SSI SPSPO/AE-18 Technical Memo ARGONNE NATIONAL LABORATORY Energy and Environmental Systems Division prepared for U. S. DEPARTMENT OF ENERGY under Contract W-31-109-Eng-38
The facilities of Argonne National Laboratory are owned by the United States Government. Under the terms of a contract (W-31-109-Eng-38) among the U.S. Department of Energy, Argonne Universities Association and The University of Chicago, the University employs the staff and operates the Laboratory in accordance with policies and programs formulated, approved and reviewed by the Association. MEMBERS OF ARGONNE UNIVERSITIES ASSOCIATION The University of Arizona Carnegie-Mellon University Case Western Reserve University The University of Chicago University of Cincinnati Illinois Institute of Technology University of Illinois Indiana University The University of Iowa Iowa State University The University of Kansas Kansas State University Loyola University of Chicago Marquette University The University of Michigan Michigan State University University of Minnesota University of Missouri Northwestern University University of Notre Dame The Ohio State University Ohio University The Pennsylvania State University Purdue University Saint Louis University Southern Illinois University The University of Texas at Austin Washington University Wayne State University The University of Wisconsin-Madison NOTICE This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government or any agency thereof, nor any of their employees, make any warranty, express or implied, or assume any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represent that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, mark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. This informal report presents preliminary results of ongoing work or work that is more limited in scope and depth than that described in formal reports issued by the Energy and Environmental Systems Division. Printed in the United States of America. Available from National Technical Information Service, U. S. Department of Commerce, 5285 Port Royal Road, Springfield, Virginia 22161
ARGONNE NATIONAL LABORATORY 9700 South Cass Avenue Argonne, Illinois 60439 ANL/EES-TM-94 MAGNETOSPHERIC EFFECTS OF ION AND ATOM INJECTIONS BY THE SATELLITE POWER SYSTEM by Y. T. Chiu, J. G. Luhmann* and M. Schulz The Aerospace Corporation El Segundo, California and J. M. Cornwall University of California, Los Angeles prepared for Energy and Environmental Systems Division Argonne National Laboratory under Argonne Contract 31-109-38-5075 Aerospace Corp. Report SSL-80(9990)-1 July 1980 Work sponsored by U.S. DEPARTMENT OF ENERGY Satellite Power Systems Project Office *Now at University of California, Los Angeles.
CONTENTS Page I. INTRODUCTION..................................................................................................................... 1 II. EMISSION MODELS.............................................................................................................. 5 A. COTV Ion Engine Exhaust................................................. 6 B. POTV Chemical Engine Exhaust... ...................... 9 III. ARGON ION ENGINE EXHAUST IN MAGNETOSPHERE...................................................... 15 A. Argon Ion Precipitation near LEO.......................... 16 B. Beam-Magnetosphere Interactions............................................................ 17 C. Further Fate of Argon Ions....................................................................... 33 IV. MAGNETOSPHERIC EFFECTS OF ARGON PLASMA EXHAUST........................................ 35 A. Artificial Airglow............................ 35 B. Artificial Ionospheric Current............................... 41 C. Thermospheric Heating............................ 43 D. Plasmaspheric Heating........... .. ................................... ............... 45 E. Ring Current Modification..................... 49 F. Radiation Belt Modif ication....................................................... 54 G. Plasma Turbulence and Space Communications............................. 58 V. CHEMICAL ENGINE EXHAUST IN MAGNETOSPHERE..................................................... 65 A. Reduction of Ring Current Activity.................. .................................. 65 B. Intensification of Geocorona........................................................... 72 VI. CO-ORDINATION WITH EXPERIMENTS............................................................................ 75 VII. SUMMARY OF MAGNETOSPHERIC EFFECTS..................................................................... 79 VIII. RECOMMENDATIONS............................................................................................................... 83 IX. REFERENCES.......................................................................................................................... 87 X. FIGURE CAPTIONS.................... 91 XI. APPENDIX: MAGNETOSPHERE ....................................................................................... A-1 iii
ABSTRACT This is the final report of a two-year assessment of magnetospheric effects of the construction and operation of a satellite power system. This assessment effort is based on application of present scientific knowledge rather than on original scientific research. As such, it appears that mass and energy injections of the system are sufficient to modify the magnetosphere substantially, to the extent of possibly requiring mitigation measures for space systems but not to the extent of causing major redirection of efforts and concepts. The scale of the SPS is so unprecedentedly large, however, that these impressions require verification (or rejection) by in-depth assessment based on original scientific treatment of the principal issues. Indeed, it is perhaps appropriate to state that present ignorance far exceeds present knowledge in regard to SPS magnetospheric effects, even though we only seek to define the approximate limits of magnetospheric modifications here. Modifications of the space radiation environment, of the atmospheric airglow background, of the auroral response to solar activity and of the fluctuations in space plasma density are identified to be the principal impacts. iv
