Radio Plasma Imaging for the Proposed Inner Magnetosphere Imager (IMI)

J. L. Green, R. F. Benson, W. Calvert, S. F. Fung, P. H. Reiff, B. W. Reinisch, and W. W. L. Taylor

February 1993
A report on remotely imaging the plasma density and magnetic field boundaries in the magnetosphere by radio sounding

NSSDC Technical Publication

PREFACE

The Inner Magnetosphere Imager (IMI) is being studied by NASA as a potential new start in the Office of Space Science and Applications. A Science Definition Team (Thomas P. Armstrong, Chairman) has been meeting since 1991 to study the scientific feasibility of imaging the inner magnetosphere from a scientific spacecraft. In July 1991, the Team published an initial report, Inner Magnetosphere Imager: Scientific Rationale and Mission Concept. To support the Science Definition Team, studies are being performed at Marshall Space Flight Center to evaluate the engineering feasibility of the concept. A Preliminary Engineering Concept Study was issued in June 1991. Both the scientific and engineering studies reached similar, positive conclusions, that the concept is feasible and that studies should continue.

The Science Definition Team is now preparing a second report and has requested an additional report to be prepared by an ad hoc science team, in another area of magnetospheric imaging, plasma sounding. This ad hoc science team, (the Plasma Sounder Team) has prepared the following report and will present its findings at the next meeting of the IMI Science Definition Team, February 22-23, 1993, in Washington, D. C. The members of the Plasma Sounder Team are given below.

EXECUTIVE SUMMARY

Imaging of the Earth's magnetosphere would be an important and exciting new initiative for the 1995-2015 time period as reported by a task group of the Space Science Board of the National Academy of Sciences [Scarf, 1988]. Such images, in fact, could be as important for studying magnetospheric morphology and dynamics as auroral images have become for studying the aurora [Frank and Craven, 1988]. The scientific objectives of the Inner Magnetosphere Imager (IMI) mission as described by Armstrong et al. [1991] are thus directly pertinent to the recommendations of the Space Science Board study.

The current IMI strawman payload includes imagers for observing the geocorona in the far ultra-violet (FUV), the aurora in the FUV and X-ray wavelengths, heavy ions in the plasmasphere from scattered extreme ultra-violet (EUV) radiation, and the ring current by energetic neutral atom detection. The purpose of this report is to introduce radio sounding techniques for the purpose of remotely measuring plasma density and to show how this technique naturally complements the instruments already defined for the IMI mission.

For probing the various magnetospheric plasma regions and determining their densities and distances a Radio Plasma Imager (RPI) will transmit and receive radio wave pulses at frequencies ranging from 3 kHz to 3 MHz. Using the echo delay and the direction of arrival of the echo signals, it will be possible to generate two-dimensional cross-sectional images of the plasmasphere and auroral zone during a single orbit, and to monitor the positions of critical plasma and magnetic boundaries such as the plasmapause and magnetopause on time scales of a few minutes.

Combining the RPI capabilities with those of the other IMI instruments would enable fundamental questions of magnetospheric morphology and dynamics to be addressed. For example, the interaction between the ring current and the inner magnetospheric plasma can be determined by the energetic neutral atom (ENA) and RPI instruments. Similarly, comparing the data from the ENA and geocorona imagers with the RPI electron density measurements would enable the study of the relationship between the loss and replenishment of neutral hydrogen from the geocorona and the inner plasmaspheric structure. In the auroral zone, RPI measurements would permit comparison of auroral emission patterns, and AKR source locations, with auroral plasma cavity density structures. While the IMI instruments are producing images of the plasmasphere and aurora, the location of the magnetopause can be monitored nearly continuously by the RPI. These combined observations would show global cause-and-effect relationships of fundamental importance to magnetospheric structure and dynamics.

The RPI considered for this study uses two long dipoles antennas in the satellite spin plane (500 meter tip-to-tip length) and a short dipole along the spin axis (10 meter). Pulses of a few milliwatts to a few watts will be transmitted from the long antennas, thus causing little if any interference with other instruments. Current estimates are that the antennas should weigh roughly 18 kg, instrument should weigh roughly 14 kg, require about 25 watts of power to operate and a data rate of about 5 kilobits/second with onboard processing and data compression.

Satellite sounders have proven to be quite successful since the mid 1960's. Ground based sounders using advanced digital techniques have proven that the RPI will face minimal technological risks. We believe that the RPI electron plasma density and range measurements will be critical for interpreting the data from other IMI instruments and for defining pertinent regions of the magnetosphere. The scientific benefits of the RPI to the IMI mission would be extremely high.

1.0 INTRODUCTION

In the last thirty years of ionospheric and magnetospheric research, there have only been a few spacecraft instruments that have been able to make remote sensing observations of extended plasma regions. There have been instruments for ionospheric sounding, observing auroral at different electromagnetic wavelengths, and for the detection of energetic neutral atoms from storm time ring current interactions. As discussed in the excellent review by Williams et al. [1992], many of the techniques reviewed could produce images of various regions of the inner magnetosphere such as the auroral zone, plasmasphere, ring current, geocorona, and plasma sheet in a way never before achieved in space plasma observations, which has been dominated predominantly by in situ measurements.

The main scientific objective of the Inner Magnetospheric Imager (IMI) Mission is to understand the global evolution of the structure of the magnetosphere and the relationships between key magnetospheric plasma regimes using imaging instruments. The IMI Science Definition Team is in the process of completing an initial scientific and engineering study with an emphasis on instruments capable of imaging the magnetosphere in the far and extreme ultraviolet radiation, X-ray radiation, and energetic neutral atoms. The purpose of this report is to introduce the technique of radio wave sounding by a Radio Plasma Imager (RPI) to detect remote magnetospheric plasma regimes and show how this technique is a natural complement to the instruments already defined for the IMI mission.

2.0 BACKGROUND AND PREVIOUS STUDIES

The investigation of the ionosphere using radio sounding techniques dates back more than a half century to the experiments performed using selected fixed frequencies by Breit and Tuve [1926]. These early experiments indicated the need for swept-frequency sounders which were developed and evolved into a global network of sophisticated instruments that produced high-resolution ionograms (displays of echo delay versus frequency) on 35 mm film [Brown, 1959]. The resulting electron-density (Ne) profiles of the bottomside of the ionosphere provided a major input toward achieving the goals of the International Geophysical Year [Berkner, 1959].

