Download Samir et al 1983 Expansion of plasma into a vacuum The moon

REVIEWS
OF GEOPHYSICS
AND SPACE PHYSICS,
VOL.
21, NO. 7, PAGES 1631-1646, AUGUST
1983
The Expansion of a Plasma Into a Vacuum'
Basic Phenomenaand Processesand Applications to Space Plasma Physics
URI SAMIR1
Space Physics Research Laboratory, University of Michigan
Ann Arbor, Michigan 48109
K. H. WRIGHT, JR.
Department of Physics, University of Alabama at Huntsville
Huntsville, Alabama 35899
N.H.
STONE
Space Science Laboratory, NASA Marshall Space Flight Center
Huntsville, Alabama 35812
In this review we call attention to basic phenomena and physical processesinvolved in the
expansionof a plasmainto a vacuum, or the expansionof a plasmainto a more tenuousplasma, in
particularthe fact that upon the expansion,ions are acceleratedand reach energieswell above their
thermal energy.Also, in the processof the expansiona rarefactionwave propagatesinto the ambient
plasma, an ion front moves into the expansionvolume, and discontinuitiesin plasma parameters
occtlr. We discussthe physical processeswhich causethe above phenomenaand point toward their
possibleapplicationfor the caseof the distributionof ions and electrons(henceplasmapotentialand
electric fields) in the wake region behind artificial and natural obstaclesmoving supersonicallyin a
rarefied spaceplasma. To illustrate this, some in situ results are reexamined.Directions for future
work in this area via the utilization of the Space Shuttle and laboratory work are also mentioned.
of a plasma into a void (vacuum) or into a more tenuous
plasma.
$amir and Fontheim [1981] performed a comparaPhenomenainvolved in the expansionof a plasma into a
vacuum,particularlyion accelerationand rarefactionwave tive theory-experimentstudy of the ion and electron distripropagation,were studiedboth theoreticallyand to a lesser bution in the wakes of the Atmosphere Explorer C and the
extent experimentallyin the last decade. Gurevich et al. Explorer 31 satellites.The theoretical model used was based
[ 1966, 1968]were the first to show theoretically that upon the on the Parker [1976, 1977] wake and sheath steady state
expansionof a plasmainto a vacuum,ionsare acceleratedto model. The latter is probably one of the more sophisticated
highenergies.While this physicalprocesswas recognizedby and elaborate numerical models which exist at the present
laboratoryplasmaphysicists,particularlyby thoseworking time. Even so, order of magnitude discrepanciesbetween
in laser fusion research, it went unnoticedby spacegeophys- theory and measurement in the very near wake zone were
icists, even though it may be one of the fundamental found. The conclusion of that work was that the discrepanprocessesunderlying many phenomena in space plasma cies between theory and experiment are due to the use of a
physics and astrophysics.Recently, $ingh and Schunk steady state theory and a singleion equation usingthe mean
ion mass (see also $amir et al. [1981]). There can be little
[1982] used computer simulationcalculationsof the expansionof a plasmainto a vaccumand the resultingproduction doubt that the spatialand temporal evolution of electron and
of energeticions in order to study the energizationof high- ion velocity and density distributions which take place upon
latitudeionosphericions in the contextof the expansionof the expansionof a plasmainto a vacuum is directly relevant
the polar wind. They indicate that there are potentially to the filling in of the wake region behind an obstaclemoving
importantphysical processesoperative in a plasma expan- supersonicallyin space. It is also possiblethat the structure
sion that are not taken into account by the existing steady (i.e., particle and field spatial and temporal distributions)of
the 'dark' or 'antisolar' side region behind Venus, behind
state modelsof the polar wind.
The distributionof chargedparticlesand potential(electric our moon, and/or in the wakes of Io and Titan is determined,
fields) in the wake behind an obstaclemoving supersonically at least partially, by the basic processesinvolved in the
in a collisionlessplasmais also an example of an expansion expansionof a plasma into a vacuum or into another, more
tenuous plasma.
Furthermore, investigationsrelevant to the electrodynam•Now at the SpaceScienceLaboratory,NASA MarshallSpace ic characteristicsof satellitesand large spacestructuresmay
Flight Center, Huntsville, Alabama 35812. On leave from the
benefit from an examination of the plasma expansion proDepartment of Geophysicsand Planetary Sciences,Tel-Aviv Unicesses in modeling the total current collection [$amir,
1.
INTRODUCTION
versity, Ramat-Aviv, Israel.
1982b].
This paper is not subjectto U.S. copyright. Publishedin 1983by
the American Geophysical Union.
Paper number 3R0866.
1631
With the advent of the Space Shuttle, includingits wide
range of capabilities, it should be possibleto perform controlled experimentsof body-plasmainteractionsin a manner
1632
SAMIR ET AL.: EXPANSION OF A PLASMA INTO A VACUUM
not possiblein the pre-Shuttle era. The study of the phenomena and the physicalprocessesinvolved in the expansionof
a plasma into a vacuum follows directly from the study of
'plasma-obstacle'interactions. Details of a new experimental philosophyincludinggeneraloutlinesfor practical modes
of experimental operation required to achieve specificscientific objectives are given by Sarnir and Stone [1980] and
Sarnir [1982a]. In addition, it would be very valuable to
perform complementaryexperimentsin the laboratory. Such
experiments, which would differ from those conducted in
laser fusion research, could be made more directly applicable to the expansionprocessesin space plasmas.
In this paper the basic physicalprocessesand phenomena
which characterizethe expansionof a variety of plasmasinto
Denavit [1979], True et al. [1981], Gurevich and Meshcher-
a vacuum are discussed in section 2. Section 3 follows with a
discussed will follow the above order.
reexamination
We now discussthe expansionprocessesby consideringa
semi-infinite plasma held by a diaphragm at its boundary
located at x = 0 (see Figure l a). At a time t = 0 the
diaphragm is removed, and the plasma expands into the
vacuum. We are interested in the evolution of the velocity
and density distributionsof the plasma particles filling in the
vacuum and the electric field they create. As the expansion
begins, the electronsmove ahead of the ions becauseof their
greater thermal velocity, and some of the ions are subsequently accelerated by the space charge electric field. A
front of plasma, called the 'expansion front,' moves into the
vacuum. The density of ions near this front decreaseswith
time. A region of decreasedplasma density, a 'rarefaction
wave,' moves into the ambient plasma.
Electron inertia in this processcan be neglectedas long as
the ion streaming velocity is less than the electron thermal
velocity. The electric field providescontinuousacceleration,
although its magnitude decreaseswith time. As a result, the
ions from the ambient (source) plasma that move to replace
the ions that move into the vacuum region are exposedto a
lower electric field and thus will not reach the velocity of the
ions that were initially near the t = 0 plasma-vacuum
interface. Indeed, it is the ions originally near this interface
that attain the highest velocities.
The electron expansion can be treated as isothermal.
Denavit [ 1979] showedthat the assumptionsof an isothermal
electron expansion and the neglect of electron inertia are
of some of the available in situ wake data and
a discussionof the relevance of laboratory experiments of
body-plasmainteractionsin light of spaceplasmaexpansion
processes.In section 4 we speculateon possibleinterpretations of phenomenaobserved in the interaction between the
solar wind and Venus, the solar wind with the earth's moon,
and the wake of Titan in terms of phenomenaand processes
which characterize the plasma expansion into a vacuum.
Finally, in section5 we summarizethe presentknowledgeof
the plasma expansion phenomenaand processesbased on
theoretical studiesand point toward the required in situ and
laboratory simulation experiments needed to examine the
present theoretical predictions.
2.
EXPANSION
PHYSICAL
OF A PLASMA INTO A VACUUM:
PROCESSES AND
PHENOMENA
In the past decadean extensiveeffort by plasmaphysicists
working in the area of laser fusion research was devoted to
the study of the electric fields and energy and density
distributionsof particles created by plasma expansioninto a
vacuum, in particular, the expansionof laser-createdplasma
from a target pellet. The study was both theoretical and
experimental. However, despite the significant achievements already attained, various aspects are still in a rudimentary state of understanding. The theoretical studies
include both analytical and numerical methods for a wide
rangeof conditions.The types of plasmasconsideredinclude
(1) plasmascomposedof a singleelectron temperatureand a
singleion species(see, for example, Gurevich et al. [1966,
1968] (the pioneering work in this area), Allen and Andrews
[1970], Widner et al. [1971], Crow et al. [1975], Bezzerides et
al. [1978], Mora and Pellat [1979], Denavit [1979], and
Gurevich and Meshcherkin [1981a, b]); (2) plasmas composed of electrons with multiple temperatures and a single
ion [e.g., Bezzerideset al., 1978;Denavit, 1979; Wickensand
Allen, 1979; True et al., 1981]; (3) plasmascomposedof a
single electron temperature and multiple ion species[e.g.,
Gurevich et al., 1973, 1979; Gurevich and Pitaevsky, 1975;
Gurevich and Meshcherkin, 1981a; Singh and Schunk, 1982;
Decoste and Ripin, 1978; Felber and Decoste, 1978; Anderson et al., 1978;Begay and Forslund, 1982]; and (4) plasmas
composedof electronswith multiple temperaturesand multiple ion species[e.g., Wickensand Allen, 1981]. The papers
cited can be divided according to whether a fluid and/or a
kinetic approach is used, whether ions are taken to be cold
and/or hot, and whether overall chargeneutrality or charge
separationis considered.Among the papers which treat the
latter case we cite Widner et al. [1971], Crow et al. [1975],
kin [1981b],and Singhand Schunk[1982]. Amongthe papers
where quasi-neutralityis assumedthroughoutthe expansion
region we cite Gurevich et al. [1966, 1968, 1973, 1979],Allen
and Andrews [1970], Gurevich and Pitaevsky [1975], Anderson et al. [1978], Bezzerideset al. [1978], Decoste and Ripin
[1978], Felber and Decoste [1978], Mora and Pellat [1979],
Wicken}andAllen[1979,1981],Gurevich
andMeshcherkin
[1981a], and Begay and Forslund [1982].
Detailed reviews of studiesregardingthe plasma expansion into a vacuum are given by Singh and Schunk [1982],
Denavit [1979], and Gurevich and Pitaevsky [1975]. Hence
we restrict the discussionhere to basic phenomena and
processesand some of the results. The plasma types to be
correctto order(ZMe/Mi)1/2,whereZ is ion charge,Me is
electron mass, and Mi is ion mass. The source of the ion
translational energy is the electron thermal energy. Therefore if the electron gas does not cool, then heat must flow
from the ambient plasma to the expansionregion. Mora and
Pellat [1979] showed that at the rarefaction wave, qe =
dEi/dt, where qe is heat flux and Ei is ion energy.