I. INTRODUCTION The space segment of the satellite power system (SPS) is projected to operate at geosynchronous orbit (GEO) at an altitude of ~ 36,000 km [~ 6.6 earth radii (RE) from the center of the earth in the equatorial plane]. During the spacecraft construction phase, transportation and assembly activities will take place between low earth orbit (LEO) at ~ 400 km altitude and GEO. Thus, the operational activities of the SPS and a major segment of the constructional activities take place in the magnetosphere, which is a region of near-earth space where the ionized medium is controlled by magnetic and electric fields. These activities in space represent a loading upon the tenuous but spatialy vast magnetospheric environment. The magnitude of this loading, in the form of injections of matter and energy, can be qualitatively accentuated by comparison of the mass of the SPS spacecraft [~ (3-5) x 107 kg] at GEO with the largest spacecraft operated to date [Skylab, ~ 7 x 104 kg] at LEO. While Skylab did not seem to have any appreciable effects upon the magnetosphere, the key question, however, is whether the scaling-up of spacecraft mass by three orders of magnitude and the scaling-up of orbit altitude by two orders of magnitude would have appreciable magnetospheric effects. Further, if magnetospheric modifications were expected, what mitigation strategies would be required in system design? The primary goal of the assessment effort is to evolve an answer to the above key questions. This report represents our assessment in FY79 and FY80 of the magnetospheric effects of SPS based upon application of present knowledge and is written with a view toward recommendations for future studies and observations needed to verify the assessments. As such, we have focused our efforts to assess the entire range of magnetospheric effects which may con1
ceivably be of importance, rather than to do original research-in-depth upon particular issues. In-depth assessment of the more important issues will be considered as follow-on studies after their priorities have been determined by simple but physically appropriate assessments of the present study. As is implicitly noted in the SPS-Skylab comparison above, a number of uncertain factors necessarily underlie the assessment of magnetospheric effects; the primary reason being that the mass scale and the altitude range of construction and operation activities of the SPS are unprecedented. In this study, theoretical knowledge is applied to bridge this gap in scaling. Including those with available observations, there is a spectrum of theoretical opinion on what the proper interpretation should be. This state of affairs is prevalent in magnetospheric physics since it is a relatively young science in which present space experiments are still attempting to amass the data needed to test theoretical interpretations. The diversity of present theoretical interpretation of magnetospheric phenomena complicates our effort because we must choose, for our assessment, what we regard to be the "present knowledge" from a spectrum of opinions. Thus, our treatment here is subjective to a degree, but it must be noted at the outset that our choice of "present knowledge" is based on consultation with what we regard as foremost experts on the particular issue. For this reason, our treatment of issues may be regarded by some as following the "scientific establishment" in the magnetospheric field; however, a program of assessment in-depth cannot be initiated unless some hypothesis and definitive concepts are established (recognizing the mutability of these concepts, of course). Indeed, we may view our efforts here as exploration and selection of issues so that a coherent program of priorities can be constructed for experimental verification of SPS magnetospheric effects assessment. 2
Obviously, our study would run the risk of being too shallow if we attempt to cover the entire multitude of identified magnetospheric issues. We consequently focus our efforts primarily upon the issues connected with the injections of free energy and of mass into the magnetosphere (including the evolution of the injected free energy) because we deem these issues to be of more immediate concern to human activities in space and on the ground. Included in our consideration are, among others, the magnetospheric injections of solar electric propulsion vehicles, which use ionized argon gas as propellant, and of chemical propulsion vehicles, which would release neutral hydrogen and oxygen in the magnetosphere. Effects induced by these magnetospheric modifications include radiation belt dosage modification, auroral activity modification, optical earth-sensor interference, possible communication interference and possible modification of the atmospheric electric circuit which may impact powerline and pipeline operations. The severity of these impacts is much more difficult to determine with a high degree of certainty without in-depth scaling up to SPS proportions. Indeed, it can be said that we have uncovered a higher degree of present ignorance than present knowledge insofar as the scaling of impacts up to the SPS level is concerned. Of those cases that we were able to consider within limits of present knowledge, it is probably fair to say that the impacts are of sufficient concern to induce consideration of design and mitigation strategies, but are probably not so severe as to put a stop to the project. We remind the reader, however, that these are present impressions on some specific issues and are subject to future rejection when (and if) new results are obtained. The reader is referred to the "CONTENTS" for a summary of the organization of this report. For the reader not well-versed in the terminology of the magnetospheric environment, we have included a brief discussion of the basic properties of the magnetosphere in the APPENDIX. 3
