BRIAN J. ANDERSON
ULTRA-LOW-FREQUENCY MAGNETIC PULSATIONS IN THE EARTH'S MAGNETOSPHERE
Regular magnetic field oscillations in the Earth's magnetosphere occur continuously and are one way solar wind energy is deposited in the ionosphere. Recent determinations of the occurrence distributions of these oscillations imply that pulsations are coupled to solar wind energy by several mechanisms and may be a more significant energy source for the sub-auroral ionosphere than previously thought.
INTRODUCTION The vast majority of satellite data comes from geosta Although we usually regard the magnetic field meas tionary or near-geostationary spacecraft, so that the region ured on the Earth as constant, many geomagnetic process of space most heavily sampled in the magnetosphere cor es introduce perturbations in the field. Auroral activity responds to a narrow annulus in the equatorial plane. Be and the associated ionospheric current systems produce cause of the small volume that spacecraft have sampled significant magnetic disturbances often as large as 1000 to date, it is not well known to what extent pulsations near nanoteslas (nT) , or about one-sixtieth of the Earth' s field geosynchronous orbit are representative of pulsations oc strength at the ground. * Other fluctuations also occur; curring in other regions of the magnetosphere. Hence, although these are smaller (typically:::::: 10 nT) , they are although various pulsation mechanisms have been iden distinguished by their remarkable regularity. These regu tified, and considerable progress in confirming theories lar fluctuations are called geomagnetic pulsations and ap of magnetic pulsations has been made, numerous ques pear as nearly sinusoidal waveforms in ground-station tions about the relationships between pulsations and mag magnetometer records with periods ranging from 0.5 s netospheric dynamics and energy transport remain to be to 10 min. ' adequately addressed. As with the auroral currents, geomagnetic pulsations originate in magnetospheric processes. They occur at all Unique Role of the AMPTE/CCE Satellite local times and under a variety of circumstances. Space The Active Magnetospheric Particle Tracer Explorers/ craft observations have shown that these pulsations, Charge Composition Explorer (AMPTE/CCE) satellite has despite their small amplitude on the ground, have ampli several features that make it useful for pulsation studies. tudes in space relative to the local magnetic field of 5 % A primary factor is the satellite's elliptical orbit with a to 10 % and occasionally much larger, up to about 50%. maximum altitude of 7.8 RE (8.8 RE apogee, 1 RE = By studying geomagnetic pulsations, a detailed compari 6380 km, where RE denotes Earth radii) and low geo son can be made between plasma physics theory and ob graphic inclination (5°), which provide ± 16 ° magnetic servations in ways not possible in laboratory experiments. latitude (MLA T) coverage.7 Equally important is the In addition, geomagnetic pulsations playa role in mag quantity of data available. The satellite functioned from netospheric dynamics and energy transport, and their August 1984 to January 1989, during which time excel study forms an integral part of increasing our understand lent data coverage (90 %) was achieved. The CCE data ing of the magnetosphere. therefore provide extensive sampling of a sizable volume Importance of Spacecraft Observations of the magnetosphere. In addition, the Magnetic Fields Experiment on the CCE spacecraft, performed by APL, was Space-based instrumentation has provided the greatest a sophisticated design with seven automatically switcha insight into pulsations. By measuring the in situ magnetic ble ranges providing 0.01 % resolution of fields from 16 field perturbations, the polarization characteristics and fre to 65 ,535 nT full scale. The sampling rate was 8.06 vec quency structure of pulsations have been determined un tor samples per second, so that the maximum detectable ambiguously. Electric field and particle instruments have frequency was 4.03 Hz, providing excellent frequency also been used to test pulsation theories in ways not pos 8 2 coverage. Fortuitously, computational power has re sible with ground observations. ,3 Multi-spacecraft and cently become more economical, allowing sophisticated satellite-ground correlation studies have been performed data processing to be performed on a routine basis that to study the spatial distribution and propagation charac 4 6 was not possible previously. This combination of teristics of pulsations. - As a result of the extensive factors-satellite orbit and data coverage, sophisticated analysis of satellite data, the primary pulsation mechan magnetic field instrumentation, and the development of isms have been identified. relatively inexpensive computational resources-allows a *The nominal value of the Earth's field near the poles is 60,000 nT; significant advance in magnetic pulsation studies based 1 nT = 10 - 5 gau ss. on the AMPTE/CCE data set.
