Lecture13– Plasmaeffects
Date:16ththSeptember2019
Bhaswa<Bha=acharyya
ElectrodynamicsandRadia<veProcessesI
August-September2019
IUCAA-NCRAGraduateSchool
bhaswa<@ncra.<fr.res.in
Addi<onalRefThePhysicsofFluidsandPlasmabyArnabRaichoudhurih=ps://www.plasma-universe.com/
Mostofthebaryonicma=erintheuniverseisplasma.Magne<cfieldsplayvitalrolesinastrophysicalprocesses:starforma<on,thermalconduc<on,accre<on,turbulence,par<cleaccelera<on,dynamos,etc.Plasmaastrophysicsallowsthestudyofphenomenaatextremeregionsofparameterspacethatareinaccessibleinthelaboratory.
PlasmaEffects
VisibleUniverseis99.999%plasma.TheSunisabout100%plasma,asareallstars.Plasmamakesupnearly100%oftheinterplanetary,interstellarandintergalac<cmedium.TheEarth'sionosphereisplasma.
Standarddefini<onofPlasma
ü “Plasma”namedbyIrvingLangmuirin1920’sü Thestandarddefini<onofaplasmaisasthe4thstateofma=er
(solid,liquid,gas,plasma),wherethematerialhasbecomesohotthat(atleastsome)electronsarenolongerboundtoindividualnuclei.Thusaplasmaiselectricallyconduc<ng,andcanexhibitcollec<vedynamics.
Aplasmaisanionizedgas,orapar<ally-ionizedgas(quasi-neutral).
ü Eventhoughtheinterac<onbetweenanypairofpar<clesistypicallyweak,thecollec<veinterac<onsbetweenmanypar<clesisstrong.2examples:DebyeShielding&PlasmaOscilla<ons.
Refer:h=ps://www.plasma-universe.com/
TypesofPlasma
ThePlasmaUniverseisatermcoinedbyNobelLaureateHannesAlfvéntohighlighttheimportanceofplasmathroughouttheUniverse.
PlasmaEffects
Sofarwehaveassumedthatourpropaga<onmediumtobevacuum.Butradia<onpropagatethroughplasma.
Aplasmaisagasinwhichanimportantfrac<onoftheatomsisionized,sothattheelectronsandionsareseparatelyfree.Globallyneutral,ionizedgasiscalledplasma.
PlasmaEffects
Ø Becausesomeorallpar<clesareelectricallychargedandcapableofcrea<ngandinterac<ngwithelectromagne<cfields,manyphenomenanotpresentinordinaryfluidsandsolidscanbefoundinplasmas.
Ø Aplasmaisaconductorofelectricity,butavolumewithdimensionsgreater
thantheso-calledDebyelengthexhibitselectricallyneutralbehavior.Ø Atamicroscopiclevel,correspondingtodistancesshorterthantheDebye
length,thepar<clesofaplasmadonotexhibitcollec<vebehaviorbutinsteadreactindividuallytoadisturbance,forexample,anelectricfield.
Mostoftheobservablema=erintheUniversehasbeenintheplasmastate.Inthisstate,normalatomshavehadsomeoralloftheirelectronsrippedawaybecauseofintensehea<ngorcollisions.Onthelargestscales,ma=erisdominatedbygravity,butonsmallerscales,thosechargedionsinteractwitheachotherandwithelectricandmagne<cfieldstohelpcreatestructureandchannelmomentumandenergy.Plasmaastrophysicsaimstostudyandhelpunderstandhowplasmasbehaveinordertounderstandthedetailedbirth,evolu<on,anddeathofthewidevarietyofstructureswecanseeintheuniverse:fromstarsandplanetarysystems,togalaxiesandclustersofgalaxies.
