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