II. EMISSION MODELS In the present section, we attempt to describe the characteristics of the SPS injectants in the magnetosphere. The description is limited to the determinable quantitative parameters from the reference system report of the SPS concept development program (U.S. DOE, 1979) and the SPS Baseline Review (U.S. NASA, 1978). The evolution of each injectant in the magnetosphere is not considered in this section, because the evolution is properly the magnetospheric effect itself. Even for this limited task at hand, we have found that the information available is not sufficient for us to completely evaluate the impacts on specific physical processes. This is particularly true in regard to thrusting schedules. We have attempted to supplement the basic information with some consideration of rocket dynamics. The primary sources of matter and energy injected into the magnetosphere are ionized argon exhaust from the solar-powered cargo orbit transfer vehicles (COTV) that ferry the payload between LEO and GEO, and neutral chemical exhaust in the form of H2O and H2 (or H and 0 atoms after photodissociation) from the personnel orbit transfer vehicles (POTV). In addition, the COTV may also use subsidiary chemical engines and the SPS spacecraft in its operational form may use argon ion (Ar+) engines for station-keeping activities. Because of this simple breakdown into two key elements of magnetospheric injection and because the present assessment effort is not expected to represent a complete scaling-up of physical phenomena to SPS dimensions, we shall consider the emissions in terms of output from a single SPS mission, rather than a sequence of SPS missions. Accumulative effects will be considered separately. 4
A. COTV Ion Engine Exhaust The current technology of ion engines is still evolving (Kauffman, 1974; Byers and Rawlin, 1976); therefore, the parameters of argon-ion engine operations in space must largely be regarded as uncertain at present, although it is by now fairly firm that the most economical and environmentally safe propellant is argon. According to the Reference System Report of the Satellite Power System Concept Development and Evaluation Program (U.S. DOE, 1979) argon-ion engines of specific impulse 13000 sec. are projected for the COTV. Other considerations (Byers and Rawlin, 1976), with perhaps less stringent requirements on projected advances on the technology of ion engines, assumed 5000 sec. specific impulse as standard for comparison. Some projected characteristics of these two options of ion engine operation are listed in Table I, in which Option I (the official concept option) will be used as reference in this report. From Table I, it is seen that the ion beam exhaust is a very dense but fairly cool plasma whose streaming kinetic energy (3.5 keV) far exceeds the thermal energy. In order to propel the COTV to geosynchronous orbit, the argon plasma beam will be directed primarily perpendicular to the geomagnetic field at the equatorial plane in the azimuthal direction (Figure 1). The COTV transfer orbit will be a spiral in the equatorial plane (Figure 2). Plasma beams propagating perpendicular to the geomagnetic field entail very interesting dynamical interactions with the magnetosphere-ionosphere system; in this case, this interaction takes place not at a single location but at all equatorial altitudes from LEO and GEO (Figures 1 and 2). Although, for purposes of considering large-scale magnetospheric modification, the argon plasma beam can be regarded as being perpendicular to the magnetic field at the equatorial plane, it is technically not entirely correct because the magnetic 5
Table I. Ion Engine Characteristics Option 1 Option 2 Specific impulse (sec) 13000 5000 Ar+ kinetic energy (keV/Ar+) 3.5 0.5 Ar+ streaming speed (km/sec) 130 50 Current density (amp/cm2) 2.5 x 10-2 2.5 x 10-2 Temperature (°K) ~ 1000* ~ 1000* Beam density (cm ) ~ 1.5 X 1010 ~ 4 x 1010 Beam diameter at exit (cm) 100 100 Beam spread at exit (deg) ~ 10° ~ 10° Number of engines required for SPS/COTV ~ 300 ~ 800 *Kauffman (1974) 6
axis is offset from the earth’s spin axis and because proposed SPS launch site at Florida would necessitate a 28.5° orbit inclination change during transfer orbit to GEO. The exact orientation of the argon plasma beam with respect to the local magnetic field depends entirely on the above factors and on the details of the planned thrusting schedule, which are not available. Considerations of particle motion in the Appendix section indicate that this exact orientation is not of great significance for global scale environmental assessment except at the vicinity of LEO where direct precipitation of a dense beam of 3.5 keV Ar+ would cause airglow (artificial aurora) emissions and atmospheric heating far exceeding that of the natural aurorae. These effects will be discussed more fully in Section IV.A. For consideration of argon plasma emission parameters, Figure 3 (taken from Chiu et al., 1979a) shows the relationship between payload mass and argon propellant mass needed to transport the payload from LEO (~ 400 km altitude) to synchronous altitude with an accompanying orbital plane change of 28.5°. Obviously, the amount of propellant required for a given payload depends on the ion-beam streaming speed. For an SPS payload of ~ 107 kg, it will be necessary to expend ~ 106 kg of argon propellants for option 1 in Table I. This is ~ 1031 Ar ions, roughly comparable to the total content of the natural plasmasphere and ionosphere above 500 km. The exhaust deposition rate in terms of the time fraction of LE0-GE0 transfer orbit, which is nominally ~ 130 days, is shown as a function of geocentric radius R on Figure 4 (Chiu et al., 1979a). Thus, 80 percent of the total propellant content is released in the plasmasphere, R <= 4 Rg (Figure 2). The number of Ar+ released at a given geocentric distance for a payload mass of ~ 107 kg is shown on Figure 5 (Chiu et al., 1979c); for comparison, the number of ambient electrons lying within a flux shell of thickness equal to twice the argon gyroradius at a 7
