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An updated theory of the polar wind
Adv. Space Res. Vol. 6, No. 3, pp. 79—88, 1986 Printed in Great Britain. All rights reserved.
0273—1177/86 $0.00 + .50 Copyright © COSPAR
AN UPDATED THEORY OF THE POLAR WIND R. W. Schunk Center for Atmospheric and Space Sciences, Utah State University, Logan, UT 84322—3400, (LS.A.
ABSTRACT
The ‘classical’ polar wind is an ambipolar outflow of thermal plasma from the terrestrial ionosphere at high latitudes. As the plasma escapes along diverging geomagnetic flux tubes, it undergoes four major transitions, including a transition from chemical to diffusion dominance, a transition from subsonic to supersonic flow, a transition from collision—dominated to collisionless regimes, and a transition from a heavy to a light ion. A further complication arises because of horizontal convection of the flux tubes owing to magnetospheric electric fields. Recent modelling predictions indicate that the polar wind has the following characteristics~ (I) The ion and electron distributions are anisotropic and asymmetric in the collisionless regime; (2) Elevated electron temperatures ( 10,000 K) act to produce significant escape fluxee of suprathermal 0+ ions; (3) The interaction of the hot magnetos— pheric and cold ionospheric electron populations leads to a localized (double layer) electric field which accelerates the polar wind ions; (4) A time—dependent expansion produces suprathermal ions; and (5) Large perturbations lead to the formation of forward and reverse shocks. These and other results are reviewed. INTRODTJC TION In the early 1960’s, it become apparent that the interaction of the solar wind with the earth’s intrinsic dipole magnetic field acts to significantly modify the magnetic field configuration in a vast region close to the earth /1,2/. The effect of the interaction is to generate intense current systems which act to compress the earth’s magnetic field on the sunward side and stretch it into a long comet—like tail on the antisunward side. The magnetic field lines which form the tail originate in the earth’s polar regions, and along these so—called ‘open’ field lines the light ionospheric ions (11+, He+) can readily escape the ionosphere and flow into the magnetospheric tail. The first study of this light ion outflow was based on an evaporation model /3/. This study suggested that the evaporation of plasma from the polar ionospheres Out along magnetic field lines would provide a significant source of relatively cool plasma for the magnetospheric tail. Subsequently, it was argued that the outflow should be supersonic and it was termed the ‘polar wind’ in analogy to the solar wind /4/. A hydrodynamic model was then used that emphasized the supersonic nature of the flow, thereby elucidating its basic characteristics /5,6,7/. It is now well—known that the ‘classical’ polar wind is an ambipolar outflow of thermal plasma from the topside ionosphere at high latitudes and that it undergoes four major transitions, including a transition from chemical to diffusion dominance, a transition from subsonic to supersonic flow, a transition from collision—dominated to collisionless regimes, and a transition from a h~avyto a light ion. Because of the complicated nature of the flow, numerous mathematical models have been constructed over the years, including hydrody— namic /5,6,7,8/, hydromagnetic /9/, generalized transport /10,11/, kinetic /12,13,14/, and semikinetic /15,16/. The models have been used primarily to study the steady state characteristics of the flow, with the emphasis on studying physical processes. Since the ‘classical’ polar wind models are based on charge neutrality and charge conservation with no field—aligned current (smbipolar flow), the models cannot be applied to auroral field lines. Also, the presence of strong localized parallel electric fields and wave-particle interactions on auroral field lines acts to further invalidate polar wind no— dels in the auroral region. Consequently, this review will not be concerned with auroral processes of any kind. Instead, the review will concentrate on the’classical’ polar wind, with the emphasis on the theoretical results obtained during the last five years.
79
80
R. W. Schunk
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DENSITY (cm3)
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2000
2600
3200
3800
TEMPERATURE (deg K)
Fig. 1. Theoretical H+ density and temperature ~rofiles as a function of altitude for different H4 escape velocities at 3000—km. The H velocities at 3000_\tm are: (a) 0.06, (b) 0.34, (c) 0.75, (d) 2.0, (e) 3.0, (f) 5.0, (g) 10.0 and (h) 20.0—km s . The shaded region shows the range of densities (from /8/). EARLY HYDRODYNAMIC SOLUTIONS In the initial studies of the polar wind, the hydrodynainic continuity and mcxnentum equations for H+ and 0+ were solved by assuming an isothermal ionosphere /5,6,7/ and the basic characteristics of the density and flow velocity structure were elucidated. Subsequently, the polar wind energy balance and the effects of magnetospheric convection electric fields were taken into account /8,17,18,19/. Typical polar wind results are shown in Figures la and lb for the case when convection electric field effects are neglected. Figure la shows the effect on the H+ and 0+ densities of different H4 escape velocities at 3000—km. Curve (a) represents near diffusive equilibrium, with H~ becoming the dominant ion at 900-km (the 0+ density in this case follows the lower curve of the shaded region). As the upper ~oundary velocity is increased, the H density is progressively reduced with a peak in the H density profile appearing near 600 — 700-km altitude. Curves (b) — (e) correspond to subsonic outflow, while for curves (g) — (h) the flow is supersonic. Curve (f) covers the transonic region with the Mach number equal to 1.17 at 1400-km and reducing to 0.89 at 3000—km. For curvy (h)~ which is for a flow velocity of 20-km s~ at 3000—km, the H+ escape flux is 8.5 x 10 ctn s~. The H4 temperature is strongly affected by the H4 flow, as shown in Figure lb. The behavior of the H4 temperature is also fairly complicated. As the escape velocity is increased, the H4 temperature at high altitudes first decreases, then increases, and th~n decreases again. This behavior is related to the relative contributions made to the H thermal balance by convection, advec tion, thermal conduction, frictional heating, and collisional cooling, and the complete details are given by Raitt etal. /8/. How~ver, we note that the general trend of increasing 11+ temperatures at high altitudes as the H escape velocity increases the subsonic regime (curves b — e) ~s due primarily to enhanced frictional heating as H moves through a gravitationally bound 0 population with an increasing speed. The decrease in the H4 temperature with increasing H+ escape velocity in the supersonic regime (curves f — h) is due both to a decrease in frictional heating as the plasma becomes collisionless and a change in the shape of the velocity profile, which acts to increase the importance of convective cooling. EARLY KINETIC SOLUTIONS The polar wind results that have been discussed in the previous section are valid at the altitudes where the flow is collision—dominated. As a rough guide, the flow is effectively collision—dominated when, U./11 1\)1 << 1, where U~is the ion field—aligned drift velocity, ~ is the ion density scale height, and is the appropriate ion collision frequency. For H pressure distribution ani— this condition generally begins to break down at 1000—km 4and is clearly violated becomes at 2000—km sotropic and the the plasma 11+ heatis flow is not simply related to the gradient in the H4 temper/8/. When not vector collision—dominated, the H ature. The collisionless characteristIcs of the polar wind can be described by kinetic, semi—kinetic, hydromagnetic and generalized transport models. The hydromagnetic and generalized transport equations are obtained by taking velocity moments of the Eoltzmann equation in an effort to derive conservation equations for the physically significant moments of the distribution function, such as density, drift velocity, temperature, stress tensor, and heat flow
vector.