Some characteristicfeatures of the expansionprocesscan
be found by solving for the ion dynamics under the assumption of charge neutrality (Ne = ZiNi). Charge neutrality
removes the Debye length (as a relevant characteristic
length) from the equations. Thus any functional dependence
on x or t will be through the combination (x/t). Solutions of
this type are commonly referred to as self-similar [Landau
and Lifshitz, 1963]. An analytical solution to the cold ion
fluid equations,i.e., continuity and momentum equations,is
obtained by assuminga space-timedependencefor density
N• and velocity Vi through the variable • = x/Sot, where So =
(ZTe/Mi)•/2is the ion acousticspeedand Teis the electron
temperature in energy units. The self-similar solutionsfor a
plasma consistingof a single ionic speciesand an ambient
SAMIR ET AL.'
Maxwellian
EXIANSION
OF A PLASMA INTO A VACUUM
1633
!N {t=O)
electron distribution are
No
Ne -- ZiNi -- ZiNo exp [-(•
(a)
+ 1)]
VACUUM
= So( + 1)
cb= -(Te/e)(•: + 1)
• + 1 -> 0
The polarization electric field E = -Ock/Oxis proportional to
(l/t).
Figures lb and lc show the self-similar density and
velocity solutions.The rarefactionwave propagatesinto the
plasma at the ion acoustic speed. Note that for large values
ofx this theory predictshigh-velocityions with a densitythat
approacheszero. The quasi-neutrality assumptionrestricts
the validity of the self-similarsolutionto - 1 -< • < •m, where
•m is determinedby equating a characteristiclength of the
expansion, L = Sot, to the local Debye length
RAREFACTION
•
WAVE
N
(b)
No
EXPANDING
PLASMA
(Te/Ne)
1/2.
The•rn-- [2In(oopit)
-- 1],wheret > •opi
-• and60pi
is the ion plasmafrequency.Namely, for valuesof • > •mthe
potentialdue to the self-similarsolution[•b= -(Te/e) (• + 1)]
is not valid. The time requiredfor the ionsto respondto the
polarizationelectric field and producea plasmaflow with Ne
= ZiNiisgivenby •ovi
-•. In otherwords,onlyaftertheions
•V
i /
respondto the rapid electron expansionand create a quasineutralplasmaflow are the self-similarsolutionsvalid. Singh
and Schunk [1982] show through their computer simulation
computations,which are basedon the Poissonequation,that
"•-LINEARLY
INCREA
Vi
the above conclusion is indeed correct. The assumed Boltz-
mann distributionfor electronswill remain valid as long as
the time required for the electrons or ions to cross the
expansionregion is shorter than the expansiontime. The
velocity at • = •mcan be interpretedas the velocity of an ion
front, Vr, moving in the expansionregion with Vr = 2S0 In
(%,•t).The energyof the ions at the front is then givenby
(c)
Vi=0
•'/
-Sot
Fig. 1. The expansion of a plasma into a vacuum. (a) Initial
condition. (b) The evolution of density according to the self-similar
solution. (c) The evolution of ion velocity according to the selfsimilar
solution.
E = «ZTe(•m+ 1)2 = 2ZTe[Intopit]
2
to-charge ratio will be accelerated in the same manner.
In the pioneering work of Gurevich et al. [1966, 1968],
numerical serf-similar solutionswere found using a kinetic
approach, i.e., the Vlasov equation for ions (further details
are given in the appendix). Comparing the results from the
kinetic approach and the results from the cold ion fluid
treatment showsthat including ion temperature smoothsout
the weak discontinuity at • = -1 (see Figure lb) and
introduces differences in the ion density values in the
rarefactionregion. As the ion temperature Ti increases,the
difference between the two approaches increases. In the
expansionregion at large • (or large x), changingthe Te/T•
solutions based on the cold ion momentum equation (see
also appendix) can be applied.
A comparison between studies using the self-similar approach and those using numerical computer simulations,
which drop the assumptionof charge neutrality and use the
potential determined from the Poisson equation, was performed more recently by Denavit [1979] and Singh and
Schunk [1982]. In Denavit's [1979] study, both single and
double electron temperatureswere considered. It was found
that the effect of charge separation is to produce (among
other local effects) an ion front (sometimescalled an 'expansion front'). In the region between the expansion front and
the rarefaction wave some of the general predictions of the
self-similartheories are applicable. In other words, in this
region the numerical solutions are in accord with those
obtainedby the self-similarapproach. As mentioned earlier,
a simple way to describethe range of applicability (say, in x
ratio was shown to introduce
or t) of the self-similar solution vis-h-vis the solutions
The energy per charge is then
E/Z = 2Te[lntoeit]
2
where%i = (4rrZe2No/Mi)
v2.All ionswiththesamemass-
small differences
between
the
two approaches. The reason for these small differences is
that at large • the ambient ion distribution function evolves
to a streaming delta-function-like distribution. The effective
ion temperaturewas found to vary as exp (-2se). Therefore
the ion dynamicsin the expansionregion for large • can be
reasonablywell describedby using the cold ion fluid equations. This is an important physical conclusion, since it
specifiesa condition (i.e., distancein space)where the fluid
obtainedby consideringthe Poissonequation is to say that
the self-similar solutions are valid for times t which satisfy t
-> o¾•
-•. Thisis thetimeit takestheionsto respond
to the
fast expansion of the electrons and create a quasi-neutral
plasma flow.
Smaller density gradients existing at t = 0 (as compared to
the large gradient shown in Figure la) affect the expansion
processby increasingthe time required for the expansionto
1634
SAMIR
ET AL'
EXPANSION
OF A PLASMA INTO
become self-similar [Felber and Decoste, 1978; Singh and
Schunk, 1982].
The case of an expansion of a dense plasma into a more
tenuous plasma was also treated by Gurevich et al. [1968]
and Gurevich and Pitaevsky [ 1975]. The boundary condition
imposed by the second plasma population existing at t = 0
for x > 0 (see Figure la) adds to the variety of phenomena
that occursin the expansionprocess.Limited accelerationof
ions is a feature of this physical situation. Depending on the
properties of the second plasma population, there can be
trappingof ions in potential wells, excitation of a two-stream
electrostatic instability, and jump discontinuitiesor shock
waves occurringwhen the two plasmashave highly dissimilar ion temperatures [Gurevich and Meshcherkin, 1981b].
These jump discontinuitiesimply the existence of charged
sheets moving with constant velocity.
In describingthe expansionof a plasma consistingof one
ionic speciesand two electron temperatureswe considerthe
case where the ambient density of the colder electron
population
(Neoc) is muchgreaterthanthedensityof thehot
electronpopulation(Neon).During the early stagesof the
expansion the ion acceleration is determined by the cold
A VACUUM
If •/> 1, we have a plasmawhere oxygen(M0 is the major
constituent and hydrogen (M2) the minor constituent. The
relatively immobile oxygen initially provides an additional
electricfield to acceleratethe hydrogenions. As a result, the
hydrogenionsgain a higherinitial velocity than in the •/< 1
case. As one might expect, the hydrogen density becomes
comparable to the oxygen density at some value of •. A
'plateau region' in ion density, velocity, and potential is
obtained,which implies constantvalues for density, veloci-
ty, andpotentialnearthe locationwhereN• (O+) = N2 (H+).
Althoughthere are quantitativedifferencesin the description
of this plateau region by the quasi-neutral (self-similar)
treatment of Gurevich et al. [ 1973]and the chargeseparation
(computer simulation) treatment of Singh and Schunk
[1982], the gross qualitative effects remain similar. Beyond
the plateauregionthe hydrogenbehavesas in the expansion
of a one-ioncomponentplasma.Oscillationsare seenbehind
the ion front. These are more pronouncedin hydrogenfor Te
> Ti. Oscillationshave also been seenin the spectraof laser
pellet interaction plasma [Decoste and Ripin, 1978]. The
hydrogenvelocity for values of • greater than the plateau
regionapproachthat given by the self-similarsolution, V2 =
electroncomponent,
becauseNe½> NeH.The ion velocity S0(•+ ¾m).Sotheenergyis
Vi is given by Vi •
Sc(• + 1), where • = x/Sct, Sc =
E2/Z2= « (re/T)(•m+ T1/2)
2 ate= •m
(ZTeC/Mi)
1/2,and Tec is the temperature
of the coldelectrons.When Nen > Nec, the hot electroncomponent
will The oxygen velocity is given by V• = So(• + 1) in the
control the ion motion according to Vi • Sie(• + 1), where •
= x/Snt, Sn = (ZTen/M•)
m, and Ten is the temperature
of
the hot electrons. The energy spectra of the ions will then
expansionregion for 1 -< • < •m.
Finally, we considerthe expansionof a plasma composed
of two ion constituents (Z•, M•; Z2, M2) and two electron
have two peaks, one proportionalto Tec and the other temperature
populations
(Tec, Ten) wherethe ambientcold
proportionalto Ten . The rarefactionwave will propagateat electron population (Nco) is much greater than the hot
the acoustic speed determined by the cold electron component.
Now consider the case of a two-ion, one-electron component plasma. From the spaceplasma point of view, this case
is of great practical value for planetary ionospheres and
magnetospheres.The dynamicsfor the two-ion plasma depend on the similarity parameter 3' = Z2M•/Z•M2. For the
casewhere the major ionic constituentis hydrogen(M•) and
the minor constituentis oxygen (M2), T • 1, each speciesis
found to behave in a self-similar manner at large se [Gurevich
et al., 1973;Anderson et al., 1978;Singh and Schunk, 1982].
Moreover, Gurevich et al. [1973] and Gurevich and Meshchefkin [1981a] point out the existenceof oscillationsin the
expansion region and conclude that they should always be
present in a two-ion componentplasma. The velocity of M1
(H +) is V• = S0(s
e + 1) andthat of M2 (O+) is V2 - S0(s
e + 3')
for se >> % and the energies of the ions at se-
sero
are
El/Z1 = «Te(•m+ 1)2 and E2/Z2= « (Te/T)(•m -{- 7)2,
respectively.Hence E2/Z2 > El/Z1 at • = •m. Gurevichet al.
[1973] give an expression for the percentage of the total
number of 'impurity ions' (i.e., the minor ionic constituent)
passingthrough a unit surface at the point x = x0 having an
energy greater than some reference energy as
electronpopulation(Nno), Z•Nlo > Z2N20,and ,/> 1. As the
expansionbegins, the initial electric field is predominantly
determined by the cold electrons and the ion constituent
with the greater charge density, in this case, Z•N•. So the
higherZ/M constituent,i.e., Z2/M2, is preferentially accelerated. As the expansion continues, there will be a spatial
region where many of the cold electrons will be reflected
from the self-consistent electric field set up by the hot
electrons. In this spatial region the charge density of the
Z2/M2 constituentbeginsto exceed the chargedensity of the
Z•/M• constituent. The remainder of the expansion is then
determinedby the hot electron component and the Z2/M2
constituent.The energy spectra of each ion constituentwill
thenhavetwo peaks,oneproportional
to Tec andthe other
proportional
to Ten . The rarefactionwavemovestowardthe
ambient plasma at a speed determinedby the cold electron
temperature and the lower Z/M constituent, i.e.,
(ZiTeC/MO
•/2.