given distance R is also shown. The energy content released into a given shell dominates the ambient energy content, however, since the streaming Ar+ kinetic energy is 3.5 keV and the ambient thermal energy is ~ 1 eV. Argon ion engine exhaust in the magnetosphere is thus unique in that it represents both matter and energy injections. The evolution of these two forms of injections follows very different paths, as we shall show. B. POTV Chemical Engine Exhaust Neutral chemical exhaust is initially emitted in the magnetosphere as H2O molecules in the exhaust of LO2/LH2 rocket engines of the POTV. In the magnetosphere, the H2O and H2 molecules are expected to be photodissociated into H and O atoms. Since chemical rocket combustion temperatures are ~ 2000° K, slightly less but comparable to the ambient magnetospheric temperature, chemical rocket exhaust does not represent injection of extra free energy, just injection of matter. The emission scenario of neutral chemical exhaust can be separated into two distinct phases: (1) dense neutral exhaust cloud expanding away from the rocket nozzle and (2) gravitational trapping in magnetospheric orbits or exit from the magnetosphere. The first phase is common to all chemical rocket burns and the emission model is characterized by a model of free jet expansion. The fate of neutral molecules and atoms in the second phase depends on the orbital dynamics of each engine burn: some burns procude neutral clouds which escape the magnetosphere through either its upper or lower boundaries, while other burns produce gravitationally trapped neutrals. We shall consider both phases of the emission scenario. 8
For the first phase, it is necessary to consider models of the exhaust jet. According to the SPS baseline concept review (U.S. NASA, 1978) the POTV engine assembly consists of two stages with 4 engines in the first stage and 2 engines in the second stage. Each engine has a mass flow rate F [[spi:math]] 104 kg/sec. Taking an averaging approach, one may assume as a working model an average total POTV exhaust rate F [[spi:math]] 310 kg/sec of H2O over an average exhaust cross-section of ~ 9 m at exit (average of 3 nozzles of 2 m diameter each). The exhaust speed is u ~ 4 km/sec. Once the exhaust leaves the nozzle it expands primarily isotropically away from the exhaust beam axis. Thermodynamically, this expansion is controlled by the temperature of the exhaust so that relatively more molecules have zero transverse speed and the abundance of molecules with higher transverse speeds fall off in a Gaussian fashion according to a thermal distribution. The proper treatment of the density distribution in such a thermally expanding jet in collisionless medium is by solution of the Boltzmann equation. The Boltzmann equation for the free expansion of a neutral gas with distribution function [[spi:math]] for a source distribution [[spi:math]] is given by: (1) Our source is a time-independent beam at the origin firing off exhaust molecules with speed v0 in the z-direction of a cylindrical coordinate system [[spi:math]]. A cylindrical system in velocity space [[spi:math]] is also used. The velocity distribution in the r-direction is assumed to be a Gaussian with a cut-off constant [[spi:math]]. We shall study the effect of this beam-spread constant [[spi:math]] upon the artificial auroral emission intensity. A properly 9 [[spi:math]
[[spi:math]] (2) From (4), we note that the beam density falls off as z-2 in the beam propagation direction but more importantly the beam is confined to a transverse region [[spi:math]]. Since z and v0 are given for our case, the constant [[spi:math]] determines the cross-sectional area of the beam. In charge-exchange considerations of Section V.A, certain complex drift path averages will be needed to determine ring current particle lifetimes. Consequently, (4) may be too complex for such purposes; instead, an averaging approach can be used to estimate the neutral jet characteristics here. Assuming the exhaust to expand away from the beam axis at an average speed w ~ u/10 [[spi:math]] 0.4 km/sec, the neutral exhaust cloud would occupy an approximately conical volume [[spi:math]] at any time t > 0. The density distribution N inside this volume depends on the details of the expansion as descibed above. For our purposes here an average estimate is N ~ Ft/V. This would imply an average density of 1013/(4t2) atoms/cm3, where t is measured in 10 normalized (to the exhaust molecules propellant flow rate F) source function is where F (molecules/sec) is [[spi:math]]. The exact solution of (1) for S given by (2) can be obtained as [[spi:math]] (3) The density N is given by [[spi:math]] . (4)
seconds. Comparison of this streaming expansion model (w is not necessarily the thermal speed) with (4) shows that [[spi:math]] and z = ut, as it should be. As we shall see, the dense neutral cloud at early times would significantly influence the lifetimes of charged particles in the magnetosphere. For the second phase of the neutral chemical exhaust emission scenario, we must consider the fate of the rocket burns. Dr. Chul Park of NASA/Ames has worked out a likely scenario of the POTV burns (private communications from Dr. Chul Park), based on an earlier version of the SPS concept which involves fewer workers at GEO requiring 561 metric tons of ignition weight at LEO for the POTV [Piland, 1979]. The official baseline concept [DOE, 1979; NASA, 1978] specified the POTV ignition weight to be 890 metric tons at LEO. We have accordingly revised Dr. Park’s scenario for the official version of the POTV chemical exhaust emissions. The fates of the various POTV burns are shown in Figure 6. According to Park’s construction, a POTV mission requires five engine burns. They are named here for convenience Burns 1 through 5 where: Burn 1 is the acceleration burn at LEO using the first stage engines to deorbit from LEO, Burn 2 is the acceleration burn at GEO using the second stage engines to circularize at GEO, Burn 3 is the deceleration burn at GEO using the second stage engines to deorbit from GEO, Burn 4 is the deceleration burn at LEO using the second stage engines to circularize at LEO, and Burn 5 is the deceleration burn at LEO of the first stage vehicle using the first stage engines for circularization at LEO. In time sequence, Burn 5 occurs prior to Burn 3. The masses of fuel burned, the absolute velocities of effluents^ and the eventual fate of the effluents are listed in Figure 6. In the figure, the negative sign denotes the direction opposite to the earth’s rotation. The finite range in the velocities given are due to the fact that the vehicles change velocity during burns. The fates of the effluents are judged 11
