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Models of the plasmaspheric thermal plasma distribution
Adv. Space Res. Vol. 6, No. 3, pp. 141—151, 1986 Printed in Great Britain. All rights reserved.
0273—1177/86 $0.00 + .50 Copyright © COSPAR
MODELS OF THE PLASMASPHERIC THERMAL PLASMA DISTRIBUTION P. G. Richards,5 D. G. Torr,5 J. L. Horwitz5 and M. R. Torr** 5Department of Physics, The University of Alabama in Huntsville, Huntsville, AL 35899, U.S.A. **NASA/Marshall Space Flight Center, Huntsville, AL 35812, U.S.A. ABSTRACT Our current understanding of the thermal plasma in the atmosphere and its coupling to the ionosphere is reviewed. Existing models appear adequate to explain the gross behavior of the cold thermal plasma, but there remain some vexing problems. Notably, (1) why does the density in flux tubes appear to saturate at lower values than are predicted theoretically, (2) what causes the sunset peak in measured Te, and (3) why does the equatorial plasmapause signature differ in latitude from the ionosphere signatures. The more difficult problem of what happens during the early stages of refilling after a magnetic storm, when the high altitude plasma is likely to be supersonic and collisionless, has received nioch attention, hut the results are not definite. A number of papers have dealt with the interaction of supersonic counterstreaming fluxes and there are now models that can handle the transition from supersonic to subsonic flows although the transition from a collisionless to a collision—dominated plasma remains difficult to deal with. INTRODUCTION The magnetosphere is the volume of space dominated by the Earth’s magnetic field. On the dayside, the dipolar magnetic field of the Earth is compressed by hot flowing plasma from the Sun. On the nightside, the “drag” of the solar wind stretches the magnetosphere into a comet—like tail millions of miles long. During periods of quiet solar activity, the inner region of the magnetosphere within several Earth radii from the center of the Earth is effectively shielded from the direct effects of the solar wind. This region is largely composed of “thermal plasma” with energies less than 1 eV. The thermal plasma population has its origin in the topside ionosphere below 1500 km altitude. Pressure gradients operate to move the charged particles along magnetic field lines to higher altitudes. Electric fields also cause the plasma to drift radially and azimuthally. During periods of enhanced solar activity, the inner regions are severely affected as increased electric fields penetrate to lower latitudes and sweep away the thermal plasma. The recovery of this region under conditions of plasma flow from the ionosphere in the presence of convecting motion of the plasma is one of fundamental importance, since, thermal plasma is the dominant constituent of the region. The plasmasphere can be divided into two regions, the inner plasmasphere where the constituents are in equilibrium with the underlying ionosphere, and the outer plasmasphere where dynamic processes prevail /1/. At the plasmapause the ion density typically drops from several hundred ions per cubic centimeter to less than one ion per cubic centimeter in a very short distance (Figure 1). It is well known that the major ion constituent above approximately 3000 km altitude is which is produced from 0+ in a reaction with H below approximately 1000 km and which then diffuses to higher altitudes. On some occasions, the density of He+, which is also produced in the topside ionosphere, can approach that of }l~ in the plasmasphere /2/. The distribution of thermal plasma in the plasmasphere is therefore inextricably linked to ionospheric processes. EXISTING MODELS Chakrabarti et al. /3/ have compared the measured intensity of the resonantly scattered He ii 304 A emission line with that obtained from a static equilibrium model of the plasmaspheric density distribution /4/. Although this approach may apply in the inner plasmasphere, the outer plasmasphere is seldom in static equilibrium, so this comparison is not adequate. Further, Waite at al. /5/ and Li et al. /6/ have shown that such models are extremely sensitive to the topside ion densities chosen as boundary conditions, and these are not well known. More importantly, there is no simple relationship between topside densities and plasmaspheric densities when flux tubes are refilling after magnetic storms. 141
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Fig. 1. Plot of density profiles(derived from plasma frequency measurements by the plasma wave experiment) for successive ISEE—1 outband passes of 4 and 7 December 1977 /1/. The do 9, which represent densities calculated assuming a constant upward flux of 5 x cm s , were added by the present authors. The ideal approach is to solve the appropriate plasma equations rigorously. A number of models have been developed to5, solve and the H+ along time—dependent closed field one—dimensional lines of the Earth’s continuity magnetic and field /7—18/. The full models momentum equations for 0~, He describe the plasma distribution realistically and are essential in gaining an understanding of the fundamental processes connected with the distribution of plasma along flux tubes. One of the main difficulties in understanding the measurements of the thermal plasma arises from the complications of plasma drifts that are c4used by electric fields. The plasma not only expands and contracts as it drifts, but also different plasma elements rotate about the Earth at different rates /19,20/. Plasma drifts that are caused by lectric fields complicate the interpretation of satellite measurements because the time evolution of the observed plasma elements is not known. Horwitz /21/ identifies six major questions which remain to be explained regarding the interchange of thermal plasma between the ionosphere and plasmasphere. (1) What is the physical interaction between the two “colliding” plasma streams emerging from conjugate hemispheres in the early stages. of the plasmasphere filling process? (2) How does the plasmasphere filling process proceed following the transition to gentle, subsonic flows from the ionosphere? (3) How does the mode of plasmasphere filling depend on the season. (4) What are the characteristic diurnal flows of plasma between the plasmasphere and ionosphere? Does plasma flowing down from the plasmasphere maintain the nighttime ionosphere? (5) How do the behaviors of the different ion species differ during flow between the ionosphere and plasmasphere? (6) Are there multiple distinctive regions of the plasmasphere .~uchas the inner and outer plasmasphere of Park /22/, and can these regions be distinguished on the basis of flow or other characteristics? In this paper, we shall restrict our attention to a brief discussion of questions 1—4. 1.
