Radio Sounding of Multiscale Plasmas

P. H. Reiff1, C. B. Boyle1, J. L. Green2, S. F. Fung2, R. Benson2, W. Calvert3, W. W. L. Taylor4

1Dept. Space Physics and Astronomy, Rice University, Houston, TX 77251
2NASA Goddard Space Flight Center, Greenbelt, MD 20771
3Dept. of Physics and Astronomy, University of Iowa, Iowa City, IA 52242
4Nichols Research Corporation, Arlington, VA 22209

in Physics of Space Plasmas, 14, edited by T. Chang and J. R. Jasperse, MIT Press, Cambridge, MA, pp. 415- 429, 1996

Reprinted with Permission from MIT Center for Theoretical Geo/Cosmo Plasma Physics, Cambridge MA, Copyright 1995

Contents

Abstract

Radio sounding, long used in ground-based and space-based studies of the ionosphere, is a powerful technique which can also be used to remotely study multi-scale magnetospheric plasmas. A radio sounder aboard a spacecraft located in the low density magnetospheric cavity will be suited for sounding the magnetopause, the cusp, and the plasmasphere. Free-space electromagnetic waves transmitted by the sounder will be reflected from remote plasma regions where the transmitted wave frequency matches the local O-mode or X-mode cutoff, and will return almost instantaneously to the sounder as O-mode or X-mode echoes wherever the density gradient at the reflection point is approximately parallel to the line of sight from the sounder. Thus, swept-frequency echoes from the magnetopause, cusp, plasmapause, and boundary layers will yield density profiles and magnetic field information, as well as position and velocity information from these remote regions. Despite the large sounding distances, the nearly paraboloid shape of the magnetopause will result in partially focused return signals. Using modern digital signal processing techniques, a radio sounder can observe remote magnetospheric regions using a fraction of the power used in previously flown topside ionospheric sounders. Large-scale (~1 RE) undulations of the magnetopause or boundary layer, as may be caused by pressure pulses or large-scale surface waves, will result in multiple echoes, permitting knowledge of the amplitude, wave length, and velocity of the waves. These extra return signals allow the inference of the 3-dimensional configuration and dynamics of the magnetopause and its boundary layers on very rapid time scales.

Introduction

Traditional in-situ measurements of magnetospheric plasmas and fields have provided a wealth of data over the last few decades. Unfortunately, in-situ measurements suffer from an inherent ambiguity in distinguishing spatial from temporal variations in the measured quantities. This problem is simply due to measuring the quantities along a single space-time trajectory. Additionally, magnetospheric regions can only be sampled on orbit time scales. For any but the lowest earth-orbiting satellites, the orbit periods (and thus the time between sampling regions of interest) can be quite long. Important time scales for magnetospheric physics, however, run from minutes (for substorm studies or sporadic reconnection events) to hours or days (for storms).

The alternative to in-situ measurements is remote sensing. Remote sensing of ionospheric and magnetospheric processes continues to mature with recent advances in technology. Until recently, passive sensing has been largely limited to auroral regions and solar physics. Active radio sounding provides a way to extend remote sensing to the rest of the magnetosphere [1], while trivially resolving the ambiguity between spatial variations and temporal variations. Active radio methods directly provide differential rather than column integrated measurements, complementing the optical, UV, and neutral particle imagers now available. Radio sounding also provides an opportunity to simultaneously measure widely separated regions of the magnetosphere. As we describe below, an active radio plasma sounder presents a unique opportunity to simultaneously study small and large scale magnetospheric plasmas.

History

Detailed, high time resolution profiles of the ionosphere from networks of ground based sounders have been available for decades. Modern "bottomside" digital sounders measure the frequency, time delay, amplitude, phase shift, Doppler shift and spread, polarization, and the return direction of echoes reflected off the underside of the earth's ionosphere. These measurements are typically shown as " ionograms " and are regularly inverted to give plasma density, velocity, and even turbulence versus altitude [2]. Ionograms represent only a fraction of the information available to a modern sounder, but they do display the echoes from ionospheric structures in a clear and graphical format. Many of the advantages of modern sounders over earlier devices are due to increased use of digital signal processing and flexible software controlled designs. Two examples of modern bottomside sounders are the Digisonde (developed at the University of Massachusetts Lowell) and the Dynasonde (developed by the U.S. Department of Commerce Laboratories in Boulder, CO).