Figure 2 summarizes the ion energy for the four types of
plasmasdiscussedabove, and the analytic self-similar solutions are quoted. Figure 3 [after Singh and Schunk, 1982] is
introduced in Figure 2 because the velocity solution for the
self-similar case [Gurevich et al., 1973] was shown to differ
with the chargeseparationcomputer simulationresult [Singh
and Schunk, 1982] for the indicated region of space.
In summary, the self-similar and computer simulation
computations have shown the following effects when a
wherep = (Z22M•/2Z1M2),
fromwhichit followsthat0.1%of plasma expands into a vacuum:
the ions acquire an energyE > E0 = 50pTe. Ifp becomestoo
1. Ions are accelerated to high energies.
large,i.e., p >> 1, thentheassumptions
usedto deriveNE>E0 2. A rarefaction wave is created which propagatesinto
break down.
the ambient plasma.
SAMIR ET AL.' EXPANSION OF A PLASMA INTO A VACUUM
1635
3. An ion front (shock)movesinto the vacuumregion.
4. Excitation of instabilitiesand plasma waves over
certainvolumesin spacetake place.
5. Strong(orjump) discontinuities
in the plasmaoccurat
The quantitative significanceand intensity of the above
phenomenaand processesdepend, in part, on the specific
ionic constituentsof the plasma and the relative concentration of the minor ion in the plasma, on the ambient electron
the expansion front.
temperature, on the ratio of a characteristic linear dimension
ION ENERGY
PLASMA TYPE
ONE ION SPECIES(M1, Zl).
(1) ONE ELECTRONDISTRIBUTION
(TeL
ONE ION SPECIES(M1, Z1).
TWO ELECTRON
DISTRIBUTIONS
•x :
Sot
EXPRESSION
E1 . «Te(•+l)2
Z
1
X
E1
x
E1
IFN,c>Nell
AND
•-Sct: • ' :• TeC
(•+1)2
(2)(Tell
' TeC)
' FOR
N•o
>>Ne•
o
c
AND
1.5< [TeH/TeC]
< 9.
IFNe
H•NeANDSSH
t : ---«Te
H(•+I)
2
ß
Z1
TWO
ION
SPECIES
(N•o
' M1,Zl)'
•-•-
X
IF•<1: Z1
E1 «Te(•+l)
2
(3)(N2oi,
M2,
Z2)
FOR
N1o 2o
ONE ELECTRON
DISTRIBUTION
E2- « Te(•+,•)2
Z2
IF'y•.l:
(TeL
•-E1 •Te(•+l
Z1
)2
FOR
,•'""
7«'ß•-SEEFIG.
E2
3
FOR
TWO
ION
SPECIES
(N•1o
' M1
' Zl),
H
Z2
X
IFNeC
•N e ANDS-set: ZlE1.. • TeC(•+1)2
E2
=_
«TeC
(•+1)2
(N•
o, M2.Z2)
FOR
ZiN•o
>Z2N•o.
(4)
TWO ELECTRON
DISTRIBUTIONS
(No,T/).(N:
ø, T,")
?
AND- X
E1
E2
=,«Te
H• +1)2
z2
WHERE'
So
=(ZlTel
«=ION
ACOUSTIC
VELOCITY;
X=SPATIAL
COORDINATE;
M1
t - TIME;M1, M2 = IONICMASSES;
Z1, Z2 - IONCHARGENUMBERS;
Neo,NoI - AMBIENT
VALUES
OFELECTRON
ANDIONCONCENTRATIONS;
Z2M1
ZlTeC)•,
Te- ELECTRON
TEMPERATURE,
?-ZIM2
, Sc-(
M1 SH=(ZITeH)
M1. «
Fig. 2. Analyticalionenergyexpressions
for self-similar
solutions
for eachof thefourplasmatypes.
1636
SAMIR ET AL.'
EXPANSION OF A PLASMA INTO A VACUUM
and g and u are nondimensionalquantities defined by
•Mi/
and
u= V
= --2 -1/2
So
4110
_
where No is ambient density, f is the ion distribution
function, Ti and Mi are ion temperature and mass, respectively, and V - Vx is the velocity in the direction of the x axis
,,,•
(see Figure 1). As seenin Figure 4, the distributionfunctions
for the ions (in [g, u] coordinates) differ for different values
of ß (see also appendix). For ß < 0 (e.g., ß - -3 or -2 in
Figure 4) the distribution function g - F(u) is the unperturbed distribution, whereas for ß > 1 the distribution
-800
-400
0
400
800
1200
1600
2000
narrows to delta-function-like shapes,which physically implies that ions are being accelerated. For a plasma with two
Fig. 3. Evolutionof the H + and O+ drift velocitiesaccordingto
ion componentsand one electron temperature distribution
the self-consistentcomputer simulationcomputations(solid curves).
The dashedcurve(s-s)is the self-similar
solution
for O+. f•o(a)is the distributionfunctionsg - F(u) for variousvaluesof ßare
thenormalized
iondriftvelocityfor sp•ecies
a (• H+, O+) defined obtained for the two differing ionic constituents. Figure $
_
_
by Po(a) = f_•+•l?f, d•/f_•+•f, dV, whereV = V/Vr(H+) and showsexamplesof distributionfunctionsfor an O+-H+Vr(H+) is the hydrogenthermalvelocity;• is the normalized electronplasmawhereH + is takento be the minorion, i.e.,
distance,equalto X/XDi(H+), where XDi(H+) is the hydrogenDebye
N0(H+) << N0(O+), where No is the ambient ion plasma
length;! is thenormalized
timeequalto t%,i(H+),where%,i(H+) is
the hydrogenplasma frequency. The computationswere made for
the caseof No(H+)/No - 0.1, No(O+)/No - 0.9, T(H+)/Te - 1, and
T(O+)/Te - 1, where No is the total ambiention density.The figure
is after Singh and Schunk [1982].
to the Debye length, and on the density gradient at the
plasma-vacuum interface.
3.
PLASMA EXPANSION
INTO A VACUUM:
THE CASE OF PLASMA WAKES
As mentioned in the introduction, the processes and
phenomenainvolved in the expansionof the plasma are of
interest to spaceand cosmicplasmasresearch,e.g., flow of
plasma out of stars, solar physics(flares), and flow interactions with artificial 'obstacles' orbiting the earth and planets
as well as flow interactions with planets and their natural
satellites. Even so, this subject went unnoticed by most of
the spacephysics community.
It should be noted that the expansion phenomena and
physical processescan be adequately examined via the
analysisof the density and energy distributionsof electrons,
ions, and potentials (or electric fields) in the wake region
behind 'artificial obstacles.' For example, the mechanisms
responsiblefor ion accelerationcan be studiedusing spacecraft or 'test bodies' orbiting in the terrestrial (or planetary)
environment, as well as in laboratory experiments.
density.
Fromthisfigureit followsthat the H + ionsare accelerated
to muchhighervelocitiesthan the O+ ions, which are the
main ion componentof the plasma. Generally, the maximum
accelerationof the minor ion dependson the values of Z, Mi,
and Te of the ambient plasma and on the ratio (Ro/ho)(where
R0 is the characteristiclength and ho is the ambient value of
the Debye length) and on the relative ambient concentration
of majorto minorion constituent,e.g., No(O+)/No(H+).We
note that when 3/ - MiZ2/M2Z• > 1 (where M and Z
represent the ionic mass and charge, respectively, and the
subscripts 1 and 2 indicate the major and minor ions), the
minor ions are initially accelerated much more than the
major ions. For this case the concentration N2 decreases
with increasing• much slower than for the case with 3/< 1.
For even larger values of ß the minor ion concentration
exceedsthat of the major ions. This can be seenin Figure 6,
g
1.o
0.8
'T = --2
0.4
3.1.
The Expansion: An Ion Acceleration Mechanism
In the brief discussiongiven below we show sometheoretical results for ion acceleration which in situ and laboratory
experiments should attempt to examine. Figure 4 [after
Gurevichand Pitaevsky, 1975] showsexamplesof computed
ion distribution functions for a singleion and electron plasma
expandinginto a vacuum. Here
•=
Mi
=
•--
So
•
2]/2
I
-3.0
-2.0
-1.0
0
1.0
2.0
3.0
4.0
Fig. 4. The variation of the normalized distribution g with the
normalized velocity u for different values of ?. The plasma consists
of oneionicspeciesandoneelectrondistribution:
g = (2,rTi/Mi)1/2
No-if, u = o(2Te/Mi)
-1/2,and r = x/t(2Te/Mi)-1/2,wherex, t, andv
are distance, time, and velocity, respectively. The figure is after
Gurevich and Pitaevski [1975].
SAMIR ET AL.' EXPANSION OF A PLASMA INTO A VACUUM
which depicts different distribution functions for different
values of •'. The results of Figure 6 are for ambient conditions (N2oZ2/N•oZl) = 0.1. It appears[Gurevich et al., 1973;
Singh and Schunk, 1982]that for •' > •'k(where •-kis a specific
critical large value of •') the distribution function hardly
varies with increasing •-; i.e., a characteristic plateau region
is obtained whose width is a function of the charge-to-mass
ratio. Beyond the plateau the plasma expands like a singleion speciesplasma. Both Gurevich et al. [1973] and Singh
and Schunk [1982] also study the opposite case, where
g2.t= -2
-2
0
I
--2
1637
r =0
2
T=0
0
;=2
4
T=4
8
10 U
T=2
2
I
I
6
8
u
N0(O+) << N0(H +).
No+ (r) • NH+ (r)
3.2.
Reexamination of Satellite Wake Measurements
A reexamination of relevant results available at present
from in situ satellite wake observations was therefore performed. Unfortunately, we find the available results to be
meager, fragmentary, and applicable only to the very near
wake zone. Hence theory-experiment comparisonis limited.
This unfortunate situation stems from the following reasons:
(1) No experimental probe complementswere ever designed
settingthe phenomenainvolved in the plasmaexpansionas a
scientific objective. Hence the available relevant data are
basically by-products of traditional geophysical observations. (2) The available data are fragmentary, sinceit was not
always possibleto gather sufficientreliable measurementsto
composethe required ensembleof plasma and body parameters. (3) The available relevant measurements are limited (a
priori) in their spatial and temporal extent, because most
observationswere made by probes which were either flush
mounted
on the surfaces
of the satellites
or mounted
on
relatively short booms. Hence, at best, only very near wake
measurements
could be examined.
Despite these shortcomingsand limitations some indirect
experimental findings can be used for a partial theoryexperiment analysis.
