Particle Ionization in Interplanetary Space

VOL.

77, NO. 28

JOURNAL

OF GEOPHYSICAL

RESEARCH

OCTOBER

1, 1972

Electromagnetic Instabilities Produced by Neutral-Particle Ionizationin Interplanetary Space C. S. Wv

Institute ]or Fluid Dynamics and Applied Mathematics University ol Maryland, College Park, Maryland 20742 R. C. DAVIDSON Department t•] Physics and Astronomy

Universityo! Maryland, CollegePark, Maryland 20742 This article examinesthe consequence of the ionization (e.g., photoionization) of a small

population of neutralatoms(hydrogen or helium)in interplanetary space. It is foundthat, even if the density of the newly ionized particles is only a very small fraction of that of the solar wind, these particles can efficiently excite electromagnetic waves by means of a new

collectiveinstability.The instabilityis driven by an anisotropyin kinetic energyof the newly ionized particles. The typical linear growth rate is •,--•

(•0•/2 •/•) (vo./c) where

is the plasmafrequencyof the newly ionized ions, and vo• i• the characteristicspeedof the newly ionized ions perpendicularto the ambient magnetic field in the frame of the solar wind. The interaction

between solar wind and inter-

the neutralparticlesandthe solar-wind particles is so long that the two classes of particlesare

stellar particles is a topic of considerableinterest, as evidencedby recent observationsthat confirm the existenceof interstellar gas in the inner solar system [Thomas and Krassa, 1971; Bertaux and Blamont, 1971] and several recent works in this general subject area [Axford, 1971; Holzer and Axford, 1971; Feldman et al., 1971]. In

this article

we consider a different

practically noninteracting.In this article we examinewhat happensif theseneutralparticles

suddenlybecomeionized,say by photoionization.

The distributionof newly ionizedparticlesis

described in the following section. In the third section it is shown that these newly ionized

but

particles can produce collective instabilities for highly relevant aspectof the subject,namely, transverse electromagneticwaves propagating the collectiveplasma effectsthat occurimmedi- parallelto the ambientmagneticfieldB0 in the ately after the interstellaratomsbecomeionized. frequencyranges It is shownthat newly ionizedparticlescan result in the local generationof electromagnetic and wavesin interplanetary space. To orient the reader, we first describe the

physicalproblem of interest. Considera dis,

tribution of neutral hydrogenor helium atoms (of interstellar origin) in the solar wind. These neutral particles have very low density, a very small fraction of the density of particles in the solarwind. Furthermore,the macroscopic propertiesof theseneutral particles (e.g., their mean velocity) can differ substantiallyfrom those of the solar wind.

Under

usual solar-wind

In (1) and (2), •o is the wave oscillation frequency (complex)as viewedin the frame of the

solarwind,andI.•,l andI.fl•]arethesolar-wind electron and proton cyclotron frequencies,respectively.Qualitative features of the nonlinear responseof newly ionized particlesto the instability are discussed in the fourth section.

condi-

DISTRIBUTION OF NEWLY IONIZED PARTICLES

tions the mean free path for collisionsbetween Copyright ¸

1972 by the American GeophysicalUnion.

In this section we discussproperties of the initial distributionfunctionfor the newly ionized 5399

5400

Wv

A•D DAVIDSON

particles. This servesas the basis for the linear stability analysis presented in the following section. For simplicity, we assume that the interplanetarymagneticfieldB0 is uniformin the senseof the local approximation.Furthermore, it is assumedthat the solarwind is homogeneous, and has a constant bulk velocity rs. If the magneticfield is moving with a uniform velocity vm, then in the absenceof collisionswe expect

So = 0 Equation 3 states that the solar wind and the magnetic field are comovingin a direction normal to the magnetic field lines. It is therefore convenientto carry out the analysisin a frame of reference that

coincides with the solar-wind

frame..

We now considerwhat happensto the neutral particles soonafter ionization has taken place. Denoting the initial bulk velocity of the neutral particles (before ionization) by v,, then in the solar-windframe the newly ionized particlesare streaming along the magnetic field lines with a mean parallel speedv0,,

Vo,= [(v, -- v,,)'nI

(4)

where n = Bo/[Bo[is a unit vector alongBo. Moreover, these newly ionized particles are gyrating around the magnetic field lines with a mean transversespeedVo• where It shouldbe noted that the transverseguiding center velocity is equal to zero. The moving magnetic field very quickly accelerates the newly ionized particlesin the transversedirection. The resultingparticle orbits in the transverse direction are circular gyrations in the solar-wind frame, with zero mean relative velocity (transverseto the magnetic field) between the solar wind and the newly ionized particles. In the solar-wind frame we therefore expect that the distributionfunction of newly ionizedparticlesis peakedat a parallelvelocity v, = Vo,and a perpendicularspeed v. = Vo.. If the particles haye a negligiblespread in vdocities relative to Vo,and Vo.,the distribution functionF,,,,(v?, v,) of newly ionizedparticles can be expressedin the approximateform

_

2z'v.