Complementing the long heritage of ground based sounders, a number of space based "topside" ionospheric sounders have been flown. Beginning with the Alouette/ISIS programs in 1962 [3], topside sounders have included Alouette 1/2, ISIS 1/2, ISS-b, EXOS-C/D, Intercosmos 19, and Cosmos 1809. During its first 3 years on orbit, Alouette 1 alone provided 1100 ionograms each day. Although the intent of the Alouette/ISIS program was to study the upper ionosphere, ISIS also demonstrated the ability to remotely sound the magnetospheric cusp [4]. A new generation of space borne sounders could use the technology of modern ground based sounders to provide a new way to observe multiscale magnetospheric plasmas.

In addition to avoiding spatial/temporal aliasing, radio sounding offers several other advantages. Most importantly, a sounder can sample points not at the spacecraft location, including points not on the spacecraft trajectory. This allows sounders to sample more regions than comparable in-situ measurements, and reduces the coupling between the orbit period and the observable time scales. Since radio sounders can perform simultaneous measurements of remotely separated regions, sounding may greatly improve our understanding of the coupling between the many regions and processes in the solar/terrestrial system.

One of the most significant advantages of active radio sounding of the magnetosphere is the large range of scales that can be observed by a single instrument. For illustrative purposes, we will consider a 10W magnetospheric sounder (less than 10% of the transmitted power of Alouette-1) with 400m dipole antennas. Using sounding frequencies from 3 kHz to 3 MHz allows detection of reflections from a range of plasma densities greater than seen in the magnetosphere. Calvert et al.═s analysis [5] (hereafter referred to as Calvert) showed that a digital radio sounder with these characteristics could resolve density structures as small as 500 km at distances of up to 4 RE from the sounder. Under appropriate conditions, a sounder can measure the positions, density profiles, velocity profiles, and field strength profiles of both flanks of the magnetopause/boundary layer simultaneously (across a total of 30 RE). It can resolve plasma structures on scales ranging from 0.08 RE to 30 RE, including line of sight density, field strength, and velocity profiles, in minutes. This is a tremendous improvement over in-situ measurements, which provide only local density and field measurements. These one-dimensional profiles can also be combined to build detailed planar sections of magnetospheric regions on time scales of 1 orbit.

Sounding

A radio plasma sounder operates by emitting a series of pulses over a range of frequencies, and listening for returned echoes. The properties of the dielectric, the surrounding plasma in this case, dictate the wave modes which propagate and their dependence on the dielectric (plasma) parameters. The cold plasma approximation [6] indicates two modes useful for sounding exist: the O mode and the X mode. The signal from the antennas propagates as two independent wave front surfaces, whose progress is guided by variations in the dielectric parameters via the dispersion relations for the relevant modes. Each wave front refracts separately and will reflect at the point where the plasma parameters indicate cutoff (when the index of refraction equals zero) for that wave mode. Excellent summaries of the physics of plasma waves can be found in either [6] or [7], while particularly relevant magnetospheric applications of the theory can be found in [8-9].

The crucial distinction between these two modes for magnetospheric sounding is that the O mode cutoff is determined solely by the plasma density, while the X mode cutoff is also a function of the total magnetic field strength. The cutoff for the O mode is the local plasma frequency fp,

(1)

when the electron density Ne is expressed in cm-3; eo is the permittivity of free space, e is the electron charge and m is the electron mass. For the X mode, the cutoff fx is

(2)

where the gyrofrequency is fg = (1/2p)eB/m ü 28 B (Hz) when B, the magnetic field strength, is expressed in nT. These two modes propagate freely with group velocity vg >> vph >> c when the wave frequencies are well beyond the mode cutoffs; thus they are also called the free-space modes.