simply by comparing the absolute velocities with the escape velocities, which are 10.76 km/sec at LEO and 4.34 km/sec at GEO. Thus, effluents from Burns 3, 4 and 5 will escape. Effluents from Burn 1 will likely fall back to earth, although, being released at LEO, it will not be in the area of concern to this study. As indicated in the figure, the effluents of Burn 2 are trapped in an earth-bound orbit at the rate of 145 metric tons per POTV mission. The center of gravity of the effluent mass has a perigee of 14,400 km above sea level, an apogee of 35,800 km above sea level (GEO), and a period of 18 hours. But the effluents (~ 1031 molecules) are spread over a wide range: some particles have a perigee as high as 30,000 km while others have only 3000 km. Since the typical densities of naturally occurring charged and neutral particles in this region are [[spi:math]] 103 cm-3, the collisional lifetimes of these injected particles are likely to be months; thus, giving rise to the possibility of accumulating a "torus” or "belt" of neutrals in the region (3-6) RE from successive POTV missions. It appears that the effects of this second phase of neutral emission scenario will be of long time scale rather than transient. We have attempted to collect and summarize the available information on emission parameters of argon ion engines and of LO2/LH2 chemical engines in the magnetosphere for the SPS program. As we can see, the information available is not sufficient for a complete environmental assessment although it does allow limits of magnetospheric modifications to be roughly defined. The evolution of each exhaust emission outside of the immediate vicinity of the relevant spacecraft represents the effects of magnetospheric modification. These will be treated separately in the rest of this report. 1 2
III. ARGON ION ENGINE EXHAUST IN MAGNETOSPHERE Argon plasma exhaust from the COTV ion engine assembly is the major source of magnetospheric effects; therefore, this section sets the foundation for major tasks in this assessment effort. A complete and quantitative description of the evolution of the injected argon plasma from the initial beam stage to the final thermalized and recombined stage is a task probably beyond present scientific capability. Yet, a satisfactory picture of the evolution can be obtained by breaking it down into a collection of important phenomena taking place at various magnetospheric regions and in various stages of argon plasma evolution. In this Section, we shall concentrate on the interactions between the Ar+ exhaust and the magnetosphere as foundation for consideration of impacts in subsequent sections. As is noted in the Appendix and in Section II.A, the geometry of Ar+ beam injection and the likelihood of Ar+ precipitation into the atmosphere can be used roughly to divide the magnetospheric effects into two regimes. First, near LEO where the loss-cone is large a substantial portion of 3.5 keV Ar+ is likely to precipitate as a dense beam, stimulating artificial local airglow and atmospheric heating some orders of magnitude above the natural aurora. Second, in the plasmasphere (>= 2500 km altitude) and up to GEO, the loss-cone becomes small and the Ar+ beam is likely to undergo magnetospheric interactions as a plasma. In what follows we shall discuss the approximate behavior of the argon ion engine exhaust in these two regimes as groundwork for assessing the various specific magnetospheric effects. 13
A. Argon Ion Precipitation Near LEO By examination of (A4), it is well-established that 3.5 keV Ar+ emitted at LEO with nonvanishing [[spi:math]] is likely to charge-exchange with neutral thermospheric constituents without first losing its initial energy by other interactions. A more quantitative consideration requires determination of the charge-exchange altitude zce [or [[spi:math]] in (A4)]. Since major thermospheric neutral constituents are O N2 and O2, the following charge-exchange processes must be considered: [[spi:math]] (5) [[spi:math]] (6) [[spi:math]]. (7) These processes at 3.5 keV incident energy are needed to determine zce for a given distribution of neutrals. The cross-sections associated with (6) and (7) were measured by Hedrick et al. [1977] but there is no known measurement of total cross-section for (5). If the incident energy far exceeds the O2 binding energy, we would expect that [[spi:math]] . (8) With the use of the CIRA/COSPAR International Reference Atmosphere (1972) at an average 1000° K exospheric temperature, it is a simple numerical procedure to determine zce from the functional relation (2) for each of the processes (5) - (7). We obtain: zce [(5)] ~ 280 km, zce [(6)] ~ 200 km, and zce 14
[(7)] ~ 140 km. Thus, the Ar+ charge-exchange altitude can be taken as 280 km. This is due to charge exchange with atomic oxygen, which is the main neutral thermospheric constituent. With [[spi:math]] = RE + 280 km, we can use (4) to calculate the loss-cone angle ([[spi:math]]) for given field line L [[spi:math]] R/RE and for various locations of injection r0 on the same field line. The relationship between [[spi:math]] and r0 is shown in Figure 7. From this figure, we determine that prompt precipitation of substantial numbers of Ar+ of 3.5 keV energy is unlikely for source radial distances greater than ~ 2000 km from LEO, primarily because the beam pitch-angle is not likely to be much less than ~ 30°. Consideration of the impacts due to precipitation of 3.5 keV Ar+ is given in Section IV.A. B. Beam-Magnetosphere Interactions In the rest of the magnetosphere at radial distances > 2000 km from LEO and up to GEO, trapping of the argon plasma, as depicted in Figure 1, is likely to occur for substantial length of time if the argon plasma beam does not pass entirely out of the magnetosphere. For this case, we must consider beam-plasma interactions. The plasma interactions can be roughly divided into the largest spatial scale interaction with the magnetospheric shell as a whole and into the spectrum of smaller scale plasma instabilities, although the two are not unrelated. Here we shall deal only with the former; discussion of the latter is found in Section IV.E. The physics of a plasma beam propagating transverse to a homogeneous vacuum magnetic field is very simple: if the beam is sufficiently dense so that polarization currents can maintain the charge separation electric field necessary to satisfy [[spi:math]] ([[spi:math]] is the beam velocity), the beam will propagate across the magnetic field. An alternative view of the effects of 15