A quantity often used as an indicator of filling-in processes
in the wake is the ratio (le,i(wake)/le,i(ambient)), where e and
i represent electrons and ions, respectively. This quantity
No (0+)•N o (H+) TWOIONS
ß
=-
1
2
=3
Fig. 6. The variationof the normalizeddistributionfunctionsg•
(O+), g2 (H +) with the normalizedvelocityu for differentvaluesof
•-. The plasma consists of two ionic species and one electron
distributionfor the case Z2N2o/Z•N•o = 0.1. The figure is after
Gurevich et al. [1973].
was determined experimentally from in situ measurements
made by a variety of probes on board the satellitesExplorer
8, Ariel 1, Explorer 31, Atmosphere Explorer, and U.S. Air
Force S3-2. A comparison with various wake models was
attempted. Such comparisons, as mentioned earlier, were
limited to the very near wake zone. 6eneral agreementwith
Gurevich_et al. [1970, 1973] was reached only for specific
situationsand for the spatialregionslocated on the edgesof
the wake zone and when it was assumed that the influence of
the acceleratedH + ions becomesdominanteven though
their relative concentrationin the ambient plasma was very
small [Sam& et al., 1973, 1975; Gurevich et al., 1973;
Al'pert, 1976]. It is in the wake edge regions where the selfsimilarapproachis valid. However, sinceno relevant energy
spectrum information was available from any of the above
satellites, it was not possibleto examine directly the acceleration of ions. Moreover, since all available in situ measurements are limited to the very near wake region, it is not
possibleto reexamine the spatial distributionsin the overall
wake region. There is one exception where the electron
angulardistributionprofile was obtained at a distanceof SRo
(where S is the averageion acousticMach number and R0 is
the radius) from the center of the Ariel 1 satellite [Henderson
and Sam&, 1967] and compared with results of Gurevich et
al. [1970] (see also Al'pert [1976]) and the degree of agreement is very good. The limitation in this case is, of course,
that the data were obtained for electrons and not for ions.
It shouldbe noted that for the practical case of the wake of
-4
-2
0
2
4
I
6
I
8
u
gl
ß
r = 1 r=2
an ionosphericsatelliteboth N0(H +) >• N0(O+) and N0(H +)
<< No(O+) casesare of interest, sincethe orbit of a standard
ionosphericsatellitewill passthrougha plasmawhich satisfies both situations and intermediate ones. Unfortunately,
none of these interesting phenomena can be examined
via the presently available in situ wake observations. The
in situ results given in Figure 7 [Sam& et al., 1979] for
(l+(wake)/l+(ambient)]= f[Te, No(O+)/No(H+)] are of inter-
1--- -2
1-o=
-4
-2
0
2
4
6
8 u
Fig. 5. The variation of the normalizeddistributionfunctionsg]
(O+), g2 (H +) with the normalizedvelocityu for differentvaluesof
•-. The plasma consists of two ionic species and one electron
distributionfor the case N•o >> N2o, where N]o and N:o are the
ambient densities of the two ionic species. The figure is after
Gurevich et al. [1973].
est, since they show the quantitative influence of the ambient electron temperature and relative ionic composition
(ambient) on the ion depletion in the wake. While the latter
quantity is related to wake filling-in processes,the resultsof
Figure 7 standingon their own cannot yield direct information on the ion distributions
as a function
of •-for
further
distances in the wake or yield unambiguous information
regarding the acceleration of ions. The results of Figure 7
1638
SAMIR ET AL.'
I
R=
R=
R=
R=
0.4
I
EXPANSION
OF A PLASMA INTO A VACUUM
I
motion of a satellite through the terrestrial ionosphere was
inferred for the first time by Samir and Willmore [1965]
through an analysis of Ariel 1 satellite measurements.These
oscillations were found to exist at least at the edges of the
R = [0.1.-.0.2]
[0.1 - 0.2]ß
[1-1.510
[4-5]V
[lO] ©
-1.5]
• = [lO2] ß
-R= [103]1 ß
wake of the satellite.
While
this result is in accord
with the
above mentioned theoretical predictions, this in situ evidence cannot be seen as conclusive. Preliminary results
obtained recently from the wave experiment [Shawhan and
Murphy, 1982; S. D. Shawhan, personal communication,
1982] from the Plasma Diagnostic Package on board the
Space Shuttle flight STS-3 showed the existence of 'electrostatic noise generated in the orbiter wake at frequencies near
the ion plasma frequency (50 KHz) and below in the ion
acoustic mode' [Shawhan and Murphy, 1982]. If the above
preliminary result can be correctly interpreted as indication
of excited waves due to the motion of the Space Shuttle,
then further supportis provided to the earlier result of Samir
and Willmore [ 1965] and is in accord with theoretical predictions [Gurevich and Meshcherkin, 1981b; Gurevich et al.,
0.3
1973, 1970].
500
1500
2500
Te (AMBIENT)
Fig. 7.
3500
"
Variation of normalized ion current a with ambient
electrontemperatureTefor variousvaluesof [N(O+)/N(H+)] = R.
[after Sam& et al., 1979].
could be used together with other in situ results (from the
Space Shuttle, for example) when they become available
(see also Samir and Stone [1980]).
Gurevich et al. [1973], Gurevich and Pitaevsky [1975],
Gurevich and Meshcherkin [1981a, b], and others discussed
the excitation of ion plasma waves, ion acoustic instability,
two-stream instability, strong or 'jump' discontinuities on
the ion expansionfront, and the dependenceof some of the
phenomena on the initial density gradient between the
plasma and the vacuum. The overall situation is complicated, and no in-depth analysis will be given here. However,
the excitation of ion plasma oscillations caused by the
4000
Samir and Wrenn [1972] through their analysis of the
angular distribution of electron temperature Te around the
Explorer 31 satellite found that Te(wake) > Te(ambient).
This is shown in Figure 8. The authors speculatedthat this
enhancement is probably due to a heat transfer process
which takes place through wave-particle interactions in the
potential 'well' which exists in the wake behind the satellite
and/or to instabilities. Troy et al. [1975] analyzed in situ
measurements from another probe mounted on the same
satellite. They confirmed the earlier finding that there exists
an electron temperature enhancementin the very near wake
region and that the enhancementis not due to some instrumental effect. We should note that no such enhancement
-
ANGLE
OF ATTACK
RANGE
180 + 15ø ,
180 + 30 ø
0+ 30ø
0 + 60ø
3000
2000
510
550
600
650
ALTITUDE
Fig. 8.
was
found at a distance of Z = 5R0 downstream in the wake of
the Ariel 1 satellite [Henderson and Samir, 1967]. A possible
interpretation for the latter result is that the temperature
enhancement is limited to distances downstream, Z, which
satisfy Z < SR0, where S is the ionic Mach number, which
was S = 4 for the above experiment. It should be noted that
the Te measurementsat Z - 5R0 represent average values.
Gurevich and Meshcherkin [1981b] attempt to explain this
temperature enhancement. They claim that the 'region of
700
750
(km)
Variation of electron temperature with altitude for several angle of attack ranges [after Samir and Wrenn,
1972].
SAMIR ET AL..' EXPANSION OF A PLASMA INTO A VACUUM
maximum
rarefaction'
in the
wake
of an obstacle
in a
streaming plasma has a sharp and not a diffuse boundary
which may lead to sharp discontinuities in the plasma
properties, among which is the electron temperature. Moreover, behind the body the converging beams of the flowing
plasmacollide [e.g., Stone et al., 1972; Stone, 1981a, b, and
references therein] and can lead to the excitation of ion
acousticwaves. Since Landau absorption of such a wave is
done mainly via the electrons it is possible that this absorption causes the enhancement in the [Te(wake)]. Despite the
above reexamination of the electron temperature data it is
clear that more experimental evidence is needed in order to
establish the existence of the excitation of plasma oscillations (mainly ion oscillations) and the instabilities in the
wake of an obstacle moving supersonically in a rarefied
spaceplasma. If the electron temperature behind an obstacle
,. ts•
1639
I
I
I
I
I
I
100ø
110ø
120ø
130ø
140ø
150ø
(9oø)
.9
.8
.7
.6
.5
.4
.3
.2
.1
can indeed serve as an indicator of the existence of waves/in0
stabilitiesin the wake region, it would be useful to determine
(experimentally and theoretically) the exact conditions for
the existence of such temperature enhancements.
We have reexamined
some of the Ariel
1 results obtained
from measurements made by a guarded planar electron
probe which was mounted on a boom [Henderson and
Samir, 1967]. The probe measures the angular electron
distribution at a distance of about Z = 5Ro (Ro is the satellite
radius) from the center of the satellite downstream in the
wake. Figure 9 shows the variation of the normalized
electron current Ie/Io with angle of attack 0. The result can be
interpreted as indicating the existenceof a 'trailing shock' or
'propagating rarefaction wave.' This is depicted by the
structure of the normalized current at the angles of attack
0 = 120ø, 240ø. Details on how this plot was obtained are
given by Henderson and Samir [1967]. Of course, it would
have been more useful to have ion density and composition
measurementseven for this single location downstream, but
such is unfortunately not available. In order to establish
unambiguouslythe existence of the rarefaction wave, similar
angular variation profiles are needed for more than one
location downstream. This is not available at the present
time. As will be shown in the next section, laboratory
experiments do indicate the existence of a rarefaction wave
propagatinginto the ambientplasma, as predicted by theory.
Recently, Samir and Fontheim [ 1981] performed a theoryexperiment comparison for the angular distribution of the
normalized ion current around the Explorer 31 and the
Atmosphere Explorer C satellites (see Figure 10). For the
maximum wake zone (0 > 150ø) a discrepancy develops
between theory and experiment, increasing to about 2.5
orders of magnitudeat 0 = 160ø, where [I(Theory)/Io] = 0.97
1.0
0.6
ß MORE THAN ONE
MEASUREMENT
I
I
I
24O
0
Fig. 9.
Variation of normalized electron current [le/10]with angle
of attack 0 [after Henderson and Sam&, 1967].
90ø
160ø
Fig. 10. Variation of normalized ion current [1+(0)/1+(90ø)]with
angle of attack 0. The dashed curve represents in situ measurements. Iteration 0 representsthe neutral approximation (where ions
are treated as neutral particles). Iteration 15 represents the selfconsistentsolution. The figure is after Samir and Fortrheim [1981].
x 10-5 and[I(meas)/Io]
= 0.58 x 10-2. Detailsaregivenby
Samir and Fontheim [1981]. The theoretical model used was
that of Parker [1976, 1977], which solved the steady state,
Vlasov-Poisson equations for a single ion self-consistently.
Although the exact cause of the discrepancy is not clear at
present, it was suggested [Samir and Fontheim, 1981] that
this discrepancy can most likely be removed by the use of
the time-dependent equations written separately for the
various ionic species.
In summary, we note that while the amount of presently
available in situ information regarding the expansion of a
plasma into a vacuum through satellite wake studies is
meager, fragmentary, and limited, some results obtained in
the past through the parametric analysis of the amount of
current depletion in the near wake, electron temperature
enhancement in the wake, etc., seem to be in accord with
theoretical predictions.
3.3. About the Relevance of Some
Laboratory Wake Experiments
Laboratory investigations of the expansion of a plasma
into the void downstream
from test bodies in collisionless
plasma streamsand of the propagationof the corresponding
rarefaction wave into the ambient plasma have been carried
out by Hester and Sonin [1970], Fournier and Pigache
[ 1975],Stone et al. [ 1978], and others. In the investigationby
Stone et al. [1978] both spherical and cylindrical test bodies
were used. The plasma stream conditionswere such that the
ion acoustic Mach number S and the Debye ratio Re remained constantwhile the normalized test body potential •b
was varied over a wide range of values.