Refilling of Depleted Flux Tubes
One of the important unresolved problems in ionosphere—magnetosphere coupling concerns the refilling of depleted plasmaspheric flux tubes after geomagnetic storms /23/. Specifically, it is not clear whether a depleted flux tube fills from the top (equator) to the bottom (ionosphere) or from the bottom to the top. Although a significant effort has been devoted
Models of Plasmaspheric Thermal Plasma
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to studying interhemispheric plasma transport (see /14/ and references therein), the hulk of this work is not targeted at the initial refilling of flux tubes, since it is based on a low—speed, collision—dominated transport formulation. In contrast, supersonic flow and collisionless plasma characteristics are expected on depleted flux tubes Shortly after magnetic storms. The hydrodynamic model of Banks et al. /24/ envisioned supersonic flows of &~plasma from the two conjugate ionospheric feet of a plasmaspheric flux tube colliding with nearly equal intensities near the equator to initiate plasmasphere replenishment, following magnetospheric storms. Banks et ml. postulated that after flux tube depletion, the resulting supersonic field—aligned plasma flows that emerge from the conjugate ionosphere interact at the equator, forming a pair of shocks. Schulz and Koons /25/ studied the stability of counterstreaming ion flows using a onedimensional analysis based on the ion—acoustic mode. They concluded that electrostatic shocks were not likely to form at the equator, but that ion trapping could occur via wave— particle interactions. Although Schulz and Koons based their analysis on the ion—acoustic mode, they recognized that the ion—cyclotron mode could be important. An extension of the treatment by /24/ was made by Grebowsky /26/ who considered both isothermal and adiabatic flow states and also the effects of cross—L drifts, resulting from magnetospheric convection, which cause compression or expansion of the magnetic flux tubes • He found that the thermal energy of the shocked plasma at the equator decreases or increases with time when a flux tube contracts, depending on whether the flow is isothermal or adiabatic, respectively. Singh and Schunk /27/ conducted one—dimensional numerical simulations that are relevant to the initial refilling of depleted plasmaspheric flux tubes. Their results support the conclusion by /25/ that slow moving, downward propagating electrostatic shocks are not likely to form at the equator. Moreover, their results also indicate that the counterstreaming plasmas are more stable than anticipated. Although there are few observations of the flows that are responsible for the initial filling stages, high—speed upward flows have been observed in the topside ionosphere /28/, and recent observations of a highly collimated, low—energy H+/Re+ field—aligned plasma flow, which is identified as the high—altitude extension of the polar wind /29/, should help to clarify many of these issues. 2.
Subsonic Filling of Flux Tubes.
After 1 or 2 days of the replenishment process, the upward flow is subsonic everywhere. Even for this gentler, extended period of plasrsasphere filling, reliable estimates for appropriate time constants and tube contents, for example, are not yet available, although some theoretical and observational estimates have been made. Bailey at al. /14/ calculated that the tube content on the L = 3.2 field line should ha still building up 6 days after initiation of recovery. The flux tube contents may be compared with the buildup in density profiles observed through whistler observations indicated by Figure 2a from Park /22/. From such data, Park estimates that the times required to attain equilibrium range from about 1 day at L = 2.5 to 8 days at L = 3. It appears then that saturation is predicted to be somewhat later in occurring than in the calculations of Bailey at al. /14/, and that the observed saturation tube contents are smaller by factors of 3 or more than in their calculations. With regard to saturation, Figure 3 from Sojka and Wrenn /30/ shows that the cold H+ density at geosynchronous orbit 3. The rate of appears to saturate at an extraordinarily low value of the order or 100 cm refilling that is observed prior to saturation is in agreement with theoretical predictions about the t1~flux from the ionosphere. According to present theory, the plasmasphere should not begin to saturate until the equatorial density reaches at least 1000 cm3. A comprehensive interhemispheric model for studying refilling has been developed by Richards and Torr /31/. It solves the continuity, momentum, energy, heat flow, and photoelectron flux equations f or subsonic flows using photochsmically determined boundary conditions in conjugate E regions. The solutions of the equations are carried out along the -full extent of the flux tubes using tilted dipole geometry which was found to have significant effects for interhemispheric thermal coupling. Calculations show that refilling by cold ionospheric plasma, can account remarkably well for the latitudinal variations in major ion density observed by the plasma wave instrument (PWI) and the retarding ion mass spectrometer (RIMS) on DE 1 but not the ion composition. The code solves for the concentrations and flow velocities of the three major ions 0~, H~, and He5, as well as the electron and ion temperatures.
JASR 6:3—3
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Fig. 2. (a) Smoothed tube content profiles on successive days of June 1965 for whistler observations of the filling of the plasmasphere. (b) Corresponding smoothed equatorial electron concentration profiles (from /22/).
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TIME (hr) FROM 00 UT. DEC. 10. 1978 Fig. 3. Thermal ion (top panel) and 50 to 509—eV electron (bottom panel) densities over a 3—day period beginning at 0000 UT on 10 December 1978. The light line represents detector A data (pitch angle range 120 to 20°)while the heavy line represents detector B data covering 60° to 110°pitch angles (from /30/). 3.
Seasonal Effects
Our results show that filling rates can change significantly under different geophysical conditions. Diurnal, seasonal, and solar cyclic effects must be taken into account in order to get realistic refilling fluxes and hence refilling times. Figure 4 shows a comparison between theory and data from RIMS and PWI for day 282 in 1981. Calculations are indicated by the large circles with central dots. These results show that the variation in plasma concentration observed by 05 could he well accounted f or by allowing the field tube to fill for 8 days. The fact that a steep density gradient occurs between L = 3.28 and L = 3.80 implies that after 8 days of filling, a depletion clown to L 3.5 occurred.
