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    A major purpose of the Techni-cal Information Center is to providethe broadest dissemination possi-ble of information contained inDOEs Research and DevelopmentF?eports to business, industry, theacademic community, and federal,state and local governments.

    Although a small portion of thisreport is not reproducible, it isbeing made available to expeditethe availability of information on theresearch discussed herein.

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    LA-uR 90-1129

    ;,o~ AIanIoS Nal)ona) LaDOraIOrv M operated By me unwerwy ot Gahlorn:a to? the Unma States Dewlmenl Of Enew underconl~aclw-~405-ENG-36

    LA-UR--90-1123DE90 o1O565

    TITLE P ART I CL E E NE RGI Z AT I ON

    AuTHOR(S) Ga l e n Gisler

    SUBMITTED0 P r o c e e d i n g s o f t h e Wo r k s h o p o n t h e I n t e r p r e t a t i o n o f Mo d e r nSy n t h e s i s Ob s e r v a t i o n s o f Sp i r a l Ga l a x i e s , A l b u q u e r q ( l e , NMMa r c h 1 1 - 1 5 , 1 9 9 0

    -.~ECLAIMERThis rqw wmpm~d aann qxwunf of-ks~botibyann~ncyof lhclJnild slataCmwrnm[lt, Nei&rlhe {Jnild Stala(iomrnmnt noranya~~ tkwf, noranyuflhir~mfdoYeca,makeswrywarranly,qaremor implkd, or usaum~unyIcgtilliability or m~~rni.t rility for the quracy,c ompletenm,u ruwfulnwtisny infwmnlim, qqMralun,prrducl,orpfomnndieArecd.or re~nls Ihat its u= would mx infrin~ privatelyownedrights. Refer.mrcc herein 10 qny ~ ml r ~crnnme~talprrxluctl pr~, w mcrviw by Ira& n-me, tra&mnrk,manufaulurer, or otherwi= dwrn not nwcmarily wrnstilu(c w im~y its cndormmenl, r~.Mendali!ln,or fmmringhy k I)niled Slutes(iovernrncntrareny qency thcr~f, The viewsand opinionsof mrthomcnprc~ hereinIJrsnot nwnarily q[~le w ~~1 Ihq ,)f IN[)nitd SIaICa (iwrnmcnt or any qgency thcra)f,

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    LosAlamos National LaboratoryLos Alamos,New Mexico 87545

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    PARHCLE ENERGIZATION

    GAI J5N GISLERSpacePlasmaPhysics,Los AlarnosNational LaboratoryLos Alamos NM 87545ABSTRACT. A first-principles approachto thephysicsof particle energi-zation is presented. The general physicsof particle accelerationis thenapplied to a number of theclassicalastrophysicalmechanismsfor accelerat-ing particles, with referencesto recent litcratum+where theseamused inspecific circumstances. The solar flare is recommendedasa microcosmforstudying pardclc accclermionbecausemany diffemtt Dmcesscsseemto beoccurring in close proximity, and them is abundanthi~ time resolutiondatafordiagrmsingthoseproccsscs.Finally, a list of possible sitesand mecha-nismsfor particle accelerationin spiral galaxies ispresented.

    1. INTRODUCTIONThis review of particle encrgizadon is intendedasa surveyof what people aremrrcntly doing and thinking in thissubdiscipliw My own interestis inhowparticles can lx extracted from a backgtmnd thermal popuhdon to form a supath-ermal population. Others, who arc interestedin how suprathennal particlesarcaccelcmtcdto relativistic energies,call my problem theinjection, orseed, problem,Both of thesepmblcms must lx! addressedin order to understandfheorigin ofenergetic particles in cosmic sources.

    There is a greatdeal of work presentlyM.ng done In this atea, but it is spreadamongastrophysics,spacephysics,sohr physics, andcosmic rayphysics. Toprepare thistalk, 1sumeyed the literature for the years 1987 tirough 1989, and fount203 paperson the subject,distributed asshown in Table 1.TABLE I Distribution of literatureon pmticlc cncrgization, 1987-89,

    Astrophys. J. 70J. Geo hvs. Rcs.R 33sol. P ys, 13Astron, Astrophys. 8Phys. Fluiak 7Mon. Not. Roy. Astr. S(JC.Astrophys. Space Sci. ;Space ,fci. Rev. 5Sov. Astr. 5variousconfcnmt: ,YW:&i!iqg S y-)

