Non-neutralPlasmaShock

工HUXiwei（胡希偉）

HEYong（何勇）

Hu

Yemin（胡業(yè)民）HuazhongUniversityofScienceandTechonology2006.10.25ZhejiangUniversity,Hangzhou,China

1OutlineIntroductionMotivationOnedimensionalcaseTwodimensionalcase(withmagneticfieldproducedbyshockcurrent)Theelectrostaticinstabilitiesonthenon-neutralshockfront2Introduction

to

non-neutralplasmashock3Plasmashock

Plasmashockcanarise:whenafluidvelocityislargerthantheionsoundvelocity(withoutmagneticfield)ortheAlfvenvelocity(withmagneticfield).A

steadyshock(orshockfront,shockprofile)istheresultofabalancebetweencompressiveanddissipativeeffects.4Front,UpstreamandDownstreamShockfront(orshockprofile):asteadywave-front,propagatingatsupersonicspeedthroughtheundisturbedfluid.Upstream⑴:theunshocked(undisturbed)fluidbeforetheshockfrontDownstream⑵:theshockedfluid(disturbed)behindthefrontfront5TheneutralplasmashockInmostcases,wedescribetheplasmashockwiththesingle(neutral)fluidormagnetohydrodynamic(MHD)equations.Sotheplasmashockisneutralessentially.Inneutralplasmashocktheremaybeplasmacurrentandmagneticfield,butthereisnot

chargeseparationandelectrostaticfield.6ElectricfieldinthefrontTheionfluidelementswillrunaheadoftheelectronfluidelementsduetoitslargerinertial.Thiscausesachargeseparation,thenaelectrostaticfieldEandapotentialdifference

Δφbetweentheup-anddownstream.7Effectsofelectricfieldinfront(I)TheelectricfieldEwillholdbacktheionfluidelementsanddrawtheelectronfluidelements.Thiseffectissimilartheroleofdissipationintheformationofsteadyshock(shockfrontorprofile).So,theEcouldplayveryimportantroleintheformationofplasmashockprofile,especiallythecollisionless(non-dissipative)shockprofile.8Effectsofelectricfieldinfront(II)ThepotentialdifferenceΔφ

willmodifythejump(discontinuity)relations–thesocalledHugoniotrelations

andthecriticalMachnumberMc(theleastvelocityforshockemergency).TheelectricfieldwilldriveanewkindofelectrostaticinstabilityintheshockfrontastheroleofdensitygradientintheRayleigh-Taylorinstability.9MotivationInoursimulationfortheimplodingshockinasinglesonoluminescingbubble,wefoundthatthereisaextremestrongelectrostaticfieldintheshockfront.Theelectricfieldiscausedbythechargeseparation.Thechargeseparationisduetothedifferenceofelectronfluidandvariousionfluidvelocities.10

ProfilesofthechargenumberdensityΔn,electricfield

E,andelectriccurrentdensity

J

stridingontheshockfrontatthemomentneartheemergenceofthemaximumelectricfield.1112ElectricfieldinstronglaserandinimplodingshockPlasmaproducedbyextreme-shortpulselaserImplodingshockfrontinSBSLE(V/m)5×10112×1010Δt

(s)10-1210-11Δr(m)10-610-8ne(cm-3)10211022PolarizationElectromagneticElectrostatic13OnedimensionalcasePlasmashockcarrieslowcurrent.Theeffectsofmagneticfieldproducedbytheshockcurrentcanbeneglected.14Staticcoupledequations

inareferenceframeonthefront

whereistheequivalentheatflowThedoublefluidequationsandPoissonequation15Profiles:━M1=1.6

┉M1=1.516Jumpconditionsacrosstheshock

Particlefluxes

Momentumfluxes

Energyfluxes

Where17CriticalupstreamMachnumber

When

,fromwecanobtaintheminimumupstreamvelocityforthenon-neutralshockemergencyZ1234M1min1.4141.73222.23618TwodimensionalcaseCylindricalNon-NeutralPlasmaShockwithCurrent,ElectricandmagneticField.Thecurrentandelectricfieldisinaxial(z)direction.Themagneticfieldproducedbytheshockcurrentisinpoloidal

(θ)direction.19Basicsteadyequationsforshockfront20Jumpconditions

ofparticle,momentum

inr

and

z

direction,and

energy

fluxes21Profilesofvelocityandtemperature22Downstreamprofiles

━2Dcase,

┉1Dcase23Shockcurrentchangesthe

24Summary(I)Thejumpconditionsacrosstheshockwillbechangedthattheparticlefluxandenergyfluxarenolongerconservative.Theprofilesofplasmaparametersindownstreamarenolongerassameastheprofilesinupstream.25Summary(II)ThecriticalMachnumber(theminimumupstreamvelocityforthenon-neutralshockemergency)islargerthanitsvalue(1.0)inneutralshock.WhenJ0=0,Thepositiveshockcurrent(fromup-todown-stream)willreducethe,andthenegativecurrentwillincreasethe.26Electrostaticinstabilities

inshockfront

(1Dcase)27Thelinearinstabilityanalysisx--thedirectionoftheshockpropagating,y–thedirectionperpendiculartoshockpropagating.28AExample

Dispersionrelationabout

kx

Disturbanceisinthedirectionofx

–theshockpropagatingdirection29labeledx=0.1,0.3,0.5,0.7,0.9

asNo.1,No.3,No.5,No.7,No.9Profilesofequilibriumparameters30ThenumericalresultsThehighfrequency()approximationvs.lowfrequency()approximation.Withelectricfield(E≠0)vs.E=0.Withdissipation–viscousandfriction--(α≠0

)vs.α=0.Adiabaticprocessapproximationvs.diabatic(energyequation)case.31Thehighfrequencyapproximation

32333435Adiabaticvs.Diabatic(E≠0)

36SummaryTheE

candrivetheelectrostaticinstabilityintheshockfrontinbothparallel(kx)