As technology advanced, ionospheric swept-frequency sounders were incorporated into satellites in order to obtain Ne profiles of the topside of the ionosphere, above the density maximum and thus inaccessible from ground based sounders. ISIS (International Satellites for Ionospheric Studies), one of the most successful long-lasting international space programs, produced more than 50 satellite-years of ionospheric topside-sounder data. These data were used to combine Ne profiles obtained from successive ionograms to produce 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]. Topside/bottomside density comparisons and multi-spacecraft rendezvous studies have indicated that the accuracy of the ISIS sounder-derived Ne values (even at the most remote distances) is typically a few percent and no greater than 10% [Jackson, 1969b; Whitteker et al., 1976; Hoegy and Benson, 1988 and references therein]. In addition, the ISIS satellites also demonstrated that the sounders could operate in a manner compatible with other instruments on the same spacecraft. This compatibility was particularly well illustrated with ISIS 2 which, in addition to producing Ne profiles, produced the first monochromatic auroral images from space for scientific investigations [Lui and Anger, 1973; Shepherd et al., 1976].

Later spacecraft-borne sounders, employing digital technology, were developed in Japan for ISS-b (Ionosphere Sounding Satellite) [Maruyama and Matuura, 1984], Ohzora (also called EXOS-C) [Oya et al., 1985], and for Akebono (or EXOS-D) [Oya et al., 1990] and in the former USSR for Intercosmos 19 and Cosmos 1809 [Shuiskaya et al., 1990]. Relaxation sounders, which transmit very low power, are designed to stimulate plasma resonances in the ambient medium near the spacecraft for diagnostic purposes, have been flown on a variety of spacecraft over the last 15 years: GEOS 1 & 2 and ISEE 1 [Etcheto et al., 1983], Jikiken (EXOS B) [Oya and Ono, 1987], Viking [Perraut et al., 1990], Oedipus A [James, 1991], and Ulysses [Stone et al., 1992].

The greatest advance in sounding techniques has been employed in bottomside (ground based) ionospheric sounders over the last few decades, the Advanced Ionospheric Sounders (AIS), as described in the recent book by Hunsucker [1991]. In addition to measuring the amplitude and time delay of the returned pulse, as done by simple ground based ionosondes, these AIS instruments measure the exact frequency, phase, Doppler shift, 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). An important feature of these instruments is the high degree of flexibility in measurement format since operations are controlled by software. Evidence that their scientific capabilities go far beyond the Ne profiles of the standard ionosondes is indicated from results that show, for example, turbulence, winds and structures, [Wright and Hunsucker, 1983 and Buchau et al., 1988]. These latest techniques can now be implemented in space-borne instruments to make sounding of the magnetosphere possible with modest power.

3.0 RADIO WAVE SOUNDING OF THE MAGNETOSPHERE

Radio wave sounding in the magnetosphere uses the same principles as ionospheric sounding. A cold magnetized plasma supports two freely propagating electromagnetic waves, the O (for ordinary) and X (for extraordinary) modes with two distinct phase velocities and polarizations [Budden, 1985; Stix, 1992]. The propagation characteristics of these electromagnetic waves are determined by the electron plasma frequency (fp) and gyrofrequency (fb) of the plasma.

As an illustration, we display in Figure 1 several plasma characteristic frequencies on a scale of increasing frequency. In this example, the cross-hatched regions show the allowed frequency ranges in which the O and X modes can propagate in a medium with fp < fb (typical of the plasma characteristics over a significant portion of the nominal IMI orbit [Armstrong et al., 1991]). The whistler and Z modes, shown as shaded regions, have upper frequency cutoffs or resonances and are referred to as trapped modes of the plasma. Thus they are unsuitable for use in direct sounding to great distances.

Figure 1. A schematic frequency diagram showing the propagation modes supported by a cold plasma when the local electron gyrofrequency is greater than the local electron plasma frequency. For the purposes of remote sensing, the O and X propagation modes are the most appealing since their lowest frequency limits are the local electron plasma frequency and the fx cutoff frequency, respectively. From a knowledge of the plasma frequency, the electron gyrofrequency can be derived. The lower frequency cutoffs of the Z and whistler mode are not shown since they are not relevant to this study.

On the other hand, the X and O modes have only lower frequency cutoffs (Figure 1). The cutoff for the O mode is the local fp,

(1)

in which Ne is the electron density (cm-3), [epsilon]0 is the permitivity of free space, e is the electronic charge and m is the electronic mass. For the X mode, the lower frequency cutoff is

(2)

where

fb = (1/2[pi])eB/m = 2.80 B(gauss) MHz (3)

and B is the magnetic field strength. These two modes can propagate freely at or near the speed of light c when the wave frequencies exceed the plasma cutoffs and hence are called the free-space modes.

A swept-frequency sounder, generally consisting of a radio transmitter and receiver, transmits pulses typically 100 microseconds long at sequentially increasing frequencies. The receiver operates at the same frequency for several milliseconds after each pulse.

When the freely propagating transmitted waves enter a density or magnetic field gradient, they will be reflected upon encountering their respective plasma cutoff (i.e., when a plasma cutoff frequency equals the wave frequency) [Budden, 1985; Stix, 1992]. Thus, the measurements of the time delays and frequencies of the radio echoes by the receiver will produce data records of the echoed signal amplitude as a function of echo delay and frequency, analogous to the ionograms.

From the swept-frequency sounder measurements, one can determine the line-of-sight electron plasma density profiles in remote plasma regions. The analysis procedure, known as "true range" analysis, is straightforward and well developed for analyzing ionospheric sounder data. It is an inversion technique that takes into account the density profile dependence of the refractive index between the sounder and the point of reflection at a given frequency. By starting with echoes having the lowest frequencies and shortest time delays, hence the nearest echoes, and extending to signals of higher frequencies and longer delays, one can then recover the plasma profile between the sounder and the remote plasma location [Jackson, 1967, 1969a; Huang and Reinisch, 1982]. Ground and space-based radio sounders have used this technique quite successfully for decades in the bottomside and topside of the ionosphere, respectively.