    .,.uft, I}lvv II(V . (m,);rf. Inl *..... ?1

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    With so many people working in this area, publishing so many papcrx in somany different journals, there must be lots of ideas for the si~csM which particleacceleration occurs, Indeed this is true, as show-nin Table II. This table wasconstructed from theAstronomy and Astrophysics Abstracts. Tk p h r a s e p ~ r t i c ka c c e l e r a t i o n sa secondary keyword in that reference, but not aprimary keyword,which means you have to look under a large number of primary keywords to do anexhaustive search. The primary keywords usually (but not always) turn out to begeneric sites. This is merely an illustmivc list, showing that the general phenom-enon encompasses an extremely broad range of physical parameters.TABLE 11 IYimary kcywords inAstronomy and Astrophysics Abstracts,under which panicle accclcration is found m a secondary keyword.

    accretionactive galactic nucleiauroracblack holesclose binariescometary atmospherescometary comaecometscosmic raysCrab nebulaEarth magnetosphereEarth ionospheregeomagnetic tailinterplanetary plasmainterplanetary shock wavesjetsmagnetic flux tubesmolecular cloudsneutron stare

    planetary magnetospheresplasmapulsar magnetospherespulsarsquasarsradio galaxiesshock wavessolar atmospheresolar coronasolar cosmic rayssolar flaressolar magnetic fieldssolar particlessolar radio burstssolar windspiral galaxiessupenlova remnantssupernovae

    In addition itvariety of physical proccsscs arc considered important forparticle cncrgization, and while at some sites there maybe just onc that is dominant,in general many processes operiitc together.In this review I introduce the subject with some gcnmd remarks on poten-tials for cross-fertilization in this branch of physics (Section 2), then touch briefly onthe subject of power laws (Section 3), bci t addnxsing the general physics ofproccsscs by which charged palticlcs can gain energy (Section /1), IIISection 5, 1give Cxarnpics, with signpats to the rcccnt Iitcratum for details, In Section 6, Isuggest that solar flares make a gwd Iabomtory for the study of pitrticlc cncrgiza!.ion,since so many different proccsscs appear to be occurring in onc plGcc,and in Scc[iorl7 I give a list of possible sites and mcch,anisms for the production of the particlesresponsible for the continuum radio emission from spiriil galaxies, Finally, inSection 8 I offer suggestions as to profitable techniques for further study,

    2. PARTICLE ENER(;IZAI10N (; ENERAL REMARKS

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    nating, as there arqxxir to be u multitude of ways in which high-energy chargedparticics can arise in collisionless plasmas.The reason for this is that a collisionlcss plasma is a highly dynamic system,made up of electrons, ions, and clcctromagnctic liclds. An outside source of energymay couple most effectively with one of those components, crczting a nonequilib-num situation. In reapportioning the energy, the plasma makes use of a large numtwof instabilities, and often the saturation mode of one instability cm supply a source offme energy to drive another instability. The plasma then cascades via these instabili-ties from higher energy states to lower energy states. With each cascade, someenergy escapes the system in the form of electromagnetic radiation, and someescapes as high energy particles. Since the high energy particles are quickly lost,they constitute a very efficient way for the plasma to dump energy.While we do not yet understand in detail the processes by which energeticparticles an produced in collisionless plasmas, we have numcmus examples ofvery-well diagnosed systems in which this occurs. In fusion laboratories, confine-ment breakdown is often associated with bumts of energetic particles, at energiesmuch higher than the thermal energy. Runaway electrons in tokarnaks are a particu-lar example. Sce the review by Benz (1987) for an account of how runaway elec-trons arc produced, with rcfcrcnccs to both tokamaks and solar flares,In space, everywhere we look (comets, planetary magnetospheres, interplan-etary bow shocks, solar flares, etc.) we see energetic pafiiclcs, and we have data(microwaves, X-rays, in situ piuticle detectors, all with high time resolution) that cantell us something about tic processes that accelerate them.In astronomy, there is evidence for energeticparticles in many differentsources, in many different parts of the electromagnetic specuum. Inaddition, cosmicray detectors see energetic particles fmm distant sources directly,Thus particle acceleration is anarea that is ideal for cross-fertilizationbetween the various disciplines that usc plasma physics. Astronomers in particularcan benefit by using data from these other fields, even though the net result may tendto blur the usefulness of synchrotrons radiation as a diagnostic tool.Because of the division of research into particle acceleration along disciplin-ary lines, this area is made to seem esoteric, Each subdiscipline uses its ownparticular terminology and specialized techniques. It is therefore useful to reacquaintounsclves with the fundamental physics of particle acceleration and to adopt across-disciplinary, first-principles approach.