- Vo,,) - Vo)

(6)

wherethe subscripta labelsthe particlespecies. The distributionfunctionin (6) is justifiablefor ions of interstellar origin, sincethe spread in velocities relative to Vol and Vo, is generally

small. It should be noted that the present analysis is mainly motivated by the study of the interaction

of interstellar

helium with

the

solar wind. Thus it is implicitly assumedthat photoionization is the dominantionizationprocess, since the photoionizationrate is much greater than the rate for charge exchange lAxford, 1971]. In the event that other ions are produced predominantly by charge exchange processes,then F• given by (6) may have to be modifiedto includean appreciable velocity spread.However,it is anticipatedthat this velocity spread is much smaller than Vo• and that the present analysis is still qualitatively correct. Note that the normalization of

F• is suchthat f d•vF•,, = nan,wherej' •v -2.•r$o© dr. v. $_• dr, and n• (constant)is the ambient density of newly ionizedparticlesof speciesa. In general,F• may be spatiallyinhomogeneous. However, if the length scale of inhomogeneity is very long in comparisonwith the typical wavelengthof excitedmodes,in a first approximationF• can be treated as spatially homogeneous. We assumethis to be the casein the subsequentanalysis. The most significantfeature of (6) is that the distributionof newlyionizedparticlescanresult in collectiveinstabilitiesthat generatelargeamplitude electromagneticwaves. Moreover, thesewavescan interactwith the newlyionized particles and alter their distribution F•.. If this interaction results in a significantdecreasein vo,,and Vo•,the newly ionizedparticlesare assimilatedby the solarwind. GENERATION OF ELECTROMAGNETICWAVES-LINEAR T•rORY

The analysisin this sectionis carried out in the frame of the solar wind. The total distribu-

tion function for speciesa, F•(v• •, v,.), can be expressedas

where F,,,(v• •, v,) is the distribution of solarwind particles and F,,,•(v•f, v,) is the distribution of newly ionizedparticlesgivenin (6). In

]'NSTABILITIES IN ]•NTERPLANETARY SPACE

the parameter regime of interest, vo• and are likely to be much smallerthan the thermal speed ve.•8 of the solar-wind electronsbut muchlargerthan the thermalspeedv•,• øof the solar-windprotons.That is,

••Vo•• (( (v•,t•)• Vol•

(8a)

•nd

+

•nd ion sound waves. Not all of these modes are

excited, however, since the density of newly ionizedparticlesis low and the solar •nd can result in a large Landau or cyclotron d•mping in some frequency and wave number ranges. For example,we neglection soundw•ves in the analysis that follows, since these waves are heavily d•mp• when the solar-•nd electron temperatureis not substantiallyhigherthan the proton temperature. Furthermore, we expect that ion cyclotronwaves are heav•y damped, owingto cyclotronabsorptionby the solarwind. We considerthe linear stability of transverse electromagneticw•ves propagating parallel to the •mbient magneticfield (k [[ B0). Attention is restrictedto frequency•nd wave n•ber ranges well removedfrom cyclotronresonances with the solar-windp•rticles. That is, we •ssume

In (9), a labelsthe p•rticle species, • = e•Bo/

(w-/CVo 2•2

2

loan I• t)Oi'

+

_-

1o)

where • and • are the ath speci• plasma frequenciesassociated•th the solar-•nd particles and the newly ionized pa•icles, respectively; i.e.,

Thereforeit is reasonable to expectthat there are w•ve modesthat c•n be excitedin the intermediate and low frequency r•nges. In general, there •re several modes of interest. These include Alfv•n waves, magnetosonicwaves,ion cyclotronw•ves,whistlerwaves,

5401

• w•

2 4wnanea 2 •o,,,,•=

4wn•e•• =

ma

ma

(11)

In (11), n•8 (constant) is the ambient density of solar-windparticlesof speciesa, and n• (constant) is the ambient density of newly ionized particles of speciesa. The upper sign (+) in the dispersionrelation, (10), refers to waves with right-handpolarization,whereasthe lower sign (-) refers to waves with left-hand polarization. The third term on the right-hand side of (10) representsthe contributionof the solarwind particles.This term is approximatewithin the context of the inequality in (9). The last two terms on the right-handsideof (10) representthe contributions of the newlyionizedparticlesto the dispersionrelation.Theseterms are exact within

the

context

of the

distribution

function given in (6). In the analysisthat followswe assumethat the solar wind is composedof two components, namely, electrons(a -- e) and protons (a -- p) with equal densities(he8 - •,). Furthermore, sincethe densityof newly ionizedparticlesis low (n•,• • np•) and.the frequencyrangesunder

consideration (equations I and2) satisfy!o•!• Ifl•l, we neglectcontributions in (10) that are

associated with electronsproducedin the ionization process.The contributionsfrom newly ionized ions (a -- i), however, are retained in of species a), (v•,•,) • = (• dayv•F•)/([ dayF•) the dispersionrelation. For a singlecomponent is the thermal speed squ•red of • solar-wind of newly ionized ions, (10) thus reducesto p•rticle of speciesa, w is the w•ve oscillation frequency(complex)in the solar-windframe, •nd z k is the wave vector p•mllel to B0. Substituting 0 = D:•(k,w) = kZc 2 2 (7) into the f•mili•r dispersion relation for 2

m•c is the cyclotronfrequency (e• •nd m• •re the charge•nd mass,respectively,of • p•rticle

parallelpropagation [Sudan, 1963;Montgo•ry and Tidman, 1964]•nd m•king useof (6) •nd (9),

wefindthat thedispersion relation c•nbe expressed to le•ding order •s 2

o:

2

(•-

- Vo6 kvollq- 9•) 2

2

2

a•i• k Voj.

2(w- kVoll--

(12)

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Wu AND DAVIDSON

In (12),a -- i canreferto protons, He+orHe++, ofthenewlyionized ions.Thesolutions oftype2 asthecasemaybe.Wenowexamine (12) in the areobtained to leading orderby balancing the intermediate (equation 1) andlow(equation 2) second andfourthtermsin (17),whichgivesthe frequency ranges.The ratio n•,•/np8 is assumed approximatedispersionrelation to be small, with

~2

2 k2•)oJ. 2

Intermediate irequency range:I'•1