Johns Hopkins APL Technical Digest, Volume 11 , Numbers 3 and 4 (1990) 239 B. 1. Anderson
The first analysis of AMPTE/CCE magnetic field data spe forces that are screened with a length scale called the cifically directed to pulsation studies was undertaken by Debye length.) Even though the particles do not collide, Mark J. Engebretson of Augsburg College in Minneapo their motions are complex and are not straight-line trajec lis, Minnesota, in collaboration with Thomas Potemra and tories. Because the particles have a charge q, they ex Lawrence Zanetti, both of APL.9 The first results clearly perience a force F = q(E + v x B), called the Lorentz showed that the AMPTE/CCE data would make a significant force, which is due to electric and magnetic fields , E and contribution, and the studies done subsequently by B, respectively. Via this force, the magnetic field con Engebretson and also by Kazue Takahashi of APL showed strains the particles to move along the magnetic field lines that a variety of pulsations was observed by AMPTEI and to gyrate around the field lines, electrons in the right CCE. IO. II Subsequent statistical studies conducted by the hand sense and ions in the left-hand sense. This perpen author in collaboration with Engebretson, Potemra, dicular circular motion occurs with the angular frequency Zanetti, and Takahashi were done to determine the Oc = qBlm and a radius rc = lJ... mlqB, where m is the occurrence distributions of pulsations in the mag particle mass and Vl. is its velocity perpendicular to B. netosphere. The results of these studies provide consider Because of the particle's charge, the circular motion able insight into the role of pulsations in magnetospheric produces a magnetic moment Il = - mv}B/2B2. Since processes and will be discussed later after introducing the Il is directed opposite to B, the plasma is a diamagnetic physics of the relevant wave phenomena in the mag medium. netosphere. Influence of the Plasma WAVES IN THE MAGNETOSPHERE The plasma also exhibits collective behavior because Before discussing the CCE observations, it is useful to the ions and electrons not only respond to electric and sketch the characteristics of the plasma medium that de magnetic fields , but they also participate in their genera termine what waves are supported in the magnetosphere. tion. Minute charge imbalances generate electric fields The waves occurring in the 0.5-s to 10-min period range and relative motion of the electrons, and ions generate are of two basic types: (I) standing wave resonances and currents and hence magnetic fields. The particles, in turn, (2) plasma instabilities. Magnetospheric standing waves react to these fields according to the Lorentz force, so are analogous to standing waves on a string (shear waves) that the large-scale fields feed back on the motions that or in an organ pipe (longitudinal sound waves) and result caused them. This interplay of particle motions and elec from the interplay of the geometry of the Earth's magnetic tromagnetic fields is given analytically by Maxwell's field and waves supported by the plasma medium. The equations: V·E = p, V·B = 0, V x E = -aB/at, and standing waves observed are those whose frequency and V x B = 1l0(J + EoaE/ at) where p is the charge den spatial structure most nearly match those of the driving sity; t is time; J is the current density; and Ilo and EO are source(s). Plasma instabilities result from the interaction the permeability and permittivity of free space, respec of charged particle distributions with electromagnetic tively. fields, and their occurrence is determined principally by In the treatment of linear plasma waves, the field per the characteristics of the magnetospheric particle distri turbations are transformed by letting the field quantities butions. vary as exp[i(k.r - wt)], where k is the wave vector, r is the position vector, w is the angular frequency, and The Magnetospheric Medium i = .J=T, to solve the problem for particular k and w. An appreciation of the variety of waves supported in With this transform and by using the Lorentz force, the the Earth's magnetosphere is afforded by a comparison particle motions can be computed, and the plasma's with sound waves. In air, the only wave mode supported response to the electromagnetic field can be written in consists of disturbances of alternating regions of compres terms of a conductivity matrix a, so that the current den sion and rarefaction. The disturbances propagate in the sity J is given by J = a·E. By using Maxwell's equa direction of the pressure variations with a uniform speed tions, an expression involving only the electric field can called the sound speed, VS' The wavelength A and fre be obtained of the form M·E = 0, where M is a matrix; quency f of the waves are related by the simple expres the equation only has solutions if the determinant of M sion Af = vS' The notation w = kvs is commonly used, vanishes. This condition yields the plasma dispersion re where w = 27rf and k = 27r/A. On the microscopic scale, lation D(k, w) = 0, and solutions of this relation for the forces between air molecules are transmitted entirely which Re(k) 1= 0 are supported as waves in the plasma. by collisions; between collisions, the molecules travel in Furthermore, those solutions with Im(w) < 0 are straight-line trajectories. damped, whereas those with Im(w) > 0 grow exponen In a magnetized plasma, the situation is vastly more tially and are unstable. Since D(k, w) is a complicated complex. Magnetospheric plasma is a fully ionized gas function, characterizing its solutions involves apprecia composed of electrons and protons with admixtures of ble effort but shows that a wide array of wave phenome He+ (~5%-10%), 0 +(1 %-2%), and He2+ (::5 1 %). na can occur. 12 The density is exceedingly low, about 10 to 1000 parti 19 Influence of the Ambient Magnetic Field cles/cm3, compared with 3 x 10 particles/cm3 in air at room temperature, so that plasma particles move essen A magnetized plasma is not isotropic but exhibits a tially without collisions. (A collision in a plasma is differ distinction between motions parallel and perpendicular to ent than in air because it is caused by long-range coulomb B. This anisotropy appears in the expression for the plas-