    3. POWER LAWSFirst it is in order to make some general remarks about power laws. since the outputof a particle acceleration calculation is often the index of a power law, which is thencompared with art obscwcd radio frequency spectrum,Fitstly, inferring a particle tmcrgy spectrum from an observed frequencyspectrum involves makmg some assumptions that may bc incomct. The often statedassumption, that [he magnetic field in the source is uniform and isotropic, is, ofcourse, a physical impossibility, Thc only possible uniform magnetic field is highlydirectional, Fields that vary in dimctioi~enough to bedescribedasisotropic will alsovary significantly in magnitude, WhCrI rcsscd on this point, a radio astronomer wiil[larify: the field may vary in strength, ut all the radiating particles arc in fickls ofdwut the same magnimdc, riindomiy oriented to the line of sight. This makes somephysic::! W?SC,iv thnt ch,w~cd particles tend m avoid places wh~rcth(; firld h high,hIIIII ignores [hc t[~clh:~tpl;~smasin highly dis[urbcd mgior]s 01qp:ILC(Iikc typi(:~1~ii(jtosour~u) i]!(it)(*vitL\!)!\vcrv l;Ir lmm(v!ltilihriurn i;wtic1~~~11p.]rll(lll:lr~lltil#J t !~di i ud Gicnisclvcs in high lwlds will mdiatc very cllccuv~i), while simli~i

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    particles in lower fields will not.I appeal to astronomers to consider other possibilities. The field in thesource is cerrainfy inhomogcncous in strength, Perhaps it has a power-law distribu-tion of magnetic field strengths. In that case, depending upon me accessibility ofenerge5c particles to the high-field regions, the output radio-frequency spectrumcould be a power law cvc ] if the energetic particle distribution is a delta function(Terry Whelan, private communication, 1985).Secondly, a power law has very little in the way of physical content. Theusual power law expn.xsion for a particle energy spectrum isNac E-y.This can also be written in the formdhL .-

    N Y~,

    o)

    (2)which simply relates the frictional loss in a population to the fractional gain inenergy by the remaining members of that population.An acceleration mechanism that satistics equation (2) is, for example, one inwhich the fractional gain in energy at each step is proportional to the energy theparticle already has, while the probability of escape at each step is independent ofenergy. It is relatively simple to concoct linear schemes that work, by makingsimplifying assumptions about conditions that we know little about. That is one wayto make progress, and diffusive shock acceleration theory (see below, Section 5,d) isan example of such a scheme, in which the power-law index y is simply related tothe shock compression ratio. A better way to study particle acceleration is to statfrom first principles, and then see what distributions we end up with.

    4. THE PHYSICS OF PARTICLE ENERGIZATIONa. The Lorentz forceNaturaUy any discussion of particle energiz,ation must begin with the 1,orentz forceon a particle of chargeq and velocity w:

    F=q(E+~x B). ( 3 )Some elementary observations follow imme&ately, in the case of static, uniformfields. Since the force of the magnetic field acts pctpcndicular to the particlesvelocity, it cannot by itself inc~ase tic particles energy. Clearly, a component of Eparallel to B yields a steady increase in the particles energy.If E is strictly perpendicular to B and IEI < IBI,it is possible to transform to aframe in which E is zero. The velocity of the transformation is the E x B drift speed,given IMOWin equation ( 11), Seen in the lab frame, the pvticles energy increasesduring half of its cyclotron period, and dccrea.scsduring meother half. Them is nonet energy gain, but the particle drifts in a direction pc~ndicular to both E and B. IfIEI> IBI, the drift speed is greater thanc. In that case a different transformation canbe made to a frame in which B is zero and the particle is acted upon by a purelyelectrostatic field am!,can thcrcforc gain energy,If the magnetic ticld is nonuniform, or there are other forces operating,particles can gain energy in even weak transvcmc electric fields. A gradient in B, forcxamnlc, will break the symmetry bctwccn the two halves of a cyclotron rotation,and tf~crciixc permit p~tti~iu accclnration in a transverse field. TIc p;miclc driftsithmg :!-,~,i~l.uicrittin~!icld (we Section 4,d).!{(:N.,,lf \V1*;~ilr~h!~lrw:I)I~10~{:~~l~r:lll:{~fli(;]csn ;islr~)ph~~l~ti~OnJKls,\tc lrlc:; : !.$ok [qr W;(YS 1:, i>r~}lio~~ [)iif;~ll~>l (.li~[ri~ fit:!~s i;; ~rc~ :,+110$ ~;i VCly ,~lii)r,gu iit)!wcmcIickh, UI~lrcumstanccs that allow acceleration in weak trimsvcr~ fields,