For a sounder in the magnetospheric cavity, where the density and field strengths are relatively low, the sounding frequencies are well above the local plasma frequency. Both wave modes travel at their group velocities, which are nearly c in this region. The O mode group velocity is:

(3)

The X mode group velocity includes the effect of the magnetic field, but is approximately given by equation (3) throughout the sounding region.

O mode cutoff, hence reflection, occurs at regions of increased plasma density such as the plasmasphere or boundary layers. At each point where the plasma frequency equals the sounding frequency, the wave will be reflected. If the density gradient points away from the sounder, the wave will be reflected in the direction of the sounder and detected. For the X mode, an additional term depending on the magnitude of the magnetic field is added, but the process is otherwise identical. Thus, at each frequency several O (and X) mode returns will be detected at the spacecraft. For each return, the sounder measures the delay time (distance), Doppler shift (line of sight velocity), and the direction from which the return is received. The sounder then increments the transmitted frequency, and detects more distant, higher density layers. Since the propagation speed is comparable to c except near the reflecting gradient, the sounder can very rapidly build up detailed profiles of even very remote regions. For the X mode wave the process is very similar, and the returns can be compared to the O mode data to distinguish magnetic field and plasma density variations [10].

Given the ability to distinguish between the plasma density and field strength of remote plasmas, the question remains as to which magnetospheric structures and phenomena could be detected with a radio sounder. Most magnetospheric regions and structures have X and O mode cutoffs between 3 kHz and 3 MHz:

Region Density
(cm-3)
|B|
(nT)
O Mode
cutoff (kHz)
O Mode
cutoff (kHz)
inner plasmasphere 104 103 900 914
plasmapause 100 500 90.0 97.3
outer plasmasphere 20 200 40.3 43.2
plasmoids 10 20 28.5 28.7
weak ring current < local dB~10 90.0 91.4 *
strong ring current < local dB~300 90.0 94.3 *
boundary layers 10-20 40 34.9 35.4
magnetpause 20-40 40 49.3 49.9
plasma sheet 1 < 50 9.0 9.7
cusp 5-10 0-20 24.7 24.8
lobes 0.1 20 2.9 3.1
convective flow 3 50 15.6 16.3 *
FTE 20 10 40.3 40.4 *

* indicates events distinguishable via secondary characteristics of the return (Doppler, etc.); the ring current is detected by means of X-mode echoes.

Table 1. Illustrative X and O mode cutoffs by region

The first figure shows schematically how a sounder might be used to study plasmasphere refilling. Since it can resolve both the large scale plasmaspheric structure and the fine scales needed to measure density gradients, under appropriate conditions a sounder could directly observe plasmasphere erosion and refilling. Since the dielectric properties of the ambient plasma only support two long distance (non-trapped, non-evanescent) sounding modes, and since the sounding frequencies in these modes encompass all major magnetospheric structures, it is theoretically possible to sound most of these regions. The implementation of sounding and the geometries of the echo returns are the remaining key issues.

Figure 1. Schematic of reflections of ~30 kHz O mode waves (corresponding to n ~10 cm-3) from the outer plasmasphere. In panel (A), the plasmasphere is large and filled, corresponding to quiet conditions. In panel (B), the plasmasphere is compressed and the outermost layers have been removed during enhanced convection. In panel (C) the plasmasphere is refilling. It may be possible for the sounder to separately, quantitatively, follow simultaneously the simple expansion of the plasmasphere (reflections from point "a"); the propagation of a refilling front from the ionosphere (point "b"); and the location of plasmas trapped in the equatorial plane (point "c"). Note that higher-frequency sounding waves will be reflected from deeper within the plasmasphere in each case (examples are shown in panel C, near "a"), allowing the construction of high time resolution density profiles which show erosion and refilling.