240 Johns Hopkins APL Technical Digest, Volume 11, Numbers 3 and 4 (1990) Magnetic Pulsations in the Earth's Magnetosphere rna pressure. The total plasma pressure is given by cyclotron frequency ranges from 1 to 10kHz, far above P = P art + B2121to, where the magnetic contribution to the sampling rate of the CCE magnetic fields instrument. the pre~sure is the magnetic energy density, just as Ppart In addition to their gyromotion, particles bounce back is the kinetic energy density of the particles. In addition, and forth between the Northern and Southern hemispheres it is useful to consider the particle pressure as derived from in the dipole field of the Earth. Those particles whose ve two contributions, Ppart = P.l. + P II , where P.l. is the locities at the magnetic equator are most aligned with the pressure due to motions perpendicular to B, and P II is magnetic field travel farthest along the field line and are that due to motions parallel to B. Because the particle reflected at the lowest altitudes. Bounce periods for typi gyromotions lead to diamagnetic moments, as discussed cal magnetospheric protons range from 50 to 150 s. This earlier, the perpendicular pressure leads to a magnetic mo motion is of interest here because of the potential for ment per unit volume of m = - P.l. BI B2. resonance between particle bounce motions and magnet The analog of sound waves in air occurs, but because ic field-line resonance frequencies. the magnetic field also contributes to the total pressure, As particles bounce between the Northern and Southern "sound-like" waves propagating parallel and perpendic hemispheres, they also drift azimuthally in the dipole field ular to the field are different. Compressional waves travel because of the combined effects of field-line curvature and ing along the magnetic field are governed only by P part ' radial gradient in field intensity. Ions drift westward and but compressions traveling perpendicular to B are affected electrons drift eastward. For typical particle energies by both Ppart and the magnetic pressure, and the wave «200 keY), the period for a complete drift around the speed is either raised or lowered according to whether Earth is much longer than 10 min, so the frequency of the magnetic and particle pressure fluctuations are in phase this motion is not of interest here. What is important is (fast mode) or out of phase (slow mode) . that the particles drift around the Earth, ions one way and In addition to longitudinal sound-like waves, the mag electrons the other. netic field introduces a new class of transverse waves called Large-scale electric fields also lead to particle drift, with shear Alfven waves. These waves occur because the mag the difference that electrons and ions drift in the same netic field provides a tension per unit area, B21 Ito, which sense. Particles respond to an imposed electric field E by acts to restore perturbations in the fieid to the equilibrium drifting with a drift velocity V DE = E x 81 B2, that is , configuration. This phenomenon is analogous to the way perpendicular to both E and B. This electric field drift waves are supported on a string. For a string under a ten will be important in a later discussion of drift waves. In sion T with a linear mass density PI , waves travel at a addition, the solar wind flow past the magnetosphere cre speed V = .J(T/PI) ' In a magnetized plasma, B21 Jlo pro ates an electric field throughout the magnetosphere that vides the tension, and the plasma provides the mass den- is generally directed from dawn to dusk. Because the mag sity Pm ' so that the speed of shear Alfven ,wave s is netic field in the equatorial plane is northward, this dawn 2 VA = .J(B IJloPm)' It turns out that shear Alfven waves to-dusk electric field causes plasma to drift sunward. This are guided along the magnetic field , so that the waves fol sunward motion of plasma plays an important role in trans low the bends in the field . porting energetic ions from the tail of the magnetosphere toward the inner magnetosphere, where they excite mag Particle Motions: Gyration, Bounce, and Drift netic pulsations. Having briefly discussed the medium in which pulsa Because of the highly structured nature of particle tions occur, we can now consider the manifestations of motions, the particles introduce waves and interactions field-line resonances and waves arising from plasma in with waves that have no corollary with sound waves. Since stabilities in the magnetosphere. the ions gyrate about the magnetic field in a left-hand sense, this motion leads to so-called ion cyclotron wave FIELD-LINE RESONANCES modes, which are left-hand waves. The presence of The dipolar field lines of the Earth's field can be regard several ionic species with different mass-to-charge ed as anchored in the northern and southern ionospheres, ratios-H+ (1 amu/e) , He+ (4 amu/e) , and 0 + (16 and shear Alfven waves guided along the field direction amu/e)-implies the existence of a set of ion cyclotron will be reflected by the highly conductive ionosphere so frequencies, so that the different species interact d.iffer that the field lines actually constitute a linear resonance ently with electromagnetic waves if the frequency 1S be cavity. Figure 1 shows two examples of field-line per tween cyclotron frequencies. Hence, several different turbations associated with different field-line resonance waves associated with particle gyromotions appear in a modes. In the figure, displaced field lines are shown rela multicomponent plasma. 