The data from a sounder can be presented in a "plasmagram" as sketched in Figure 2 as it may appear to a receiving spacecraft at 6 Re (see similar plasmagram examples in Ondoh et al., [1978]; Green and Fung, [1993]; and Green et al., [1993]). The plasmapause density step is assumed here to increase from 10 to 100 cm-3 at a distance of 2 Re. The O and X echo delays, from which the electron density profile is determined, begin at zero range at the local plasma and X cutoff frequencies. They gradually increase with frequency as the echo point moves further from the satellite. Once the plasmapause is reached, waves with frequencies between 30 and 90 kHz will be reflected with decreasing delays as the frequency increases. At higher frequencies, the corresponding echo points migrate into the plasmasphere or even the topside ionosphere (with fp ~ few MHz), resulting in longer time delays of the associated echoed pulses.

Figure 2. A schematic plasmagram of the magnetosphere. Note that echoes from the magnetopause as well as the plasmapause can readily be obtained.

Since echoes from other remote plasma regions in other directions are also possible, echoes from, e.g. , the magnetopause should also appear simultaneously at low frequencies. Thus, the salient features of the global magnetosphere such as plasma density profiles and distances to the magnetopause and plasmapause as well as the density structure of the plasmasphere could be measured from the RPI data. From a sequence of line-of-sight density profiles taken during a single orbit (or partial orbit), it would be possible to produce two-dimensional, cross-sectional images of the plasmasphere on the same time scale as the other IMI images (10 to 30 minutes) as illustrated in Figure 3. As mentioned previously, this technique has been used in the ionosphere [e.g., Nelms and Lockwood, 1966; Benson, 1985 and references therein]. Complete images can also be obtained by fitting several sounder-observed density profiles with standard models of the plasmasphere and magnetopause such as Angerami and Thomas, [1964],Gallagher et al., [1988] and Sibeck et al., [1991].

Figure 3. An idealized sketch of a combined set of images. The RPI instrument will be able to remotely sense the magnetopause, the plasmapause, and much of the plasmaspheric structure.

The construction of images from multiple echoes requires the determination of echo directions. Echo wave polarization and direction of arrival are determined from the amplitudes and phases of the echo signals received separately on three orthogonal antennas. This techniques has been used extensively on DE-1, ISEE-3, and other spacecraft [see for example: Calvert, 1985; Fainberg et al., 1985; Huff et al., 1988; Kurth et al., 1975] for direction finding of natural emissions. However, three new aspects not previously pertinent to radio sounding of ionospheric plasma must now be considered:

1) Since the sounding distances will no longer be negligible compared to the radius of curvature of reflecting surfaces, curvature focusing effects are significant.

2) Since the echo direction (previously predominately vertical because of the horizontal stratification of the ionosphere) will now vary, it is necessary to measure or otherwise determine the echo direction of arrival.

3) Since the echoes will be from greater distances and there will be a lower signal to noise ratio, modern digital techniques will be needed to sufficiently enhance the echo signals.

Using today's technologies, all three of these aspects can now be adequately addressed.

As described in detail in Appendix A, the effect of a curved reflecting surface is to enhance (or decrease) the echo amplitude by a factor of F,

(4)

where r is the range and R (positive for a convex surface) is the reflecting surface radius of curvature [see Davies, 1990]. The factor F reduces the echo signal strength from the plasmasphere by roughly 10 dB, whereas for the magnetopause, it is increased by a comparable amount. Thus, the negative (concave) curvature focusing effect makes it possible to routinely sound the magnetopause.

Plasma densities in the magnetosphere range from 0.1-1 cm-3 in the auroral plasma cavity and magnetospheric lobes to 10-30 cm-3 at the magnetopause and 102- 106 cm-3 in the plasmasphere and ionosphere. The pertinent frequencies for magnetospheric sounding, therefore, range from 3 kHz to 3 MHz. The corresponding echo delays for a satellite sounder at a few Earth radii above the plasmapause would be a few tenths of a second (using an average propagation speed of c/2 or 43 ms per Re).

Although finding the echo direction generally requires three orthogonal antennas, signal directions can be determined with only one or two antennas under certain circumstances (see the techniques developed by Kurth et al., [1975]; Fainberg et al., [1985]; Calvert, [1985]; Huff et al., [1988]). In such cases, stronger signals are required to determine echo directions, but such measurements should be possible to an accuracy of about one degree throughout most of the plasmasphere (where they are needed most), and outside the plasmasphere during quiet times for the soundings of the plasmapause and magnetopause.

4.0 SCIENTIFIC OBJECTIVES

4.1 Primary Scientific Objectives

The primary scientific objective of the RPI will be to study the global structure and dynamics of the plasmasphere, a region of dense cold plasma of ionospheric origin surrounding the Earth and often having a sharp field-aligned outer boundary, the plasmapause. The plasmasphere is known to be very dynamic. The equatorial plasmapause has been observed at distances varying between 2 and 7 Re as the magnetospheric conditions change from active to quiet [Carpenter, 1966]. A recent statistical study by Horwitz et al. [1990] shows that plasmaspheric (cold plasma) ion density profiles exhibit significant complex structure (such as multiple plateaus and/or troughs) about 60% of the time. These complex profiles are presumably the plasmaspheric responses to the variations in time of magnetospheric convection and magnetic activity. The distinct advantage of the RPI over previous in situ measurements of the plasmasphere will be the nearly instantaneous determination of plasmaspheric electron density profiles. Therefore, nearly the same region can be probed repeatedly within minutes, allowing separation of spatial from temporal phenomena in the plasmasphere and at the plasmapause, and thus providing for the first time observations of plasmaspheric evolution.

The plasmasphere constantly interacts with the much higher energy plasmas in the radiation zones and the ring current in the equatorial boundary regions of the inner magnetosphere. The dynamics of these regions have been studied in the context of magnetospheric storms and substorms [Horwitz et al., 1984]. During magnetospheric substorms, the changes in the global electric and magnetic fields during the growth and expansion phases significantly change the plasmapause location. The enhanced convection and induced electric fields energize and inject magnetospheric particles into the ring current region. Although charge exchange between the ring current ions and the neutral hydrogen in the geocorona is believed to be the primary loss mechanism for depleting the inner ring current ions, wave-particle interactions also cause ring current ions to be lost through pitch-angle diffusion, resulting in precipitation into the ionosphere. Simultaneous measurements by the energetic neutral atom instrument and the RPI instrument will provide the opportunity to observe directly the interaction processes between the cold plasma of the plasmasphere and the hot plasmas of the ring current.

