2. Physics of Space Plasma

2.PhysicsofSpacePlasma

LetUniformB,E=0,Binthezdirection

2.2 SINGLE-PARTICLE MOTION

Gyrofrequency,cyclotronfrequency

Gyroradius,cyclotronradius,Larmor radius

ExB driftNocurrent

Externalforce driftCurrent

GradientBdrift

Thefirstadiabaticinvariant

Themirrorpoint

Thethirdadiabaticinvariant

ThesecondadiabaticinvariantThefirstadiabaticinvariant

The total magnetic flux Φ enclosed by a drift surface is the third adiabatic invariant

• Characteristicsofplasma:Quasineutrality,collectivebehavior,goodconductor.

• Phasespace:3Ddisplacement+3Dvelocity• Thephase-spacedensityfunctionf(r,v,t)isalsocalledthesingle-particledistributionfunction.

• Volume=dv dr =dvx dvy dvz dxdy dz• Thedifferentialphase-spacevolume=f(r,v,t)dv dr

2.3 COLLECTIONS OF PARTICLES

Thezerothmomentofthedistribution

Thefirstmomentofthedistribution

Theaveragekineticenergyperparticleofstypeinaunitvolumeoftheplasma

Thehydrostaticpartialpressure

whereN isthenumberofindependentcomponentsofvelocity,Ps isinPascale(Pa),1Pa=1N/m2.

V t

IdealGasLaw:P=nKT

Forthesysteminequilibrium

Maxwellian distribution

V t

ForUs=0

2.4 THE PASMA STATE

DebyeShieldingPlasma Density

ne(m-3)Electron temperatureT(K)

Magnetic fieldB(T)

Debye lengthλD(m)

Gas discharge 1016 104 -- 10−4

Tokamak 1020 108 10 10−4

Ionosphere 1012 103 10−5 10−3

Magnetosphere 107 107 10−8 102

Solar core 1032 107 -- 10−11

Solar wind 106 105 10−9 10

Interstellar medium 105 104 10−10 10

Intergalactic medium

1 106 -- 105

Source:Chapter19:TheParticleKineticsofPlasmahttp://www.pma.caltech.edu/Courses/ph136/yr2002/

Spacecraft (satellite) potential

ND>1=>g<<<1(hightemperature,lowdensity)

characteristictime,characteristiclength,collisionfrequency,meanfreepath,gyrofrequency,gyroradius,plasmafrequency,Debyelength

Fp =9000N1/2,plasmafrequencyFp inHz,electrondensityNin#/cm3

Plasmafrequency

0eexnE e=

Gyro-motion

Gyro-radius

Gyro-frequency

Meanfreepath

http://abyss.uoregon.edu/

l>>rH (ν<<ω),Collisionlessplasmal<<rH (ν>>ω),Collisionplasma

Scaleheight

Height

Density,N

A

B

在溫度相同時，物種A的質量___物種B的質量

在質量相同時，物種A的溫度___物種B的溫度

在電漿中，同時考慮電子與質子兩種不同的物質

經過簡化後可得到標尺高為：

2.4 THE FLUID DESCRIPTION OF A PLASMA

Hydrodynamicsvs.Magnetohydrodynamics (MHD)Individualparticlemotionsvs.Propertiesofacollectionofmanyparticles

Frozen-influx

Frozeninmagneticfield

òò ×= sdB !!fMagneticflux

[ ]òò òòòòòòòòD

×+×´´Ñ=D

×+׶¶

=×=dtsdBsdBu

dtsdBsd

tBsdB

dtd

dtd )()()( !!!!!

!!!!

!!f

[ ] 0)()()()( =´×+×´=D

×+×´´Ñ= òòòò òò lduBldBudtsdBsdBu

dtd !!!!!!

!!!!!f

0=dtdf

Solarwind