13 It turns out that ion cyclotron tive to their equilibrium positions. The coordinate sys waves occur principally in the vicinity of the He+ gy tem indicated by the unit vectors is the dipole system rofrequency, which varies from 4.4 Hz near 3 RE to O. 16 discussed later. The azimuthal perturbation, Figure lA, Hz at 9 RE in the equatorial plane of the Earth's field. consists of a side-to-side motion of the field line, and the The CCE magnetic fields instrument, which has a Nyquist outward perturbation, Figure IB, consists of stretching frequency (upper frequency limit) of 4.03 Hz, is there (compression one-half cycle later) of the field line. fore well suited to detecting the waves in this region. Elec trons gyrate in a right-hand sense and are associated with The String Analogy right-hand waves. Because the electron mass is a factor As with waves on a string, the field-line resonances are of 1830 less than the mass of H +, however, the electron standing waves, and each field line admits a harmonic ser- fohns Hopkins APL Technical Digesc, Volume 11 , Numbers 3 and 4 (1990) 241 B. J. Anderson
A 8 Field-line Magnetic field displacement perturbation A
1\ ell
Figure 1. Field·line displacements. A. Fundamental toroi· dal (azimuthal) field-line resonances. B. Poloidal (outward) 8 field-line resonances. The dipole coordinate system-v, Il,
242 fohns Hopkins APL Technical Digest, Volume 11, Numbers 3 and 4 (1990) Magnetic Pulsations in the Earth's Magnetosphere
is the poloidal mode, where the magnetic field perturba 200 tion is purely outward, that is, radial at the equator. Refer ring to Figure 1, we see that part A corresponds to DB = DB AMPTE/CCE magnetometer YrDay = 85037 80- a: co 40 200-r - 2 0 80 N I E.. 0 >. u c w 40 - -1 Q) co :::J CT u:Q) 0- - -2 0 - -3 80 - -4 z co 40 - -5 -200- - -6 llB Log power 0 llB I I I I I UT 1900 2100 2300 0100 0300 0500 0700 0900 1100 L 3.8 6.9 8.5 9.0 8.5 7.7 5.7 1.9 MLT 1.6 3.5 4.3 5.1 5.9 6.8 8.0 12.4 MLAT -10.5 -12.6 -11.1 -8.1 -4.5 -1.0 1.4 -1.3 0200 0210 0220 0230 0240 0250 0300 Universal time Figure 4. Example of the toroidal fundamental mode field·line resonance observed by the AMPTE/CCE Magnetic Fields Experiment. The spectrograms show wave power as a function of frequency versus universal time (UT) for one satellite orbit. The magnetic field components are BR, radially outward; BE, azimuthal; and BN northward and approximately along the field direction. Spacecraft coordinates are indicated below the spectrogram: L is the equatorial crossing distance of the field line passing through the spacecraft in units of RE, MLT is magnetic local time, and MLAT is magnetic latitude. The one hour segment of detrended data illustrates the sinusoidal nature of the wave and the dominance of the azimuthal component. 244 fohns Hopkins APL Technical Digest, Volume 11 , N umbers 3 and 4 (1990) Magnetic Pulsations in the Earth 's Magnetosphere determined by taking the ratio of the elapsed occurrence A Maximum occurrence rate = 47.1% time of particular pulsation types to the total observation 1200 MLT time in each latitude and L/MLT bin. The distributions for fundamental toroidal resonances are shown in Figure 5. The latituQe distribution clearly shows a node at 0 0 MLAT with monotonically rising occurrence frequency , reflecting the nodal structure in the magnetic perturba tion of the fundamental mode. The equatorial distribu tion shows a clear maximum at 0500 to 0700 MLT , L = 8-9. The dawn/dusk asymmetry is remarkably strong, although several other pulsations often occur at dusk (as discussed later); thus, it is difficult to conclude 1800 - :-·I~""'I-·-I·-~ -0600 that the asymmetry of occurrence reflects a correspond ingly strong asymmetry in resonance excitation. Interfer ence from other pulsations does not occur on the dayside (0900-1500 MLT) or the nightside (2100-0300 MLT) , so the preference for excitation at the flank does reflect the localization of the energy source. The decrease in oc currence frequency with L may be due to the low frequen cy of the source as follows: because the resonance frequencies increase with decreasing radial distance, the 0000 frequency-matching condition will not be met on inner field lines if the driving source frequency is sufficiently B low, and hence resonance will not occur. 0.20.------,---,..------,------, 0> A primary candidate for the source of these waves is -(J) ~:g 0.15 the Kelvin-Helmholtz, or wind-on-water, instability ex 0> :l cited by sheared plasma flows occurring near or just in g~ side the magnetopause at the flanks. Theoretical studies ~.~ 0.10 0 00 have shown that the flanks are an appropriate site for Oeo 0- 0.05 generating long wavelength (= 10 RE) surface waves, whereas near noon, the flow speeds are too low to drive O~---L---~--~---~ the instability.20 o 4 8 12 16 Toroidal Harmonic Series Magnetic latitude (deg) Figure 5. Occurrence distributions of fundamental toroi An example of a second population of field-line dal mode field-line resonances in the Earth's magneto resonances is shown in Figure 6. From 0530 to 1000 UT sphere. A. Equatorial occurrence distribution. B. Latitude and again from 1500 to 1800 UT, toroidal harmonic occurrence distribution. The equatorial occurrence frequen resonances occur over the frequency range from 15 to 40 cies are a percent of total observation time, and the latitude mHz. The waveform shows small-amplitude sinusoidal occurrence frequency scale is arbitrary. MLT is magnetic local time, and L is the equatorial crossing distance of the pulsations, but it is difficult to discern the harmonic struc field line passing through the spacecraft in units of RE. ture from the line plot illustrating the advantage of