the polarization electric field E seen by a co-moving observer above is that, in the coordinate system of the stationary magnetic field outside of the cloud, the plasma cloud, under the force of E, appears to be drifting with a velocity [[spi:math]]. But [[spi:math]] above is also the drift velocity of magnetic field lines in the cloud induced by the electric field [[spi:math]]; hence, the field lines in the cloud are said to be "frozen" into the plasma, drifting with velocity [[spi:math]] relative to the field lines outside of the cloud. For this condition to apply, the beam density nA must satisfy [[spi:math]] (9) where mA is the argon-ion mass (Curtis and Grebowsky, 1980). Numerically, (9) yields (500-30000) nA (cm-3) [[spi:math]] 1 for 2 <= L <= 4, which would seem to be well- satisfied for the beam parameters of Table I; if so, the beam simply moves out of the magnetosphere to be dissipated in space. Unfortunately, this conclusion is conditionally false. The magnetosphere cannot be considered in terms of a vacuum magnetic field because disturbances of the magnetospheric plasma must necessarily involve the dissipative ionospheric plasma. In their latest consideration, Curtis and Grebowski (1980) invoke a non-propagating sheath to shield the beam from interaction with the rest of the magnetosphere and ionosphere. Such a situation depends critically on how and if a sheath, and especially a non-propagating one, can be formed. Since there is no present knowledge of this mechanism, we shall, without prejudice, assess the beam-magnetosphere interaction according to the "estab- lishmentarian" picture of plasma interactions in the magnetosphere, whose origin can be traced to considerations of Alfven. In this picture, plasmas in the magnetosphere, and especially in the ionosphere, act to short out the 16
charge-separation electric field E and transfer to the magnetosphere the major portion of the beam energy in a distance of ~ 1000 km. The basic physics of beam plasma cloud interaction with the magnetosphere and ionosphere is well-known, and was worked out by Scholer (1970) and Pilipp (1971) in connection with the HEOS release of an ionized barium cloud at L = 12 (Haerendel and Lust, 1970). This high-altitude release had, as will the argon engines, a high initial [[spi:math]], where [[spi:math]] is the pressure perpendicular to the field lines of the injected plasma). The beam expands rapidly, in a direction perpendicular to [[spi:math]] and to [[spi:math]], to the point where [[spi:math]] <= 1. Of course, the beam also spreads without constraint (except for mirroring forces) along B as in Figure 1 and as discussed above. One could calculate the final beam spread Ay in the y-direction (or [[spi:math]] direction; see Figure 1) using zero-Larmor-radius magnetohydrodynamics, that is, by equating [[spi:math]] (including thermal pressure nAkT plus dynamic pressure (l/2)nAmA v2 tan2 [[spi:math]] to the asymptotic plasmaspheric pressure, which is essentially B2/8[[spi:math]]. Flux conservation requires [[spi:math]], where n0A and A are the initial beam density and area (see Table I) and Az is the beam spread along the field. Assuming [[spi:math]], one finds that Ay is less than ~ 1 km for L < 4, much smaller than the argon Larmor radius RA. In effect, this calculation of the confinement of gyration centers tells us that [[spi:math]] is of the order of the argon Larmor radius (40-80 km at L = 4) because the gyration centers are confined to a [[spi:math]] much smaller than the argon Larmor radius, at least for the first ten or so Larmor radii downstream from the nozzle; past this, the ~ 10° angular divergence of the beam could produce substantially larger [[spi:math]] [as long as (9) continues to hold]. In first approximation, then, we have a beam of [[spi:math]] propagating across the earth's field as shown in Figure 8. In this figure, the dotted 17
lines show schematically earth’s magnetic field lines at various times. The condition [[spi:math]] means that these lines are frozen into the plasma beam at the equator; their distortion is an Alfven wave (t = 1, in Figure 8). At t = 2, the wave reaches the ionosphere, where the foot of the field line slips, because of the ionosphere’s finite conductivity; the wave then reflects back to the beam (t = 3,4). The field lines act somewhat like rubber bands, tending to retard the cloud. The physical mechanism is that the polarization charges responsible for [[spi:math]] move along the field lines at the Alfven speed vA, accelerating magnetospheric plasma and transferring momentum out of the beam. Ultimately, the Alfven wave reaches the ionosphere and drives dissipative Pedersen currents (in the absence of dissipation, the argon beam would oscillate like a mass on a rubber band field line). Let MAbe the mass density of the argon beam, integrated along field lines passing through the beam: [[spi:math]] (10) When this mass density is equal to the mass per unit area incorporated by the Alfven wave, namely [[spi:math]], the beam is essentially stopped. Here [[spi:math]] is the time it takes the Alfven wave to travel a distance vA [[spi:math]], and n0 mp is the magnetospheric mass density per unit volume. For the argon beam, [[spi:math]], this gives [[spi:math]] few seconds. The beam’s velocity behaves like [[spi:math]] , so the beam can only travel a distance of the order of v0 [[spi:math]] <= 103 km. In this qualitative example, the beam momentum is soaked up by magnetospheric plasma extending at most a few thousand kilometers down the field line on either side of the beam. 18
