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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]. 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