the spectrogram display. The latitude and L/MLT distributions of these harmonic resonances are shown in Figure 7. The latitude distribution is fairly uniform with indicating a poloidal mode. The latitude and L/MLT only a shallow minimum at 0 0 MLA T , indicating the distributions (Fig. 9) show that the occurrence probability presence of both even and odd harmonics. The L/MLT maximizes at the equator, implying an even harmonic. distribution shows that the waves are a dayside phenome The wave period is in the range from 50 to 100 s, non and occur with roughly equal probability over a wide also suggesting that it is probably a second harmonic (cf. L range. This distribution implies that the energy source Fig. 3). The LlMLT distribution is markedly different from is on the dayside and that inward propagation of energy the fundamental and harmonic mode field-line resonances. is relatively efficient. Other work has shown that these The occurrence pattern is a band that shifts from L > 7 harmonic pulsations are correlated with the alignment of at night to L < 7 on the dayside, with an absence of waves the interplanetary magnetic field with the Earth-Sun in the morning. It has a significant population of nightside line;21.22 thus, the excitation of these waves is caused events, a condition that does not suggest a direct energy directly by the solar wind/magnetosphere interaction. source in the solar wind/magnetosphere interaction. That the waves are even harmonics implies that the energy Poloidal Mode Oscillations source acts asymmetrically about the equator. Research An example of the third class of field-line resonance ers have suggested previously, on the basis of these proper pulsations identified in the CCE data is shown in Figure 8. ties, that poloidal resonances are second harmonics in The pulsations occur from 2200 to 0200 UT and again bounce resonance with energetic ions ,23 and Takahashi et from 0500 to 0630 UT and are predominantly radial, al. 11 showed directly in one case study with simultaneous fohns Hopkins APL Technical Digest, Volume 11 , Numbers 3 and 4 (1990) 245 B. J. Anderson AMPTE/GGE magnetometer YrDay = 85339 80 ~ 40 200-- 2 N I S o ;>, () c (1) ~ 40 -1 ::J 0- (1) u: 0 -2 0 80 -3 -4 ~ 40 -5 -6 LlB Log power 0 LlB r UT 0400 0600 0800 1000 1200 1400 1600 1800 2000 L 5.4 7.7 8.7 8.9 8.4 7.0 4.3 MLT 12.0 13.5 14.1 14.7 15.3 16.0 17.5 MLAT -12.4 -10.2 -6.8 -2.6 -1.9 5.9 8.1 L "0 ~ .Q Qi c Cl ('Cl E "0 (1) "0 C (1) ~ o 0700 0710 0720 0730 0740 0750 0800 Universal time Figure 6. Harmonic toroidal mode field·line resonances observed by AMPlE/GGE in the same format as Figure 4. The detrended data (line plot) show that although the presence of azimuthal pulsations can be detected in line plots, the harmonic structure is virtually impossible to discern. magnetic field and ion flux measurements that energetic gesting that the energetic ions are indeed the energy source ions are in bounce resonance with this type of wave, sug- for the wave. 246 Johns Hopkins APL Technical Digest, Volume 11 , Numbers 3 and 4 (1990) Magnetic Pulsations in the Earth '5 Magnetosphere A Maximum occurrence rate = 62.6% Storm-Time Compressional Waves 1200 MLT Storm-time compressional waves derive their name I from their tendency to occur during geomagnetic storms, as observed at geostationary orbit. The reason for this as sociation is that the ion populations required to excite the waves are energized and transported to geostationary dis tances during periods of high geomagnetic activity. An example of a storm-time compressional wave is shown in Figure 10. The pulsation occurs from 0000 to 0500 UT, and the wave has a large compressional, BN , com ponent. The latitude and LlMLT distributions of these waves are shown in Figure 11 . A maximum occurrence at dusk and late evening at large L and confinement near the equator are evident. The prominence of activity on the nightside and to the west of midnight strongly sug gests that ion populations injected from the nightside are responsible for the waves (recall that ions drift westward), consistent with their association with magnetic storms. A rough idea of the physics behind these waves can be obtained by considering the interplay between particle mag 0000 netization currents and field inhomogeneity. Recall that the B total pressure of the plasma is P part + B2/2j.to , and that the 0.10,------.----,------.-- ---, particle pressure can be written as P part = P.l. + PII' The perpendicular pressure provides a magnetic moment per *;U '~c 0.08 unit volume of m = - P.l. B/B 2, reflecting the diamagnetic u ::J nature of the plasma, and is associated with magnetiza C ~ 0.06 Q)C\l tion currents circulating in the left-hand sense. Note that B~ 0.04 m is inversely proportional to the field strength. A spa u ~ 0- . 0 02 tially uniform plasma in a uniform field is stable, but spa tial inhomogeneities in the plasma density and field OL-__-L ___ L- __-L __ ~ strength can lead to instabilities of spatial irregularities o 4 8 12 16 in the plasma density. 