RPI sounding measurements can also be used to determine the extent of auroral zone density cavities. In situ and remote plasma density measurements of the high altitude auroral zone over the last ten years have revealed density depletion regions or cavities associated with the auroral acceleration regions and sources of the auroral kilometric radiation (AKR) [see for example, Benson and Calvert, 1979; Calvert, 1981a; Benson, 1985; Persoon, et al., 1988; and Hilgers, et al., 1992]. Density cavities in the auroral zone have major roles in auroral plasma dynamics, the auroral acceleration processes, and in the generation and propagation of many auroral zone plasma and radio emissions such as AKR.

The actual density profiles of the auroral density cavities, how they are created, what role they play in the generation of AKR and how they relate to auroral arcs and substorm activities are still not clear. For instance, Benson [1985] found by using the ISIS I topside sounder data, that cavities below 1.5 Re have latitudinal widths ranging from a few degrees to a few tens of degrees. Calvert [1981a] obtained a statistical picture of a large (20[ring] wide in latitude) auroral plasma cavity structure by combining the observations of multiple auroral zone crossings by the Hawkeye spacecraft (radial distances of 1.5 to 2.5 Re). More recently, Hilgers, et al. [1992] found that the auroral zone density cavities observed by the Viking spacecraft at altitudes between 6500 to 8500 km were associated with regions of upward (field-aligned) ion beams and downward electron beams, and that the latitudinal extent of these cavities were much smaller. Simultaneous measurements by the Auroral Imager and the RPI instruments on IMI will provide the opportunity to relate the wide variety of observed auroral zone density structures with auroral FUV and radio emissions and substorm activities.

4.2 Additional Science Capabilities

Effects of magnetospheric substorms have been observed for many years by instruments on the ground and on orbiting satellites. Substorms and the associated phenomena play critical roles in determining the global structure and dynamics of the magnetosphere [Akasofu, 1977; Kan et al., 1991 and references therein]. Despite the effort of many researchers to develop various substorm models [see review by McPherron, 1991], the lack of coherent and global observations of magnetospheric substorm processes renders the synthesis of a global substorm model a formidable task in modern space plasma physics.

Since it has been shown that AKR is a sensitive indicator of auroral and magnetic activity [see for example: Gurnett, 1974; Voots et al., 1977; Benson and Akasofu, 1984], the RPI will be used to monitor inner magnetospheric conditions by observing the occurrence of AKR during magnetospheric substorms. The RPI receiver can also observe the fine structure of AKR [Anderson and Gurnett, 1981; Benson et al., 1988] to study its relationship with substorm phases.

Acting as a ranging instrument, the RPI can determine the distances of the IMI spacecraft to the magnetopause. By comparing the sounder observations with appropriate magnetopause models such as Sibeck et al., [1991] a determination of the solar wind plasma pressure can also be made, thereby monitoring the size of the magnetosphere as a function of solar wind conditions. In addition, from the magnetopause echoes the time evolution of the density structures of the magnetopause boundary layers can be measured, to determine the variability of plasma mantle density and thickness in response to the southward component of the IMF, and the passage of Kelvin-Helmholtz wave structures in the low-latitude boundary layer [Rosenbauer et al., 1975; Paschmann et al., 1978; Paschmann, 1984].

It is important to note that RPI can operate throughout the entire IMI orbit, even during periods when other IMI instruments may not be operating when the spacecraft is in the deep plasmasphere or near perigee. When the IMI spacecraft is located inside the plasmapause, the local plasma density can be obtained accurately by in situ relaxation sounding of the various plasma resonances. In addition, duct sounding as proposed by Calvert [1981b] and investigations of whistler mode wave-particle interactions and plasmaspheric irregularities and motions will also be possible.

5.0 FEASIBILITY AND INSTRUMENT CHARACTERISTICS

Imaging of magnetospheric plasmas by utilizing radio wave sounding techniques as described in this study requires observations to be made in the frequency range from 3 kHz to 3 MHz. The widespread use of sounders, both from the ground and from satellites, for the study of the Earth's ionosphere, has led to a comprehensive understanding of many of its global physical characteristics. As discussed in a previous section, the ISIS program provided a wealth of new information. The latest technology commercially available makes a remote plasma imager realistic and fits well within the scientific goals and objectives of the IMI mission. The use of this type of mature and existing technology thus reduces costs and risks normally associated with the development of new concepts and instrument designs.

In recent years, compact, low power, and highly sophisticated ground based ionosondes, have become available [see for example Reinisch et al., 1992]. Ground based sounders measure all observables contained in the reflected electromagnetic waves: echo range, Doppler spectrum (amplitude and phase spectrum), angle of arrival, and wave polarization. Precision digital frequency synthesis, multiple receiving antennas, and high speed digital processing are combined to characterize, in real-time, the data received. Phase coding and pulse compression techniques together with coherent spectral integration provide typically 20-40 dB of digital processing gain enabling successful operation with low transmitted power even in regions with high levels of interference. For an RPI on the IMI satellite, a system of three orthogonal antennas (a pair of long dipoles in the spin plane and a very short dipole antenna along the spin axis) would be needed to measure the wave polarization and assist in the determination of the arrival angles.

5.1 Transmitter Power and Antenna Length

Franklin and Maclean [1969] concluded that a magnetospheric radio sounder would be capable of receiving echo signals from densities as low as 5 cm-3 at apparent ranges of at least 6000 km. This conclusion was based on extrapolation of the observed performance of the ionospheric sounders on the low altitude Alouette and ISIS satellites. This section analyzes the power requirements necessary to probe different plasma regions of the magnetosphere using technology a quarter century more advanced than that available to Franklin and Maclean [1969]. In Appendix A the maximum radar range rmax (in Re) equation for a given transmitted signal is derived

(5)

where S/N is the desired signal to noise ratio, L is the tip-to-tip dipole antenna length in meters, Va the rms voltage in volts at the transmitting antenna terminals, F the focusing factor (see equation A4.0), [lambda] the wavelength in meters, and [lambda]1 ~ L2 /40 m is the breakpoint wavelength at which the wavelength dependence of the noise in the receiver switches from [lambda]-3 (at lower frequencies) to [lambda]-2 (at higher frequencies). A cosmic noise level of [Phi]= 10-22 W/m2Hz, a receiver bandwidth of B = 1 kHz and a temperature of T = 300 K was assumed. The value for the cosmic noise level corresponds to a frequency of 100 kHz and is based on an extrapolation of measurements by the ISEE-3 Radio Astronomy Instrument [Bougeret et al., 1984]. These measurements indicate higher cosmic noise levels at higher frequencies but lower levels at lower frequencies which are of prime interest to the RPI. At these low frequencies plasma thermal noise must be considered [Meyer-Vernet, 1979]. This noise should not limit the reception of long range echoes by the RPI, however, because they will correspond to frequencies well above the ambient fp.