Signal Strengths and Signal Processing

While Calvert discusses the expected signal strengths and signal processing in detail, it is worth reviewing the highlights. Initially, the radiated signal spreads out roughly spherically from the sounder. When the transmitted waves reflect off magnetospheric structures, the round trip signal strength is approximately proportional to d-2 (where d is the distance to the structure), with some corrections.

One of the modifying factors to the d-2 power law is focusing/defocusing by the reflecting surface. If the critical frequency surface (which is an isodensity surface for O mode waves) presents a concave surface towards the sounder, the echo return will be enhanced. This is obviously the case for sounding the magnetopause and boundary layers, where the focusing factor could increase the echo strength by a factor of ~2.8. The plasmasphere, on the other hand, will appear convex to a sounder located in the tail lobes or most magnetospheric cavities, and will return less than if this factor were neglected. If the plasmasphere were a simple 4 RE sphere, the defocusing could reduce the signal by approximately a factor of 1/2 for a sounder 1 RE beyond the plasmapause [5]. Of course the plasmasphere is not a sphere, and a sounder is likely to be much closer to the plasmasphere than to the magnetopause (see however [11,12]).

Again assuming a 10W transmitter, orthogonal 400m spin plane dipoles, and a much shorter spin axis antenna, Calvert determined that reactancetuned and impedance-matched antennas were essential. To verify the feasibility of tuning and matching 400m dipoles to existing sounder transmitter and receiver circuits at the frequencies needed, B. Reinisch and others successfully constructed and tested the proposed dipole with modified Digisonde circuitry in an end-to-end test [13]. Calvert also identified several other operational techniques and signal processing methods from ground based sounding as appropriate for magnetospheric operations. Since the waves propagate at speeds close to c, a sounder can significantly reduce noise by combining repeated measurements (digital signal integration) despite the long distances to the reflecting surfaces. Further, modern sounders use onboard processing to perform techniques such as pulse compression and spectral integration to dramatically improve signal to noise ratios. These techniques have been used in many ground-based ionosondes, providing confidence in the methods and in the resulting gains in the signal to noise ratio.

Another key feature of modern digital sounders, which could prove valuable in magnetospheric sounding, is their ability to automatically adjust their operations and transmissions. This can be used to minimize the effect of auroral kilometric radiation (AKR), which occurs at discrete frequencies [14-15]. Modern sounders can receive without transmitting, and adjust their operations to avoid noisy frequencies. This technique is used in ground based sounders to minimize the effects of man-made signals. A somewhat thornier problem is posed by continuum radiation. Escaping continuum radiation is, despite its name, also discrete [16], and can be avoided by frequency side-stepping, as for AKR. The trapped continuum, however, is too smooth in frequency to be avoided by this method. However, by its nature it tends to be trapped near the equatorial plane between the density gradients at the plasmapause and the magnetopause [17]. Thus the signal to noise ratio may be worse when operating near the equatorial plane. It is also reasonable to avoid transmitting near the equator, so that the sounder signal will not contribute to the trapped continuum.

Magnetospheric Raytracing

Given the relatively simple physics of reflecting artificial X and O mode plasma waves off density (and field) gradients, it is possible to model the sounding process with a high degree of realism. Two tools have been developed which use models of the magnetospheric environment to simulate the propagation of X and O mode waves for sounding purposes. Both are fundamentally raytracing programs; they numerically track the propagation, reflection, and refraction of simulated waves. Both use empirical models of the magnetosphere and plasmasphere, although each uses different models and methods. Finally, although the two simulations generate similar results, each has its strengths.

Figure 2. The shape of the dayside magnetosphere, hence the sounding geometry, is a function of solar wind pressure and IMF [18,19]. This is an example of the largest scales observable by radio sounding of the magnetopause/boundary layers. On a much finer scale, the detailed boundary layer structure can be distinguished by a radio sounder. The diagram on the right shows two types of boundary layer structure which could be unambiguously observed by sounding at several frequencies. Additionally, motion of the boundary would be resolved by the Doppler shift of the echoes. Radio sounding would allow determination of the boundary type, its location, and its motion. Adapted from [1].