24 Magnetic latitude (deg) Consider what happens when a cloud of high-P.l. plas Figure 7. Occurrence distributions of harmonic toroidal mode resonances in the same format as Figure 5. ma is injected into an inhomogeneous magnetic field , as illustrated in Figure 12. The boundary of the high-P.l. region is assumed to have a slight ripple structure, and the magnetic field increases to the right in the figure. Be The fundamental toroidal, harmonic toroidal, and poloi cause the plasma magnetic moment is largest in the low dal (second harmonic) modes are the three dominant class er field regions, the associated magnetization currents are es of field-line resonances observed in the near equatorial most intense in the portions of the ripple extending into magnetosphere, and their occurrence distributions sug .. the low field region and weaker along the valleys of the gest that three separate energy sources are responsible for ripple. Because the magnetization currents are inhomo them. Fundamental and harmonic resonances appear to geneous, charge imbalance occurs, creating electric fields. be excited by a mechanism associated directly with the The plasma responds to the electric field by drifting with solar wind/magnetosphere interaction, whereas the poloi a velocity E x B/B 2, causing the rippled structure to dal second harmonic waves appear to be driven by ions grow larger, providing positive feedback. Gradients in in the magnetosphere. the magnetic field and plasma density also cause drift motions of the plasma perpendicular to the gradients, so PLASMA INSTABILITIES that the ripple structure moves parallel to the boundary Field-line resonances are a property of the magnetic of the high-P.l. region, creating a traveling wave. A com field geometry, and their excitation reflects the distribu mon feature of these waves is that the magnetic field in tensity and ion flux oscillate out of phase, consistent with tion of energy sources whose frequencies and spatial struc 25 tures match the frequency and spatial structure of the this picture. field-line perturbations. Two other types of pulsations oc cur commonly in the magnetosphere and result from in Ion Cyclotron Waves stabilities in the magnetospheric ion population rather than The second type of plasma wave with which we are con from frequency matching to field lines. These additional cerned is associated with the ion cyclotron instability. This pulsations are storm-time compressional waves with peri wave is also driven by an ion population with large P.l. , ods of 2 to 10 min , and electromagnetic ion cyclotron but rather than being a pressure instability, the wave is waves with frequencies of 0.1 to 4 Hz. generated by the cyclotron motion of the ions. Consider Johns Hopkins APL Technical Digest, Volume 11, Numbers 3 and 4 (1990) 247 B. 1. Anderson AMPTE/CCE magnetometer YrDay = 85193 80 a: co 200 - 2 N I E- O >. () c w Q) co - -1 :::J 0" Q) u: 0- - -2 - -3 - -4 z - -5 co -200- - -6 flB Log power flB I UT 1700 1900 2100 2300 0100 0300 0500 0700 0900 L 5.0 7.4 8.6 9.1 8.7 7.3 4.7 MLT 19.1 20.5 21 .3 21.9 22.4 23.1 0.4 MLAT -0.9 1.0 4.1 6.7 8.0 8.4 9.5 () ~ c: Cl C"CI E "0 Q) "0 c: ~ 0500 0510 0520 0530 0540 0550 0600 Universal time Figure 8. Poloidal mode field-line resonances observed by AMPlE/CCE in the same format as Figure 4. The dominance of the radial component is apparent in the waveform. 248 fohns Hopkins APL Technical Digest, Volume Il, Numbers 3 and 4 (1990) Magnetic Pulsations in the Earth 's Magnetosphere A Maximum occurrence rate = 17.6% verse to B , and the wave power parallel to B. In the se 1200 MLT cond and third panels, the dotted lines show the He+ and H + cyclotron frequencies, respectively. The bottom panel shows energetic particle data from the Medium Energy Particle Analyzer instrument. Waves occur from 0700 to 0930 UT for L > 8 and also at 0200 and 1445 UT at low L. For the L > 8 waves, onset occurs simul taneously with an enhancement in the energetic particle fluxes, indicating that the particles are intimately related to the waves. The wave occurs above the He + cyclotron frequency and is predominantly left-hand polarized. The L/MLT distribution of these waves (Fig. 14) shows a clear preference for occurrence in the early afternoon for L > 7 and a secondary population for L > 8 in the morning (0300-1000 MLT). The association with enhanced flux es of ::::: 100-keY ions and theoretical expectations lead us to associate these waves with energetic ions. The high occurrence rate implies a significant energy transport out of the ion population into waves and eventually into the ionosphere. B 0.12 ,------,---...... ------y------, ENERGY FLOW Cll_ These results have implications for the role of pulsa .... III ~ .... tions in energy flow in the magnetosphere. The pulsations ~'§ 0.08 discussed here all ultimately derive their energy from the g~ ~ ~ interaction between the solar wind and the magnetosphere, :; .1:: 8 -e 0.04 and the energy delivered to the pulsations is eventually O~ dissipated in the ionosphere. Magnetospheric pulsations therefore constitute a stage in the energy flow from the solar wind to the ionosphere, and the various pulsations 4 8 12 16 can be viewed in terms of their position in an energy cas Magnetic latitude (deg) cade. Possible energy pathways for the pulsations dis Figure 9. Occurrence distributions of poloidal mode resonances in the same format as Figure 5. cussed here are shown schematically in Figure 15. The five classes of pulsations discussed earlier derive their energy from different mechanisms, but all of the mechan isms correspond to only two basic energy pathways: (I) a particle with a velocity along the field line of V II ' An direct excitation from the solar wind/magnetosphere in Alfven wave propagating parallel to the field can interact teraction, and (2) instabilities driven by ion distributions resonantly with the particle if the matching condition that, in turn, result from acceleration processes occurring W = nc - k· VII is met, that is, if the wave as viewed in in the anti-sunward portion, or tail , of the magnetosphere. the particle frame has the frequency n c' the angular cy clotron frequency introduced earlier. Because ions gyrate Direct Conversion from the Solar Wind in the left-hand sense, left-hand waves will be excited. Some energy from the solar wind appears to be con To determine the frequencies that are unstable to growth, verted directly into pulsations, namely, harmonic and one must turn to the plasma dispersion relation, D(w, fundamental toroidal mode resonances. Because these k) = 0, and solve for w(k) = Wr + iWi' where Wr and Wi resonances