Figure 11 shows tranverse ion current density profiles
taken at 2 and 3 radii downstream
from the maximum
cross-
sectional area of the spherical test body. Similar transverse
profiles were obtained at several distancesdownstream from
the various
test bodies.
In each case the distance
that the
leading edge of the rarefaction wave had propagated away
1640
SAMIR ET AL.' EXPANSION OF A PLASMA INTO A VACUUM
wake and/or via the excitation
I
-13
-4
-2
0
2
4
[X/Ro]
I
•oo=2.0
-13
-4
-2
0
i
•
2
4
of ion acoustic
waves which
are absorbed (Landau absorption) by the electrons.
Intriligator and Steele [1982] reported interesting results
from experiments performed at the University of Southern
California's AstrophysicalPlasma Laboratory. Although the
experimentsare basicallysimilar to thosereported by Hester
and Sonin [1970], Fournier and Pigache [1975], Stone et al.
[1972], Oran et al. [1974], and Stone [1981a, b, c], they differ
in that the ionic constituent of the synthesized plasma was
[X/Ro]
Fig. 11. Variation of normalizedion currentdensity(I/1o)with
normalized transverse distance (X/Ro) at two normalized distances
(Z/Ro) downstreamfrom a conductingsphere [after Stone et at.,
1978].
from the wake axis and into the ambient plasma stream, AW,
was determined. As seen in Figure 12, the variation of
AW(S/Ro)is a linear function of Z/Ro, which showsthat the
leading edge of the rarefaction wave propagatesinto the
ambientplasma stream at the ion acousticspeed.This result
is in agreementwith an earlier theoreticaltreatmentof bodyplasma electrodynamicinteractions by Martin [1974].
The data in Figure 12 were obtained for several different
test body geometriesand for a wide variety of applied test
body potentials. The fact that the data from all of thesecases
fall on the same line shows that the rarefaction
wave is not
affectedby body geometry or by the appliedbody potential.
It is apparentlydependentonly on the characteristicsof the
plasma stream and is generated by plasma moving into the
void region swept out by the test body. This is analogousto
the theoretical case treated by Gurevich et al. [1966, 1970],
where a plasma occupyinga half spacewas releasedat time
to and allowed to expand into the vacuum of the remaining
half space.In experimentalstudiesof the type conductedby
Stone et al. [1978] the plasma density gradient is created at
time to by the motion of the test body through the plasma,
and at all subsequenttimes the ambient plasmaexpandsinto
the void left in the wake of the test body. Since in the
reference frame of the test body the rarefaction wave
propagatesaway from the wake axis at the ion acoustic
H + with an energyof the orderof KeV. HencetheIntriligator and Steele [1982] results represent the case of the
interaction between an obstacle (sphere) and a high-energy
plasma, whereas the earlier experiments represent the case
of low-energy, plasma-body interactions. Intriligator and
Steele [1982] suggestthat their experiments may be more
realistically related to the interactions of the high-energy
solar system and astrophysical plasmas with planetary,
lunar, and astrophysicalobjects.
Intriligator and Steele [1982] indicate that strong fluctuations in the current occur on the edges('transition region') of
the wake, that these fluctuations occur at a low frequency,
and that these phenomena are a direct result of the bodyplasma interaction. It is very tempting to claim similarity
between the above findingsand the in situ results of Samir
and Willmore [1965] and Henderson and Samir [1967],
related to fluctuationson the edgesof the wake of the Ariel 1
satellite and the excitation of ion plasma waves in the
frequency range of a few kilohertz. However, we feel that at
presentsucha claim is highly speculative.It shouldbe noted
that Intriligator and Steele [1982] do not report on the
propagationof a rarefaction wave expanding into the ambient plasma or on the enhancementin electron temperature in
the near-wake region.
It should be noted that the laboratory data available at
present, with the exception of the work of Eselevich and
Fainshtein [1980], do not deal explicitly with the ion acceleration mechanismor with the specificsof discontinuitiesas
discussedby Gurevich and Meshcherkin [1981a, b]. Moreover, most of the laboratory work done until now does not
25-
Machangle,0s= sin-l (l/S); in the referenceframeof the
plasma stream the rarefaction wave propagates into the
ambient plasma from the initial void-plasmainterface at the
ion acousticspeed, as predicted theoretically.
Another, presumably permanent, feature of the wake
under
certain
conditions
is the enhancement
of electron
temperaturein the very near wake region. This finding was
first reported by Samir and Wrenn [ 1972], as discussedin the
previous section. In the laboratory, similar results were
reported by Oran et al. [1974] and Shuvalov [1979, 1980].
The [Te(wake)/Te(ambient)] values from the laboratory experiments significantly exceed the in situ results. There is
not yet a clear physical explanation for the heating process
that causes this enhancement. Samir and Wrenn [1972] and
Gurevich and Meshcherkin [1981b] speculated that the enhancementis probably due to a heat transfer processwhich
takes place via wave-particle interactions in the potential
well which exists [Gurevich et al., 1970;Al'pert, 1976]in the
O
•
0
,•
•
.,•'•
I
5
/'
-25
OPEN
- SPHERE
CLOSED- CYLINDER (ñ)
•b
=-3.8
ESTIMATEDERROR: •
I
10
I
15
I
20
I
25
[Z/Ro]
Fig. 12. Variation of the normalized propagationdistanceof the
ion rarefaction wave away from the wake axis [(AW/Ro)S] with
normalized distance downstream (Z/Ro), where $ is the ion acoustic
speed [after Stone et at., 1978].
SAMIR ET AL..' EXPANSION
OF A PLASMA INTO A VACUUM
deal with cases where Ro (-- Ro/ho) >> 1, which may be of
greater relevance to space applications. However, laboratory studies have shown the creation of a rarefaction wave
which propagatesat the ion acoustic velocity, as predicted
by theoretical treatments of plasma expansion, and clearly,
specializedexperimentscan be designedto study aspectsof
the ion acceleration process and the theoretically predicted
strong discontinuities and oscillations.
4.
THE EXPANSION
PHENOMENA
INTERACTIONS
4.1.
OF A PLASMA:
OF POTENTIAL
WITH
PROCESSES AND
INTEREST TO SOLAR WIND
'PLANETARY
OBSTACLES'
1641
-•
•
øo
. •n•Hi••
'•e
_•
CLOUD
ZONE
DUSK
SUN--;
-• --180•
VENUS
WAKE•
A Few Comments Regarding the Wake of Venus
The depletion of particles in the boundary layer mentioned
in the recent review paper by Russell and Vaisberg [1983]
may perhaps be connected with the acceleration of ions into
the wake of Venus upon the expansion of the postshock
ionosheath/magnetosheath
plasma. In any case, fluctuations
in velocity [Russell and Vaisberg, 1983] are possiblein the
rarefaction wave (or rarefaction shock) region. It is also
possiblethat predictions based on viscousinteractions [e.g.,
Perez-de-Tejada, 1980] can be alternatively seen in light of
the discussiongiven in this paper regardingthe region which
is in the proximity of the plasma-vacuum interace and the
location of the onset of the rarefaction wave. In this region
the self-similar approach is valid, as shown theoretically by
Singh and Shunk [1982] and as could be inferred from
theory-experiment comparisons [e.g., Gurevich et al., 1970;
Sam& et al., 1975]. The slowing down and cooling (or
heating)of ions approachingthe center of the wake [Russell
and Vaisberg, 1983] should be examined in depth through
the processesinvolved in the 'expansionof the plasma into a
vacuum.
'
Jumps in flow properties such as density, velocity, and
potential are in general accord with some theoretical predictions discussed earlier (see also Gurevich and Meshcherkin
[1981a, b]), particularly the flows in the wake with properties
which are different from those of the external flow. Jumpsin
the flow properties at the boundary of the wake are of
particular interest and perhaps directly relevant to the phenomena and processes involved in the 'plasma expansion.'
Although the planetary origin of these ions may complicate
the issue, it is worthwhile examining the findings in light of
the latter processes in the wake, ignoring the question of
particle origin. From our earlier discussion it follows that
higher-energy accelerated ions should exist in the wake,
while their concentration
varies with location
downstream.
Ion acceleration associated with magnetic field fluctuations
[Russell and Vaisberg, 1983] may be correlated with the
rarefaction wave region. If the clouds observed by Brace et
al. [1982b] are created outside the ionopause of Venus (see
Figure 13), an examination of the nature of the clouds
(overall location, energy, etc.) vis-h-vis the discussion of
phenomenainvolved in the plasma expansion, in particular
in the wake edge regions may be worthwhile. Moreover, it
may not be unfounded to consider the energization of ions
from the Venusian ionospheric 'holes' [Brace et al., 1982a;
Grebowskyand Curtis, 1981] through the processof plasma
expansion. This may, perhaps, provide another relevant
acceleratingmechanism.Reports on far-wake measurements
of particles and fields are given by Russell et al. [1981] and
Mihalov and Barnes [1981, 1982]. Mihalov and Barnes [1982]
have surveyed the plasma observations from the Pioneer
_
IONiAUSE
o•
•
•
120
•
e•
o
Fig. 13. Location of plasma clouds around Venus [after Brace et
al. 1982b].
Venus Orbiter during the first series of orbits that intersected
the planet's wake in the region 8-12 Rv (Rv is the Venusian
radius) downstream behind the planet. Their results, contrary to those of Venera 9 and 10, do not point toward a welldefined plasma cavity which narrows with increasing distance from the planet and which terminates at -<3-4 Rv.
Overall they find the wake region to vary strongly in space
and time and to display turbulence. They also discuss the
energyspectra(intensityand shift) for H+-O + in the wake
and the originof the O + ions.
We suggestthat in addition to the interpretations given by
Mihalov and Barnes [ 1982] it might be useful to examine the
energy and shift of the particle spectra in terms of phenomena (particularly acceleration mechanisms, instabilities, and
wave-particle interactions) involved in the expansion of a
plasma into a vacuum for the case of a two-ion plasma with
one and/or two electron
distributions
discussed in section 2.
One possibleexplanationof the existenceof O+ in the
Venusian wake is that the neutral oxygen which extends
above the ionopause on the dayside is being ionized by
photoemission and charge exchange processes and then
convected
down
the
Venusian
tail.
Mihalov
and Barnes
[ 1982]statethat suchan explanationis in accord with plasma
measurementsin the region near the planet and in the wake.
However, they statethat the thermalspeedof theseO + ions
is much smaller than the magnetosheathflow speed. Althougha possibleexplanationof the latter was given in terms
of a coolingprocess,it is not impossiblethat the O+ ions in
the Venusian wake are caused by the plasma expansion
processesdiscussedin this paper.