The hydromagnetic equations correspond to the collisionleas moment equations.
The generalized transport equations are similar to the hydromagnetic equations, except that collisional terms are retained, and therefore, these equations provide a continuous transi—
Updated Theory of Polar Wind
81
tion from the collision—dominated to the collisionless regimes. The kinetic models, on the other hand, are obtained by directly integrating the collisionless Boltzmann equation, and consequently, they satisfy the full hierarchy of moment equations deduced from the colli— sionless Boltsmann equation. Semi—kinetic models correspond to a hybrid approach whereby some species are described by transport equations and others by kinetic equations. Our aim is not to compare the different mathematical models of the polar wind but rather to present the results that have been obtained from the various models in order to elucidate the basic characteristics of the flow. Reviews on the various transport equations have been written by Schunk /20/ and Barakat and Schunk /21/, while an excellent review of kinetic models of the solar and polar winds is given by Lemaire and Scherer /14/. With regard to the polar wind, the hydromagnetic, generalized transport, kinetic and semi—kinetic models produce density and drift velocity profiles that are similar to those obtained from the hydrodynamic equations for the case of supersonic flow. However, the ion temperature distributions are different, with the collisionlesa models yielding large ten— peratu~e aniso~ropies at high altitudes. Some early results are shown in Figure 2, where the H and 0 temperatures parallel and perpendicular t~ the geomagnetic field are. plotted as a function of altitude for collisionless, supersonic H outflow. The ion temperature distributions were calculated with both kinetic and hydromagnetic models and the results are similar. The parallel ion temperatures are essentially constant with altitude at high altitudes, while the perpendicular ion temperatures decrease monotonically with altitude. The net result is a parallel—to—perpendi~ular temperature anisotropy that grows with altitude, reaching nearly a factor of 50 for H ions at a distance of 10 earth radii. GENERALIZED TRANSPORT MODElS
Generalized transport equations were used by Schunk and Watkins /10,11/ to obtain polar wind solutions that are continuous through the tr~nsition from collision—dominated to collision— less regimes. Both subsonic and supersonic H outflows were considered. The dramatic result to emerge from these studies was that the character of th~ solution to the generalized transp~rt equations was different for subsonic and supersonic H outflows. Figure 3 show~ the H temperatures parallel and perpendicular to the geomagnetic field for supersonic H outflow and for both cold (left panel) and hot (right panel) electron temperature distributions. For both cases, there is an appreciable H÷temperature anisotropy with T,,~ 1> T at all altitudes above 1500—km. The perpendicular H temperature displays a rap~d de~rease with altitude at low altitudes and then tends to go constant at high altitudes. The variation of F with altitude, on the other hand, is more complicated. At low altitudes, T displays ~ decrease with altitude that is similar to the T decrease. Above about 3000—kE T exhibits little variation with altitude all the way to~’the top boundary for the low e~ctron temperature case • However, for the high electron temperature case, T is roughly constant with altitude between 3000 and 5000—km and then decreases with altitud~ above this altitude range. The behavior of the parallel and perpendicular H+ temperatures shown in the left panel of Figure 3 for the cold T distribution is in good qualitative agreement with that obtained from the kinetic and hydroLgnetic models (Figure 2). +The main qualitative difference is that the generalized transport equations produce an H temperature anisotropy that tends to go constant at high altitudes, whereas the anisotropy obtained from the kinetic and hydro— magnetic models does not disp’ay this tendency. Also, solutions to the gene~alized transport equations for supersonic H outflow can be obtained only with an upward H heat flow from the lower ionosphere. For subsonic H+ outflow, it i~possible to obtain solutions to the generalized transport equations with a downward H heat flow, which implies that a high altitude h~atsource exists above the altitude range of interest. Figure 4 shows that for subsoni~H outflow with a downward heat flow, the variation of the parallel and perpendicular H temperatures is different from that found for supersonic outflow. For subsonic outflow, the anisotropy is opposite to that found for supersonic outflow, with T > T below about 3500-km and T T above this altitude. Also, in contrast4to what wa~foun~for supersonic outflow, f~r th?s case the parallel and perpendicular H temperatures increase with altitude above 3500—km, owing to the high—altitude heat source. 4 outflow Different is subsonic results or supersonic are also obtained (Figurefor5).theFor electron subsonic gasH~epending outflow, onthewhether electron thegas H remains collision—dominated to high altitudes; that is, the electron temperature anisotropy is small, the electron temperatures are low, the electron temperature profile is isothermal at high altitudes, and the electron heat flow is ‘iven by the classical 5ollision—dominated expression at all altitudes. For supersonic H outflow, on the other hand, the electron gas becomes collisionlesa above about 3000—km. In the collisionless regime an electron temperature anisotropy develops such that the electron temperature perpendicular to the geomagnetic field, Ta.&~ is greater than the temperature parallel to the geomagnetic field, T ~. Thi anisotropy increases with altitude, and at 12,000—km Tej. /Te~ 2. Also, for aup~rsonic H
R. W. Schunk
82
12
I I
ION TEMPERATURES
-
\
— — —
-
KINETIC HYDRODYNAMIC
8~lH~
2 10’
~
TEMPERATURE (K) Fig. 2. o~and ll~temperatures parallel and perpendicular to the geomagnetic field obtained from kinetic and hydroinagnetic models of the collisionless, supersonic polar wind (from /9/).
O~
TEMP (thousands K)
TEMP (thousands K)
4 temperatures parallel and perpendicular to the geomagnetic field versus altiFig. 3. H tude . for supersonic flow and for both cold (left panel) and hot (right panel) electron temperature distributions (from /11/). 2
E
T 5
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4 temperatures parallel and perpendicular tude flow (from /11/). Fig. for 4. subsonic H
6
to the geomagnetic field
versus
alti-
Updated Theory of Polar Wind
83
outflow the magnitude of the downward electron heat flux at 1500—km has a dramatic effect on the individual parallel and perpendicular electron temperatures. For small Tower—boundary electron heat fluxes, F 011 and Te~are low at all altitudes (Tea < 70000K), but for large electron heat fluxes at the lower boundary, Te_j_ can exceed 100,000°K at 12,000—km. HIGH THERMAL ELECTRON TEMFERATIJRES Although the early polar wind models predicted a negligible 0+ escape flux, satellite measurements clearly indicate that the magnetosphere contains a significant population of both energetic and suprathermal 0+ ions. In order to determine the possible contribution of the polar wind to this nagnetospheric 0 population, a systematic parameter study was conducted by Barakat and Schunk /15/ using a semi—kinetic model to describe the steady state, colli—
sionleas polar wind. This study indicated that for h3gh e~ectfontemperatures 0~is not g~avitationallybound and significant escape fluxes (- 10 cm s ) of suprathermal (—2 eV) 0 ions can occur. 4 outflow
Figure and for6 electron shows representative temperatures ion of 3000 density and and 10,000 MachK.number The case profiles of Ffor = 3000 supersonic K is essentially H the same case considered by Holzer et al. /9/, except for a cons~a~tmultiplier of the ion densities at the lower boundary (4500—km). For this case, the ~ density decreases rapidly with altitude, the 0~escape flux is negligibly small, and the 0 Mach number is l~ss than unity over most of the altitude range. For T 10,000 K, on the oth~r hand, the 0 density profile tends to follow the H4 profile, and s~gnificantly elevated 0 densities ~ccu~ at high altitudes. The 0+ ~acapg flj 1ix also
increases
dramatically,
from 1.8 x ~0
cm
s
for
3000 K to 0.44 x 10 om~ s for T = 10,000 K. In addition, the 0 Mach number, d~ift velocity, and energy increase markedly when F is increased from 3000 to 10,000 K. The 0~outflow is supersonic at most altitudes and the ~ach number approaches 20 at the upper boundary. T
=
I
0
50
I
I
100
I
50 0
50
~.