Assuming a transmitter power of 10 W, but limiting the antenna voltage to 1 kV, the maximum radar range for S/N = 1 and F = 1 can be calculated from equation (5). Figure 4 shows rmax versus frequency for L = 100, 200, 500, 1000 and 2000 m. As shown in Appendix A, the radiated power at 30 kHz is only 4 mW, and even a very lossy antenna would require less than one watt of transmitter power. For example, a 500 m dipole at 100 kHz will reach out to about 100 Re with a signal to noise ratio of 1 (before digital processing), while a 200 m antenna would only reach to 6 Re. We could have indicated in this same figure the target ranges, r, to the magnetopause, plasmasphere, etc. (see Table 1). Instead we located the target regions at their effective ranges reff = r/F. For a concave reflecting surface, like the magnetopause, the focusing F is larger than one, and in terms of the reflected signal strength the echo seems to come from a target at a distance smaller than the actual distance; the opposite is of course true for convex reflecting surfaces. To estimate the expected signal-to-noise ratio (S/N) for a given target, Figure 4 gives the ratio of rmax/reff. If this ratio equals one, then S/N = 1, since rmax was calculate for S/N = 1. If rmax/reff = 10, then S/N = 10 or 20 dB since the received signal amplitude is proportional to 1/r. Correspondingly, S/N = -20 dB if rmax/reff = 0.1.

Figure 4. The maximum radar range rmax is plotted versus frequency for different untuned antennas of length L, assuming the same antenna length for transmission and reception. L = 100m, 200m, 500m, 1000m and 2000m was used in equation (5), Va < 1000 V, and S/N = 1. Superimposed on these plots are the "effective" locations of the different target regions, where the actual ranges of the targets are reduced by the focusing factor F, reff = r/F. If reff/rmax < 1, then S/N > 1.

Table 1 summarizes the characteristics of the different target regions assuming a satellite at 6 Re. The effective range reff is larger than the actual range r for the plasmapause, the plasmasphere, the ionosphere and the plasmoids because of defocusing, and smaller than r for the magnetopause and possibly for the auroral cavity. In Figure 4, the different target regions are positioned at their respective effective radar ranges for their characteristic plasma frequency intervals. The degree of focusing can, of course, only be estimated because it is influenced by the structure and roughness of the reflecting surface. As an example, the expected signal-to-noise ratios for a 500 m antenna and Va < 1 kVolt are shown in the last column of Table 1.

Table 1. Target radar ranges and expected S/N ratios for satellite at 6 Re

  fp (kHz) r (Re) R (Re)(1) reff (Re) S/N (dB)(2)
Plasmapause 3 to 100 2-4 +(2 to 4) 3 to 12 >= 0
Magnetopause 20 to 50 4-9 -(10 to 15) <2.9 >= 0
Plasmasphere 30 to 1000 2-5 +(1 to 4) 3 to 30 20 to 30
Ionosphere >1000 5 +1 55 20
Auroral Cavity 3 to 30 0.5 +-5? 0.5 -30 to +10
Plasmoids 1 to 10 >10 ~10 >20 <-50

(1) + defocusing, -focusing.
(2) S/N for L = 500 m and Va<1000 Vrms<=10 W.

Modern digital processing can add another 20 to 40 dB of processing gain to the analog S/N ratios shown in Table 1, which means that all target regions except the plasmoids will have a post-processing S/N ratio of more than 10 dB, which is adequate for their detection under quiet conditions, i.e., for [Phi] = 10-22 W/m2Hz.

The expected noise margin for echoes from the plasmasphere, for L = 500 meters, should be 20 to 30 dB, and, after digital signal processing, 40 to 70 dB. Accurate density and direction-of-arrival measurements should therefore be possible throughout this region during quiet times. Even in the presence of solar or magnetospheric noise 40 dB above the cosmic noise (as occurs during relatively rare solar noise storms) the measurements should still be possible near the ionosphere, where they are needed most. At the plasmapause, where the post-processing noise margin is expected to be 20 to 50 dB, it should be possible to measure the direction frequently and the distance and density most of the time. For the magnetopause it should be permissible to sacrifice range resolution by using longer coded pulses and a 100 Hz bandwidth (with 0.25 Re resolution) in order to increase the noise margin to 30 to 60 dB and hence permit adequate distance and direction measurements more often in the presence of stronger solar noise. Measuring low density contours of the auroral cavity, on the other hand, will require integration and must rely upon magnetic models for direction, since the noise margin with integration will probably be only -10 to +40 dB, and detecting plasmoids in the tail will probably not be possible.

If a short antenna is used for reception (see Appendix A, equations A15 to A18), the antenna must be tuned in order to obtain a similar performance as the one discussed for the 500 m transmit/receive antenna. This is illustrated in Figure 5, where the maximum range curves are shown for reception with an untuned and a tuned 10 m antenna and an untuned 500 m antenna; a 500 m transmit antenna was again assumed.

Figure 5. Same as Figure 4, except for tuned and untuned receiving antennas of length L = 10m. Transmission from an untuned 500m antenna was assumed.

5.2 Potential Instrumentation

An RPI could be based on the design of the Digisonde Portable Sounder, or DPS [Haines et al., 1989; Reinisch et al., 1992] developed at the University of Massachusetts, Lowell for ground based ionospheric observations. The large echo ranges involved allow a long pulse width of 10 msec resulting in a range resolution of 1,500 km for the sounding of the magnetopause. A 1 msec pulse width would be selected for sounding of the near satellite environment. The pulse repetition rate would be limited by the largest distances to be probed (~ 25 Re or 1 sec of travel time). The pulse repetition frequency would not be higher than 1 Hz. A 12 dB (S/N = r(16)), processing gain could be obtained by transmitting a 16 bit phase coded signal, resulting in a 160 ms transmitter pulse for magnetopause sounding. For the near satellite sounding, the 1ms pulse would be transmitted uncoded. The maximum transmission duty cycle would therefore be 16 percent. Figure 6 shows a block diagram of a possible RPI instrument.