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    It is of coursewell known that large-scale. staticelectric fields cannot bemaintainedin space, becauseof tic existenceof highly mobile free chtugcs,.s0we look for waysof producingdynumic electric fields. Suchfields can be said to come in five catego-ries: indkctive, electrostatic, magnetohydrodynamic, electrodynurnic, and resis-tive. To seehow theyarisewc examine Maxwells equations andOhms law.b. Maxwells equationsMaxwells ccmationsfor theelect.mmagneticfield arc conventionally wnuen:aB -=c VXEat ( 4 )

    (5)V@ E=4Zp (6)VOB=() (n

    wherep andJ arc the local chargeandcurrent densities.An inducrive Clcctric field arises from a Limcdcpcndent magnetic field viaFaradayslaw, equation (4). This is what acceleratesparticles in laixxatory deviceslike betatrons. 11alsoworks in space,for particles diffusing into regionsof strongerfield, or particles in a fluid being compmsed. The inductive electric field is animpottant componentof Fermf acceleration, which isthe bestknown of the tradi-tional astrophysicalmechanismsfor particle aceelcradon (seeSection 5a).h efectmstatic electric field arisesfrom chargesepamtionthroughCou-lombs law, equation(6). Lnspace,suchfields m of small spatial scaleor of shortduration, but they do form, and can accelerateparticles. The usualsignatureofelectrostaticaccelerationis a very narrow spmmdn theenergyof theacceleratedparticles. Electrostaticfields can form where there isa shmpgradient in density, andan increasein temperaturein thedensermedium, The more mobile charge speciesrunsaheadinto the lowdensity medhtm, and actsup anelectric field. This occursinso/.arj7ares (Lin and Schwartz, 1987;Mamns, 1988; Smith and Orwig, 1988;Winglee, 1989), atsheds (Chiueh, 1988; Ohsawa andSakal, 1987; Ohsawa andSakai, 1988; Schwanz et al., 1988: Schwarw.eta!., 1987), in&uble layers(Borovsky, 1988), and in general in anyexpanding pfasma (Gislcr, 1989).c. ohms lawTo look at theother varieties of dynamic electric fields, wc alsoneedOhmslaw for a moving mediumwith conductivityu and fluid velocity v:

    J=~E+:xB). (8)In a fluid with infinite conductivity thisgives anclcctnc field

    F=- +xBo ( 9 )~s isequivalent to a Loremz transformationof a laboratory-frame II into E in tieframeof a moving fluid. UnLcr uniform conditions, this electric field can betransformeditway.However, if eitherB orv isnonuniform, asat a shock,there is notmiquetransformation10get rid of E. Thismagnetohydrodynurnfc flcld does no work on thePlukl. though it does wok on dccoupicd pardclc~, Since it is a munsww rlnctficMd. il &L~iCiMG pv?icics only wncncurnbincdwith ptiniclc drifts (see4,(1~Ifthr c(mducung tllclliun~ISn)[~ling, IIFC;In ~~~t~[i[)n(ii*h, J plimcls!wih)Spl lCLC 01 u .k b il (Ai .-M! :I [t .lir a UICIT IS v IIIII(JU(lWMjlUl iiiiiLiSR i:; &Ci IL L. -.i .f LIn this ca.sc,the field from equation (9) may he termed cfcctrodynurnic. in andogY