00
_________________
150 0
50
100
150
TEMP (thousands K) Fig. 5. Itiectron temperatures parallel and perpendicular to the geomagnetic field altitude for supersonic flow and for low~rboundary electron temperature gradients (left panel), 1 (middle panel), and 2 K-km (right panel) (from 110/).
versus of 0.1
I~ I
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111111
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DENSITY (cm Fig. 6. Ion density (left panel) and Mach number (right panel) profiles for supersonic 11+ outflow and for F 0 = 3000 K (dashed curves) and Fe curves) (from /15/).
versus =
altitude
10,000 K (solid
84
R. W. Schunk
HOT MAGNETOSPHERIC ELECTRONS Precipitating hot electrons of magnetospheric origin are a common feature of the polar cap. Specifically, three hot electron populations have been identified, including the polar rain, polar showers and polar squall /22,23/. Recently, the effect of such hot electron populations on the polar wind has been studied by Barakat and Schunk /16/ using a semi—kinetic model to describe the collisionless regime at high altitudes. Estimates of hot electron parameters based on characteristic energy and flux measurements indicate that the hot/cold electron temperature ratio varies from 10 to io~and that the percentage of hot electrons varies from 0.1% to 10% at 4500-km. For ratios at the lower ends of these ranges, the polar wind solutions with hot electrons are similar to those obtained previously without hot electrons. However, for higher hot electron temperatures and a greater percentage of hot electrons, there is a discontinuity in the kinetic solution, which indicates the presence of a sharp transition. 4 This is shown outflow, for ina Figure 7, where H+ density profiles are shown for the case of supersonic H hot/total electron density ratio of 1% at 4500—km, and for hot/cold electron temperature ratios of 10, 100 and 1000. The transition corresponds to a contact surface between the hot and cold electrons. Along this surface, an outwardly directed, parallel electric field exists which reflects cold ionospheric electrons and prevents their escape. The ‘double layer’ electric field also acts to increase the supersonic H+ outflow velocity and escape energy. The H energy gain may be as large as 1 to 2 keV, depending on the ionospheric and magnetospheric conditions. With 4regard to O~,the hot electrons act to reduce the pot~ntial barrier, thereby allowing more 0 ions to escape. A significant enhancement in the 0 escape flux can occur depending on the hot electron density and temperature. TThIE-DEPENDENT EXPANS ION
All of the polar wind studies discussed up to this point were for steady state conditions, and therefore, the energization that occurs during the initial plasma expansion was not modelled. Recently, however, the temporal evolution of density perturbations in the supersonic, collisionless polar wind was modelled with the aid of time-dependent hydrodynamic equations /24,25/. Extended density depletions as well as localized density bumps and holes were considered. For ‘extended’ density depletions, the results obtained depend on the degree of the depletion. When the density depletion is small, the expansion is headed by a shock. On the other hand, when the extended density depletion is severe, the expansion is headed by a pair of forward and reverse shocks. The extent of the ion acceleration depends both on the mag4, and profiles nitude of the density depletion and on the ion mass. Figures 8a and Sb He4 showdensity the effect of for the a ion typical mass for polara wind given situation density depletion. are perturbed At tby= imposing 0, the 0+, an extended H density depletion at altitudes above about 2800-km (geocentric distance of 9188—kin), while the velocity profiles are left unchanged. At later times, the expansion of each ion species is headed by a density front, which appears as a shock in the hydrodynamic model. A significant acceleration of all of the ion species occurs behind the fronts. Note that over certain altitude ranges each ion species can be the mos~energetic (Figur~8b); the maximum en~rgies(W) of the different ions are limited to W(H ) < 10 eV, W(He ) < 5 eV, and W(0 ) < 1.5 eV. These energies, however, are considerably larger than typical ionospheric thermal energies (Ti - ç~.33 eV). Theref~re, the relative sn~xiinum energization of the ions is: Wmex(H )/T 1 29, Wmax(He )/Ti = 16, and Wmex(O )/Ti 4. I 1111119 I 1111119 I IIIlI~ 111111,
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H~DENSITY (cm3) Fig. 7. H4 density profiles versus altitude for supersonic H~ outflow, for a hot/total electron density ratio of 1E at 4500—km, and for hot/cold electron temperature ratios of 0 Th/Tc = 10 (left panel), 100 (middle panel), and 1000 (right panel). The dashed curves correspond to the solutions obtained without including the effect of hot electrons (from
/161)
Updated Theory of Polar Wind
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Fig. 8b. Ion kinetic energy profiles at two times after an initial extended t9-e’~r’.ty depletion in the topside polar ionosphere (from /25/).
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DENSITY N (RELATIVE SCALE) Fig. 9. Temporal evolution of a localized density enhancement created polar wind (from /24/).
at
t
=
t
in
the
86
R. W. Scliunk
When the polar wind is perturbed by a ‘localized’ density bump or hole, the perturbation propagates upward in the direction of the polar wind, but it undergoes a considerable modification, evolving into forward—reverse shock pairs. Figure 9 shows the temporal evolution of a density bump. The density profile at t_ 1 is a typical, steady state, supersonic polar wind profile. At t the polar wind is perturbed by a density bump, which peaks at a geocentric distance of 1~,OO0—km and is approximately Gaussian with a width of about 500—km. The density bump is initially given a zero drift velocity along the flux tube to simulate the release of plasma from a spacecraft moving horizontally through the polar ionosphere. At later times (t2, t4), distinct ‘forward’ and ‘reverse’ shocks can be clearly seen. The forward shock moves with a velocity of about 36—km/s until it crosses the upper boundary, while the reverse shock undergoes a continual acceleration, crossing the upper boundary with a speed of about 14.5—km/s. After the reverse shock crosses the upper boundary, the polar wind returns to a steady state situation, which typically takes only tens of minutes. ION HEATING The effect of ‘localized’ ion heating on the polar ionosphere has been studied by Gombosi et al. /26/ with the aid of a time-dependent hydrodynamic model. The ionosphere was initially assumed to be in a state of diffusive equilibrium and then a localized ion heat source was applied. The distributed ion heating had a Gaussian shape with the peak at32009_km and a half—width of 250—km. The ion heating rate was increased up to 0~O25 er~s cm s over a time period of 150 a. The absorbed heat was divided between H and 0 according to their mass densities. The topside pressure was kept at a very low value to simulate ‘open’ geomagnetic field lines. Figure 10 shows the effect of the io~heating on the ionosphere 2.5 minutes after the heating was initiated. At this time, the 0 temperature already ~xceeds 20,000 K between 2000 and 5000-kin, which causes a significant (but subsonic) upward 0 flow. Consequ~ntly,intense ion heating ~pplied for brief periods of tine can produce subsonic upward 0 flows, but supersonic 0 outflows are obtained only if the ion heating is applied for 1 hour or longer. In this latter time period, the flux tube of plasma can convect a significant distance across the polar cap owing to magnetospheric electric fields, and therefore, it is hig~ly unlikely that a naturally occurring, localized, ion heat source can produce supersonic 0 outflows of the polar wind type.
