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.