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    with clccmical gcnermmrs.Elcctrodynamic fields can produce very Iargc potentialdrops @ctwccn equator and pole, or between the outer and inner edgeof a disk),giving riseto vacuum fields with E parallel to Bin some regions. Such fields aredischargedby theproduction of intensebeamsof chargedparticles, but the condi-tions arcsuchthat they are quickly regenerated,since t-heenergy reservoirsarcvast.Parti:lcsin suchfields can gain large amountsof energy very uickly (Gisleret af.,198!; Lcinemann and l%iclheim, 1988: Mclia and Fatuzzo, 19 9; Sorrdl, 1987).With finite conductivity, Ohms law (equation 8) gives resistive ekcuicllelds with finite componentsparallel to B. Combining Ohms law with Amp&eslaw (equation5) and neglectingthe displacementcurrent~E@t givesE =-:x B+-&vx B. (lo)

    TIE parallel componentof E is thenthe right handsideprojected onto B, to whichonly the secondterm contributes.A rapid increasein msistivity due to a micminstability in a solarcoronal lcMpcan rapid]y producea strongparal.lclelectric field (Takakura, 1987). This M amanifestationof magnetic rceomection, where magnetic energy is converted intc thekinetic energyof field-aligned fastparticle beams. Magnetic reconnectionisextensive y sludicd in both solar flaresand planetary magnetospheres(Ambrosiano eruf. 1988; Mancns, 1988; Schindleret uf., 1988).Weakly ionized gaseslike molecular cloudsare resistive plasmas,since freeelectronsin suchgaseshave a low mean flee path for collisions with neutral atomsormolecules. It is thuspossiblein thesecloudsto produceresistiveelectric fields thatcan accelerate particles(~giel etd., 1987).Eleetmna.dc double layers (Borovsky, 1988) can also be viewed asmanifes-tationsof finite resistivity, althoughhemthe resistivity is due to plasmacollectiveeffects, and is temmdanomalous.

    d. Particle driftsAs mentioned above, a !ransverseelectric field canaccelerateparticleswhencom-W with a panicle drift in the samedirection. So here we write someof h drifbthat thargcd particlesare subjectto. These are all derived from the Lorentz fome byaveragingover the gyromotion, and they therefore provide no new information,1. E x B drift (same direction for both chargespecies):

    (Ex B)VEg=C . 2 (11)1!e include thisdrift for rcfcrcnceeven thoug it isnot useful for particle accelera-tion, since the drift is perpendicular to bothE and B. This drif?enables theconvec-tion of a neutral plasmaacrossamagnetic field, aslong as it hassufficient polariza-tion charge toproduceE. This equation is effectively the inverseof cquat.ion(9) fortie convective electric field.2. Grad-B drift (opposite directionsfor+ and - charges):

    v@B + A(Bx VB). ( 1 2 )1 ?his is the drift mostcommonly invo cd for tmnsverscacceleration.3. Curvature drill (opposite directiom~for + and - charges):

    (13)

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    In a time-stationary magnetic Iicld, bothK and~ arc invarian~ if the particlegyroradiusissmall comparedto tie lengrh over which the field changes. As themagneticfield seenby tie particle increases,# remainsconstantw v increases. To~ -OandeepK constant,v=decreases. If fhe minor issrrongenough,eventu yVX-thepanicle reflccrs. Clearly, W condition for the panicle to reflect is(rQ

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    tion of minors along a flux tubemoving in different directions, a particle willexpiencc more approaching enmunms thart receding ones, and the particle gainsenergyon average. This issecond-order, or stochastic Fermi acceleration fFermi,1949). If the mirrors converge, then all encountersam approaching,and this isjlrst-order Fermi acceleration (Femi, 1954).In either case,there is a firm limit to he process. Since the pitchanglealways decreaseswith increasingenergy, eventually the particle is boostedinto thelossconeof themimer and cannotbe acceleratedfur!~er without pitchangle scatter-ing. This limit is suchthatmost particlesdo not boost their energiesby factorsofmore than a few for a minor ratio of 4 (such aswould be found in a strongshock, forexample). Particleswith very high initial pitchzmglesare the bestcandidatesforstrongaccderatiomPerhapsthemost interestingresult of first-order Fermi acceleraticmin a trapis the division of the input distribution into fragments,according to the numberofparticle reflections. Since a particle is either reflected ~r not at a given encounter,dependingon ils pitchangle at minimum B, particles that arevery closeneighbors ininitial conditionscan becomewidely sepamtedin the output phasespace. This rigidsorting canproduceseveredistortionsin the output distribution fimction, andmaycontribute to the productionof a suprathenml tail, asstrewnin the next sectiomb. Results of first-order Fermi acceleration in a curved trap at a perpendicularshock.As an illustration of how test-pmicle calculations in collapsingmagnetic traps(asillustrated in the txeviowsSecxion)can ix armlied to Fermi acceleration.Gisler andlemons (1990) ~xamined the geometry sho-~ in Figure 3.