PlasmaAstrophysics
Reference:h=p://www.bu.edu/csp/files/2014/08/Zweibel_BU_2014-v2.pdf
Dispersionincoldisotropicplasma
Foramediumwithdielectricconstantε
Dielectricconstantε
Plasmafrequency
Rela<onbetweenωandkarecalleddispersionrela<onConsiderplasmaofelectronswithdensityn
Plasmafrequencyforelectron
Dispersionrela<on
Dispersionrela<onAlltheinforma<onaboutthepropaga<onofagivenplasmawavemodeiscontainedintheappropriatedispersionrela<on,whichrelatestheangularfrequencywtothewavenumberk(magnitudeofthepropaga<onvectork).Someoftheimportantparametersreadilyseenfromthedispersionequa<onare:(i)Phasevelocity:v(ph)=w/k(ii)Groupvelocity:v(g)=dw/dk(iii)Propaga<onregionfrequencyrangewherethewaveisabletopropagate(iv)Reflec<onpoints:frequencyatwhichthepropaga<onregionislimitedbyinfinitephasevelocity(iv)Resonancepoints:frequencyatwhichenergycanbetransferredtoplasmapar<cles(zerophasevelocity,andinfinitegroupvelocity)(v)Wavegrowthordamping
Dispersionincoldisotropicplasma
Dispersionrela<onconnec<ngkandωcanbewri=enas
Whenω<ωpthewavenumberisimaginary
ωp:plasmacutofffrequencybelowwhichnoelectromagne<cpropaga<on.Example:Earth’sionospherepreventsradia<on<1MHzfrombeingobservedfromEarth’ssurface(correspondington~104cm-3)
plasmafrequency
Plasmafrequencycutoffhelpstoprobeionosphere.Electrondensitycanbedeterminedasafunc<onofheight.
Apulseofradia<oninanarrowrangeaboutωbedirectedstraightupwardfromEarthWhenthereisalayerwherenislargeenoughtomakeωp>ω,thepulsewillbetotallyreflectedfromlayer.Getinforma<onofheightfrom<medelayofpulseRepea<ngthesemeasurementsatmanydifferentfrequencieselectrondensityasafunc<onofheightcanbedetermined
FaradayRota<onAplanepolarizedwavewillnotkeepaconstantplaneofpolariza<on,butitsplanewillrotateasitpropagates.
Decomposi<onoflinearpolariza<onintorightandlescircularpolariza<on
Faradayrota<onoftheplaneofpolariza<on
ü Waves
ü Shocks
ü Instabili<es
ü Turbulence
ü Par<cleaccelera<on
ü Dynamo:Convertskine<cenergytomagne<cenergy
ü Reconnec<on:Convertsmagne<cenergytokine<c/thermalenergyandpar<cleenergiza<onaltersmagne<cfieldconnec<vity
Fundamentalprocessesinplasmaastrophysics
AboutFinalExam25thAugust(9AM-12PM)
Closedbook/notesCalculatorsallowed
Total:100marks
Objec<ve:20 Theory:20 Problem:60
Prac<ceproblemsdiscussedinLectures,Assignments,RybickiandLightmanandmore
Explainallthesymbolsyouuse.Completenumericalcalcula<ons.Writeneatly.
Request
Exampleques<onsFinalExam25thAugust(9AM-12PM)
Objec<veques<on(eachfor2marks,total20)
1)The Electric field of a moving charge “q”is composed of two terms. What are they and how do they depend on the distance to the charge?
2)WritedownexpressionforLorentztransformedspace-timefourvectorandcharge-currentfourvector.Howwillthelengthfourvectorsvarybetweeninertialframes.
Exampleques<onsFinalExam25thAugust(9AM-12PM)
Theoryques<on(eachfor6marks,total20)
When a charge is accelerated by the Coulomb force, its emission is called Bremsstrahlung. Draw the spectrum (specific intensity as a function of frequency), assuming that there is a frequency νa below which the medium is optically thick and that hνa << kT (T is the temperature of the medium). What will happen at hν ~ kT . Draw Bremsstrahlung spectra for two different temperature T1 and T2 with same number density. For what particular situation does the Bremsstrahlung spectrum become a Black Body spectrum? Mention two astrophysical situations where free-free emission is observed. Comment on the polarisation state of the overall emission in Bremsstrahlung process.
Exampleques<onsFinalExam25thAugust(9AM-12PM)
Problems(eachfor15marks,total60)
Similartotheproblemsfromyourassignments
EndofLectures