Models of Plasmaspheric Thermal Plasma
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5 Fig. 4. Sample Dynamics Explorer data showing H+ and He densities approximately in the equatorial plane on orbit 282. The dots are theoretical densities assuming 8 days of refilling. Another problem is illustrated in Figure 5 which shows that the full flux tubes of Figure 4 ware virtually empty 1 day earlier. There is no known way in which the state of the tubes could change so quickly, given theoretical refilling rates. Since the data in question were taken at different longitudes, this suggests that the state of depletion of a flux tube depends on its longitude at the time the magnetic activity occurs, and that some tubes may be more depleted of plasma than others. The relationship between Kr, and the plasmapause has been discussed by Chappell /19/ and Higel and Wu Lei /32/. Although there appears to be a close relationship between K~and the position of the plasmapause in an average sense, there are many instances when the plasmapause behaviour is anomalous /32/. It is well known /33,9/ that the H5 density is well represented by a diffusive equilibrium profile in the inner plasmasphere, though not in the topside ionosphere, even when there are large flows. The recent calculations of Khazanov at al. /34/ indicate that even for supersonic flows, the 8+ density follows a diffusive equilibrium profile above approximately 3000 km. Measurements also indicate that in less than 1 day after magnetic activity decrease, the outer plasmasphere forms and consists of cold, essentially Maxwellian plasma with ion characteristics generally similar to those of the inner plasmasphere, albeit at significantly lower densities /35/. Richards and Torr /31/ have derived a simple analytical expression-for calculating the limiting H5 flux. Comparisons with the full model over a wide range of conditions show agreement generally to within 30%. Figures 6 and 7 point to a problem in calculating refilling rates. Two different models of the neutral atmosphere produce markedly different solar cyclical variations of the H’~~escape flux. Figure 6 was obtained using the older MSIS model of Hedin et al. /36/ while Figure 7 was obtained using the latest version of the MSIS model /37/. The latter fluxes are higher because the H density is higher at solar maximum. A recent study by Breig et al. /38/ found an [NJ variation intermediate between the two MSIS model variations. 4.
Characteristic Flows and the Maintenance of the Nocturnal Ionosphere
Several authors have examined the effects of interhemispheric flows on the state of the F region /12,16/. Solstice calculations of Bailey at al. /14/ suggest that, for an L = 3 flux tube, the flow during the first few days of plaemasphere replenishment is upward at all local times in the summer hemisphere, and in the daytime in the winter hemisphere. At later times, the flow is upward during the day and downward during the night in both hemispheres, reflecting the dominance of diurnal variations at these later stages of fillinq. The winter and summer ionospheric F2 layers are not tightly coupled and, although interhemispheric transport does occur, the plasmasphere mainly acts as a reservoir whose H~ content is variable and prevents direct mass coupling between the conjugate F2 layers. Thermal coupling is strong however, and this is discussed later.
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Variation of the limiting H~flux with solar activity index F
107 from the full model (full line) and the simple analytical formula (dot—dash line). The MSIS—77 model was used f or theme calculations. The neutral hydrogen variation is also shown (broken line) (from /31/). One of the major ongoing questions in the area of ionosphere—plasmasphera coupling is whether the nighttime F region ionosphere is maintained by plasma flowing down the magnetic field lines from the plasmasphere. Jam et al. /39/ have measured ionospheric density profiles as a function of local time using the Malvern incoherent scatter radar and find that following sunset, the ionosphere decays rapidly in the first few hours in a manner consistent with reconthtnation, but then decay essentially ceases f or the remainder of the night. Torr and Richards /40/ have also investigated the effect of interhemispheric flow on the nocturnal F region densities under solar maximum equinox conditions at mid—latitudes (L = 2.5). They found that the modeled diurnal variation of the peak electron density of the F region at night is sustained by a downward flow of ions. This is evident in Figure 8 which
Models of Plasmaspheric Thermal Plasma
147
displays a well—known enhancement of the nocturnal ionosphere near midnight, which occurs in all seasons. Figure 8 shows that the enhancement occurs even when the field tube is empty. Furthermore, during these times, the H+ flux for the cases examined is upward throughout the night. The 0+ flux is downward at the tines of the enhancement. Normally, it would be expected that the protonompheric 0+ would drain fairly rapidly after sunset because of a thermally induced collapse at that time. We have also investigated the effects of winds on the F2 layer. Our calculations revealed that for the case we studied, 0+ fluxes are driven upward by normal the 2s~ which until sunset, 3 hours LT. 5mospharic winds persists shortly after reversing at 19 hours LT to a downward flux of 5 x 10 cm 28 IlIIIIIll 28
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LOCAL TIME (hours) Fig. 8. Diurnal variation of NmF2 in the northern hemisphere at L = 2.5 near the fall equinox, illustrating the nighttime increase. Sethia et al. /41,42/ demonstrated that the electron content responds markedly to the magnitude and phase of the neutral air winds. Figure 9 illustrates their computed
P. G. Richards et a!.
148
percentage daylight change in total electron content of Lancaster due to neutral winds. They conclude that the effect of the neutral wind on the ionospheric end protonospheric electron contents depends on the duration of the poleward wind in relation to daylight, and whether or not the wind reverses while the ionosphere is sunlit.