t
V (kmls) -6
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Fig. 10. Flow velocities, Mach numbers, number densities, and temperature distributions an ion heated ionosphere 2.5 minutes after ion heating was initiated (from /26/).
in
Updated Theory of Polar Wind
87
CONCLUSION In recent years, theoretical models of the polar wind have produced a number of new predictions with regard to its characteristics and temporal evolution. As in the past, the theoretical predictions are still way ahead of experimental verification. However, some important characteristics of the polar wind have recently been confirmed. EE—1 satellite date were used to show ‘indirectly’ that the polar wind is ‘supersonic’ in the polar cap most of the time /27/. Altitude profiles of electron density were constructed from measurements made on many traveraals ~f the polar cap, and the measurements strongly support the model results for supersonic H outflow. Also, individual ‘direct’ measurements of the polar wind by Nagai etal. /28/ and Gurgiolo and Burch /29/ indicate that the flow is supersonic. More recently, T.~—l satellite data obtained at an altitude of 4500-km by Biddle at al. /30/ have directly verified the predi~tionsregarding ion heat flux asymmetries /ii/T’ On open 4) were observed to be supersonic, and the shape and field lines, light ions and He direction of thetheasymmetry of (H the distribution functions were consistent with the presence of upward heat fluxes. On closed field lines, on the other hand, the outward flows were subsonic and the heat fluxes were downward /11/. In addition, measurements of photoelectron spectra by Winningham and Heikkila /22/ and Winningham and Gurgiolo /23/ suggest the presence of a spatially and/or temporally varying large—scale outwardly directed parallel electric field over the polar cap. This suggestion is consistent with the prediction of a contact surface (double layer electric field) between the hot niagnetospheric and the cold’ ionospheric electron populations 116/. Acknowledgement.
This
research
was
supported
by
NASA
grant
NA~T—77 and
NSF
grant
ATh—841788O to Utah State University. REFERENCES
1.
W.I. Axford and C.0. Hines, A unifying theory of high—latitude and geomagnetic storms, Can. J. Phys., 39, 1433—1464 (1961)
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W.J. Raitt, R.W. Schunk, and P.M. Banks, The influence of convection electric fields on thermal proton outflow from the ionosphere, Planet. Space Sci., 25, 291—301 (1977)
18.
W.J. Raitt, R.W. Schunk, and P.M. Banks, Helium ion outflow from the terrestrial ionosphere, Planet. Space Sci., 26, 255—268 (1978)
19.
W.J. Raitt, R.W. Schunk, and P.M. Banks, Quantitative calculations of helium ion escape fluxes from the polar ionospheres, 3. Geophys. Keg., 83, 5617—5624 (1978)
20.
R.W. Schunk, Mathematical structure of transport equations Rev. Geophys. Space Phys., 15, 429—445 (1977)
21.
A.R. Barakat and R.W. Schunk, Transport equations for space plasmas: A review, Plasma Phys., 24, 389—418 (1982)
22.
J.D. Winningham and W.J. Heikkila, Polar cap auroral electron ISIS, 3. Geophys. Rea., 79, 949-957 (1974)
23.
J.D. Winningham and C. Gurgiolo, ~—2 photoelectron measurements consistent with a large-scale parallel electric field over the polar cap, Geophys. Res. Lett., 9, 977—979 (1982)
24.
N. Singh and R.W. Schunk, Temporal evolution of density perturbations wind, J. Geophys. Res., 90, 6487—6496 (1985)
25.
N. Singh and R.W. Schunk, Ion acceleration in expanding ionospheric plasmas, Presented at the Chapsan Conference on Ion Acceleration in the Magnetosphere and Ionosphere, Boston, Massachusetts (1985)
26.
T.I. Gombosi, T.E. Cravens, and A.F. Nagy, A time-dependent theoretical model of the polar wind: Preliminary results, Geophys. Res. Lett., 12, 167—170 (1985)
27.
A.M. Persoon, D.A. Gurnett, and S.D. Shawhan, Polar cap electron densities from 1~1 plasma wave observations, J. Geophys. Res., 88, 10,123—10,136 (1983)
28.
T. Nagai, J.H. Waite, J.L. Green, and C.R. Chappell, First measurements of supersonic polar wind in the polar magnetosphere, Geophys. Keg. Lett., 11, 669—672 (1984)
29.
C. Gurgiolo .J.L. 12,Burch, of the polar wind Geophys. Res. and Lett., 69—72 Composition (1985)
30.
A.P. Biddle, T.E. Moore, and C.R. Chappell, Evidence for ion heat flux in the ion polar wind, 3. Geophys. Res., 90, 8552—8558 (1985)
for
on
the
polar
multi—species
multicomponent
—
fluxes
not
dust
wind,
flows,
anisottopic
observed
in
the
4
H
and
with
polar
He4, light
0273—1177/86 $0.00 + .50 Copyright © COSPAR
AN UPDATED THEORY OF THE POLAR WIND R. W. Schunk Center for Atmospheric and Space Sciences, Utah State University, Logan, UT 84322—3400, (LS.A.