Recently, Intriligator and Scarf [1982] compared particle
and wave measurementsin the Venusian ionosheath. They
found continuously changing ion distributions and correspondingenhanced plasma wave activity. They also found
ion acousticwaves generatedby plasma instabilitiesassociated with the changing plasma distributions and predict
rarefaction and compression of the ionosheath. The observed enhancements in plasma waves were related to
interpenetrating ion beams. More details regarding the ion
1642
SAMIR ET AL..' EXPANSION OF A PLASMA INTO A VACUUM
populationin the Venusian wake (at 11.5 Rv) are given by
Intriligator [1982]. A point of interest here is the statement
by Intriligator and Scarf [ 1982] that the results from Venus
and Titan suggest that the interaction of a nonmagnetic
objectwith a streamingplasmamay producehigh turbulence
levels, in agreement with the recent laboratory results of
Intriligator and Steele [1982].
The orientationof planetaryO+ fluxesand magneticfield
lines in the Venusian wake were discussed by Perez-de-
Tejada et al. [1982]. A result of this study is that the
direction of motion of the O + ions is uncorrelated with
changesin the direction of the magnetic field vector. This
may indicatethat [E x B] pickup processesare not sufficient
to account for the acceleration
and the direction of motion of
the ions and that wave-particle interactions associatedwith
turbulence processesare called upon.
The discussionshere and in section 3 clearly indicate the
existenceof common signaturesin the following interactions
between a streaming collisionlessplasma and a nonmagnetized obstacle: solar wind-Venus, streaming laboratory plasma-target body, and spacecraft-ionosphere.The understandingof commonprocesseswill undoubtedlylead toward
a unified approach in treating collisionlessspace plasmabody interactions.
4.2.
A Few Comments Regarding the Wake of Titan
It is difficult at present to comment meaningfully on the
direct application of our discussion to the case of Titan's
wake. However, speculations pointing toward additional
directions of thought in interpreting this part of the Voyager
1 fly-by observations may not be unwarranted. As mentioned recently by Gurnett et al. [1982], Titan can interact
either with the magnetosphere of Saturn or with the solar
wind dependingon its orbital position and the position of the
magnetopause. If the interaction is with Saturn's magnetosphere, then the flow regime for the interaction is qualitatively similar to that of an artificial satellite moving in the
terrestrial ionosphere/magnetosphere.On the other hand,
differencesbetween these casesare due to plasmacorotation
and to the fact that Titan has a substantial atmosphere. In
this respect there is a similarity with the interaction of Venus
with the solar wind or, to a lesser degree, the interaction of a
comet with the solar wind. However, it may be possible to
consideraspectsof our discussionin the interpretation of the
wave experiment measurements[Gurnett et al., 1982]for the
'low-frequency noise.' It is also possiblethat the questionof
the 'slow-mode shock' mentioned by Gurnett et al [1982] in
the context of the low-frequency noise is a signature of a
'propagatingwave' or a 'trailing shock.'
It is tempting to speculatethat the structureof the electron
density observed on the edgesof Titan's wake is of the kind
known to occur in satellite-ionosphereinteractions [Henderson and Samir, 1967]. At present, nothing more definitive
can be said. However, if and when more in situ and
laboratory measurements relating to body-plasma interactions become available, it would be possible to support or
opposethe above speculation.
4.3.
A Few Comments Regarding the Lunar Wake
Another kind of body-plasma interaction which takes
place in the solar system is that of the solar wind with the
moon. The moon has neither an intrinsic magnetic field nor
an atmosphere. Hence the solar wind interacts essentially
with the surface. In the present study, seeking 'model
unification' for some wake structure in terms of phenomena
typical of the expansion of a plasma into a vacuum, we
examined some of the moon's experimental wake results
[e.g., Lyon et al., 1967; Ness et al., 1968; Serbu, 1969;
$iscoe et al., 1969] and theoretical results [e.g., Michel,
1968; Wolf, 1968; Whang, 1968a, b, 1969;Moskalenko, 1972;
Lipatoy, 1976]. We find that the existence of a region
depletedof chargedparticles in the very near wake zone was
established in qualitative accord with results from satellite
ionosphere interactions [e.g., Samir and Willmore, 1965;
Samir, 1981] and from laboratory simulation data [e.g.,
Stone and Sam&, 1981].
Siscoeet al. [ 1969]investigatedthe distributionof normalized flux in the near lunar wake. They found the wake to be
depleted of charged particles, while the edges of the wake
showed fluxes larger than the ambient values. It should be
noted that the 'leading edge' of the disturbance as it spreads
out downstream from the moon, mentioned by Siscoe et al.
[1969], is at the location of the rarefaction wave associated
with the plasma expansion as discussedin section 2. Relevant laboratory results are given by Podgorny et al. [1975]
and Dubinin et al. [1977]. Theoretically, regions of rarefaction, recompression, and the existence of an inner shock
were predicted [Wolf, 1968; Michel, 1968].
The semiquantitative theoretical diagrams show the main
features of the flow in the lunar wake to be in line with our
knowledge from laboratory work and, to a degree, from in
situ work. However, we did not find any in situ measurements or discussionwhich directly relate to the ion-accelerating mechanismsdue to the expansion of the plasma into a
vacuum. It should be noted that the approach of Michel
[1968], Wolf[1968], and Siscoe et al. [1969] is conceptually
similar to that of Gurevich et al. [1966, 1968] for the regions
where a self-similar approach holds, including the region
between the rarefaction wave and the 'plasma free region'
[Gurevich and Pitaevsky, 1969, 1971].
A particle approach rather than a fluid approach(as taken
by Wolf[1968], Michel [1968], and Siscoe et al. [1969]) was
adopted by Whang [1968a, b, 1969], Moskalenko [1972], and
Lipatoy [1976]. However, neither approach provided any
significantinformation regarding the acceleration of ions in
the wake. A review of lunar wake theoretical studiesis given
by Sprieter et al. [1970], and the question of the validity of
each approachwas discussedby Ness et al. [1968] and Dryer
[1968].
We believe that an in-depth reexamination of available
lunar wake measurements (particles and fields) is worthwhile, particularly in light of the basic phenomena and
processesinvolved in the expansion of the solar wind into
the lunar wake ('dark side'). The results from such a study
may undoubtedly help in the understandingof plasma-body
interactionsin spaceplasma physics.
5.
SUMMARY
AND FUTURE
STUDIES
The fact that phenomena such as ion acceleration, excitation of plasmaoscillations,propagationof rarefactionwaves
and ion fronts, creation of strong and weak discontinuitiesin
the plasma parameters, plasma instabilities, and turbulence
are all caused by processes involved in the expansion of a
plasma into a vacuum makes this area of plasma physics
very interestingbut quite difficult to study. However, we are
dealing with processesand phenomena which are of funda-
SAMIR ET AL.: EXPANSION OF A PLASMA INTO A VACUUM
mental scientific interest with relevant applications to both
laser fusion and spaceplasma research. This was recognized
by laser fusion researchers, and an extensive effort, both
theoretical and experimental (but mainly theoretical), has
been devoted to this area in the past decade. Unfortunately,
the importance of the complex of phenomena and physical
processesinvolved in the expansion of space plasmas into a
vacuum, particularly to solar system plasma phenomena,
and the possibility of studying them via the interactions of
spaceplasmas with natural and artificial 'obstacles' in space
went almost unnoticed by the space geophysicscommunity.
While the existence of rarefaction waves and possible
trailing shocks was discussed in the context of the lunar
wake and, to a lesser extent, in the context of the Venusian
wake, there was no overall comprehensive and systematic
study or discussionalong the general lines shown in summary in Figure 14.
We hope that the discussiongiven in this review will be
seen as a step toward a unified approach in dealing with the
interaction between an obstacleand a spaceplasma, particularly the extremely complicatedwake region. Specificpractical situations may require variability in the significanceand
intensity of specific processes, but there are undoubtedly
basic processesand permanent features which are relevant
to a wide range of interactions.
Even the state of in situ investigations of the basic
processesrelevant to space plasma physics for the practical
case of spacecraft-ionosphereinteractions is still not well
understood. An in-depth, comprehensive reexamination of
measurements from spacecraft-ionosphere, solar windmoon, and solar wind-Venus interactions, together with
relevant available results from laboratory studies, should
constitute a first stage aimed toward a unified approach to
the understandingof plasma-obstacleinteractions in space
plasma research. The structure of the wake, the more
complicated region of the interaction, could be largely
understood through the phenomena and processes of the
expansionof a plasma into a vacuum.
While the above reexamination is essential, it will not
suffice for gaining an overall knowledge and understanding
of the spatial and temporal structure of the wake region of
the interaction. More in situ and laboratory experiments
supported by computer simulations and semianalytic, semiquantitative theoretical work will be needed.
Measurementsdirectly relevant to the study of the expansion of a plasma into a vacuum can be performed partly in
laboratory simulation studies and via in situ measurements
utilizing the Space Shuttle. It would be very valuable to
conduct laboratory experiments (different from those oriented toward laser fusion research) suitableas much as possible
to realistic situations met in spaceplasma physics. This can
be done through the study of wakes. Although it is often
difficultto generate, in the laboratory, syntheticplasmasand
conditionswhich are exactly identical to those which exist in
space, it may not always be essentialto do so. This depends
on the scientific objectives of the study. If the major
objective is to seek physical understandingof processesand
causeand effect relationships, then there may be no need to
seek exact scalingbetween laboratory and space. There can
be no doubt that laboratory studies are of scientific importance and have potential applicationsto spaceplasma physics. From our present physical understanding,it is possible
to speculate that some features observed in the wakes of
1643
EXPANSION OF A PLASMA INTO A 'VACUUM'
(SUMMARY)
(A)
PHENOMENA/PROCESSES
(1)
ION ACCELERATION IN THE 'VACUUM' REGION.
(2)
RAREFACTION WAVE (SHOCK) PROPAGATION INTO THE AMBIENT
PLASMA REGION.
(3)
ION FRONT MOVES IN THE DIRECTION OF EXPANSION
(IN
(4)
THE VACUUM),
EXCITATION OF PLASMA OSCILLATIONS AND INSTABILITIES,
OVER CERTAIN VOLUMES.
(5)
STRONG ('JUMP')
DISCONTINUITIES
IN PLASMA PARAMETERS
AT THE EXPANSION FRONT.
(B)
THE ABOVE DEPEND ON:
(A)
SPECIFIC
IONIC CONSTITUENTS OF THE PLASMA.
(B)
RELATIVE CONCENTRATION OF IONS IN THE PLASMA.
(c)
AMBIENT ELECTRON TEMPERATURE,
(D)
DENSITY GRADIENT AT THE PLASMA-VACUUM INTERFACE.
(E) RATIO
OFCHARACTERISTIC
LENGTH
TOAMBIENT
•'D'
Fig. 14. Expansion of a plasma into a vacuum: phenomena and
processes.
bodies inserted in laboratory streamingplasmas may be
permanent features for body-plasma interactions at large.