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Fig. 9. Example of the computed percentage ‘change in NmF2 at Lancaster, England due to neutral winds (from /41/). Sethia at al. /42/ investigated conjugate thermal coupling and found that conjugate photoelecton heating has a major effect on the shape of the daily variation of slant slab thickness and the protonospheric content. Some of the main features were found to be related to sunrise and sunset times in the conjugate ionosphere. Also, it was found that the nighttime increase in total electron content and the F2 region peak density in winter are natural consequences of ionization loss at low altitudes causing an enhanced flow of plasma from the protonosphere which is coupled to the summer hemisphere. Richards and Torr /43/ pursued the effects of conjugate thermal coupling further, taking into account the tilt of the Earth’s dipole axis, and confirmed the results of Sethia et al. /42/ that it is very strong. Heating from the conjugate hemisphere can produce electron temperatures which are 1000 K higher in the dark than in the sunlit hemisphere. The high temperatures have little effect on NmF2 but cause a sharp rime in the 0+ density in the topside ionosphere and the consequent rapid expulsion of H+ into the plasmasphsre. The tilt of the Earth~smagnetic field means that the conjugate illumination effects can actually be observed in the dark hemisphere 2 hours in local time before they appear in the sunlit hemisphere, and 5 hours before local illumination. Figure 10 shows the H+ fluxes through the 3000 km level as a function of local time in both hemispheres at June solstice. There is a prominent peak in the upward 8+ flux at 0220 hours LT in the southern winter hemisphere several hours before local sunrise when the solar zenith angle is still 135°. We have also compared calculations of the diurnal variation of Te measured at 300 km with ISIS—2 /44/. In Figure 11, we compare our theoretical results for 1400 km at equatorial latitudes with the ISIS—i observations. The bars indicate the spread in the data points. Although the agreement is generally fairly good, the afternoon peak in the data is not reproduced. Figure 12 shows the Te variation at 3000 1cm in the equatorial region. The data are from Figure lOb of Brace and Theis /44/. Here, the calculated temperature is substantially lower than the data at all times other than near noon where the agreement is good. The high temperatures at night suggest a nighttime heat source. EFFECTS
ASSOCIATED
WITH MAGMETOSPHERIC
CONVECTION
The effects of convective electric fields on the high latitude ionosphere have been studied extensively by Sojka and Schunk (/45/ and references therein), while the convecting highlatitude topside ionosphere and plasmasphere has been studied by /16—18/. Using the model of Quegan at al. /17/, Allen at ml. /18/ have carried out calculations taking into account convection of field tubes at high latitudes using convection paths based on the semi— empirical model of Spiro et al. /46/, assuming that the geographic and magnetic poles are coincident. The cross—tail potential used was 60 kV. The calculatiune were done for low
Models of Plasmaspheric Thermal Plasma geomaguetic used.
and sunspot
activity.
The neutral
149
air winds of Fuller—Rowell
and Fees /47/ were
SOLAR ZENITH ANGLE (deg) S N
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Fig. 10. Diurnal variation of the fluxes through the 3000 km level as a function of local time in the northern hemisphere at L = 3 at the June solstice (from /43/).
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LOCAL TIME (hours) Fig. 11. Comparison of model values of Ta at 1400 km at equatorial latitudes with the data frets /44/. The bars indicate the spread in the data. 5, and O~ densities and flows. Figure 13 shows contours of The model computes H~, He concentration. Similar plots were also given for He5 and H+. It was found that many of the
150
et al.
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features of the 0+ at 500 km could be accounted for in terms of the behavior of 0+ at F layer heights, which is determined by the presence of various sources and sinks along the convection paths. One example is the O~trough in the afternoon dusk sector which is a consequence of the mid—latitude trough in NmF2. Another example is the Thigh latitude hole~ feature around 75° latitude in the post-midnight sector.
6000
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LOCAL TIME (hours) Fig. 12. Comparison of model values of Ta at 3000 km altitude at equatorial latitudes compared with the observations of /44/.
n (0~)AT 500 km IN WINTER MLT
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2400 Fig. 13. Contours of calculated 0+ concentration for 500 km altitude in winter /18/. The 3): 1, 4.3 x 106; 2, 1.2 x iO~ 3, 3.6 x contour 4, 1.1 x values 108; 5,are3.1as x follows 108; 6, (in 9.0 units x 108;of7,m 2.6 x 1O~ 8, 7.6 x 1O~ 9, 2.2 x 1010. Lines of constant solar zenith angle are also shown. 8+ is controlled by chemical interaction with 0~. The H~contours show that 8+ is the dominant ion in the hole and the trough as predicted by Quegan at al. /17/. The Ha~ ions become dominant at times when there is solar illumination of the atmosphere at high altitudes. Ha+ ions are produced by photoionization while there is no significant equivalent source of 0~ and H~ which are in the process of decaying.
.
Models of Plasmaspheric Thermal Plasma
CONCLUSION
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The state of our current modeling capability of the thermal plasma in the ionosphere and plasmasphere has been reviewed. Earlier discrepancies between theory and measurement have been reduced by improvements in both theory and data collection. However, a number of fundamental problems that were discussed in this review remain to be solved. ACKNOWLEDGEMENTS
This work was supported by NSF grants APM—8545227 and ATM-8506642 and NASA grants 1IAGW—922, NAG8—054, and NAG8—O58 at The University of Alabama in Huntsville. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47.