ABSTRACT
The ‘classical’ polar wind is an ambipolar outflow of thermal plasma from the terrestrial ionosphere at high latitudes. As the plasma escapes along diverging geomagnetic flux tubes, it undergoes four major transitions, including a transition from chemical to diffusion dominance, a transition from subsonic to supersonic flow, a transition from collision—dominated to collisionless regimes, and a transition from a heavy to a light ion. A further complication arises because of horizontal convection of the flux tubes owing to magnetospheric electric fields. Recent modelling predictions indicate that the polar wind has the following characteristics~ (I) The ion and electron distributions are anisotropic and asymmetric in the collisionless regime; (2) Elevated electron temperatures ( 10,000 K) act to produce significant escape fluxee of suprathermal 0+ ions; (3) The interaction of the hot magnetos— pheric and cold ionospheric electron populations leads to a localized (double layer) electric field which accelerates the polar wind ions; (4) A time—dependent expansion produces suprathermal ions; and (5) Large perturbations lead to the formation of forward and reverse shocks. These and other results are reviewed. INTRODTJC TION In the early 1960’s, it become apparent that the interaction of the solar wind with the earth’s intrinsic dipole magnetic field acts to significantly modify the magnetic field configuration in a vast region close to the earth /1,2/. The effect of the interaction is to generate intense current systems which act to compress the earth’s magnetic field on the sunward side and stretch it into a long comet—like tail on the antisunward side. The magnetic field lines which form the tail originate in the earth’s polar regions, and along these so—called ‘open’ field lines the light ionospheric ions (11+, He+) can readily escape the ionosphere and flow into the magnetospheric tail. The first study of this light ion outflow was based on an evaporation model /3/. This study suggested that the evaporation of plasma from the polar ionospheres Out along magnetic field lines would provide a significant source of relatively cool plasma for the magnetospheric tail. Subsequently, it was argued that the outflow should be supersonic and it was termed the ‘polar wind’ in analogy to the solar wind /4/. A hydrodynamic model was then used that emphasized the supersonic nature of the flow, thereby elucidating its basic characteristics /5,6,7/. It is now well—known that the ‘classical’ polar wind is an ambipolar outflow of thermal plasma from the topside ionosphere at high latitudes and that it undergoes four major transitions, including a transition from chemical to diffusion dominance, a transition from subsonic to supersonic flow, a transition from collision—dominated to collisionless regimes, and a transition from a h~avyto a light ion. Because of the complicated nature of the flow, numerous mathematical models have been constructed over the years, including hydrody— namic /5,6,7,8/, hydromagnetic /9/, generalized transport /10,11/, kinetic /12,13,14/, and semikinetic /15,16/. The models have been used primarily to study the steady state characteristics of the flow, with the emphasis on studying physical processes. Since the ‘classical’ polar wind models are based on charge neutrality and charge conservation with no field—aligned current (smbipolar flow), the models cannot be applied to auroral field lines. Also, the presence of strong localized parallel electric fields and wave-particle interactions on auroral field lines acts to further invalidate polar wind no— dels in the auroral region. Consequently, this review will not be concerned with auroral processes of any kind. Instead, the review will concentrate on the’classical’ polar wind, with the emphasis on the theoretical results obtained during the last five years.
79
80
R. W. Schunk
~: ~
Hill__IIIIIiII~
________________
ic
2
io
~3
io~
DENSITY (cm3)
o~
06800
1400
2000
2600
3200
3800
TEMPERATURE (deg K)
Fig. 1. Theoretical H+ density and temperature ~rofiles as a function of altitude for different H4 escape velocities at 3000—km. The H velocities at 3000_\tm are: (a) 0.06, (b) 0.34, (c) 0.75, (d) 2.0, (e) 3.0, (f) 5.0, (g) 10.0 and (h) 20.0—km s . The shaded region shows the range of densities (from /8/). EARLY HYDRODYNAMIC SOLUTIONS In the initial studies of the polar wind, the hydrodynainic continuity and mcxnentum equations for H+ and 0+ were solved by assuming an isothermal ionosphere /5,6,7/ and the basic characteristics of the density and flow velocity structure were elucidated. Subsequently, the polar wind energy balance and the effects of magnetospheric convection electric fields were taken into account /8,17,18,19/. Typical polar wind results are shown in Figures la and lb for the case when convection electric field effects are neglected. Figure la shows the effect on the H+ and 0+ densities of different H4 escape velocities at 3000—km. Curve (a) represents near diffusive equilibrium, with H~ becoming the dominant ion at 900-km (the 0+ density in this case follows the lower curve of the shaded region). As the upper ~oundary velocity is increased, the H density is progressively reduced with a peak in the H density profile appearing near 600 — 700-km altitude. Curves (b) — (e) correspond to subsonic outflow, while for curves (g) — (h) the flow is supersonic. Curve (f) covers the transonic region with the Mach number equal to 1.17 at 1400-km and reducing to 0.89 at 3000—km. For curvy (h)~ which is for a flow velocity of 20-km s~ at 3000—km, the H+ escape flux is 8.5 x 10 ctn s~. The H4 temperature is strongly affected by the H4 flow, as shown in Figure lb. The behavior of the H4 temperature is also fairly complicated. As the escape velocity is increased, the H4 temperature at high altitudes first decreases, then increases, and th~n decreases again. This behavior is related to the relative contributions made to the H thermal balance by convection, advec tion, thermal conduction, frictional heating, and collisional cooling, and the complete details are given by Raitt etal. /8/. How~ver, we note that the general trend of increasing 11+ temperatures at high altitudes as the H escape velocity increases the subsonic regime (curves b — e) ~s due primarily to enhanced frictional heating as H moves through a gravitationally bound 0 population with an increasing speed. The decrease in the H4 temperature with increasing H+ escape velocity in the supersonic regime (curves f — h) is due both to a decrease in frictional heating as the plasma becomes collisionless and a change in the shape of the velocity profile, which acts to increase the importance of convective cooling. EARLY KINETIC SOLUTIONS The polar wind results that have been discussed in the previous section are valid at the altitudes where the flow is collision—dominated. As a rough guide, the flow is effectively collision—dominated when, U./11 1\)1 << 1, where U~is the ion field—aligned drift velocity, ~ is the ion density scale height, and is the appropriate ion collision frequency. For H pressure distribution ani— this condition generally begins to break down at 1000—km 4and is clearly violated becomes at 2000—km sotropic and the the plasma 11+ heatis flow is not simply related to the gradient in the H4 temper/8/. When not vector collision—dominated, the H ature. The collisionless characteristIcs of the polar wind can be described by kinetic, semi—kinetic, hydromagnetic and generalized transport models. The hydromagnetic and generalized transport equations are obtained by taking velocity moments of the Eoltzmann equation in an effort to derive conservation equations for the physically significant moments of the distribution function, such as density, drift velocity, temperature, stress tensor, and heat flow
vector.
The hydromagnetic equations correspond to the collisionleas moment equations.