Modern digital techniques developed in recent years, like those now used routinely in advanced ground based sounders, include simultaneous Doppler integration and pulse compression. For Doppler integration, pulses are transmitted N times at the same frequency providing N complex measurements, for each range. The N measurements are Fourier transformed to give a Doppler spectrum. This spectrally coherent integration results in a signal to noise (S/N) improvement equal to r(N). For example, with N = 128 the S/N improvement becomes r(128) = 11.3 or 21 dB. There is an additional advantage to spectral integration. Assuming that the observed spectrum is primarily the result of the satellite motion, it will give additional information on the direction of echo arrivals.

Figure 6. An instrument schematic of the Radio Plasma Imaging instrument.

For pulse compression, a long pulse consisting of M short pulses, each of length [tau], is transmitted. The phase is constant within each short pulse, but the phase changes between short pulses. In reception, the long pulse of length M[tau] is compressed to length [tau], by cross correlating the received signal with the transmission sequence. The S/N improvement in pulse compression equals r(M). For M = 64, the S/N improvement is 8 or 18 dB. Using both Doppler integration and pulse compression as in the examples above, the total S/N improvement would be 39 dB.

The computational requirements to perform the doppler integration and pulse compression processing are minimal, and an 8 bit microprocessor could easily handle the required correlation and Fourier transform algorithms. For example, integration over 128 pulses would require approximately 2 minutes for collection of the raw data samples. At the end of this reception period, the processor would have to pulse-compress 200 range bins (100 for ordinary and 100 for extraordinary polarization) requiring 6400 operations and compute 200 Doppler spectra, requiring an additional 80,000 operations. Sixteen bit integer processing will provide sufficient (96 dB) dynamic range. Since relatively simple microprocessors perform one million instructions per second (1 MIPS), or 120 million instructions in 2 minutes, this is a trivial load.

The Doppler processing of the received signals provides a number of advantages: (1) S/N improvement by phase coherent integration on all Dopplers; (2) direction of arrival information based on observed radar velocities relative to the satellite velocity; (3) spectral characterization of local plasma resonances.

Not all ranges can be simultaneously sampled with the same resolution and the RPI will, therefore, have to operate in a number of modes with varying transmission and processing characteristics. Two examples are shown below:

Long Range (Magnetopause) Mode

Receiver Bandwidth : 100 Hz (0.25 Re resolution)
Pulse Waveform : 160 msec (16, 10 msec phase code bits, 18 dB processing gain)
Pulse Integration : 32 pulses (15 dB processing gain)
Pulse Repetition Rate : 1 Hz (about 25 Re range ambiguity)
Transmitter Power : 10 W
Frequency Range : 20 kHz to 100 kHz in 4 kHz steps
Measurement Run-Time : 11 minutes (32 sec per frequency step)

Short Range Mode

Receiver Bandwidth : 1 kHz (150 km resolution)
Pulse Waveform : 1 msec unmodulated pulse
Pulse Integration : 64 pulses (18 dB processing gain)
Pulse Repetition Rate : 100 Hz
Transmitter Power : 10 W
Frequency Range : 100 kHz to 3 MHz in 100 kHz steps
Measurement Run-Time : 20 sec

A multitude of different modes can be provided for optimal deployment.

The power consumption of the RPI is estimated to be 25 Watts. A telemetry rate of 5 kbits/s would allow sending 160 kbit of data for each transmitted frequency in the Long Range Mode. This is more than adequate to characterize signal amplitude, polarization, Doppler and incidence angle for 200 range bins. Data compression will be required in the Short Range Mode where the integration time is only 0.64 seconds.

6.0 SUMMARY

The importance of global imaging to studies of magnetospheric structure and dynamics has clearly been demonstrated by the use of the DE-1 auroral images in magnetospheric and auroral substorm studies. Using computer analysis, images of the magnetosphere can also be constructed from measurements of energetic neutral atoms and UV and X-ray radiation. These remote imaging techniques have clearly opened new dimensions in magnetospheric research and are expected to have significant impact on space physics research in the years to come [Scarf, 1988]. The Inner Magnetospheric Imager Mission will provide the first opportunity to simultaneously obtain images of the various parts of the magnetosphere in different wavelengths, providing a coordinated set of global views or images of the magnetosphere.

As described in this study, the techniques of probing remote plasma characteristics by radio waves have been well established for ionospheric studies but no such U.S. instruments have been flown in the magnetosphere. The successful Alouette-ISIS program has spawned numerous investigations leading to much of our current understanding and producing a global view of the topside ionosphere [Jackson, 1986]. With the new generation of ground based digital radio signal instrumentation and processing techniques developed over the last several years, it will be possible to apply the same radio wave sounding techniques to measure distant plasma parameters and to construct two dimensional images of various magnetospheric plasmas.

It has been shown that such images produced by a radio plasma imager, are feasible and would be of fundamental importance in achieving the scientific objectives of the IMI mission.

ACKNOWLEDGMENTS

We would like to gratefully acknowledge Drs. T. Armstrong and D. Gallagher for allowing the plasma sounder team to present their ideas on an exciting new instrument approach for possible inclusion on the IMI mission. In addition, we gratefully acknowledge discussions and comments from Drs. R. R. Anderson, J. Fainberg, D. M. Haines, D. A. Gurnett, R. G. Stone, and C. S. Wu as well as from many members of the IMI Science Definition Team. We thank Robert Kilgore and Robert Candey for their excellent graphic support and Dr. Kolya Tsyganenko for providing us with background information on changes in the inner magnetosphere due to external currents. We especially thank Margie Layfield for her expert typing and editorial suggestions.