    Fig.advect into a quasipmpendicularshock, as in this cartoonof a bow shoesuccessionof rna~ctic traps is formed. The uaps arecurved, so that themimx velocities can becomearbitrarily high asrheUapsclose.

    I dc ,a

    The magnetic tmps fomnedunder thesecircumstance aresimilar to the caseillustrated in Figure 2, except that theminur speedsarenot constantin time, butreach arbitrarily high valuesasthe trap close. This gives a very strongdepmdenceon the t!!ehut mirror encounterexperienced by the particle, enhancing the rigidsating mentioned in the previousSection. Such a trap can beeffective at extractinga small number of particles out of anupstreamthenrtal distribution into a supratherma! ~nil(SCCFigure 4). 71-ICSCmathcnnal paniclc$ can be fi,r!!cr zcc~icra[cd hy a;crmi process only If lhcy undcr& piwhanplc sr;urcring tirs[. (% thcv m:ly kIl!flhcr ;Kxm:>xro!:dI)y o[hcr mc[.hnnisms

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    numbt r of particles

    100.

    10rd

    11.0E4 1.oE-3 1.OE-2 1.OE-1 1.OE+Okinetic energyfig. 4. The input pardclc disuibution to a curved tmp (filled circles) is aMaxwellian. The outputdistribution (open circles) is mildly heatedandgrossly distorted,with 5% of the particles in a non-MaxweUian suprathcnnaltail. The dashedline is a Maxwellian that has the sameenergymoment astheoutputdistribution.

    c. Drift accelerationDrift accelerationcan occur when a particle drift is in the samedireetion asaUansvcmeelectric Iicld. The bestknown example or rh.isis shock drift aecelemtion(Anagncstopouloser al., 1988; Burgess,1987; Chiuch, 1988; Chiueh, 1989; Decker,1988; Krauss-Varban and Wu, 1989), bul it can occur al other interfacesaswell.Egum 5 i!lustra[est.hcgeometry. -

    Fi

    d===- shock x ion drift 1direction VB5. Gcomcny of shockdnh accclcrtmonat a perpendicular shock.

    With B in the direction shown, the drift direction for posilivc ionsis inlo thepage, vhicl] i:; :Iic .wmcdirection asthecorncc[ivcclcwic field E. Both posilivc:al; ncg;uiw charge spccicsgain cticigy throughdrift tit th:s sil~~k Cinc? u13*vi:;Iwlsi!ivc torIx)ll), If 11is in lhc mllcr dirccli(ln. Ml] F. :IIId Y ;irc (IU1 01!11(p;lj:c. :u!diiytiin ltil[b~pi:cic:,g;lil] ~n~rgvfhcmaximum energygain Possihlc in shock drift accclcr~tion is rclalcd 10

