During the NASA Space Physics Strategy-Implementation Study of 1990, we suggested using radio sounders to study the magnetopause and its boundary layers [Reiff, 1991], and to study the plasmasphere [Green and Fung, 1994]. The magnetopause, plasmasphere, as well as the cusp and boundary layers, can be remotely monitored if a radio sounder is placed on a high-inclination polar-orbiting spacecraft with a reasonable (>=6 RE) apogee (Figure 1, from Reiff et al. ).
Radio sounding techniques date back to the study of the ionosphere by Breit and Tuve . Swept-frequency ground-based sounders are used to monitor the electron number density (Ne) structure of the ionosphere up to the F-layer density peak with high time resolution. The early instruments evolved into a global network which produced high-resolution ionograms (displays of echo delay versus frequency) on 35 mm film. The bottomside electron density profiles deduced from these records provided one of the cornerstones of the success of the International Geophysical Year [Berkner, 1959].
Topside ionospheric densities, above the F-layer density maximum, were first measured in the Alouette/ISIS (International Satellites for Ionospheric Studies) program [Franklin and Maclean, 1969; Jackson et al., 1980]. A series of consecutive profiles can be combined to create orbital-plane Ne contours from the satellite altitude to the altitude of the F layer peak density [Nelms and Lockwood, 1966 and Benson, 1985 and references therein]. Comparisons of densities from topside and bottomside sounders, and multi-spacecraft studies have indicated that the error of the Alouette/ISIS-derived Ne values is typically within 10%, even at the most remote distances [Whitteker et al., 1976; Hoegy and Benson, 1988 and references therein]. ISIS demonstrated the synergism between sounders and optical imagers on the same spacecraft [Lui and Anger, 1973; Shepherd et al., 1976]. Digital technology was used in later spacecraft sounders, such as in Japan's ISS-b (Ionosphere Sounding Satellite), Ohzora (also called EXOS-C), and Akebono (or EXOS-D) spacecraft; and in the USSR's Intercosmos 19 and Cosmos 1809 missions [see Green et al. 1994 and references therein]. ISIS also showed the ability to remotely sound the magnetospheric cusp [Dyson and Winningham, 1974]. The ISIS-C spacecraft would have contained a sounder with a similar orbit and similar science objectives to that discussed here, but was never flown [J. D. Winningham, personal communication, 1994].
Bottomside (ground-based) ionospheric sounders have enjoyed great advances over the last few decades [Hunsucker, 1991]. These advanced ionospheric sounders can measure the frequency, time delay, amplitude, phase, Doppler shift and spread, polarization, and direction of arrival of the echo. Two sounders in this class are the Dynasonde (developed at the U.S. Department of Commerce Laboratories in Boulder) and the Digisonde (developed at the University of Massachusetts Lowell). These instruments offer a high degree of flexibility in measurement format since their operations are controlled by software [Reinisch, 1986]. Evidence that their scientific capabilities go far beyond the Ne profiles of the standard ionosondes is indicated from results that show, for example, turbulence, drifts, winds and structures [Wright and Hunsucker, 1983; Buchau et al., 1988]. A new generation of spaceborne sounders can use these latest techniques [Reinisch et al., 1992] to make sounding of the magnetosphere possible with very modest power requirements by taking advantage of spread spectrum pulse compression and Fourier transform processing. A 500m tip-to-tip dipole is planned as transmitting antenna.
Figure 2 shows the variation of the square of the ratio of the wave phase velocity vph to the speed of light c on a scale of increasing frequency, for several wave modes. The cross-hatched regions represent the forbidden frequency ranges in which the indicated waves cannot propagate. The Z mode has a lower frequency cutoff fz (when vph2/c2 = [[infinity]]) and an upper frequency resonance (when vph2/c2 = 0) that restricts its propagation and is thus referred to as a trapped mode of the plasma. This wave mode is unsuitable for use in direct sounding to great distances. The whistler mode (not shown in the figure) is also a trapped mode.
Since the X and O modes have no propagation restrictions above their low frequency cutoffs (Figure 2), they are suitable for remote radio sounding. The cutoff for the O mode is the local plasma frequency fp,
when Ne is expressed in cm-3; [[epsilon]]o 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
fg = (1/2[[pi]])eB/m = 28.0 B (Hz) (3)
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 plasma cutoffs; thus they are called the free-space modes.
A swept-frequency sounder transmits and receives a sequence of X and O mode pulses, with the frequencies increasing stepwise. When the transmitted waves enter a region of increasing plasma density or magnetic field strength, the pulse is reflected when the wave frequency matches the cutoff frequency. Most of the inner magnetosphere has a relatively low density - thus a satellite lies between increasing density gradients at the magnetopause and at the plasmasphere (see Figure 1). For most magnetospheric applications the primary echo paths will be approximately perpendicular to the plasma density contours at reflection. A data record (plasmagram) consists of the time delay and amplitude, along with complex Doppler and angle-of-arrival information, for each sounding frequency and polarization.