appear to be driven by different interactions, are the real and imaginary parts of the angular frequen at least two pathways must exist for channeling solar wind cy, respectively. Determining the k for which Wi is the energy directly into pulsations. Two conventional mechan largest positive value gives the growth rate versus Wr . isms are (I) propagation of compressional wave power Results of these calculations show that growth occurs for across the magnetopause and throughout the dayside mag O.lnH+ < W < n H+, where n H+ is the proton angular netosphere, and (2) the Kelvin-Helmholtz (or wind-on cyclotron frequency. The maximum frequency is deter water) instability between shear plasma flows at the mag mined by Pj.J P II ; larger p.l.J P II gives growth closer to netopause and/or boundary layer regions just inside the n H+. The calculations also show that the presence of magnetopause. These mechanisms are both shown sche He+ inhibits wave growth in the vicinity of the helium matically in Figure 15. In addition, evidence suggests that angular gyrofrequency, n He+ .26.27 modulated ionospheric precipitation is associated with har An example of electromagnetic ion cyclotron waves ob monic resonances. Turbulence just outside the magneto served by AMPTE/CCE is shown in Figure 13. The top sphere may lead to modulated dayside ionospheric particle three panels in the spectrogram show the wave ellipticity precipitation and hence conductivities and currents that in the plane perpendicular to B, the wave power trans- could drive toroidal harmonic pulsations.28 fohns Hopkins APL Technical Digest, Volume 11 , Numbers 3 and 4 (1990) 249 B. 1. Anderson AMPTE/CCE magnetometer YrOay = 85249 80-- a: co 40 200 - 2 0 80 N I .s 0 >- u c: w 40 Q) co - -1 :J 0- Q) U: 0- - -2 0 - -3 80 - -4 z - -5 co 40 -200- - -6 ilB Log power 0 t:B I UT 1900 2100 2300 0100 0300 0500 0700 0900 1100 L 4.7 7.3 8.6 8.9 8.5 7.2 4.8 MLT 16.0 17.4 18.2 18.8 19.5 20.3 21.5 MLAT 6.9 7.3 6.5 4.4 1.6 -1.1 -1 .5 L l "0 ~ u 0-m c: g> E "0 Q) "0c: ~ Q) a 0000 0010 0020 0030 0040 0050 0100 Universal time Figure 10. Storm-time compressional pulsations observed by AMPTE/CCE in the same format as Figure 4. The amplitude of the compressional component is large in contrast to the previous examples in which the compressional component was not appreciable. 250 Johns Hopkins APL Technical Digest, Volume 11, Numbers 3 and 4 (1990) Magnetic Pulsations in the Earth's Magnetosphere A Maximum occurrence rate = 35.4% 1200 MLT B I \ ·····r··········!' ...... >.""",. 8 VOE 8 Et )tJ ~ .~, . '··'\.. L= 9 + 8 ...... ~\\ \ 8~E~(tJ 8 1800 - i -'.)- 0600 VOE ~ 8 \. Et )tJ \ ! 8 + \\ /l 8 \\ I/.! , / ~ E~(tJ "",.".<.. ' j// ... ,. .1 .. ,.", ..... [...... :.--... . \ 0000 Figure 12. Illustration of the instability to wave growth of B high·perpendicular·pressure plasma in an inhomogeneous 0.20 ~-----.----.------.-----, magnetic field. The ripple corresponds to inhomogeneous <1>_ magnetization currents that cause charge imbalance a~d "§ .~ 0.15 hence electric fields. The electric fields cause plasma dnft <1> c o ::J motions, making the ripple grow larger. In the figure, B is c~ ~ ~ 0.10 the magnetic field, E is the electric field, J is the current den· ~.1: sity, and V is the plasma drift velocity. 0.0 OE o (ij 0-0.05 4 8 12 16 Energy Budget Magnetic latitude (deg) In terms of the overall magnetospheric energy budget, the majority of solar wind energy entering the mag Figure 11. Occurrence distributions of storm·time com· pressional wave resonances in the same format as Figure 5. netosphere is converted into ionospheric currents and par ticle precipitation in the auroral zone and amounts to a total power of roughly 1011 W. The power converted directly into pulsations is expected to be about 1% of this Excitation due to Magnetospheric Ions value. The existence of multiple pathways for energy in put into pulsations may increase this percentage, however. Many pulsations are driven by magnetospheric ion dis In addition, pulsations deposit energy into the ionosphere tributions. Ions energized in the magnetotail drift sunward equatorward of the auroral zone, so they will be relative under the influence of the dawn/dusk electric field , and ly more important in these regions. It also appears that close to the Earth they experience westward gradient cur pulsations are one of the means by which ions that are vature drift that diverts most of the ions to the dusk side accelerated during magnetically active periods convert of the magnetosphere. This drift pattern is illustrated in their energy into forms that are deposited in the iono Figure 15. Poloidal second harmonic field-line reso sphere. After a major magnetic storm, the energy content nances, storm-time compressional waves, and electromag of energetic ions in the Earth's equatorial magnetosphere netic ion cyclotron waves all depend on magnetospheric can be considerable (l015 J), so mechanisms for divert ions for their energy , and all of these waves occur primar ing some of this energy into the ionosphere may provide ily on the dusk side. Because the spatial distributions of an appreciable source of energy. these waves are different, however, the ion distributions Determining more precisely how the different types of responsible for each type must also be different. Previ pulsations are driven in the magnetosphere is a major ob ous work has shown that storm-time compressional waves jective of future pulsation research. As progress is made correlate with periods of geomagnetic activity, but the pre in this area, the role of pulsations in magnetosphere/ cise mechanisms responsible for producing the particle ionosphere energy flow will be evaluated quantitatively. distributions responsible for each type of pulsation have not yet been identified. Nonetheless, for each of these pul sations, the energy conversion sequence is as follows: The solar wind/magnetosphere interaction generates electric REFERENCES fields, and the fields energize magnetospheric ions, which I Orr, D ., " Magnetic Pulsations within the Magnetosphere: A Review," J. in turn excite geomagnetic pulsations. Almos. Terr. Phys. 35, I- 50 (1973). fohns Hopkins APL Technical Digest, Volume 11, Numbers 3 and 4 (1990) 251 B. 1. Anderson AMPTE/CCE magnetometer YrDay = 84274 4 ~~------~=_~. J. 2 Right 0 'c," ~ -1 -2 -3 -4 Left [ 2 ~- -5 co Log spectral density 0 107 I" ~ ... .