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    thewansvcrscdimensionof the shock, The principal diffcrcncc belwccn shocksinthesolarsyslcmand shocksof interestm rixlio wonomcrs is Lhatthe Iaucr haveimmcn.sclygreaterscales. Hcncc astrophysicalshocksarc rcgmdcdM very promis-ing candidatesfor thesitesw which relativistic pm.iclcs am accclcratcd. Driftaccclcrauondoesnot occurm strictly parallel shocks,while Fermi accelerationcanoccural bolh pamllcl and pcrpcndicuku shocks. In gencml bm.htypesof accelerationshouldbe included.d. Acceleration at shocks: applicationsDiflwive shock acceleration (Bcrczinsky and Ptuskin, 1989; Ellison and Mdbius,1987: Jokipii, 1987: Kirk, 1988: Kirk and Schncidcr, 1987; Vdlk and Bicnnann,1988; Webb, 1987) isno[a scpara[cmechanismin its own ngh~ but a methodofcalculating firw-order Fermi accelerationat shocks. An extensive mvicw isgiven byBlandford and Eich.lcr( 1987). As tic namesuggests,it usesa dit thsion approxim-ation.In h...simplcslform, it works as follows. A delta function distribution ofcncrgctic particles is advcctcdinto a shock. The individual particle speedis muchgreater than theadvcctionspeed,but theparticles arcstatistically trappxt by scatter-ing off hydromagnc[ic waves in M flow. The velocity of the scatteringcentersisgrmcr upsmxtmthan downstreamof the shock,so there is a frame in which thescattcnngccmcrsme unifonnl y converging. The scatteringccntcrs arcassumedtoMeet the particles and scat[crtheir pitchanglcssothat the limit discussedalmve insection 4.a for ordimuy Fermi accelerationis held not to apply. Them is assumedtobe a finite probability for panicle escapeat eachcncoumcr, yielding thepower-lawdistribution asdiscussedin section 3.This mctttodhasbeen applied to theEarthsbow shock (many authors),supernovaremnantshocks(many authors), solar wind termination shocks(Pc@ietcrand Moraal, 1988), and galactic wind termination shocks(Jokipii and .MortlU, 1987).Ofpanicular intmcstm radio astnmomcrtrare interplanetary spiral shocks(@We,1989; Moussasetuf., 1987), where relativistic electrons up to 7 MeV have &en seen.It musthe noted that the diffision approximation breaksdown if the fluidspeedM comparableto theparticle speed(KinkandSchneider 1988), soitcannotbeusedfor accelerationof particles out of a tiennat distribution at moderateMachnumbers. It alsobmks down for finite amplitude perturbations in the field (Os-tmwski 1988),In addilion to first-order Fermi and drift accclcration, other mechanismsforacceleratingparticleshave beenconsideredto exist at shocks, One is thesecond-ordcr Fcnni prouss m the disturbed field oneither sideof a quasiparallcl shock,ordownstreamof a quasipcrpcndicularshock (Ellison and Jones, 1988; Dtige et d.,1987). Another is theelectrostaticheating of clcctronaby thecross-shock ptentird(EIlison and Jones, !988).e. Other roles for Fermi accelerationFirsl-order Fermi accdcration is not limited to shocks, It mcwrs in any convergingflow like accretion flows [Schncidcr and Bogdan, 1989; Webb and Bogdm, 1987;Katz andSmith 1988), or in collapsingmolecular clouds(Dogicl et uf , 1987;RichardsonandWolfcndalc, 198W, Second-order(or stochastic) Fermi accdcmtionis invoked in shciwIluws (WCbb, 1989), comets(Bartmsa, 1989; Gombosi, 1988;Gombosi et ul,, 19119),JCL%Eilck and Shore, 1989), and solar flares (StcinachcretU1,, 19WI;Smith and Brccht, 19119),for example,

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    and isheld in an accelerating Iicld associmcdwith tic wave. Rcsonam-panicleaccelcmtion hasrcccntly beenapplied to comets(Pncc and Lee, 1988), to the solarcommt (deLaBeaujardiLm and Zweibcl, 1989), and to solar flares (Miller andRamaty, 1989; Ohsawa andSakai, 1987; Ohsawa andSakai, 1988).

    LExotic processesmc cncrgcticparticlesmay beborn, notrnade, energetic. High energy gammarays interacting with intensemagnetic fields canspontarmusly generatepairsofenergetic psitrons and ckxrons in active galactic nuclei (Lightman and Zdziarski1987) or in pulsars(Sul.kancnandGislcr, in preparation). Vc~ high energy protonsgeneratedin active ga!acticnuclei canccdlidcinelastically with cold matter, produc-in$ gamma rdysthat can scatteroff other photonstomake uhrarelativistic e]cctrons(Slkoraet al., 1987: Sikora and Shlosman 1989: Stanevand Vankov 1989), orproducing high energyneutronsthat can tmvcl long distancesbefore they decayorcdidc inelastically, making tdghenergy electronsfar away fmm the primary energysource(Sikora et al., 19S9].