This picture of argon beam plasma cloud interaction with the magnetosphere is based on high [[spi:math]] explosive barium releases in the far magnetosphere (Pilipp, 1971; Scholer, 1970). The 0 of ion engine exhaust is much greater, but a second indication of the action of an Alfven shock to short out the polarization electric field can be found in the stopping of Starfish debris motion perpendicular to the magnetic field (Zinn et al., 1966), although for this case [[spi:math]] is again not as large as the case of the argon ion beam. The basic physics invoked here have also been applied to the resolution of the observed anomalous magnetic drag on satellites of the ECHO series (Drell et al., 1965); and more recently, applications to the Jupiter-Io momentum transfer problem have also been made (Southwood et al., 1980). This mechanism allows the major part of the beam momentum to be soaked up by the magnetospheric and ionospheric plasma, resulting not necessarily in a uniformly cold argon plasma, but in one with some hot argon plasma components trapped in the magnetic field due to pitch angle scattering. These hot components act much like an argon ring current. Numerical models of this process for realistic plasmaspheres have been constructed in FY80 and our results have essentially borne out these expectations. The essential point to be recognized is that the momentum transfer process takes place via the Alfven speed (~ 10 times the beam speed). It is sometimes claimed that the beam regime is trans-Alfvenic , i.e., vA <= v, and that the physics of beam stopping is different because the beam speed is too fast for the Alfven shock to act. However, actual calculation of plasmaspheric Alfven speeds, as in Figure 9, based on a plasmasphere model which compares favorably with observations (Chiu et al., 1979b), shows conclusively that the 3.5 keV argon ion beam is everywhere sub-Alfvenic. 19
In FY80 we have developed a scientific program to study this beammagnetosphere interaction problem for realistic plasma distributions on a dipolar magnetic field. These aspects of the problem are very important because the plasma density and magnetic field strength along a plasmaspheric field line vary by orders of magnitude. Consequently, the simple constant density and magnetic field considerations of Scholer (1970) do not apply. Numerical calculations verify that the momentum transfer process has a time constant of < 20 sec, so the argon beam has a length of < 2000 km. To formulate the problem we use the coordinate system of Fig. 1 and assume the following magnetohydrodynamic equations: (a) We assume the frozen-field condition that the displacement [[spi:math]] of the plasma (displacement of the beam and the ambient plasma) coincides with the displacement of the magnetic field [[spi:math]] , i.e., [[spi:math]] (11) In this calculation, we shall always assume that [[spi:math]] and [[spi:math]]. Eq. (11) can be integrated over time t, yielding [[spi:math]] (12) b) In our case of inhomogeneous magnetic field and plasma distributions, the equations of momentum conservation must be expressed in terms of the energy component of the Maxwell stress tensor [[spi:math]] [[spi:math]] (13) 20
where [[spi:math]]. The ambient plasma mass density [[spi:math]] is the sum of various constituents (H+, He+, O+) and is given by the model of Chiu et al. (1979). Eq* (13) can be rewritten as [[spi:math]] (14) Using these relations we derive differential equations for the plasma displacement [[spi:math]] and the Alfven wave magnetic field Bx. [[spi:math]] (15) (16) The boundary and initial conditions for [[spi:math]] and Bx are somewhat more complex. The initial condition is obviously that the plasma speed at the equator (z=0) at t=0 is the beam speed v0. To derive the boundary condition of (15) at the equator (z=0), we assume that the beam plasma (speed in the z-direction but concentrated at z=0) moves with the same displacement [[spi:math]] near z= so that we can integrate (15) once over z to obtain 21 [[spi:math]] [[spi:math]] (17) [[spi:math]] (18)
where [[spi:math]] (19) At the ionospheric end of the field line ([[spi:math]]), the Alfven wave electric field Ey = vx B0/c drives a conduction current [[spi:math]] where [[spi:math]] is the ionospheric Pedersen conductivity. Ampere’s law then requires that [[spi:math]]. (20) From Fig. 9 we note that the Alfven speed [[spi:math]] varies a great deal along z; therefore, the assumption of piecewise constancy of [[spi:math]] and B0 above is valid only if we divide up the field line into many segments in order to perform the numerical analysis. We have divided each field line into 15 segments. At the intersection of adjacent segments the continuity of [[spi:math]] and their first derivatives with respect to z are maintained. The reader 22 Integration of Ampere’s law over the entire ionospheric layer yields the ionospheric boundary condition on [[spi:math]] [[spi:math]] where [[spi:math]] is the height integrated ionospheric Pedersen conductivity. The problem is then solution of (15) with the initial condition (17) and boundary conditions (18) and (19). The solution of this problem is rather difficult, even numerically, primarily because of the complexities of the boundary conditions. On the other hand, it is noted that if [[spi:math]] and B0 are piecewise constant over a segment of z the entire problem can be solved in closed form, albeit with the use of a summation of an infinite set of Laguerre functions. familiar with potential field problems of quantum mechanics will immediately recognize in (15) that with the aid of the transformation
[[spi:math]] (21) we can transform (15) into the Schrodinger equation (22) in which [[spi:math]] is the potential function. This recognition, provides us with the adoptation of quantum mechanical methods in solving (15) and (16) which is more suitable for numerical procedures than the highly non-linear transformation (21). Further, implementation of the boundary conditions (18) and (20) is much simpler in (z,t) coordinates than in (u,t) coordinates. Under the assumption of constancy of [[spi:math]] and B0, both (15) and (16) reduce to the same wave-equation form. As in Scholer (1970), we can write the general causal solution in terms of the Laplace transform for each segment j=1, ..., 15. [[spi:math]] In (25) B0(j) and [[spi:math]] are constant magnetic field and ambient plasma density 23 [[spi:math]] where (23) [[spi:math]] (24) [[spi:math]] (25)