J.L. Horwitz, C.R. Baughar, C.R. Chappell, E.G. Shelley, D.T. Young, and R.R. Anderson, J. Gaophys. Res. 86, 9989 (1981). J.L. Horwitz, R.R. Comfort, and C.R. Chappell, Space Bee., (this issue). S.F. Chaktabarti, F. Paresce, S. Bowyat, Y.T. Chiu, and A. Aikin, Geophys. Rem. Lett. 9, 151 (1982). Y.T. Chiu, J.G. Luhmann, m.K. Ohing, and D.J. Boucher, Jr., J. Geophys. Has. 84, 909 (1979). J.FI. Waite, J.L. Horwitz, and R.H. Comfort, Planet. Space Sci. 32, 611 (1984). Li Wenxiu, J. J. Sojka, and W. J. Raitt, Planet. Space Sci. 31, 1315 (1983). E.R. Young, P.G. Richards, and D.G. Torr, J. Coup. Phys. 38, 141 (1980). E.R. Young, D.G. Torr, P. Richards, and A.F. Nagy, Planet. Space Sci. 28, 881 (1980). R.J. 1’Soffett and J.A. Murphy, Planet. Space Sci. 21, 43 (1973). P.M. Banks, R.W. Schunk, and W.J. P.aitt, J. Geophys. Rem. 79, 4691 (1974). C.G. Park and P.M. Banks, J. Geophys. Rae. 79, 4661 (1974). 8.8. Mayr, E.G. Fontheim, L.H. Brace, H.C. Brinton, and H.A. Taylor,Jr., J. Atmom Terr. Phys. 34, 1659 (1972). K. Marubashi, Planet. Space Sci. 27, 603 (1979). G.J. Bailey, R.J. Moffett, and J.A. Murphy, Planet. Space Sci. 26, 753 (1978). G.J. Bailey, R.J. Moffett, and J.A. Murphy, J. Atmos. Tart. Phys. 41, 417 (1979). S. Quegan, G.J. Bailey, R.J. Moffett, R.A. Healis, T.J. Fuller—Rowall, D. Ream, and R.W. Spiro, 3. Atmos. Terr. Phys. 44, 619 (1982). S. Quegan, G.J. Bailey, R.J. Moffett, Planet. Space Sci. 32, 791 (1984). 8.T. Allen, G.J. Bailey, and R.J. Moffett, 3. Atmos. Terr. Phys. 48, 25 (1985). C.R. Chappell, Rev. Geophys. Space Physics 10, 951 (1972). 3. Lemaire and L. Kowalkowski, Planet. Space Sci. 29, 469 (1981). J.L. Horwitz, J. Atmos. Tarr. Phys. 45, 765 (1983). C.G. Park, J. Geophys. Rem. 79, 169 (1974). C.G. Park, J. Geophys. Has. 75, 4249 (1970). P.M. Banks, A.F. Nagy, and W.I. Axford, Planet. Space Sci. 19, 1053 (1971). M. Schulz and H.C. Koons, 3. Geophys. Bee. 77, 248 (1972). J.M. Graboweky, Planet. Space Sci. 20, 1923 (1972). N. Singh and R.W. Schunk, 3. Geophys. Has. 88, 7867 (1983). J.H. Hoffman and W.H. Dodson, J. Gaophys. Res. 85, 626 (1980). C.R. Chappell, J.L. Green, J.F.E. Johnson, and J.H. Waite, Jr., Geophys. Bee. Lett. 9, 933 (1982). J.J. Sojka and G.L. Wrenn, 3. Geophys. Has. 90, 6379 (1985). P.G. Richards and D.G. Tort, J. Geophys. Rem. 90, 5261 (1985). B. tilgal and Wu Lei, 3. Geophys. Has. 89, 1583 (1984). W.J. Raitt, R.W. Schunk, and P.M. Banks, Planet. Space Sci. 23, 1103 (1975). G.V. Xhazanov, M.A. Koen, Yu.V. Konikov, and I.M. Sidorov, Planet. Space Sci. 32, 585 (1984). J.L. Horwitz, R.H. Comfort, and C.R. Chappell, Geophys. Has. Lett. 11, 701 (1984). A.E. Hedin, C.A. Reber, G.P. Newton, N.W. Spencer, H.C. 2lrinton, E.G. Mayr, and W.E. Potter, 3. Geophys. Rae. 82, 2148 (1977). A.E. Iledin, 3. Geophys. Res. 88, 3515 (1983). E.L. Breig, S. Samatani, and W.B. Hanson, J. Geophys. Rae. 90, 5247 (1985). A.R. Jam, G.M. Taylor, and P.J.S. Williams, 3. Atmos. Terr. Phys. 35, 1717 (1973). D.G. Tort and P.O. Richards, EOS, Trans. Psner. Gaophys. Union 66, 334 (1985). G.C. Sethia, G.J. Bailey, R.J. Moffatt, and J.K. llargreavas, Planet. Space Sci. 31, 377 (1983). G.C. Sethia, G.J. Bailey, R.J. Moffett, and 3.K. Hargreaves, Planet. Space Sci. 33, 321 (1985). P.G. Richards and D.G. Torr, .3. Geophys. Has. 91, 9017 (1986). L.H. Brace and R.F. Theis, .3. Atsuos. Tarr. Phys. 43, 1317 (1981). .3.3. Sojka and R.W. Schunk, 3. Geophys. Rae. 91, 259 (1986). R.W. Spiro, R.A. Heelis, and W.B. Hanson, J. Geophys. Rae. 83, 4255 (1978). T.J. Fu].ler—Rowell and D. Rees, 3. Atatos. Sci. 37, 2545 (1980).
