that the layer forms (e.g. from meteorite ablation). However, unreasonably large gravity-wave amplitudes would be required to explain the more intense sporadic-E and neutral sodium layers which are observed on many other occasions.

Paper VI presents measurements of several more, low-altitude, sporadic E layers, including one where a simultaneous neutral sodium layer was observed. In these cases, the possibility that the ions are compressed into thin layers by electric field action is examined. Computer simulations of layer formation are made using the observed electric field values, and are found to fit the observations rather well, although some extra compressive effect from, for instance, small upward winds is needed to explain the thinness of the layers in some cases. As regards the neutral sodium layers, these cannot be formed directly by electric field action so that it seems likely that they are a secondary result of the formation of the ion layer. Paper VI goes on to discuss how the sodium might be released from atmospheric dust particles within the sporadic E layer. 12

3. Acknowledgments

I would like to thank the many colleagues with whom I have worked - the staff of EISCAT, particularly those at the Tromsö site, for their efforts in making the radar work the way I wanted it to and the staff of IRF in Kiruna for their help in preparing manuscripts, keeping the computer running and discussing the science. I would also like to thank the Swedish Naturvetenskapliga Forskningsråd for paying my salary and Prof. Bengt Hultqvist at IRF for arranging that I could devote 4 years entirely to research.

Most of all I would like to thank my two sons, Robert and Michael, for taking care of themselves when I was too busy. 13

4. References

Akasofu, S.I., The development of the auroral substorm, Planet. Space Sci. 12, 273- 282, 1964 Akasofu, S-l., Auroral arcs and auroral potential structure, in : ' The Physics of Auroral Arc formation, eds. S.-l. Akasofu and J.R. Kan, AGU Washington, 1981 Appleton, E.V., Barnett, M.A.F., Local reflections of wireless waves from the upper atmosphere, Nature 115, 333-334, 1925 Birkeland, Kr. , The Norweigan Aurora Polaris Expedition, 1902-1903. On the cause of magnetic storms and the origin of terrestrial magnetism, H. Aschenhoug & Co., Chrisiania , 1908 Bjömå, N., Kirkwood, S., Observations of natural plasma-lines in the E region and lower F region with the EISCAT UHF radar, Ann. Geophys. 4, 137-144, 1986 Brekke, A., Doupnik, J.R., Banks, P.M., A preliminary study of the neutral wind in the auroral E-region, J. Geophys. Res. 78, 8235-8250, 1973 Brekke, A., Doupnik, J.R., Banks, P.M., Incoherent scatter measurements of E region conductivities and currents in the auroral zone, J. Geophys. Res. 79, 3773- 3790, 1974 Brekke, A., Hall, C, Auroral ionosphere quiet summer time conductances, Ann. Geophys. 6, 361-376, 1988 Greenwald, R.A., Weiss, W., Nielsen, E., Thomson, N.R., STARE: A new radar auroral backscatter experiment in northern Scandinavia, Radio Sci. 13, 1021-1039, 1978 Hedin, A.E., MSIS-86 thermospheric model, J. Geophys. Res. 92, 4649-4662, 1987 Hiorter, O.P., Om magnet-nålens åtskillige ändringar, som af framledne Professoren Herr And. Celsius bifvit i akt tagne och sedan vidare observerade, samt nu framgivne, Kungl. Sv. Vetensk. Akad. Handl. 8, 27-43, 1747 Hundhausen, A.J., Direct observations of solar wind particles, Space Sci. Rev. 8, 690-749, 1968 Huuskonen, A., High resolution observations of the collision frequency and temperatures with the EISCAT radar, Planet. Space Sci. 37, 211-221, 1989 Johnson, R.M., Wickwar, V.B., Roble, R.G., Luhmann, J.G., Lower-thermospheric winds at high latitude - Chatanika radar observations, Ann. Geophys. 5, 383- 404, 1987 K

Kirkwood, S., Seasonal and tidal variations of neutral temperatures and densities in the high-latitude lower ionosphere measured by EISCAT, J. Atmos. Terr. Phys. 48, 817-826, 1986 Lopez, R.E., Lui, A.T.Y., Sibeck, D.G., Takahashi, K.. McEntire, R.W., Zanetti, L.J., Krimigis, S.M., On the relationship between the energetic particle flux morphology and the change in the magnetic field magnitude during substorms, J. Geophys. Res. 94, 17105-17119, 1989 Mcllwain, C.E., Direct measurements of particles producing visible aurora, J. Geophys. Res. 65, 2727-2747, 1960 Nygren, T., Jalonen, L, Huuskonen, A., A new method of measuring the ion-neutral collision frequency using incoherent-scatter radar, Planet. Space Sci. 35, 337- 343, 1987 Nygren, T., Lanchester, B.S., Jalonen, L, Huuskonen, A., A method for determining ion-neutral collision frequency using radar measurements of ion velocity in two directions, Planet. Space Sci. 37, 493-502, 1989 Opgenoorth, H.J., Pellinen, R., Baumjohann, W., Nielsen, E., Marklund, G., Eliasson, L, Three-dimensional current flow and particle precipitation in a westward travelling surge, J. Geophys. Res. 88, 3138-3152, 1983

Rathbone, A.J., Johnson, J.F.E. , EISCAT observations of a sequential Es layer, J. Atmos. Terr. Phys. 74, 1071-1074, 1985 Rostoker, G., Eastman, T.E., A boundary layer model for magnetospheric substorms, J. Geophys. Res. 92, 12187-12202, 1987 Roux, A., Generation of field-aligned current structures at substorm onset, Proc. ESA Workshop ESA SP-235, 151-159, 1985 Russel, C.T., McPherron, R.L., The magnetotail and substorms, Space Sci. Rev. 15, 205-266, 1973 Virdi, T.S., Jones, G.O.L, Williams, P.S.J., EISCAT observations of the E-region semidiurnal tide, Nature 324, 334-336, 1986 von Zahn, U., Hansen, T.L., Sudden sodium layers : a strong link to sporadic E layers, J. Atmos. Terr. Phys. 50, 93-104, 1988 Örsted, H.C., Naturvidenskaplige Skrifter, 2, 214, Copenhagen, 1820