The first uses a modified optical raytracer in an optical analog of a Stern [18] magnetosphere. Since the sounding frequency is well above the ambient plasma frequency except near the reflection points, this technique should provide a realistic idea of where returns might be expected for a magnetospheric sounder. It includes simple models of the cusps, ring current, plasmasphere, magnetopause and boundary layers. The models are adjustable to simulate different solar wind conditions (Fig. 2), sounding frequencies, and sounder locations. It includes reflection, focusing, and numerical tracing of ray paths to produce 'sky maps' of echo return strengths (Fig. 3). The only effect not included in this raytracing simulation is the refraction at points other than the reflection point. As noted, this is effectively a 'high frequency' approximation. Its primary advantage is that it provides a test of the geometric optics of waves in the magnetosphere, without excessive computational requirements. It also cannot produce plasmagrams.


Figure 3. These images show the effects of irregularities in the cutoff surfaces. Only the magnetopause/boundary layer model [18] was used, and echoes from smooth, irregular and sinusoidal boundary layers were created using the high frequency raytracer. Echoes from the three surface types were simulated for two sounder positions, as illustrated in the diagrams on the right hand side. Mosaics of echo return 'skymaps' each spanning 90 ° in azimuth and elevation about +ZGSM, +XGSM, and -ZGSM for each surface are shown. These images do not include plasmasphere or cusp models, and the magnetopause standoff distance is 11 RE. The sinusoidal waves used here had amplitudes of ~1.5 RE, and wavelengths of ~1.5 RE. A typical amplitude of the irregularities in the rough boundary simulations was 0.5 RE. Darker regions indicate stronger echoes.

The more accurate of the two raytracers used to simulate magnetospheric sounding, the GSFC raytracer, was developed specifically to trace plasma waves in the magnetosphere [20]. This simulation does not currently include a ring current, or cusp models, although these may be added to future revisions of the software [23]. It does include refraction at every step in the ray path, as the dielectric properties vary. This tool been evolving since the early 1970's, and been applied to a variety of problems in terrestrial and non terrestrial magnetospheres [8-10] resulting in over 25 publications. Simulations of plasmoid sounding using the GSFC raytracer are described in [21].

In Figure 4 the simulated returns for frequencies corresponding to several densities using the high frequency simulation are shown. The figures have been inverted to make viewing easier, so that dark areas indicate strong signal returns. Each panel is comprised of 3 sub-panels, each of which shows a 90 degree field of view along a GSM axis (+ZGSM, +XGSM, and -ZGSM from top to bottom). The subpanels have been combined to form mosaics which show strips running from below the spacecraft to above it along the nose of the magnetosphere. The spacecraft was assumed to be at <0,0,8 RE>GSM (i.e. above the north pole) for these simulations. The panels were all generated at the 1 ° x1 ° resolution estimated by Calvert . The first panel shows returns from 900 kHz waves which penetrate everything but the polar ionosphere. At this frequency, the sounder is acting as a topside sounder, since the transmitted frequency exceeds the plasma frequency of all other magnetospheric structures. The second panel shows echoes from a 40 kHz sounding, where the returns highlight more of the geometry of the plasmasphere as well as two reflections off the boundary layers to the north and south. The third panel uses a 28 kHz transmission to reveal Kelvin-Helmholtz waves on the inner boundary layers, as well as the plasmasphere. Comparing the second and third panels illustrates a sounder's ability to distinguish between different boundary layer configurations, which can be difficult to differentiate via in-situ measurements (Fig. 5) [22]. The final panel is at 20 kHz, which is high enough to pass through the tail lobes and the auroral cavity, but low enough to be reflected by most magnetospheric structures. Although most of the cusp returns are very weak, one segment and one spot have gradients which return waves to the sounder. The locations of the returns depend on the location of the sounder as well as the geometry of the cusp and magnetopause/boundary layers. At certain sounding frequencies, the cusp shows clearly by virtue of its blocking of portions of the boundary layer echoes from the dayside magnetopause. The rapid sampling of the cusp position and velocity by the sounder would significantly aid in understanding the response of the high altitude cusp to changing IMF conditions. The sounder design discussed by Calvert would sound to both higher and lower densities than are shown here.