0273—1177/86 $0.00 + .50 Copyright © COSPAR
MODELS OF THE PLASMASPHERIC THERMAL PLASMA DISTRIBUTION P. G. Richards,5 D. G. Torr,5 J. L. Horwitz5 and M. R. Torr** 5Department of Physics, The University of Alabama in Huntsville, Huntsville, AL 35899, U.S.A. **NASA/Marshall Space Flight Center, Huntsville, AL 35812, U.S.A. ABSTRACT Our current understanding of the thermal plasma in the atmosphere and its coupling to the ionosphere is reviewed. Existing models appear adequate to explain the gross behavior of the cold thermal plasma, but there remain some vexing problems. Notably, (1) why does the density in flux tubes appear to saturate at lower values than are predicted theoretically, (2) what causes the sunset peak in measured Te, and (3) why does the equatorial plasmapause signature differ in latitude from the ionosphere signatures. The more difficult problem of what happens during the early stages of refilling after a magnetic storm, when the high altitude plasma is likely to be supersonic and collisionless, has received nioch attention, hut the results are not definite. A number of papers have dealt with the interaction of supersonic counterstreaming fluxes and there are now models that can handle the transition from supersonic to subsonic flows although the transition from a collisionless to a collision—dominated plasma remains difficult to deal with. INTRODUCTION The magnetosphere is the volume of space dominated by the Earth’s magnetic field. On the dayside, the dipolar magnetic field of the Earth is compressed by hot flowing plasma from the Sun. On the nightside, the “drag” of the solar wind stretches the magnetosphere into a comet—like tail millions of miles long. During periods of quiet solar activity, the inner region of the magnetosphere within several Earth radii from the center of the Earth is effectively shielded from the direct effects of the solar wind. This region is largely composed of “thermal plasma” with energies less than 1 eV. The thermal plasma population has its origin in the topside ionosphere below 1500 km altitude. Pressure gradients operate to move the charged particles along magnetic field lines to higher altitudes. Electric fields also cause the plasma to drift radially and azimuthally. During periods of enhanced solar activity, the inner regions are severely affected as increased electric fields penetrate to lower latitudes and sweep away the thermal plasma. The recovery of this region under conditions of plasma flow from the ionosphere in the presence of convecting motion of the plasma is one of fundamental importance, since, thermal plasma is the dominant constituent of the region. The plasmasphere can be divided into two regions, the inner plasmasphere where the constituents are in equilibrium with the underlying ionosphere, and the outer plasmasphere where dynamic processes prevail /1/. At the plasmapause the ion density typically drops from several hundred ions per cubic centimeter to less than one ion per cubic centimeter in a very short distance (Figure 1). It is well known that the major ion constituent above approximately 3000 km altitude is which is produced from 0+ in a reaction with H below approximately 1000 km and which then diffuses to higher altitudes. On some occasions, the density of He+, which is also produced in the topside ionosphere, can approach that of }l~ in the plasmasphere /2/. The distribution of thermal plasma in the plasmasphere is therefore inextricably linked to ionospheric processes. EXISTING MODELS Chakrabarti et al. /3/ have compared the measured intensity of the resonantly scattered He ii 304 A emission line with that obtained from a static equilibrium model of the plasmaspheric density distribution /4/. Although this approach may apply in the inner plasmasphere, the outer plasmasphere is seldom in static equilibrium, so this comparison is not adequate. Further, Waite at al. /5/ and Li et al. /6/ have shown that such models are extremely sensitive to the topside ion densities chosen as boundary conditions, and these are not well known. More importantly, there is no simple relationship between topside densities and plasmaspheric densities when flux tubes are refilling after magnetic storms. 141
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Refilling of Depleted Flux Tubes
One of the important unresolved problems in ionosphere—magnetosphere coupling concerns the refilling of depleted plasmaspheric flux tubes after geomagnetic storms /23/. Specifically, it is not clear whether a depleted flux tube fills from the top (equator) to the bottom (ionosphere) or from the bottom to the top. Although a significant effort has been devoted
Models of Plasmaspheric Thermal Plasma
143
to studying interhemispheric plasma transport (see /14/ and references therein), the hulk of this work is not targeted at the initial refilling of flux tubes, since it is based on a low—speed, collision—dominated transport formulation. In contrast, supersonic flow and collisionless plasma characteristics are expected on depleted flux tubes Shortly after magnetic storms. The hydrodynamic model of Banks et al. /24/ envisioned supersonic flows of &~plasma from the two conjugate ionospheric feet of a plasmaspheric flux tube colliding with nearly equal intensities near the equator to initiate plasmasphere replenishment, following magnetospheric storms. Banks et ml. postulated that after flux tube depletion, the resulting supersonic field—aligned plasma flows that emerge from the conjugate ionosphere interact at the equator, forming a pair of shocks. Schulz and Koons /25/ studied the stability of counterstreaming ion flows using a onedimensional analysis based on the ion—acoustic mode. They concluded that electrostatic shocks were not likely to form at the equator, but that ion trapping could occur via wave— particle interactions. Although Schulz and Koons based their analysis on the ion—acoustic mode, they recognized that the ion—cyclotron mode could be important. An extension of the treatment by /24/ was made by Grebowsky /26/ who considered both isothermal and adiabatic flow states and also the effects of cross—L drifts, resulting from magnetospheric convection, which cause compression or expansion of the magnetic flux tubes • He found that the thermal energy of the shocked plasma at the equator decreases or increases with time when a flux tube contracts, depending on whether the flow is isothermal or adiabatic, respectively. Singh and Schunk /27/ conducted one—dimensional numerical simulations that are relevant to the initial refilling of depleted plasmaspheric flux tubes. Their results support the conclusion by /25/ that slow moving, downward propagating electrostatic shocks are not likely to form at the equator. Moreover, their results also indicate that the counterstreaming plasmas are more stable than anticipated. Although there are few observations of the flows that are responsible for the initial filling stages, high—speed upward flows have been observed in the topside ionosphere /28/, and recent observations of a highly collimated, low—energy H+/Re+ field—aligned plasma flow, which is identified as the high—altitude extension of the polar wind /29/, should help to clarify many of these issues. 2.