The generalized transport equations are similar to the hydromagnetic equations, except that collisional terms are retained, and therefore, these equations provide a continuous transi—
Updated Theory of Polar Wind
81
tion from the collision—dominated to the collisionless regimes. The kinetic models, on the other hand, are obtained by directly integrating the collisionless Boltzmann equation, and consequently, they satisfy the full hierarchy of moment equations deduced from the colli— sionless Boltsmann equation. Semi—kinetic models correspond to a hybrid approach whereby some species are described by transport equations and others by kinetic equations. Our aim is not to compare the different mathematical models of the polar wind but rather to present the results that have been obtained from the various models in order to elucidate the basic characteristics of the flow. Reviews on the various transport equations have been written by Schunk /20/ and Barakat and Schunk /21/, while an excellent review of kinetic models of the solar and polar winds is given by Lemaire and Scherer /14/. With regard to the polar wind, the hydromagnetic, generalized transport, kinetic and semi—kinetic models produce density and drift velocity profiles that are similar to those obtained from the hydrodynamic equations for the case of supersonic flow. However, the ion temperature distributions are different, with the collisionlesa models yielding large ten— peratu~e aniso~ropies at high altitudes. Some early results are shown in Figure 2, where the H and 0 temperatures parallel and perpendicular t~ the geomagnetic field are. plotted as a function of altitude for collisionless, supersonic H outflow. The ion temperature distributions were calculated with both kinetic and hydromagnetic models and the results are similar. The parallel ion temperatures are essentially constant with altitude at high altitudes, while the perpendicular ion temperatures decrease monotonically with altitude. The net result is a parallel—to—perpendi~ular temperature anisotropy that grows with altitude, reaching nearly a factor of 50 for H ions at a distance of 10 earth radii. GENERALIZED TRANSPORT MODElS
Generalized transport equations were used by Schunk and Watkins /10,11/ to obtain polar wind solutions that are continuous through the tr~nsition from collision—dominated to collision— less regimes. Both subsonic and supersonic H outflows were considered. The dramatic result to emerge from these studies was that the character of th~ solution to the generalized transp~rt equations was different for subsonic and supersonic H outflows. Figure 3 show~ the H temperatures parallel and perpendicular to the geomagnetic field for supersonic H outflow and for both cold (left panel) and hot (right panel) electron temperature distributions. For both cases, there is an appreciable H÷temperature anisotropy with T,,~ 1> T at all altitudes above 1500—km. The perpendicular H temperature displays a rap~d de~rease with altitude at low altitudes and then tends to go constant at high altitudes. The variation of F with altitude, on the other hand, is more complicated. At low altitudes, T displays ~ decrease with altitude that is similar to the T decrease. Above about 3000—kE T exhibits little variation with altitude all the way to~’the top boundary for the low e~ctron temperature case • However, for the high electron temperature case, T is roughly constant with altitude between 3000 and 5000—km and then decreases with altitud~ above this altitude range. The behavior of the parallel and perpendicular H+ temperatures shown in the left panel of Figure 3 for the cold T distribution is in good qualitative agreement with that obtained from the kinetic and hydroLgnetic models (Figure 2). +The main qualitative difference is that the generalized transport equations produce an H temperature anisotropy that tends to go constant at high altitudes, whereas the anisotropy obtained from the kinetic and hydro— magnetic models does not disp’ay this tendency. Also, solutions to the gene~alized transport equations for supersonic H outflow can be obtained only with an upward H heat flow from the lower ionosphere. For subsonic H+ outflow, it i~possible to obtain solutions to the generalized transport equations with a downward H heat flow, which implies that a high altitude h~atsource exists above the altitude range of interest. Figure 4 shows that for subsoni~H outflow with a downward heat flow, the variation of the parallel and perpendicular H temperatures is different from that found for supersonic outflow. For subsonic outflow, the anisotropy is opposite to that found for supersonic outflow, with T > T below about 3500-km and T T above this altitude. Also, in contrast4to what wa~foun~for supersonic outflow, f~r th?s case the parallel and perpendicular H temperatures increase with altitude above 3500—km, owing to the high—altitude heat source. 4 outflow Different is subsonic results or supersonic are also obtained (Figurefor5).theFor electron subsonic gasH~epending outflow, onthewhether electron thegas H remains collision—dominated to high altitudes; that is, the electron temperature anisotropy is small, the electron temperatures are low, the electron temperature profile is isothermal at high altitudes, and the electron heat flow is ‘iven by the classical 5ollision—dominated expression at all altitudes. For supersonic H outflow, on the other hand, the electron gas becomes collisionlesa above about 3000—km. In the collisionless regime an electron temperature anisotropy develops such that the electron temperature perpendicular to the geomagnetic field, Ta.&~ is greater than the temperature parallel to the geomagnetic field, T ~. Thi anisotropy increases with altitude, and at 12,000—km Tej. /Te~ 2. Also, for aup~rsonic H
R. W. Schunk
82
12
I I
ION TEMPERATURES
-
\
— — —
-
KINETIC HYDRODYNAMIC
8~lH~
2 10’
~
TEMPERATURE (K) Fig. 2. o~and ll~temperatures parallel and perpendicular to the geomagnetic field obtained from kinetic and hydroinagnetic models of the collisionless, supersonic polar wind (from /9/).
O~
TEMP (thousands K)
TEMP (thousands K)
4 temperatures parallel and perpendicular to the geomagnetic field versus altiFig. 3. H tude . for supersonic flow and for both cold (left panel) and hot (right panel) electron temperature distributions (from /11/). 2
E
T 5
0 ~
lj
8-
-
c
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-
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4 temperatures parallel and perpendicular tude flow (from /11/). Fig. for 4. subsonic H
6
to the geomagnetic field
versus
alti-
Updated Theory of Polar Wind
83
outflow the magnitude of the downward electron heat flux at 1500—km has a dramatic effect on the individual parallel and perpendicular electron temperatures. For small Tower—boundary electron heat fluxes, F 011 and Te~are low at all altitudes (Tea < 70000K), but for large electron heat fluxes at the lower boundary, Te_j_ can exceed 100,000°K at 12,000—km. HIGH THERMAL ELECTRON TEMFERATIJRES Although the early polar wind models predicted a negligible 0+ escape flux, satellite measurements clearly indicate that the magnetosphere contains a significant population of both energetic and suprathermal 0+ ions. In order to determine the possible contribution of the polar wind to this nagnetospheric 0 population, a systematic parameter study was conducted by Barakat and Schunk /15/ using a semi—kinetic model to describe the steady state, colli—
sionleas polar wind. This study indicated that for h3gh e~ectfontemperatures 0~is not g~avitationallybound and significant escape fluxes (- 10 cm s ) of suprathermal (—2 eV) 0 ions can occur. 4 outflow
Figure and for6 electron shows representative temperatures ion of 3000 density and and 10,000 MachK.number The case profiles of Ffor = 3000 supersonic K is essentially H the same case considered by Holzer et al. /9/, except for a cons~a~tmultiplier of the ion densities at the lower boundary (4500—km). For this case, the ~ density decreases rapidly with altitude, the 0~escape flux is negligibly small, and the 0 Mach number is l~ss than unity over most of the altitude range. For T 10,000 K, on the oth~r hand, the 0 density profile tends to follow the H4 profile, and s~gnificantly elevated 0 densities ~ccu~ at high altitudes. The 0+ ~acapg flj 1ix also
increases
dramatically,
from 1.8 x ~0
cm
s
for
3000 K to 0.44 x 10 om~ s for T = 10,000 K. In addition, the 0 Mach number, d~ift velocity, and energy increase markedly when F is increased from 3000 to 10,000 K. The 0~outflow is supersonic at most altitudes and the ~ach number approaches 20 at the upper boundary. T
=
I
0
50
I
I
100
I
50 0
50
~.
