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Space Plasma Physics: An Introduction
Part I
Basic Theoretical Considerations
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What we mean by “space” ?
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Solar-Terrestrial Environment
• Earth’s ionosphere• Magnetosphere and bow shock
• Interplanetary space• Planetary magnetospheres
• Solar corona• Solar chromosphere and the low
corona
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What is space physics
• Early definition
• Solar-terrestrial relation
• Space weather
• Space plasma physics
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Why plasma physics is important inspace research ?
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What is space plasma physics ?
It studies plasma processes commonly
occur in the solar-terrestrial space.
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?
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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。
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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.
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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 =
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In Space Plasma Physics
It is well known
2 2
10 5 10 pe
e
ω −
≤ ≤ ×Ω
310 10Thermal pressure
Magnetic pressure β − ≤ = ≤
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From Theoretical Point of View
Space plasma physics is a challengingand exciting field
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Space plasma physics involvingprocesses such as:
Collisionless shock waves
Magnetic field reconnectionOrigins of energetic particles
Production of exceedingly hot plasmasSource mechanisms of intense radiation
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Difficulties
• On the theoretical sideBroad parameter regimes
Complicated processes
Unknown physical situations
• On the observational side
Experimental methods
Limitation of instruments
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Methodology
• Fluid-dynamic description
• Kinetic-theory approach
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Limitations of fluid approach
• Comparison between plasmas
with neutral gas• Non-equilibrium situations
• Wave-particle interactions
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Kinetic Theory of Plasmas
• Statistic concepts
• Phase space density
• Velocity distribution functions
• Self-consistent fields
• Vlasov-Maxwell equations
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Non-equilibrium States
• Energetic particle beams
• Thermal anisotropy
• Temperature and density gradients
• Two different temperature states
• Loss-cone distribution
• Cross-field current
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Plasma turbulence and effects
• Heating and acceleration of particles
• Collisionless dissipation
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Classification of Plasma Instabilities
• MHD Instabilities• Fluid instabilities
• Kinetic instabilities• Reactive instabilities
• Resistive instabilities
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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
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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.
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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
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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
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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.
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Landau Damping
• Historical development
• Landau prescription• Micro- or kinetic-instabilities
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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
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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
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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
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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。
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Many Instabilities In Space Physics
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Instabilities in Ionosphere
• Low frequency drift-wave instabilities
due to density gradient
• Mirror-drift instability
Instabilities in Magnetosphere
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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
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Instability in the magnetosheath
• Mirror-wave instability
• Ion cyclotron wave instability
• Magnetosonic and Alfven waves
excited by helium ions behind the
bow shock
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Instabilities in the shock layer
• Electron cyclotron drift instability
• Modified two stream instability
• Cross-field stream instability
• Lower hybrid drift instability
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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
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Instabilities in the corona
• Excitation of ULF waves by minorheavy ions
• Instabilities associated with hot minorions with a loss-cone distribution
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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.