For comparison, a sequence of skymaps showing the motion of a surface wave in the boundary layers is shown using the GSFC raytracer in Fig. 5. These images are analogous to the +ZGSM facing segments of Figs. 2 and 3 at several subsequent times. This simulation also conforms to the sounder described by Calvert, but does not have as many sub-models as the high frequency simulation. In this figure the gray scale does not correspond to a true intensity (as in Figs. 2, 3), but rather to a 'ray missed distance', which is an analog for echo power flux.


Figure 4. The high frequency raytracing simulations of a sounder 8 RE above the north pole show the locations of O mode returns at several frequencies. Darker regions indicate stronger returns. A wave on the inner boundary layer is visible at frequencies corresponding to the boundary layer's plasma frequency. The cusp reflects only very low frequency waves. At intermediate frequencies, the model predicts a weak reflection from the southern hemisphere magnetopause (dashed arrow). However, this ray path will suffer significant refraction passing through the plasmasphere, and the more accurate GSFC raytracer should be used for these ray paths. At each frequency, 90 ° fields of view centered along -ZGSM, +XGSM, and +ZGSM are shown.


Figure 5. A simulated K-H wave is visible via the enhanced return from O mode waves off the boundary layer in these 'skymaps' from the GSFC raytracer. Each frame corresponds to successive soundings, showing the wave phase advancing on times comparable to the sounding repetition period (~ 1 minute).The gray scale corresponds to the ´missed distance═ of returning echoes, which is an analog to echo power flux, while polar look-angles about +ZGSM (the center of each figure) are shown in overlaid on the echo returns. The thin vertical stripe corresponds to echoes from the wave crest, the curves correspond to echoes from the wave troughs. Adapted from [10].

These simulated radio images are only one way of organizing the echo data. From the returns and their time delays, it is possible to determine the density and field strength at each point that reflects a wave to the sounder. At the same time, from Doppler and other information, velocity profiles can also be constructed from the same returns. Simulated plasmagrams, and the density profiles that were used by the Goddard plasma wave raytracer to generate them, are shown in Fig. 6. Plasmagrams are another selectable output of the simulation software which directly simulate the process by which an actual sounder would probe the magnetosphere.


Figure 6. A model magnetopause/boundary layer density profile and the resulting O mode plasmagram from the Goddard raytracer. These plasmagrams are analogous to bottomside ionograms, but are only a fraction of the information that would be returned by echoes to a magnetospheric sounder. A sounder will typically receive echoes from several locations at each frequency, allowing construction of plots such as these for each reflection point. The analogous X mode plasmagrams are not shown, but when combined with O mode data may yield information on magnetic structures. Adapted from [10].

Summary

Radio sounding offers a way to simultaneously measure the largest and some of the smallest scales in the magnetosphere, plasmasphere, and boundary layers. Calculations and simulations indicate a sounder will be able to measure many aspects of virtually all major nearearth plasma and field structures. In the plasmasphere, a sounder could observe scales as small as a few hundred kilometers, and as large as the plasmasphere itself. At the magnetopause, a sounder could quantify the overall response of the magnetosphere to changes in solar wind pressure and IMF while simultaneously observing small scale structures and waves. Additionally, the ability to simultaneously measure several remote regions at high time resolution could provide valuable information on the interconnections of and interactions between magnetospheric regions. At a time when magnetospheric models still have relatively large disagreements concerning issues as major as the location of the plasma cusp as a function of the IMF and the methods of plasmasphere refilling, an instrument which can provide both small scale and large scale measurements at high time resolution throughout the magnetosphere should be a high priority. Given the possible rewards from a new class of spaceborne digital sounder, and the long flight and ground history of sounding, magnetospheric sounding may offer one of the best new techniques for studying multiscale plasmas.