00
_________________
150 0
50
100
150
TEMP (thousands K) Fig. 5. Itiectron temperatures parallel and perpendicular to the geomagnetic field altitude for supersonic flow and for low~rboundary electron temperature gradients (left panel), 1 (middle panel), and 2 K-km (right panel) (from 110/).
versus of 0.1
I~ I
I
I
IO~IO~ O~ 102
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I
I
0° 0° 3) 0’
I
02
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irl I I III! I I l0~ NUMBER 10° MACH
111111
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DENSITY (cm Fig. 6. Ion density (left panel) and Mach number (right panel) profiles for supersonic 11+ outflow and for F 0 = 3000 K (dashed curves) and Fe curves) (from /15/).
versus =
altitude
10,000 K (solid
84
R. W. Schunk
HOT MAGNETOSPHERIC ELECTRONS Precipitating hot electrons of magnetospheric origin are a common feature of the polar cap. Specifically, three hot electron populations have been identified, including the polar rain, polar showers and polar squall /22,23/. Recently, the effect of such hot electron populations on the polar wind has been studied by Barakat and Schunk /16/ using a semi—kinetic model to describe the collisionless regime at high altitudes. Estimates of hot electron parameters based on characteristic energy and flux measurements indicate that the hot/cold electron temperature ratio varies from 10 to io~and that the percentage of hot electrons varies from 0.1% to 10% at 4500-km. For ratios at the lower ends of these ranges, the polar wind solutions with hot electrons are similar to those obtained previously without hot electrons. However, for higher hot electron temperatures and a greater percentage of hot electrons, there is a discontinuity in the kinetic solution, which indicates the presence of a sharp transition. 4 This is shown outflow, for ina Figure 7, where H+ density profiles are shown for the case of supersonic H hot/total electron density ratio of 1% at 4500—km, and for hot/cold electron temperature ratios of 10, 100 and 1000. The transition corresponds to a contact surface between the hot and cold electrons. Along this surface, an outwardly directed, parallel electric field exists which reflects cold ionospheric electrons and prevents their escape. The ‘double layer’ electric field also acts to increase the supersonic H+ outflow velocity and escape energy. The H energy gain may be as large as 1 to 2 keV, depending on the ionospheric and magnetospheric conditions. With 4regard to O~,the hot electrons act to reduce the pot~ntial barrier, thereby allowing more 0 ions to escape. A significant enhancement in the 0 escape flux can occur depending on the hot electron density and temperature. TThIE-DEPENDENT EXPANS ION
All of the polar wind studies discussed up to this point were for steady state conditions, and therefore, the energization that occurs during the initial plasma expansion was not modelled. Recently, however, the temporal evolution of density perturbations in the supersonic, collisionless polar wind was modelled with the aid of time-dependent hydrodynamic equations /24,25/. Extended density depletions as well as localized density bumps and holes were considered. For ‘extended’ density depletions, the results obtained depend on the degree of the depletion. When the density depletion is small, the expansion is headed by a shock. On the other hand, when the extended density depletion is severe, the expansion is headed by a pair of forward and reverse shocks. The extent of the ion acceleration depends both on the mag4, and profiles nitude of the density depletion and on the ion mass. Figures 8a and Sb He4 showdensity the effect of for the a ion typical mass for polara wind given situation density depletion. are perturbed At tby= imposing 0, the 0+, an extended H density depletion at altitudes above about 2800-km (geocentric distance of 9188—kin), while the velocity profiles are left unchanged. At later times, the expansion of each ion species is headed by a density front, which appears as a shock in the hydrodynamic model. A significant acceleration of all of the ion species occurs behind the fronts. Note that over certain altitude ranges each ion species can be the mos~energetic (Figur~8b); the maximum en~rgies(W) of the different ions are limited to W(H ) < 10 eV, W(He ) < 5 eV, and W(0 ) < 1.5 eV. These energies, however, are considerably larger than typical ionospheric thermal energies (Ti - ç~.33 eV). Theref~re, the relative sn~xiinum energization of the ions is: Wmex(H )/T 1 29, Wmax(He )/Ti = 16, and Wmex(O )/Ti 4. I 1111119 I 1111119 I IIIlI~ 111111,
\.(
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H~DENSITY (cm3) Fig. 7. H4 density profiles versus altitude for supersonic H~ outflow, for a hot/total electron density ratio of 1E at 4500—km, and for hot/cold electron temperature ratios of 0 Th/Tc = 10 (left panel), 100 (middle panel), and 1000 (right panel). The dashed curves correspond to the solutions obtained without including the effect of hot electrons (from
/161)
Updated Theory of Polar Wind
_______
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profiles
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times
-4
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after
an initial
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tion in the topside polar ionosphere (from /251).
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Fig. 8b. Ion kinetic energy profiles at two times after an initial extended t9-e’~r’.ty depletion in the topside polar ionosphere (from /25/).
37
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DENSITY N (RELATIVE SCALE) Fig. 9. Temporal evolution of a localized density enhancement created polar wind (from /24/).
at
t
=
t
in
the
86
R. W. Scliunk
When the polar wind is perturbed by a ‘localized’ density bump or hole, the perturbation propagates upward in the direction of the polar wind, but it undergoes a considerable modification, evolving into forward—reverse shock pairs. Figure 9 shows the temporal evolution of a density bump. The density profile at t_ 1 is a typical, steady state, supersonic polar wind profile. At t the polar wind is perturbed by a density bump, which peaks at a geocentric distance of 1~,OO0—km and is approximately Gaussian with a width of about 500—km. The density bump is initially given a zero drift velocity along the flux tube to simulate the release of plasma from a spacecraft moving horizontally through the polar ionosphere. At later times (t2, t4), distinct ‘forward’ and ‘reverse’ shocks can be clearly seen. The forward shock moves with a velocity of about 36—km/s until it crosses the upper boundary, while the reverse shock undergoes a continual acceleration, crossing the upper boundary with a speed of about 14.5—km/s. After the reverse shock crosses the upper boundary, the polar wind returns to a steady state situation, which typically takes only tens of minutes. ION HEATING The effect of ‘localized’ ion heating on the polar ionosphere has been studied by Gombosi et al. /26/ with the aid of a time-dependent hydrodynamic model. The ionosphere was initially assumed to be in a state of diffusive equilibrium and then a localized ion heat source was applied. The distributed ion heating had a Gaussian shape with the peak at32009_km and a half—width of 250—km. The ion heating rate was increased up to 0~O25 er~s cm s over a time period of 150 a. The absorbed heat was divided between H and 0 according to their mass densities. The topside pressure was kept at a very low value to simulate ‘open’ geomagnetic field lines. Figure 10 shows the effect of the io~heating on the ionosphere 2.5 minutes after the heating was initiated. At this time, the 0 temperature already ~xceeds 20,000 K between 2000 and 5000-kin, which causes a significant (but subsonic) upward 0 flow. Consequ~ntly,intense ion heating ~pplied for brief periods of tine can produce subsonic upward 0 flows, but supersonic 0 outflows are obtained only if the ion heating is applied for 1 hour or longer. In this latter time period, the flux tube of plasma can convect a significant distance across the polar cap owing to magnetospheric electric fields, and therefore, it is hig~ly unlikely that a naturally occurring, localized, ion heat source can produce supersonic 0 outflows of the polar wind type.