[[spi:math]] (26) At the ionosphere z=[[spi:math]] we have the boundary condition (20), while at the equator we have the boundary condition (18). It must be noted that (18), with the subsidiary condition (19), assumes the beam spread in the z direction (along magnetic field lines) to be small so that the Alfven wave is assumed to be generated by a sheet source at the equator moving with the entire momentum of the beam. A cursory look at Figure 1 will indicate that this assumption is at best an abstraction since the beam plasma will spread along the magnetic field line at about one tenth the beam speed. Thus, the Alfven wave source is distributed rather than sheet-like, albeit the parallel spreading speed is much smaller than the Alfven speed. Since our causal solution is in effect a Green’s function solution, the construction of a solution for distributed sources is straightforward but somewhat tedious. In FY80, we have made stu- dies of the distributed Alfven wave source model, but the numerical analysis is so complex that it would be more appropriate to confine ourselves to the results of the sheet-source model in this report. Hopefully, we will be able to report on the distributed source analysis as we proceed with further analyses of SPS magnetospheric effects. Without going into the details of how the causal Laplace transform of (23) can be inverted exactly so as to obtain the solution [[spi:math]]. in terms of 24 of the jth segment. At the jthinterface zj between segments, we have the boundary conditions [[spi:math]] (27)
[[spi:math]], we obtain the exact solution for the velocity field of the Alfven wave at location zi of the ith segment, ai-1 <= zi <=ai where aj is the jthinterface. [[spi:math]] [[spi:math]] and [[spi:math]] 25 [[spi:math]] (28) where [[spi:math]] and [[spi:math]] (29) In (29), [[spi:math]] and where [[spi:math]] can be [[spi:math]] or [[spi:math]] as in indicated in (28). Further Lq(x) in 4 (29) is the Laguerre function of order q and [[spi:math]] is the causal Heaviside function such that [[spi:math]] = 1 if x > 0 and [[spi:math]] otherwise. In (30) [[spi:math]] is the Alfven wave bounce time (30) (31) (32)
[[spi:math]] (33) [[spi:math]] is sometimes referred to as the Alfven wave transit time [[spi:math]] . Even though the exact solution (28) - (33) looks complicated, the interpretation turns out to be very simple. Examination of (28) shows that contributions to the Alfven wave velocity field are made up of two terms of opposite sign, with the negative contribution being associated with an extra factor of [[spi:math]]. Since [[spi:math]] is the ionospheric reflectance for the Alfven wave, i.e., the fraction of wave amplitude reflected by the dissipative conducting ionosphere, we can interpret the positive term of (28) to be due to Alfven waves arriving at the space-time point (zi, t) from the equator while the negative term is due to Alfven waves arriving from the ionosphere, having been reflected once more than the corresponding waves of the positive term. Now the structure of (29) has three significant elements: (1) it consists of an infinite sum of contributions, (2). each contribution is causal (as indicated by the Heaviside function [[spi:math]]), and (3) each contribution has been reflected q times from the ionosphere (as indicated by the factor [[spi:math]]). Examination of (30) with [[spi:math]] and [[spi:math]] indicates that the former is the arrival time at zi from the direction of the equator of an Alfven wave which has been reflected q times from the ionosphere, whereas the latter is the arrival time at zi from the direction of the Alfven wave which has been reflected (q+1) times. The two contributions are 180° out of phase because one is propagating in the opposite direction from the other. If the reflectance of the ionosphere is low [[spi:math]], the Alfven wave field decays with time constant [[spi:math]] after the 26
causal arrival of the wave front at [[spi:math]], although the contribution of the Laguerre function must be taken into account. Hence, the key parameters in the problem are: (1) the ionospheric reflectance [[spi:math]], (2) the Alfven transit time [[spi:math]], and (3) the momentum transfer time characterized approximately by 1/ p. If the ionospheric reflec- tance approaches unity, i.e., [[spi:math]], the two contributions in (28) are of approximately equal strength and the Alfven wave velocity field switches sign as each subsequent reflection arrives at zi and there is no net wave energy dissipation, just beam energy redistribution into the magnetospheric plasma. The time constant for beam energy redistribution to the magnetosphere is the Alfven transit time [[spi:math]] if [[spi:math]], and is somewhat longer (perhaps a few transit times) if [[spi:math]] approaches unity. The momentum transfer time [[spi:math]] measures the time constant of beam energy transfer to the local plasma at the vicinity of the wave front. If [[spi:math]] there is very little reflected wave and only [[spi:math]] is important. For realistic mid-latitude ionospheres, [[spi:math]] so the only important time constants are [[spi:math]] and [[spi:math]]. Thus, it is of interest to examine the time constant [[spi:math]] for the COTV beam. By definition, [[spi:math]] (34) where mA is defined by (19). Thus, it is somewhat unfortunate that this important time constant is subjected to the uncertainties concerning the difference between sheet-source and distributed-source models of beam-magneto- sphere interactions discussed earlier. Recognition of this feature indicates that distributed-source models must be looked into in the future. In the case of an ion engine beam, mA is related to the exhaust flux FA and the beam speed 27
by flux conservation. As has been discussed in the foregoing the perpendicular width of the beam is about one argon gyroradius [[spi:math]] Thus, considering (37) along with (34), the time constant [[spi:math]] is inversely porportional to the beam speed because the higher the beam speed the larger the perpendicular beam width and consequently the less beam momentum density is injected into each flux tube requiring less time for the ambient magnetospheric plasma to soak up the beam energy injected into the given flux tube. So, other things being equal, increasing the beam speed does not necessarily cause an increase in momentum transfer time because the corresponding increase in beam width implies that there is more magnetospheric plasma available to soak up the beam energy injected into a given flux tube. In FY 80 we have implemented the model of beam-magnetosphere interactions described in the foregoing, using a model of ambient plasmasphere (Chiu et al., 1979b). The detailed simulation results are summarized in Fig. 10. This figure contains the simulation results at two field lines: L=3 and L=4. The 28 (35) where Am is the argon mass. Invoking the concept of frozen-in field lines and the conservation of beam particle flux, we have [[spi:math]] (36) whereupon, [[spi:math]] (37)
RkJQdWJsaXNoZXIy MTU5NjU0Mg==