space plasma physics an introduction

7/31/2019 Space Plasma Physics an Introduction

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Space Plasma Physics: An Introduction

Part I

Basic Theoretical Considerations



What we mean by “space” ?



Solar-Terrestrial Environment

• Earth’s ionosphere• Magnetosphere and bow shock

• Interplanetary space• Planetary magnetospheres

• Solar corona• Solar chromosphere and the low

corona



What is space physics

• Early definition

• Solar-terrestrial relation

• Space weather

• Space plasma physics



Why plasma physics is important inspace research ?



What is space plasma physics ?

It studies plasma processes commonly

occur in the solar-terrestrial space.



?



Introductory Remarks

• Space plasma physics covers much

broad parameter regimes than fusion

related plasma physics。

• Historically fusion research initiatedplasma physics which plays a key role

in space research now。

• The two fields are closely related and

can mutually benefit。



A good example is plasma heating

• In fusion research we try to find

method that can help us to achieve

high temperature plasmas withlaboratory experiments.

• In space plasma physics we try tounderstand the physical origin of the

hot solar corona.



Some Basic Parametersin Plasma Physics

• One is the ratio of plasma frequency toelectron gyro frequency

• The other is plasma beta

pe

e

ω

Ω

Thermal pressure

agnetic pressure

β =



In Space Plasma Physics

It is well known

2 2

10 5 10 pe

e

ω −

≤ ≤ ×Ω

310 10Thermal pressure

Magnetic pressure β − ≤ = ≤



From Theoretical Point of View

Space plasma physics is a challengingand exciting field



Space plasma physics involvingprocesses such as:

Collisionless shock waves

Magnetic field reconnectionOrigins of energetic particles

Production of exceedingly hot plasmasSource mechanisms of intense radiation



Difficulties

• On the theoretical sideBroad parameter regimes

Complicated processes

Unknown physical situations

• On the observational side

Experimental methods

Limitation of instruments



Methodology

• Fluid-dynamic description

• Kinetic-theory approach



Limitations of fluid approach

• Comparison between plasmas

with neutral gas• Non-equilibrium situations

• Wave-particle interactions



Kinetic Theory of Plasmas

• Statistic concepts

• Phase space density

• Velocity distribution functions

• Self-consistent fields

• Vlasov-Maxwell equations



Non-equilibrium States

• Energetic particle beams

• Thermal anisotropy

• Temperature and density gradients

• Two different temperature states

• Loss-cone distribution

• Cross-field current



Plasma turbulence and effects

• Heating and acceleration of particles

• Collisionless dissipation



Classification of Plasma Instabilities

• MHD Instabilities• Fluid instabilities

• Kinetic instabilities• Reactive instabilities

• Resistive instabilities



Distribution Function and Temperature

• In general a temperature may bedefined as

• F is the distribution function.

• The broader the distribution function,the higher the temperature.

2 3 31

2( , )T mv F d rd v= ∫ ∫ v r



Temperature

• If the system is not in thermal

equilibrium the temperature is calledkinetic temperature.

• The temperature is statisticallyrepresentative only for a system that

is in thermal equalibrium.



Vlasov Equations

It is a nonlinear equation. For practical

purpose, linearization is needed.

0

F F F e

t M

∂∂ ∂

+ ⋅ + ⋅ =∂ ∂ ∂

E

v r v

3

4 ne d vF π ∇⋅ = ∫E



Phase Space Continuity Equation'( ') '( ')

0

' ' ' ' ' '

F dF F d t F d t

dt t dt dt

∂∂ ∂= + ⋅ + ⋅ =

∂ ∂ ∂

r v

r v

''

'

d

dt

=r

v

'

'

d e

dt M

=v E

34 ne d vF π ∇ ⋅ =

∫E



In linearized Vlasov theories

• Particle orbits are not affected by theperturbation (or wave). It implies thatthermal energy density is much higher

than wave energy density.• In unmagnetized plasmas electrons and

ions are moving with constant velocities.

• In magnetized plasmas, particles are onlyinfluenced by the ambient magnetic field.



Landau Damping

• Historical development

• Landau prescription• Micro- or kinetic-instabilities



Conventional Method of Solution

,

( , , ) ( , ) i t i f t f e

ω

ω

ω − + ⋅= ∑ k r

k

k

r v v

( ),

( , ) i t it e

ω

ω

δ δ ω − + ⋅= ∑ k r

k

k

E r E

0( ) ( , ) 0k k

e F i f

δ ω ω

∂− − ⋅ + ⋅ =∂

Ev k v

v

3( ) 4 ( , )k k i ne d vf δ ω π ω ⋅ = ∫k E v



Vlasov’s Theory

0

( , ) ( )k

F ie

f m

δ

ω ω

∂

= ⋅− ⋅ ∂k

E

v v k v

1 1

r

d d P

ω ω − ⋅ − ⋅∫ ∫v v

k v k v

Vlasov suggested how to treat the following integral



Landau’s Prescription

0( , )( )

k

F ie f

m

δ ω

ω

∂= ⋅

− ⋅ ∂

kE

v

v k v

r iω ω = + 0γ →

1 1( )

r

P iπδ ω

ω ω

− − ⋅

− ⋅ − ⋅

k v

k v k v

Plemelj formula



Physical Significance of the Delta

Function Term

• It describes the contribution due to

wave-particle resonance。

• It has far-reaching effects on modernplasma physics。

• It leads to the discovery of kineticinstabilities。



Many Instabilities In Space Physics



Instabilities in Ionosphere

• Low frequency drift-wave instabilities

due to density gradient

• Mirror-drift instability

Instabilities in Magnetosphere



Instabilities in Magnetosphere

• Whistler instabilities in radiation belt

• Kelvin-Helmholtz instability at themagnetopause and tail region

• Tearing mode instabilities

• Lower hybrid drift instability in the tail

• Loss-cone instability in the cusp region

• Cyclotron-maser instabilities in the

auroral acceleration region



Instability in the magnetosheath

• Mirror-wave instability

• Ion cyclotron wave instability

• Magnetosonic and Alfven waves

excited by helium ions behind the

bow shock



Instabilities in the shock layer

• Electron cyclotron drift instability

• Modified two stream instability

• Cross-field stream instability

• Lower hybrid drift instability



Instabilities in the solar wind

• Firehose instability

• Instabilities due to nowborn ions

• Excitation of Langmuir waves bystreaming energetic electrons

• Excitation of low-frequency wavesby reflected ions



Instabilities in the corona

• Excitation of ULF waves by minorheavy ions

• Instabilities associated with hot minorions with a loss-cone distribution



Concluding Remarks

• Owing to the numerous instabilities in

various regions, plasma turbulence plays

important roles in space plasma physics.

• Studies of the nonlinear effects of these

waves have attracted much attention in

space plasma physics.

space plasma physics an introduction

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