Thus the swept-frequency measurements permit the determination of the electron plasma density profiles of remote plasma regions [see, e.g., Jackson et al., 1980; Huang and Reinisch, 1982], so long as the density is generally increasing with distance. Magnetospheric density structures are quite dynamic in space and in time. Thus each transmission will typically result in more than one echo (Figure 3). Returns will usually be obtained from several directions for the same frequency transmission, but each will exhibit a different time delay, angle of return, and Doppler shift, thereby allowing a rough cross-section within minutes. From a sequence of profiles taken during a portion of a single orbit, one can produce two-dimensional, cross-sectional magnetospheric images (Figure 1). Raytracing studies indicate that from a dayside position much as in Figure 1, signal returns would also be received from the dawn and dusk magnetopause [Fung et al., 1994]. Thus information on the 3-D magnetospheric Ne structures will also be obtained. For more information on the technique and applications of magnetospheric radio sounding, see Green et al. , Reiff et al. , Fung et al., Green et al., and Calvert et al. .
A sounder, by monitoring the location of the magnetopause and the time evolution of the magnetopause boundary layers, can determine (1) the variability of plasma mantle density and thickness in response to the southward and westward components of the IMF, and (2) the passage of wave structures in the low-latitude boundary layer [Rosenbauer et al., 1975; Paschmann et al., 1978; Paschmann, 1984]. One can readily determine from a sequence of sounder measurements whether the inner edge of the boundary layer moves only in phase with the magnetopause motion (Figure 3, left), or whether the thickness of the layer varies in time as the plasmas move downstream (Figure 3, right [from Reiff et al., 1994]).
A radio sounder, by using its direction-finding capability [Calvert et al., 1994], can determine the distance from the spacecraft to one or more locations on the magnetopause simultaneously [Fung et al., 1994]. By comparing sounder observations with simultaneous solar wind data from solar wind monitoring spacecraft such as WIND and IMP-8, one can test the solar wind dependence of empirical magnetopause models such as Sibeck et al. , Roelof and Sibeck , and Petrinec and Russell [1993a, b].
In the special case of spacecraft near apogee in the near-Earth magnetotail (or a lunar-based instrument when the Moon is in the magnetotail [Reiff, 1991; Green and Fung, 1994]), one can receive the reflected signals from both the dawn and duskside equatorial magnetopause and north and south high latitude magnetopause nearly simultaneously (Figure 4). It can then determine whether the magnetospheric tail is flattened and/or twisted by the IMF, as has been proposed [e.g. Fairfield, 1992 and references therein]. By determining the size of the magnetotail and having some information about the field strength derived from the X mode echoes, it will be possible to monitor the magnetic flux in the magnetotail and thus the net (dayside minus tail) magnetic merging rates [Russell and McPherron, 1973]. Note that a sounder system located in the high-latitude lobes may be able to sound through the low-density plasmasheet to the far side magnetopause.
In certain geometries, it may also be possible to monitor the growth and motion of plasmoids in the magnetotail. In the near-earth neutral line model of a substorm [Hones, 1979], a plasmoid forms, grows, and disconnects in a substorm cycle [e.g. Baker et al., 1987; Slavin et al., 1989]. If a sounder is situated in the high-latitude lobes (e.g., at XSM ~-20 RE, |ZSM| ~10), it may be able to sound off the density enhancement of the growing and moving plasmoid. A schematic of this reflection geometry is shown in Figure 5 (adapted from Richardson and Cowley, 1987]. In the near-earth magnetotail (<100 RE), the magnetotail lobe density is much smaller than the plasmasheet density [Slavin et al., 1985] and a sounder should be able to remotely sense a plasmoid. In the distant (>100 RE) magnetotail, however, the lobes have a great deal of plasma in them and the density contrast is not sufficient to return an echo from the plasmoid [Frank and Paterson, this volume].
A plasmoid moving down tail past the sounder may allow a sequence of soundings to yield information on the growth and motion of the plasmoid, and monitoring of the deformation of the magnetopause as the plasmoid moves [e.g. Slavin et al., 1993]. A schematic of the possible geometry is shown in Figure 6. As a first test of this idea, we have taken the MHD plasmoid model developed by Omura and Green  and performed raytracing calculations with a test sounder in the near-Earth magnetotail lobe. A set of sample rays emanating from the spacecraft are shown bouncing off of the plasmoid (Figure 7). Here the sounding frequency is near 11 kHz, corresponding to a density of about 1.5 cm-3. Divergence of the rays as they refract off the plasmoid indicate the defocusing aspect of the convex surface [Reiff et al., 1994; Calvert et al., 1994].
Higher sounding frequencies can penetrate the plasmoid and may allow sounding of the far side magnetopause. Figure 8 shows a raytracing at 14 kHz (corresponding to 2.4 cm-3 density), the minimum frequency which will traverse the plasmoid. Higher frequency pulses will exhibit less refraction than shown here. The return signal from the far magnetopause will be weak, since the reflecting surface is far away; however, the signal should be focused from the concave nature of the magnetopause and may well be detectable.
Acknowledgements We would like to acknowledge early discussions of this idea with Stan Shawhan, who gave us (PHR and JLG) strong encouragement. We acknowledge helpful discussions with David Winningham and Roger Anderson. The work at Rice University was supported by NASA under grant NAGW 1655, and at Nichols Research Corporation under contract 507854-f.
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