After all, basicphysicalprocessesare not necessarilybounded by specificplasma and body properties. Their significanceand intensity may vary with specificsituationsbut not
necessarilytheir basic existence. Moreover, employing the
principle of 'qu,•litative scaling' [e.g., F•ilthammar, 1974;
Samir and Stone, 1980] may be sufficient in many cases
[e.g., Podgorny and Sagdeev, 1970;Podgorny et al., 1975;
Podgornyand Andrijanov, 1978;Andrijanovand Podgorny,
1975; Dubinin et al., 1979, 1981; Stone and Samir, 1981].
The commonbelief that the exact Vlasov scalinglaws have
to be adheredto if we are to reflect from laboratory work to
spaceis not necessarilyapplicable.
The availability of the Space Shuttle and its extensive
capabilities make it possible to study the expansion of a
plasma in situ through a series of well-conceived controlled
experiments. To achieve this goal, relatively small instrument packages(i.e., simplesmall satellites)could be ejected
from the Space Shuttle to measure the rarefaction waves,
convergingstreams, energy spectrum of ions, and the variety of discontinuitiesin the plasmapropertieswhich occur in
the interfacebetweenthe ambientplasmaand the plasmain
the wake. The wake into which the plasmaexpandswould be
generated by 'test bodies' such as inflatable balloons, tethered spheres, and spheres and/or cylinders mounted on
booms.The test bodiescan have differentsurfaceproperties
(e.g., different conductivities), sizes, and geometry. It is
possibleto examine the characteristicsof the plasma in the
wake for different ratios of [N(H+)/N(O+)] as well as for
differentratios of [Ro/ho]of interest in spaceplasmas.The
target bodies selected can be nonmagnetized,magnetized,
and bodies surroundedwith an atmosphere/ionosphere.A
1644
SAMIR ET AL'
EXPANSION OF A PLASMA INTO A VACUUM
detailed discussionof some possible experimental modes of
operation and shuttle flight configurationsis given elsewhere
[Sam& and Stone, 1980].
Finally, we submit that studies of body-plasma interactions, particularly wake studies, provide an excellent framework through which the basic physical phenomenainvolved
in the expansionof a plasma into a vacuum can be investigated and the physical processesexamined.
APPENDIX: THE BASIC EQUATION TREATED BY GUREVICH
ET AL. [1966, 1968, 1973] AND GUREVICH AND PITAEVSKY
[1975] UNDER THE ASSUMPTIONOF QUASI-NEUTRALITY
The plasmais describedby the kinetic equationfor the ion
distribution function f:
Of
--+
Ot
v
Of
e
O6
.....
Ox
Mi
Of
Ox
0
(1)
and by the Poissonequation
024,
•
= -4rre(NiOx2
Ne)
Equation (9) can also be written in the form
=
4•N
re= In
Ni = Ne
(4)
and Ne is given by
Ne = No exp (ecb/Te)
(5)
Hence
ecb= Te In (Ni/No)
(6)
Substituting in (1), we obtain
Ox
....
Oo Mi
Ox
In
fdv
dr
No=
g
1/'•(rr/3)
•--•
ri
(10)are r--->-o•, g --->exp(-/3u2) andr--->+o•,g --->0.
For large r > 0 (which correspond to large x) the ions are
strongly accelerated; hence their thermal motion can be
neglected. In this case, one deals with the continuity and
momentum equations
ONi
O
•
+ • (Nivi) = 0
Ot
[Ot
Ox
(11)
Ox/l
(3)
Assuming quasi-neutrality, (2) reduces to
v
20u
Equation (9) or (10) is the basic equation treated by Gurevich
et al. [1966, 1968, 1973] and Gurevich and Pitaevsky [1975].
For t -< 0, x --> -o• the plasma is not disturbed (ambient),
while for x --> +o• the plasma vanishes. If it is assumedthat
the undisturbed plasma obeys a Maxwellian distribution,
then the boundary conditions of the 'basic equation' (9) or
where Mi is ionic mass, •b is electrostatic potential (E =
-Ocb/Ox),and
•+
Ot
10g dqbN
=0
Or
(10)
(2)
Ni=
f•o,
fdv
Og
(u-r)
=0
(7)
As mentioned in the text, after a time t when quasineutrality is reached, the motion can be treated in the selfsimilar approach, and f = f(x/t; v). Note that the element of
length ('characteristic length') was eliminated.
Introducing the parameters
A discussion of the relation and analogy between the
Riemann solution [Landau and Lifschitz, 1963] for simple
waves in ordinary hydrodynamics and the self-similar solutions for the collisionless kinetic equation for the case of a
quasi-neutral plasma [Gurevich et al., 1966, 1968, 1973;
Gurevich and Pitaevsky, 1975] is given by Gurevich and
Pitaevsky [1969]. The breaking of the simple wave in the
kinetics of a rarefied plasma is discussedby Gurevich and
Pitaevsky [1971]. In the latter paper the stability of the selfsimilar solutions of the kinetic equation in a rarefied quasineutral plasma was investigated, and the existence of undamped ion acoustic oscillations was demonstrated.
Moreover, a class of distribution functions for which solutions (stationary solitary waves) exist, even if the thermal
motion of the ions is considered, is shown.
Acknowledgments. U. Samir acknowledgesthe supportof the
NRC/NAS Associateship Office, the interest of R. Manka, the
Program Administrator, and the hospitality of the Space Science
Laboratory at NASA/MSFC. K. H. Wright acknowledgessupport
from NASA
under contract NAS8-33982.
REFERENCES
r=-t
.= V
g=[MiJ fNo-'
(8)
the equation
(u......r)Or 20u dr In
is obtained for the nondimensional
Allen, J. E., and J. G. Andrews, A note on ion rarefactionwaves, J.
Plasma Phys., 4, 187, 1970.
Al'pert, Y. L., Wave-like phenomenain the near earth plasmaand
interactionswith man-made bodies, in Handbuch de Physik,
Geophysics,vol. III, Part V, editedby S. Flugge,p. 217, SpringerVerlag, New York, 1976.
Anderson, D., J. Faulkner, H. Wilhelmsson, K. Nishikawa, and T.
Tange, Study of similarityflows of two componentlaserproduced
plasmas,Phys. Sci., 18, 141, 1978.
Andrijanov, Yu. V., and I. M. Podgorny, Effect of the frozen-in
magneticfield on the formationof Venus' plasmashellboundary:
Experimental conformation, NASA Spec. Publ., SP-397, 101,
g du
= 0
ion distribution
(9)
function
g. Note that (9) does not impose any requirement of f. (Note
thatr andsc (givenin thetext) satisfysc = r(2)1/2.
1975.
Begay, F., and D. W. Forslund, Accelerationof multi-speciesions
in CO2 laser-producedplasmas:Experimentsand theory, Phys.
Fluids, 25, 1675, 1982.
SAMIR ET AL..' EXPANSIONOF A PLASMA INTO A VACUUM
Bezzerides, B., D. W. Forslund, and E. L. Lindman, Existence of
rarefaction shocks in a laser-plasma corona, Phys. Fluids, 21,
2179, 1978.
Brace, L. H., R. F. Theis, H. G. Mayer, S. A. Curtis, and J. G.
Luhman, Holes above the nightside ionosphere of Venus, J.
Geophys. Res., 87, 199, 1982a.
Brace, L. H., R. F. Theis, and W. R. Hoegy, Plasma clouds above
the ionopauseof Venus and their implications, Planet. Space Sci.,
30, 29, 1982b.
Crow, J. E., P. L. Auer, and J. E. Allen, The expansionof a plasma
into a vacuum, J. Plasma Phys., 14, 65, 1975.
Decoste, R., and B. H. Ripin, High-energy ion expansion in laserplasma interactions, Phys. Rev. Lett., 40, 34, 1978.
Denavit, J., Collisionlessplasma expansion into a vacuum, Phys.
Fluids, 22, 1384, 1979.
Dryer, M., Hypothesis for absence of lunar bow and wake shock
waves, J. Geophys. Res., 73, 3583, 1968.
Dubinin, E. M., I. M. Podgorny, Yu. M. Potanin, and C. P. Sonnet,
Laboratory simulation of the lunar magnetosphere, Geophys.
Res. Lett., 4, 391, 1977.
Dubinin, E. M., I. M. Podgorny, Yu. M. Potanin, and S. I.
Shkolnikova, Determining the magnetic moment of Venus by
magnetic measurementsin the tail, Cosmic Res., Engl. Transl.,
16, 693, 1979.
Dubinin, E. M., P. L. Israelovich, I. M. Podgorny, and S. I.
Shkolnikova, The magnetic tail and electrodynamic forces in
Halley's comet, Cosmic Res., Engl. Transl., 18, 642, 1981.
Eselevich, V. G., and V. G. Fainshtein, Expansion of collisionless
plasma in a vacuum, Soy. Phys. JETP, Engl. Transl., 52, 441,
1980.
Ffilthammar, C.-G., Laboratory experiments of magnetosphereinterest, Space Sci. Rev., 15, 803, 1974.
Felber, F. S., and R. Decoste, Fast expansions of laser-heated
plasmas, Phys. Fluids, 21,520, 1978.
Fournier, G., and D. Pigache, Wakes in collisionlessplasma, Phys.
Fluids, 18, 1443, 1975.
Grebowsky, J. M., and S. A. Curtis, Venus nightsideionospheric
holes: the signature of parallel electric field acceleration regions,
Geophys. Res. Lett., 8, 1273, 1981.
Gurevich, A. V., and A. P. Meshcherkin, Ion acceleration in an
expanding plasma, Soy. Phys. JETP, 53, Engl. Transl., 937-945,
1981a.
Gurevich, A. V., and A. P. Meshcherkin, Jump discontinuity on the
front of a rarefaction wave front in a plasma, Soy. Phys. JETP,
Engl. Transl., 54, 688-693, 1981b.
Gurevich, A. V., and L. P. Pitaevsky, Simple waves in the kinetics
of a rarefied plasma, Soy. Phys. JETP, Engl. Transl., 29, 954,
1969.
Gurevich, A. V., and L. P. Pitaevsky, Breaking of a simple wave in
the kinetics of a rarefied plasma, Soy. Phys. JETP, Engl. Transl.,
33, 1159, 1971.
Gurevich, A. V., and L. P. Pitaevsky, Non linear dynamics of a
rarefied ionized gas, Prog. Aerosp. Sci., 16, 227, 1975.
Gurevich, A. V., L. V. Paryiskaya, and L. P. Pitaevsky, Self-similar
motion of rarefied plasma, Soy. Phys. JETP, Engl. Transl., 22,
449, 1966.
Gurevich, A. V., L. V. Paryiskaya, and L. P. Pitaevsky, Self-similar
motion of a low density plasma, II, Soy. Phys. JETP, Engl.
Transl., 27, 476, 1968.
Gurevich, A. V., L. P. Pitaevsky, and V. V. Smirnova, Ionospheric
aerodynamics, Soy. Phys. Usp., Engl. Transl., 99, 595, 1970.
Gurevich, A. V., L. V. Paryiskaya, and L. P. Pitaevsky, Ion
acceleration upon expansion of a rarefied plasma, Soy. Phys.