t
V (kmls) -6
-3 —
I
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=
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Fig. 10. Flow velocities, Mach numbers, number densities, and temperature distributions an ion heated ionosphere 2.5 minutes after ion heating was initiated (from /26/).
in
Updated Theory of Polar Wind
87
CONCLUSION In recent years, theoretical models of the polar wind have produced a number of new predictions with regard to its characteristics and temporal evolution. As in the past, the theoretical predictions are still way ahead of experimental verification. However, some important characteristics of the polar wind have recently been confirmed. EE—1 satellite date were used to show ‘indirectly’ that the polar wind is ‘supersonic’ in the polar cap most of the time /27/. Altitude profiles of electron density were constructed from measurements made on many traveraals ~f the polar cap, and the measurements strongly support the model results for supersonic H outflow. Also, individual ‘direct’ measurements of the polar wind by Nagai etal. /28/ and Gurgiolo and Burch /29/ indicate that the flow is supersonic. More recently, T.~—l satellite data obtained at an altitude of 4500-km by Biddle at al. /30/ have directly verified the predi~tionsregarding ion heat flux asymmetries /ii/T’ On open 4) were observed to be supersonic, and the shape and field lines, light ions and He direction of thetheasymmetry of (H the distribution functions were consistent with the presence of upward heat fluxes. On closed field lines, on the other hand, the outward flows were subsonic and the heat fluxes were downward /11/. In addition, measurements of photoelectron spectra by Winningham and Heikkila /22/ and Winningham and Gurgiolo /23/ suggest the presence of a spatially and/or temporally varying large—scale outwardly directed parallel electric field over the polar cap. This suggestion is consistent with the prediction of a contact surface (double layer electric field) between the hot niagnetospheric and the cold’ ionospheric electron populations 116/. Acknowledgement.
This
research
was
supported
by
NASA
grant
NA~T—77 and
NSF
grant
ATh—841788O to Utah State University. REFERENCES
1.
W.I. Axford and C.0. Hines, A unifying theory of high—latitude and geomagnetic storms, Can. J. Phys., 39, 1433—1464 (1961)
2.
J.W. Dungey, Interplanetary magnetic field and the auroral zones, Phys. Rev. Lett., 6, 47—48 (1961)
3.
A.J. Dessler and F.C. 1421—1426 (1966)
Michel, Plasma in the geomagnetic tail,
J. Geophys. Res.,
71,
4.
W.I. Axford, The polar wind and the terrestrial helium budget, 6855 (1968)
J. Geophys. Res.,
73,
5.
P.M.
6.
P.M. Banks and T.E. 1-lolzer, Features of plasma transport J. Geophys. Res, 74, 6304—6316 (1969)
7.
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Holzer, The polar wind, J. Geophys. Res., 73, 6846—6854 (1968)
T.E.
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High—latitude
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8.
W.J. Raitt, R.W. Schunk, and P.M. Banks, A comparison of the temperature and density structure in high and low speed thermal proton flows, Planet. Space Sci., 23, 1103—1117 (1975)
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T.E. Holzer, J.A. Fedder, and P.M. Banks, A comparison of kinetic and hydrodynamic models of an expanding ion—exosphere, J. Geophys. Res., 76, 2453—2468 (1971)
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R.W. Schunk and D.S. Watkins, Electron temperature J. Geophys. Res., 86, 91—102 (1981)
anisotropy
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11.
R.W. Schunk and D.S. Watkins, Proton .1. Geophys. Res., 87, 171—180 (1982)
anisotropy
in
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12.
J. Lemaire, 0~, H+, and He4 ion distributions J. Atmos. Terr. Phys., 34, 1647—1658 (1972)
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13.
J. Lemaire and N. 103—120 (1970)
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J. Lemaire and M. Scherer, Kinetic models Rev. Geophys. Space Phys., 11, 427—468 (1973)
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A.R. Barakat and R.W. 7887—7894 (1983)
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A.R. Barakat and R.W. Schunk, Effect 3. Geophys. Res., 89, 9771—9783 (1984)
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17.
W.J. Raitt, R.W. Schunk, and P.M. Banks, The influence of convection electric fields on thermal proton outflow from the ionosphere, Planet. Space Sci., 25, 291—301 (1977)
18.
W.J. Raitt, R.W. Schunk, and P.M. Banks, Helium ion outflow from the terrestrial ionosphere, Planet. Space Sci., 26, 255—268 (1978)
19.
W.J. Raitt, R.W. Schunk, and P.M. Banks, Quantitative calculations of helium ion escape fluxes from the polar ionospheres, 3. Geophys. Keg., 83, 5617—5624 (1978)
20.
R.W. Schunk, Mathematical structure of transport equations Rev. Geophys. Space Phys., 15, 429—445 (1977)
21.
A.R. Barakat and R.W. Schunk, Transport equations for space plasmas: A review, Plasma Phys., 24, 389—418 (1982)
22.
J.D. Winningham and W.J. Heikkila, Polar cap auroral electron ISIS, 3. Geophys. Rea., 79, 949-957 (1974)
23.
J.D. Winningham and C. Gurgiolo, ~—2 photoelectron measurements consistent with a large-scale parallel electric field over the polar cap, Geophys. Res. Lett., 9, 977—979 (1982)
24.
N. Singh and R.W. Schunk, Temporal evolution of density perturbations wind, J. Geophys. Res., 90, 6487—6496 (1985)
25.
N. Singh and R.W. Schunk, Ion acceleration in expanding ionospheric plasmas, Presented at the Chapsan Conference on Ion Acceleration in the Magnetosphere and Ionosphere, Boston, Massachusetts (1985)
26.
T.I. Gombosi, T.E. Cravens, and A.F. Nagy, A time-dependent theoretical model of the polar wind: Preliminary results, Geophys. Res. Lett., 12, 167—170 (1985)
27.
A.M. Persoon, D.A. Gurnett, and S.D. Shawhan, Polar cap electron densities from 1~1 plasma wave observations, J. Geophys. Res., 88, 10,123—10,136 (1983)
28.
T. Nagai, J.H. Waite, J.L. Green, and C.R. Chappell, First measurements of supersonic polar wind in the polar magnetosphere, Geophys. Keg. Lett., 11, 669—672 (1984)
29.
C. Gurgiolo .J.L. 12,Burch, of the polar wind Geophys. Res. and Lett., 69—72 Composition (1985)
30.
A.P. Biddle, T.E. Moore, and C.R. Chappell, Evidence for ion heat flux in the ion polar wind, 3. Geophys. Res., 90, 8552—8558 (1985)
for
on
the
polar
multi—species
multicomponent
—
fluxes
not
dust
wind,
flows,
anisottopic
observed
in
the
4
H
and
with
polar
He4, light