Subsonic Filling of Flux Tubes.
After 1 or 2 days of the replenishment process, the upward flow is subsonic everywhere. Even for this gentler, extended period of plasrsasphere filling, reliable estimates for appropriate time constants and tube contents, for example, are not yet available, although some theoretical and observational estimates have been made. Bailey at al. /14/ calculated that the tube content on the L = 3.2 field line should ha still building up 6 days after initiation of recovery. The flux tube contents may be compared with the buildup in density profiles observed through whistler observations indicated by Figure 2a from Park /22/. From such data, Park estimates that the times required to attain equilibrium range from about 1 day at L = 2.5 to 8 days at L = 3. It appears then that saturation is predicted to be somewhat later in occurring than in the calculations of Bailey at al. /14/, and that the observed saturation tube contents are smaller by factors of 3 or more than in their calculations. With regard to saturation, Figure 3 from Sojka and Wrenn /30/ shows that the cold H+ density at geosynchronous orbit 3. The rate of appears to saturate at an extraordinarily low value of the order or 100 cm refilling that is observed prior to saturation is in agreement with theoretical predictions about the t1~flux from the ionosphere. According to present theory, the plasmasphere should not begin to saturate until the equatorial density reaches at least 1000 cm3. A comprehensive interhemispheric model for studying refilling has been developed by Richards and Torr /31/. It solves the continuity, momentum, energy, heat flow, and photoelectron flux equations f or subsonic flows using photochsmically determined boundary conditions in conjugate E regions. The solutions of the equations are carried out along the -full extent of the flux tubes using tilted dipole geometry which was found to have significant effects for interhemispheric thermal coupling. Calculations show that refilling by cold ionospheric plasma, can account remarkably well for the latitudinal variations in major ion density observed by the plasma wave instrument (PWI) and the retarding ion mass spectrometer (RIMS) on DE 1 but not the ion composition. The code solves for the concentrations and flow velocities of the three major ions 0~, H~, and He5, as well as the electron and ion temperatures.
JASR 6:3—3
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2345
Fig. 2. (a) Smoothed tube content profiles on successive days of June 1965 for whistler observations of the filling of the plasmasphere. (b) Corresponding smoothed equatorial electron concentration profiles (from /22/).
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TIME (hr) FROM 00 UT. DEC. 10. 1978 Fig. 3. Thermal ion (top panel) and 50 to 509—eV electron (bottom panel) densities over a 3—day period beginning at 0000 UT on 10 December 1978. The light line represents detector A data (pitch angle range 120 to 20°)while the heavy line represents detector B data covering 60° to 110°pitch angles (from /30/). 3.
Seasonal Effects
Our results show that filling rates can change significantly under different geophysical conditions. Diurnal, seasonal, and solar cyclic effects must be taken into account in order to get realistic refilling fluxes and hence refilling times. Figure 4 shows a comparison between theory and data from RIMS and PWI for day 282 in 1981. Calculations are indicated by the large circles with central dots. These results show that the variation in plasma concentration observed by 05 could he well accounted f or by allowing the field tube to fill for 8 days. The fact that a steep density gradient occurs between L = 3.28 and L = 3.80 implies that after 8 days of filling, a depletion clown to L 3.5 occurred.
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5 Fig. 4. Sample Dynamics Explorer data showing H+ and He densities approximately in the equatorial plane on orbit 282. The dots are theoretical densities assuming 8 days of refilling. Another problem is illustrated in Figure 5 which shows that the full flux tubes of Figure 4 ware virtually empty 1 day earlier. There is no known way in which the state of the tubes could change so quickly, given theoretical refilling rates. Since the data in question were taken at different longitudes, this suggests that the state of depletion of a flux tube depends on its longitude at the time the magnetic activity occurs, and that some tubes may be more depleted of plasma than others. The relationship between Kr, and the plasmapause has been discussed by Chappell /19/ and Higel and Wu Lei /32/. Although there appears to be a close relationship between K~and the position of the plasmapause in an average sense, there are many instances when the plasmapause behaviour is anomalous /32/. It is well known /33,9/ that the H5 density is well represented by a diffusive equilibrium profile in the inner plasmasphere, though not in the topside ionosphere, even when there are large flows. The recent calculations of Khazanov at al. /34/ indicate that even for supersonic flows, the 8+ density follows a diffusive equilibrium profile above approximately 3000 km. Measurements also indicate that in less than 1 day after magnetic activity decrease, the outer plasmasphere forms and consists of cold, essentially Maxwellian plasma with ion characteristics generally similar to those of the inner plasmasphere, albeit at significantly lower densities /35/. Richards and Torr /31/ have derived a simple analytical expression-for calculating the limiting H5 flux. Comparisons with the full model over a wide range of conditions show agreement generally to within 30%. Figures 6 and 7 point to a problem in calculating refilling rates. Two different models of the neutral atmosphere produce markedly different solar cyclical variations of the H’~~escape flux. Figure 6 was obtained using the older MSIS model of Hedin et al. /36/ while Figure 7 was obtained using the latest version of the MSIS model /37/. The latter fluxes are higher because the H density is higher at solar maximum. A recent study by Breig et al. /38/ found an [NJ variation intermediate between the two MSIS model variations. 4.
Characteristic Flows and the Maintenance of the Nocturnal Ionosphere
Several authors have examined the effects of interhemispheric flows on the state of the F region /12,16/. Solstice calculations of Bailey at al. /14/ suggest that, for an L = 3 flux tube, the flow during the first few days of plaemasphere replenishment is upward at all local times in the summer hemisphere, and in the daytime in the winter hemisphere. At later times, the flow is upward during the day and downward during the night in both hemispheres, reflecting the dominance of diurnal variations at these later stages of fillinq. The winter and summer ionospheric F2 layers are not tightly coupled and, although interhemispheric transport does occur, the plasmasphere mainly acts as a reservoir whose H~ content is variable and prevents direct mass coupling between the conjugate F2 layers. Thermal coupling is strong however, and this is discussed later.