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APPENDIX A: Range Capability of a Magnetospheric Sounder

In order to estimate the power needed to sound the magnetosphere, it is necessary to compare the received echo power Pr to the noise Pnoise at the receiver. The echo power, for a pulse radiated power Pt at a distance r from the target, as shown in Figure A1, is

(A1)

where the first factor represents the effective collection area of an antenna [see Jordan, 1950], the second represents the echo power flux for a plane reflector [which is proportional to 1/(2r)2 rather than 1/r4 because the reflection is coherent], F2 is a focusing factor for reflection from a curved surface, M is a receiver impedance mismatch factor, S/N is the signal-to-noise ratio, and Gt and Gr are the antenna pattern gains of the transmitting and receiving antennas (typically 0.75 for a short dipole antenna and circular echo polarization). If wave

Figure A1. The radiation cone subtended by the sounder antenna at a distance r from a coherent reflector, effectively originating from an image at 2r and producing an echo power proportional to 1/(2r)2.

retardation (usually not a major factor) is also considered, r should be replaced by the so-called "virtual range" r' = ct/2, where t is the echo delay, [Franklin and Maclean, 1969]. Since a magnetospheric sounder should presumably be shielded from terrestrial interference by the ionosphere, the principal noise sources should be incoming cosmic or magnetospheric radio noise and receiver thermal noise:

(A2)

where [Phi] is the spectral power flux of the external noise, B is the receiver bandwidth, n is the noise factor of the receiver (typically 3 for a good design), k = 1.38 x 10-23 J/K is Boltzmann's constant, and T is the temperature. The required radiated power thus becomes

(A3)

For curved reflecting surfaces, the echo power becomes proportional to

(A4)

where R1 and R2 are the principal radii of curvature of the reflecting surface and R is the equivalent spherical radius of curvature [see Davies, 1990, p. 213]. As a result, the focusing caused by curved surfaces can be allowed for by substituting

(A5)

for r in Equation A3, where reff is the effective range of the equivalent planar target.

The receiver impedance mismatch factor, for the receiver input circuit shown in Figure A2, where Ra is the radiation resistance, Xa is the antenna reactance, and Ri is the receiver input impedance, is

(A6)

for Xa > Ri. Since the approximate radiation resistance and reactance, in

Figure A2. Circuit diagram for reception, where V1 is the induced voltage causing antenna current Ia = V1/(Xa2 + Ri2)1/2.

ohms, of a short dipole antenna of tip-to-tip length L and radius a, according to Jordan [1950, Ch. 13], are

(A7)

Equation A6 becomes

(A8)

and second term in the square brackets in Equation A3 becomes

(A9)

where [lambda]1 is the breakpoint wavelength at which receiver noise begins to dominate external noise for longer wavelengths, and hence where the range capability of a sounder (see text) changes slope. For L/a = 10,000, Ri = 600 [Omega], [Phi] = 10-22 W/m2Hz (cosmic radio noise), n = 3, T = 300 K, and L in meters, this breakpoint wavelength is approximately:

(A10)

The required radiated power, for Gr = Gt = 0.75, B = 1 kHz, and [Phi] = 10-22 W/m2Hz, therefore becomes

(A11)

Although this indicates that only a few milliwatts are sufficient for sounding over distances of a few Earth radii, at the low frequencies required for magnetospheric sounding, relatively long antennas and high transmitter voltages are required to radiate such power because of the large reactance of antennas which are substantially shorter than the wavelength. For the circuit in Figure A3, where Va is the transmitter voltage, Xa is the antenna reactance, and Ra is the radiation resistance:

Figure A3. Circuit diagram for transmission, the transmitter voltage Va causing an antenna current of Ia = Va/(Xa2 + Ra2)1/2.

(A12)

For example, although only about 10 mW is sufficient for sounding at distances of 10 RE, according to Equation A11 (with S/N = 1), for an antenna length of L = 0.05 l (500 m at 30 kHz), this would require antenna voltages of about one kilovolt.

A transmitter for magnetospheric sounding thus needs to supply high voltages at low frequencies, in addition to relatively high currents at higher frequencies where the antenna reactance is less (e.g., 12 ma or more at 300 kHz, where the antenna becomes a resonant half-wave dipole). It is suggested that the transmitter might thus be of high power, high impedance design (e.g., 400 watts at 2500 ohms), but limited to a suitable maximum power on the order of 10 watts at the higher frequencies, using active feedback circuits.

From Equations A7, A11, and A12,

(A13)

where again [lambda] is the wavelength, L is the tip-to-tip antenna length, Va is the antenna voltage, Gr = Gt = 0.75, a = 10-4L is the antenna radius, [Phi] = 10-22 W/m2Hz is the cosmic noise spectral power flux, B = 1 kHz is the receiver bandwidth, and [lambda]1 is given by Equation A10. For a given S/N ratio, this represents the range capability of a magnetospheric sounder at low frequencies, and it should be noted that rmax is proportional to Va and L2, decreasing as 1/[lambda]2 for wavelengths shorter than [lambda]1, and as 1/[lambda]3 for longer wavelengths [where, according to Equation A10, the breakpoint frequency corresponding to [lambda]1 is f1 = c/[lambda]1 = 1.2 x 107/ L2 kHz.m2 (e.g., 48 kHz for L = 500 m) and at that frequency rmax = 120 Va/[lambda]1 REm/volt =  Vaf1/2500 RE/volt.kHz (e.g., 19.2 RE for and Va = 1 kV)].

At frequencies where the output is power limited, the maximum range is given directly by Equation A11:

(A14)

where it has been assumed that [lambda] < [lambda]1.

Special Considerations for a Short Receiving Antenna

When the receiving antenna is different from the transmitting antenna, the L in Equation A10 is the length of the former, whereas that in Equations A12 and A13 is the length of the latter. Consequently, for Lr << Lt:

(A15)

where Lt is the transmitting antenna length and Lr is the receiving antenna length, both in meters. On the other hand, if the receiving antenna is tuned by switching in suitable series inductors in order to cancel the Xa in Figure A2, Equation A6 becomes

(A16)

and Equation A9 thus becomes

(A17)

where Ri = 50 [Omega] in this case (since it is now advantageous to use a low receiver impedance), the other quantities being the same. This gives

(A18)

For Lr = 10 meters (tip-to-tip), therefore, a tuned receiving antenna would give roughly half the range of an untuned antenna of length equal to the transmitting antenna, (i.e., a 6 dB weaker echo signal), whereas without tuning, the factor becomes Lr2/40[lambda] = 2.5/[lambda] = 2.5 x  10-5 (-92 dB) at 3 kHz ([lambda] = 100 km). It is therefore critical to tune the receiving antenna if a short antenna is used, and with such tuning, a length of about 10 meters should be adequate.

Although the ohmic resistance of the antenna is presumably not a significant limiting factor for untuned antennas at low frequencies, since the antenna currents which determine radiation and reception are controlled primarily by the antenna reactance, this could become significant for reception on a short tuned dipole, hence dictating that short antennas for reception must be made of high-conductivity material.

APPENDIX B: Key Questions and Answers

Listed below are potential questions that might be asked about magnetospheric sounding, and answers.