References

[1] P. H. Reiff, J. L. Green, R. F. Benson, D. L. Carpenter, W. Calvert, S. F. Fung, D. L. Gallagher, B. W. Reinisch, M. F. Smith, and W. W. L. Taylor, EOS, 75, 129 (1994).

[2] B. W. Reinisch, Radio Science, 21, 331 (1986).

[3] J. E. Jackson, AlouetteISIS Program Summary, NSSDC/WDCAR&S 86, NASA Goddard Space Flight Center, Greenbelt MD (1986).

[4] P. L. Dyson and J. D. Winningham, J. Geophys. Res., 79, 521 (1974).

[5] W. Calvert, R. F. Benson, D. L. Carpenter, S. F. Fung, D. L. Gallagher, J. L. Green, D. M. Haines, P. H. Reiff, B. W. Reinisch, M. F. Smith, and W. W. L. Taylor, in press, Radio Science (1995).

[6] F. F. Chen, Introduction to Plasma Physics, Plenum Press, New York (1974).

[7] T. H. Stix, Waves in Plasmas, American Institute of Physics, New York (1992).

[8] J. L. Green, and D. A. Gurnett, Geophys. Res. Lett., 7, 65 (1980).

[9] Y. Omura, and J. L. Green, J. Geophys. Res., 98, 9189 (1993).

[10] S. Fung, J. L. Green, W. W. L. Taylor, M. F. Smith, R. F. Benson, W. Calvert, D. L. Carpenter, D. L. Gallagher, P. H. Reiff, and B. W. Reinisch, submitted to Geophys. Res. Lett. (1995).

[11] P. H. Reiff, Magnetopause Mapper (Ionosonde), Section 6.5, Space Physics Missions Handbook, R. A. Cooper and D. H. Burks eds., NASA OSSA (1991).

[12] J. L. Green and S. F. Fung, Adv. Space Res., 14, 217(1994).

[13] B. W. Reinisch, private communication, 1995.

[14] D. A. Gurnett and R. R. Anderson, in Physics of Auroral Arc Formation, Geophys. Monogr. Ser., 25, Akasofu and Kan, eds. (American Geophysi cal Union, Washington, D.C., 1981), p. 341.

[15] R. F. Benson, M. M.. Mellott, R. L. Huff, and D. A. Gurnett, J. Geophys. Res., 93, 7515 (1988).

[16] W. S. Kurth, D. A. Gurnett, R. R. Anderson, J. Geophys. Res., 86, 5519 (1981).

[17] D. Morgan and D. A. Gurnett, J. Geophys. Res., 96, 9595 (1991).

[18] D. P. Stern, J. Geophys. Res. 86, 5839 (1981).

[19] D. G. Sibeck, R. A. Lopez, and E. C. Roelof, J. Geophys. Res., 96, 5489 (1981).

[20] J. L. Green, Raytracing of planetary radio emissions, Planetary Radio Emissions II, Proceedings of the 2nd international workshop held at Graz, (Austrian Academy of Science, Vienna, 1988), p. 355.

[21] P. H. Reiff, J. L. Green, R. F. Benson, D. L. Carpenter, W. Calvert, S. F. Fung, D. L. Gallagher, Y. Omura, B. W. Reinisch, M. F. Smith, and W. W. L. Taylor, Remotes sensing of substorm dynamics via radio sounding, Substorms 2, Proceedings of the Second Intl. Conference on Substorms, J. R. Kan, J. D. Craven, and S. I. Akasofu, eds. (U of Alaska Press, Fairbanks, 1994), p. 261.

[22] N. Sckopke, G. Paschmann, G. Haerendel, B. U. Sonnerup, S. J. Bame, T. G. Forbes, E. W. Hones, and C. T. Russell, J. Geophys. Res., 86, 2099 (1981).

[23] Since this talk was given, ring current models have been added to the GSFC simulation.

[24] The authors may also be reached via electronic mail at:


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