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Waves, Fluctuations and Turbulence. General concept of waves Landau damping Alfven waves Wave energy Collisions and fluctuations. Definition. Any perturbation that propagates in plasmas. In general a wave is either damped or grow in time while it propagates

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waves fluctuations and turbulence
Waves, Fluctuations and Turbulence
  • General concept of waves
  • Landau damping
  • Alfven waves
  • Wave energy
  • Collisions and fluctuations
definition
Definition
  • Any perturbation that propagates in plasmas.
  • In general a wave is either damped or grow in time while it propagates
  • Certain dispersion relation is satisfied.
  • Coherent waves
  • Fluctuations
  • Disturbance induced by large scale motion
  • Weak turbulence
some conventional usage
Some Conventional Usage
  • In plan wave solutions we usually consider

with . (Landau prescription)

alfven and magnetosonic waves
Alfven and Magnetosonic Waves
  • Alfven waves
  • Magnetosonic waves
wave energy spectral density
Wave-energy spectral density
  • General expression
  • Unmagnetized plasma
wave energy spectral density1
Wave-energy spectral density
  • Alternative general expression
  • Spectral density associated with kinetic energy
three special wave modes
Three special wave modes
  • Alfven and magnetosonic wave
  • Langmuir wave
  • Physical implication is important.
in all three cases
In all three cases
  • Particle motion induced by a spectrum of turbulent waves can be stochastic, rather than fluid like.
  • The kinetic energy density is equal to the energy density of the wave field.
  • To the best of my knowledge no other wave mode has this special property.
general considerations
General Considerations
  • Traditional concept of “collision” is based on binary particle-particle interactions
  • The issue of Debye sphere
  • Physical picture of “collisions” is not very clear based on intuition.
balescu lenard collision integral
Balescu-Lenard Collision Integral
  • It was derived in 1960 independently by R. Balescu and A. Lenard.
vlasov equations
Vlasov Equations

Kinetic equation neglecting fluctuations

The neglected term is

klimontovich formalism
Klimontovich Formalism
  • According to Klimontovich (1967) the “collision integral” may be simply written as
implications
Implications
  • So-called “collisions” are closely related to the correlation function
  • For plasma that is unstable according to linearized Vlasov theory the fluctuations may be enhanced so that “collisions” become more important than we have assumed.
thermal fluctuations
Thermal Fluctuations
  • The physical origin
  • Spontaneous emission
  • Induced emission
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