    & SOLAR FLARES: ,MICR&OSM.% R PARTICLE ACCELERATIONBccauscsomany of the mcchitnismstim cdn~dcmd for panicle accelerationin%strophysicsarc rcprcsentcd,al~ough at o Icr sca@in the solak3ystem, it isuseful for radio astronomersto acquaint thcm~vcswith solar physicsandspace~ys&6data. An cxcellcnt example is the solar hare, schematically illustrated in

    MHDShork

    Elrc

    Fig. (5. A cartoonof a solarflare cvcm. Scc tc~t for dcscriwiqr

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    from tic rcconncclionsite. on bm.hopen and closed field Iincs. Electrons in thedownward-propagating beamsradiatea burstof microwaves in theconstricting field,then a burstof X-rays asthey hit the denserplasma below. The heatedplasmaof thechromosphcrethenexpandsup the flux tubes,ciectrons first, creating an electrostaticfield that acceleratesionsupward. Theseaccelerated ions have an energy given bythe electrostaticptcntial, and hence ionsof diffcrcru massesmove M differentsgnxxis.Relative streamingbetween the different ion spccicsdrives an instability L h a td e c e l e r a t e sight ionsand acceleratesheavy ionsup to the initial speedsof the lightions. In this way, Ilarc-producedheavy ionsarc seenat energiesup to -1 Ml GeV.Fermi and drift accelerationoccur in tic shock that propagatesaway from themxxmnectionsite. This picture is gradual]y Iming picccd together (WingIec 1989;Benz, 1987; Benz andSmith, 1987; Smith and Brcch~ 1988; Stcinachererd., 1988;Miller and Ramaly 1989), with the help of high-resolution dataon the obsmables.7. PARTICLE ACCELERATION IN SPIRAL GALAXIEST& subjectof Ibis workshopbeing radio continuum emission from spiral galaxies, Inow attempt to list someof the sitesandmechanismsthat might beexpectedtocontribute10the populationofcncrgetic elccwonsin spiral arms (Table 11[). Them isno strongevidcncc that all these electrons come from a single source, and since all ofthe sites listed herecan bearguedaspossiblesites for accclcration, it is msonablc tosuppxe thatmany of thcmdo actually contribute in somemeasure.TABLE III Sites andmechanismsfor particle accelerationin spiral galaxies

    supernovaremnantshocks shock*neutronstarsutiaccs electrostatic,electrodynamicsneutmrtstarmagnetospheres electrodynamlc, reconnectioncloud mllisions shockcloud collapses Fermi, reconnection, shockdensitywaves Fermi, drift, mcmnectionaccretion Fermi, recmtncction,shockhot-star (O,B) winds rcconncction, shockstellar wind termination shocks shockStellar flares reconnection,electrostatic, shockgakt~c wind termination shock shockgalactlc l!ams rcwnncction, electrostatic,shock(shock ishcm an abbreviation for Fcnni, drift, electrostatic)

    I have put thesein somewhatarbitrary order, but influcm ed by Fig 1ofDUriC ( ]988) ] tCndCdto plaCCthe primary energetic ,sOurccs!tt.hctopof the ]is~going down to (mostly) maccclcration sites. The odcr is certainly arguable. Most.but nol all, of the sites arc associatedwith a youngstellar population and the encr-gctlc pitrticlcs resultingfrom thcm should thcrcforc reflect the diminution of starformation. All of the mechanismsshownhere arc opcrab]c to someextent in thesolarsystcm,wtd analysisof existing in situ d ata g re at] y cnhanccsour understandingdhow Ihcsc pnrxxww might rmc:m In Icmotc ~yslrms,

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    8. FUTURE DIRECTIONS IN PARTICLE ACCELERATI(lNWe know hat astrophysicalshocksarestrongly modified by tic prcscnccof cosmicrays,and that the diffusive approximation is not adequatefor the extraction problcm,or for shockswith substantialfield perturbations. Yc[ conventional diffusive shockaccclerat.ionm unmodified shocksis still widely used.We alsoknow that Lhccxuactkm of elcctmns from a thcnmd population is avastly different problcm from the cxwactionof ions. Yet theoriesdeveloped for oncam widely used to draw conclusionsaoout the other, or a simple proportionality}isassumed.Sowhat needs to be done? Mom explicit particle trajectoriesin moderatingfield configurations startingwith thcrmd particles. These shouldbc full orbitcalculations, andnot guiding-center approaches.so Umtthe breakingof adiabaticinvariantsand pitchanglcscatteringby steepfield gradients can bcobsmed. Beyondthahwe need self-consistent3D simulationsof shocks, trconncction events, plasmaexpansionsand collapses. These shouldb elcctmmagnctic, rchttivistic simulationswith particle ions and part.iclcelectrons.

    I wish to acknowledge helpful discussionswith Martin Sulkancn iind Ncb Dune.

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