JETP, Engl. Transl., 36, 274, 1973.
Gurevich, A. V., D. Anderson, and H. Wilhelmsson, Ion acceleration in an expanding rarefied plasma with non-Maxwellian electrons, Phys. Rev. Lett., 42, 769, 1979.
Gurnett, D. A., F. L. Scarf, and W. S. Kurth, The structure of
Titan's wake from plasma wave observations,J. Geophys. Res.,
87, 1395, 1982.
Henderson, C. L., and U. Samir, Observations of the disturbed
region around an ionospheric spacecraft, Planet. Space Sci., 15,
1499, 1967.
Hester, S. D., and A. A. Sonin, A laboratory study of the wakes of
ionospheric satellites, AIAA J., 8, 1090, 1970.
Intriligator, D. S., Observation of massaddition to the shockedsolar
1645
wind of the Venusian ionosheath, Geophys. Res. Lett., 9, 727,
1982.
Intriligator, D. S., and F. L. Scarf, Plasma turbulence in the
downstream ionosheath of Venus, Geophys. Res. Lett., 9, 1325,
1982.
Intriligator, D. S., and G. R. Steele, Observations of structuring in
the downstream region of a large spherical model in a laboratory
simulated solar wind plasma, J. Geophys. Res., 87, 6053, 1982.
Landau, L. D., and E. M. Lifshitz, Fluid Mechanics, Pergamon,
New York, 1963.
Lipatov, A. S., Three dimensionalstructure of the plasma wake of
the moon, Cosmic Res., Engl. Transl., 14, 115, 1976.
Lyon, E. F., H. S. Bridge, and J. H. Binsack, Explorer 35 plasma
measurementsin the vicinity of the moon, J. Geophys. Res., 72,
6113, 1967.
Martin, A. R., Numerical solutions to the problem of charged
particle flow around an ionospheric spacecraft, Planet. Space
Sci., 22, 121, 1974.
Michel, F. C., Magnetic field structure behind the moon, J.
Geophys. Res., 73, 1533, 1968.
Mihalov, J. D., and A. Barnes, Evidence for the acceleration of
ionospheric[O+] in the magnetosheathof Venus, Geophys.Res.
Lett., 8, 1277, 1981.
Mihalov, J. D., and A. Barnes, The distant interplanetary wake of
Venus: Plasma observations from Pioneer Venus, J. Geophys.
Res., 87, 9045, 1982.
Mora, P., and R. Pellat, Self-similar expansion of a plasma into a
vacuum, Phys. Fluids, 22, 2300, 1979.
Moskalenko, A.M., The wake of the moon, Cosmic Res., Engl.
Transl., 10, 791, 1972.
Ness, N. F., K. W. Behanon, H. E. Taylor, and Y. C. Whang,
Perturbation of the interplanetary magnetic field by the lunar
wake, J. Geophys. Res., 73, 3421, 1968.
Oran, W. A., U. Samir, and N.H. Stone, Parametric study of the
near-wake structure of spherical and cylindrical bodies in the
laboratory, Planet. Space Sci., 22, 379, 1974.
Parker, L. W., Computation of collisionless steady-state plasma
flow about a charged disk, NASA Contract. Rep., CR-144159,
1976.
Parker, L. W., Calculation of sheath and wake structure about a
pillbox-shapedspacecraftin a flowing plasma, Proceedingsof the
Spacecraft Charging Technology Conference, Rep. AFGI-TR-?7O051/NASA TMX-73537, 1977.
Perez-de-Tejada, H., Evidence for a viscous boundary layer at the
Venus ionopause from preliminary Pioneer Venus results, J.
Geophys. Res., 85, 7709, 1980.
Perez-de-Tejada, H., D. S. Intriligator, and C. T. Russell, Orienta-
tion of planetaryO + fluxesand magneticfield lines in the Venus
wake, Nature, 299, 325, 1982.
Podgorny, I. M., and Yu. V. Andrijanov, Simulation of the solar
wind interaction with non-magnetic celestial bodies, Planet.
Space $ci., 26, 99, 1978.
Podgorny, I. M., and R. Z. Sagdeev, Physics of the inter-planetary
plasmaand laboratory simulation, Soy. Phys. Usp., Engl. Transl.,
98, 445, 1970.
Podgorny, I. M., Yu. V. Andrijanov, and G. B. Kulikov, Laboratory simulationof the solar wind-moon interaction, Cosmic Res.,
Engl. Transl., 13, 819, 1975.
Russell, C. T., and O. Vaisberg, The interaction of the solar wind
with Venus, in Venus, edited by D. M. Hunten, L. Colin, and T.
M. Donahue, University of Arizona Press,Tucson, in press, 1983.
Russell, C. T., J. G. Luhmann, R. C. Elphic, and F. L. Scarf, The
distant bow shock and magnetotail of Venus: Magnetic field and
plasma wave observations, Geophys. Res. Lett., 8, 843, 1981.
Samir, U., Bodies in flowing plasmas: Spacecraft measurements,
Adv. Space Res., 1, 373, 1981.
Samir, U., The interaction of rapidly moving conductorswith space
plasmas, in Contributed Papers to the International Conference
on Plasma Physics, edited by H. Wilhelmssonand J. Weiland, p.
11c:2, Chalmers University of Technology, G6teborg, Sweden,
1982a.
Samir, U., The interaction of large space structures with the nearearth environment, paper presented at Workshop on Natural
Charging of Large Space Structures in Polar Orbits, Air Force
Geophys. Lab., Bedford, Mass., Sept. 14-15, 1982b.
Samir, U., and E.G. Fontheim, Comparison of theory and in-situ
1646
observations
$AMIR ET AL..' EXPANSION OF A PLASMA INTO A VACUUM
for electron and ion distributions
in the near wake of
the Explorer 31 and AE-C satellites, Planet. Space $ci., 29, 975,
1981.
Samir, U., and N.H. Stone, Shuttle-era experiments in the area of
plasma flow interactions with bodies in space, Acta Astronaut., 7,
1091, 1980.
Samir, U., and A. P. Willmore, The distribution of charged particles
near a moving spacecraft, Planet. Space Sci., 13, 285, 1965.
Samir, U., and G. L. Wrenn, Experimental Evidence of an electron
temperature enhancementin the wake of an ionosphericsatellite,
Planet. Space $ci., 20, 899, 1972.
Samir, U., E. J. Maier, and B. E. Troy, Jr., The angular distribution
of ion flux around an ionospheric satellite, J. Atmos. Terr. Phys.,
35, 513, 1973.
Samir, U., M. First, E. J. Maier, and B. E. Troy, A comparisonof
the Gurevich
et al. and Liu-Jew
models for the ion flux around a
satellite, J. Atmos. Terr. Phys., 37, 577, 1975.
Samir, U., L. H. Brace, and H. C. Brinton, About the influence of
electron temperature and relative ionic composition on the ion
depletion in the wake of the AE-C satellite, Geophys. Res. Lett.,
6, 101, 1979.
Samir, U., P. J. Wildman, F. Rich, H. C. Brinton, and R. C.
Sagalyn, About the parametric interplay between ionic Mach
number, body-size, and satellite potential in determining the ion
depletion in the wake of the S3-2 satellite, J. Geophys. Res., 86,
11,161, 1981.
Serbu, G. P., Explorer 35 measurementsof low-energy plasma in
Lunar orbit, J. Geophys. Res., 74, 372, 1969.
Shawhan, S. D., and G. B. Murphy, Orbiter generated¾xB potentials and electrostatic noise, paper presented at Workshop on
Natural Charging of Large Space Structure in Polar Orbits, Air
Force Geophys. Lab., Bedford, Mass., Sept. 14-15, 1982.
Shuvalov, V. A., Flow of a nonequilibriumrarefied plasmaarounda
sphere, Geomagn. Aeron., Engl. Transl., 19, 670, 1979.
Shuvalov, V. A., Structure of the near wake behind a cylinder in a
nonequilibrium rarefied plasma flow, Geomagn. Aeron., Engl.
Transl., 20, 293, 1980.
Singh, N., and R. W. Schunk, Numerical calculations relevant to
the initial expansionof the polar wind, J. Geophys.Res., 87, 9154,
1982.
Siscoe, G. L., E. F. Lyon, J. H. Binsack, and H. S. Bridge,
Experimental evidence for a detachedlunar compressionwave, J.
Geophys. Res., 74, 59, 1969.
Sprieter, J. D., M. C. Marsh, and A. L. Summers, Hydromagnetic
aspectsof solar wind flow past the moon, CosmicEiectrodyn., 1,
50, 1970.
Stone, N.H., The plasma wake of mesosonicconductingbodies, 1,
An experimental parametric study of ion focusingby the plasma
sheath, J. Plasma Phys., 25, 351, 1981a.
Stone, N.H., The plasma wake of mesosonicconductingbodies, 2,
An experimental parametric study of the mid-wake ion density
peak, J. Plasma Phys., 26, 385, 1981b.
Stone, N.H., The aerodynamicsof bodiesin a rarefiedionized gas
with applications to spacecraft environmental dynamics, NASA
Tech. Pap., 1933, 1981c.
Stone, N.H., and U. Samir, Bodies in flowing plasmas:Laboratory
studies,Adv. Space Res., 1, 361, 1981.
Stone, N.H., W. A. Oran, and U. Samir, Collisionlessplasmaflow
over a conductingsphere, Planet. Space $ci., 20, 1787, 1972.
Stone, N.H., U. Samir, and K. H. Wright, Jr., Plasmadisturbances
created by probesin the ionosphereand their potential impact on
low-energymeasurementsconsideredfor Spacelab,J. Geophys.
Res., 83, 1668, 1978.
Troy, B. E., Jr., E. J. Maier, and U. Samir, Electron temperatures
in the wake of an ionosphericsatellite,J. Geophys.Res., 80, 993,
1975.
True, M. A., J. R. Albritton, and E. A. Williams, Fast ion
production by suprathermal electrons in laser fusion plasmas,
Phys. Fluids, 24, 1885, 1981.
Whang, Y. C., Interaction of the magnetized solar wind with the
moon, Phys. Fluids, 11, 969, 1968a.
Whang, Y. C., Theoretical study of the magneticfield in the lunar
wake, Phys. Fluids, 11, 1713, 1968b.
Whang, Y. C., Field and plasmain the lunar wake, Phys. Rev., 186,
143, 1969.
Wickens, L. M., and J. E. Allen, Free expansionof a plasmawith
two electron temperatures, J, Plasma Phys., 22, 167, 1979.
Wickens, L. M., and J. E. Allen, Ion emissionfrom laser-produced,
multi-ion species,two electron temperatureplasmas,Phys. Fluids, 24, 1894, 1981.
Widner, M., I. Alexeft, and W. D. Jones, Plasmaexpansioninto a
vacuum, Phys. Fluids, 14, 795, 1971.
Wolf, R. A., Solar wind flow behind the moon, J. Geophys.Res.,
73, 4281, 1968.
(Received January 28, 1983;
accepted May 6, 1983.)