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107 from the full model (full line) and the simple analytical formula (dot—dash line). The MSIS—77 model was used f or theme calculations. The neutral hydrogen variation is also shown (broken line) (from /31/). One of the major ongoing questions in the area of ionosphere—plasmasphera coupling is whether the nighttime F region ionosphere is maintained by plasma flowing down the magnetic field lines from the plasmasphere. Jam et al. /39/ have measured ionospheric density profiles as a function of local time using the Malvern incoherent scatter radar and find that following sunset, the ionosphere decays rapidly in the first few hours in a manner consistent with reconthtnation, but then decay essentially ceases f or the remainder of the night. Torr and Richards /40/ have also investigated the effect of interhemispheric flow on the nocturnal F region densities under solar maximum equinox conditions at mid—latitudes (L = 2.5). They found that the modeled diurnal variation of the peak electron density of the F region at night is sustained by a downward flow of ions. This is evident in Figure 8 which
Models of Plasmaspheric Thermal Plasma
147
displays a well—known enhancement of the nocturnal ionosphere near midnight, which occurs in all seasons. Figure 8 shows that the enhancement occurs even when the field tube is empty. Furthermore, during these times, the H+ flux for the cases examined is upward throughout the night. The 0+ flux is downward at the tines of the enhancement. Normally, it would be expected that the protonompheric 0+ would drain fairly rapidly after sunset because of a thermally induced collapse at that time. We have also investigated the effects of winds on the F2 layer. Our calculations revealed that for the case we studied, 0+ fluxes are driven upward by normal the 2s~ which until sunset, 3 hours LT. 5mospharic winds persists shortly after reversing at 19 hours LT to a downward flux of 5 x 10 cm 28 IlIIIIIll 28
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P. G. Richards et a!.
148
percentage daylight change in total electron content of Lancaster due to neutral winds. They conclude that the effect of the neutral wind on the ionospheric end protonospheric electron contents depends on the duration of the poleward wind in relation to daylight, and whether or not the wind reverses while the ionosphere is sunlit.
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ASSOCIATED
WITH MAGMETOSPHERIC
CONVECTION
The effects of convective electric fields on the high latitude ionosphere have been studied extensively by Sojka and Schunk (/45/ and references therein), while the convecting highlatitude topside ionosphere and plasmasphere has been studied by /16—18/. Using the model of Quegan at al. /17/, Allen at ml. /18/ have carried out calculations taking into account convection of field tubes at high latitudes using convection paths based on the semi— empirical model of Spiro et al. /46/, assuming that the geographic and magnetic poles are coincident. The cross—tail potential used was 60 kV. The calculatiune were done for low
Models of Plasmaspheric Thermal Plasma geomaguetic used.
and sunspot
activity.
The neutral
149
air winds of Fuller—Rowell
and Fees /47/ were
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LOCAL TIME (hours) Fig. 11. Comparison of model values of Ta at 1400 km at equatorial latitudes with the data frets /44/. The bars indicate the spread in the data. 5, and O~ densities and flows. Figure 13 shows contours of The model computes H~, He concentration. Similar plots were also given for He5 and H+. It was found that many of the
150
et al.
P. G. Richards
features of the 0+ at 500 km could be accounted for in terms of the behavior of 0+ at F layer heights, which is determined by the presence of various sources and sinks along the convection paths. One example is the O~trough in the afternoon dusk sector which is a consequence of the mid—latitude trough in NmF2. Another example is the Thigh latitude hole~ feature around 75° latitude in the post-midnight sector.
6000
I
I
I
I
I
I
~0~Tei1I’~0~4
LOCAL TIME (hours) Fig. 12. Comparison of model values of Ta at 3000 km altitude at equatorial latitudes compared with the observations of /44/.
n (0~)AT 500 km IN WINTER MLT
1200 9
8 7
90
9
6
95
90 95 JSZAO
100 8 1805
100
0600 105
.
80 60
6
5 ~‘
6
40
A°
2400 Fig. 13. Contours of calculated 0+ concentration for 500 km altitude in winter /18/. The 3): 1, 4.3 x 106; 2, 1.2 x iO~ 3, 3.6 x contour 4, 1.1 x values 108; 5,are3.1as x follows 108; 6, (in 9.0 units x 108;of7,m 2.6 x 1O~ 8, 7.6 x 1O~ 9, 2.2 x 1010. Lines of constant solar zenith angle are also shown. 8+ is controlled by chemical interaction with 0~. The H~contours show that 8+ is the dominant ion in the hole and the trough as predicted by Quegan at al. /17/. The Ha~ ions become dominant at times when there is solar illumination of the atmosphere at high altitudes. Ha+ ions are produced by photoionization while there is no significant equivalent source of 0~ and H~ which are in the process of decaying.
.
Models of Plasmaspheric Thermal Plasma
CONCLUSION
151
-
The state of our current modeling capability of the thermal plasma in the ionosphere and plasmasphere has been reviewed. Earlier discrepancies between theory and measurement have been reduced by improvements in both theory and data collection. However, a number of fundamental problems that were discussed in this review remain to be solved. ACKNOWLEDGEMENTS
This work was supported by NSF grants APM—8545227 and ATM-8506642 and NASA grants 1IAGW—922, NAG8—054, and NAG8—O58 at The University of Alabama in Huntsville. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47.
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