1. Won't sounding cause electromagnetic interference (EMI) to other instruments and spacecraft systems?

Although clearly a valid concern, the power levels of a magnetospheric sounder are comparable to those of a cellular or portable telephone, at frequencies (3 kHz - 3 MHz) which are easily eliminated by filtering. For well designed equipment, therefore, EMI caused by the sounder should not be a problem. Only the in situ plasma and particle instruments on ISIS spacecraft detected EMI from the sounder pulses and this interference could have been eliminate or avoided by only sampling in the passive interval between pulses (L. H. Brace, private communication, 1993).

2. Why does sounding require such long antennas?

Because of its high capacitive reactance, transmitting with a short antenna is quite inefficient, requiring large voltages to radiate significant power, and as a result, antenna lengths of 500 meters or more are needed to avoid unreasonably high antenna voltages.

3. How will the long antennas affect the other instruments?

Although a solvable problem, antennas may restrict the field of view for certain instruments. Also, because of thermal flexing as the solar heating varies, long antennas can slightly affect the rotation rate of a spacecraft. The change in spacecraft rotation rate due to long antennas was found to pose little or no problems for the auroral imagers on ISIS-2.

4. Is manmade interference a problem?

At the frequencies involved, a magnetospheric sounder is nearly completely shielded from man-made interference by the ionosphere, and it also operates above the altitudes that whistler-mode transmissions can reach. At frequencies below 1 MHz, a RPI should therefore be virtually immune to interference from terrestrial sources, and this is borne out by wave observations showing no such signals in the pertinent regime [private communication, R. R. Anderson]. At frequencies from 1 to 3 MHz, ground-based broadcast emissions do occasionally leak though the ionosphere. These transmitter frequencies are relatively narrow-band and can be avoided in real time by the instrument.

5.What limitations are imposed by natural interference?

The principal sources of natural interference are cosmic radio noise, solar bursts, magnetospheric continuum, and AKR, all but the first being highly variable and the last two consisting of narrowband discrete components. For tip-to-tip antenna lengths of 500 meters or more, the noise margin should be adequate to overcome interference by cosmic noise, magnetospheric continuum, and all but the strongest (and hence infrequent) solar radio bursts. AKR, on the other hand, can be eliminated, as broadcast stations are, by clear-channel detection and automatically setting the transmitter frequency to interference-free channels. The effect of magnetospheric continuum and solar radio bursts is generally loss of directional information, and of AKR, a localized loss of spatial resolution.

6. How do you know the direction of the echo?

As discussed in this study the primary method for the determination of an echo's direction is by measuring the amplitude and phase of the echo signals received on the three antennas. It is important to note that there are several other independent methods which will can also be used to confirm the echo direction determinations derived from the phase information. These methods are:

(1) Since echoes are generated perpendicular to the density gradient, and the plasma density is presumably distributed uniformly along the magnetic field throughout most of the magnetosphere, except near the ionosphere and in certain other special situations, one can generally assume that echoes originate perpendicular to the magnetic field.

(2) Since Doppler integration will yield primarily the Doppler shift caused by the known velocity of a satellite, one can thus apply the techniques of synthetic-aperture radar.

(3) Finally, once the magnetospheric and plasmaspheric density profiles have been constructed from the above methods of echo determination, these can be verified through ray tracing techniques [see for example: Ondoh et al., 1978; Green and Fung, 1993; Green et al., 1993] which should reproduce the plasmagrams and therefore verify the echo directions.

Green, J. L., and S. F. Fung, Radio sounding of the magnetosphere from a lunar-based VLF array, to be published in Adv. Space Res., 1993.

Green, J. L., S. F. Fung, J. R. Thieman, L. Aist-Sagara, R. M. Candey, Probing the magnetosphere by radio sounding techniques, submitted to J. Geophys. Res., 1993.

Ondoh, T., Y. Nakamura, and T. Koseki, Feasibility of plasmapause sounding from a geostationary satellite, Space Sci. Instrum., 4, 57-71 (1978).

7. How can one distinguish the expected echoes from those of ducting, scattering, or other such phenomena?

Experience with Alouette and ISIS spacecraft has shown that such echoes invariably produce easily recognized signatures in ionograms, and in fact, has clearly demonstrated that such features can often be used to advantage in conjunction with the usual echoes to determine specific aspects and certain details of the density distribution not otherwise accessible.

8. Will a magnetospheric sounder be capable of triggering AKR?

It is a matter of considerable interest whether auroral kilometric radiation can be stimulated by natural or artificial radiation. Calvert et al. observed AKR and suggested that the auroral radio emissions were triggered by solar Type II and Type III radio bursts [Calvert, 1981; Calvert, 1985; Farrell et al., 1986]. Although the emission mechanism may still be a cyclotron maser effect such as that proposed by Wu and Lee [1979], a sounder wave with intensity above some threshold may cause the formation of a particle distribution suitable for exciting the cyclotron maser instability, thus triggering the emission of AKR. [C. S. Wu, personal communication, 1993]. If the RPI sounder signal does trigger AKR, the resultant return signal should be distinguishable from a more normal return pulse signal (which should preserve the encoded pulse pattern). By transmitting at different power levels, we should be able to determine the threshold level at which such stimulated emission occurs. By varying the sounder wave frequency, we may also be able to determine the magnetic field strength (and thus the altitude) at which the emission was generated. Thus although the sounder's principal science objective is not the study of AKR, we may nevertheless end up learning a great deal about its properties from the instrument.

Calvert, W., The stimulation of auroral kilometric radiation by type III solar radio bursts, Geophys. Res. Lett., 8, 1091-1094, 1981.

Calvert, W., Auroral kilometric radiation triggered by type II solar radio bursts, Geophys. Res. Lett., 12, 377-380, 1985.

Farrell, W. M., W. Calvert, and D. A. Gurnett, AKR signal increases caused by triggering, Geophys. Res. Lett., 13, 370-372, 1986.

Wu, C. S., and L. C. Lee, A theory of the terrestrial kilometric radiation, Astrophys. J., 230, 621-626, 1979.

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Dr. D. R. Williams, dwilliam@nssdc.gsfc.nasa.gov, (301) 286-1258
NSSDC, Mail Code 633, NASA/Goddard Space Flight Center, Greenbelt, MD 20771

NASA Approval: J. L. Green, green@nssdca.gsfc.nasa.gov
Last Revised: 13 April 1998, DRW