-.;:;,I.-~ ?""" -;::- 6 II) 10 II) ...'<'~: :\ N E 105 ~ Energy (keV) \:.: . ~ .....•...... x ) ::J .... 25-34 \: :;::: -'. i\ 34-50 . c 4 ~>~: .2 10 ...... : .... . :~...... \~ 2 Cahill, L. J., Jr. , Lin, N. G., Engebretson, M. J., Weimer, D. R., and Sugiura, 7 Bryant, D. A., Krimigis, S. M. , and Haerendel , G., " Outline of the Active M., " Electric and Magnetic Observations of the Structure of Standing Waves Magnetospheric Particle Tracer Explorers (AMPTE) Mission ," IEEE Trans. in the Magnetosphere," J. Geophys. Res. 91 , 8895-8907 (1986). Geosei. Remote Sensing GE-23, 177- 181 (1985). 3 Takahashi, K. , McEntire, R. W., Lui , A. T . Y., and Potemra, T. A., " Ion 8 Potemra, T. A., Zanetti, L. J., and Acuna, M. H., "The AMPTE CCE Mag Flux Oscillations Associated with a Radially Polarized Transverse Pc 5 Mag netic Field Experiment," IEEE Trans. Geosci. 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Res. 69, 4515- 4522 (1964). 14 Alfven, H., Cosmical Electrodynamics. Oxford University Press. New York (1950). 15 Cummings, W. D .. O'Sullivan. R. J., and Coleman. P. 1.. Jr. , "Standing Alfven Waves in (he Magnetosphere." 1. Geophys. Res. 74,778- 793 (1969). 16 Lee, D .-L. , and Lysak, R. L., "Magnetospheric ULF Wave Coupling in the Dipole Model: The Impulsive Excitation ," 1. Geophys. Res. 94. 17,097- 17 ,103 (1989). Figure 15. Diagram of energy sources and conversion path 17 Chen. L., and Hasegawa. A., .. A Theory of Long-Period Magnetic Pulsations: ways to geomagnetic pulsations. The solar wind flow is I. Steady State Excitation of Field Line Resonances," 1. Geophys. Res. 79 , supersonic and develops a shock upstream of the magneto 1024- 1032 (1974). sphere. Energy is coupled to pulsations via several mechan 18 Chen, L. , and Crowley, S. c., . 'On Field Line Resonances of Hydromagneti c isms: wave power is generated by turbulence outside the Alfven Waves in Dipole Magnetic Field ," Geophys. Res. Lel/. 16, 895- 897 (1989). magnetosphere near noon and by Kelvin-Helmholtz waves 19 Anderson, B. J., Engebretson, M. J. , Rounds, S. P. , Zanetti, L. J., and Potem at the magnetosphere flanks caused by velocity flow shear. ra, T . A. , "A Statistical Study of Pc 3- 5 Pulsations Observed by the AMPTEI This wave power propagates inward and couples to toroi CCE Magnetic Fields Experiment. I. Occurrence Distributions, " 1. Geophys. dal field-line resonances. Ions energized in the nightside Res. 95 , 10,495- 10,523 ( 1990) . magnetosphere are injected during magnetic activity and 20 Kivelson, M. G., and Pu , Z.- Y. , "The Kelvin - Helmholtz Instability on the drift westward, through the late evening and dusk, provid Magnetopause," Planet. Space Sci. 32, 1335- 134 1 (1984). ing energy for poloidal field-line resonances, storm-time 21 Takahashi , K. T ., McPherron, R. L. , and Terasawa, T., " Dependence on the compressional waves, and electromagnetic ion cyclotron Spectrum of Pc 3- 4 Pulsati ons on the Interplanetary Magnetic Field ," 1. Geophys. Res. 89, 2770-2780 (1984). waves. 22 Engebretson, M. J., Zanetti, L. J., Potemra , T. A., Baumjohann , W ., LUhr, H ., et aI. , " Simultaneous Observation of Pc 3-4 Pulsations in the Solar Wind and in the Earth's Magnetosphere," J. Geophys. Res. 92, 10,053- 10,062 (1987) . 23 Hughes, W . 1.. Southwood, D. J .. Mauk. B., McPherron, R. L. , and Barfield , J. N. , "Alfven Waves Generated by an Inverted Plasma Energy Distribution," 27 Gomberoff, L. , and Niera. R oo "Convective Growth Rate of Ion Cyclotron Nature 275 , 43- 45 (1978). Waves in a H+-He + and H+- He +-O+ Plasma." J. Geophys. Res. 88 . 2170-2 174 (1983). 24 Miura, A. , Ohtani, S .. and Tamao, T ., " Ballooning Instability and Structure 28 Engebretson, M. Anderson, B. J. , Cahill , L. Jr .. Arnoldy, R. L.. Rosen of Diamagnetic Hydromagnetic Waves in a Model Magnetosphere. " J. Geophys. J., J., Res. 94, 15 ,23 1- 15 ,242 (1989). berg, T. J. , et aI., " Ionospheric Signatures of Cusp Latitude Pc 3 Pulsations." J. 25 Kremser, G., Korth, A., Fejer, J. A. , Wilken, B., Gurevich, A. V., et aI., Geophys. Res. 95, 2447-2456 (1990). "Observations of Quasi-Periodic Flux Variations of Energetic Ions and Elec trons Associated with Pc 5 Geomagnetic Pulsations," 1. Geophys. Res. 86. 3345- 3356 ( 1981 ). ACKNOWLEDGMENTS: Analysis of AMPTE/ CCE magnetic field data 26 Gomberoff, L. , and Cuperman, S., "Combined Effect of Cold H + and He+ was supported by NASA, by the National Science Foundation (NSF), and by Ions on the Proton Cyclotron Electromagnetic Instability," J. Geophys. Res. the Office of Naval Research. Support for computational work completed at 87,95-100 (1982). Augsburg College was provided by NSF. fohns Hopkins APL Technical Digest, Volume 11, Numbers 3 and 4 (1990) 253 B. 1. Anderson THE AUTHOR BRIAN J. ANDERSON was born in Minneapolis, Minnesota, in 1959. He obtained a B.A . in physics from Augsburg College, Minneapolis, Minnesota, in 1982 and a Ph.D. in physics, specializing in experimen tal mass spectroscopy, from the University of Minnesota in 1987. He returned to Augsburg College as an Assistant Professor of Physics, where he began his research on mag netospheric pulsations. He came to APL'S Space Department in 1988 as a Postdoctoral Associate. 254 Johns Hopkins APL Technical Digest, Volume J J, Numbers 3 and 4 (1990)