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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. 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

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  1. Waves, Fluctuations and Turbulence • General concept of waves • Landau damping • Alfven waves • Wave energy • Collisions and fluctuations

  2. 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

  3. A Simple Explanation of Landau Damping • Considering

  4. Some Conventional Usage • In plan wave solutions we usually consider with . (Landau prescription)

  5. Conventional Definition of Wave Vector x z y

  6. General Dispersion Equation (cold)

  7. Alfven and Magnetosonic Waves • Alfven waves • Magnetosonic waves

  8. Conventional Definition of Wave Vector x z y

  9. Wave-energy spectral density • General expression • Unmagnetized plasma

  10. Wave-energy spectral density • Alternative general expression • Spectral density associated with kinetic energy

  11. Three special wave modes • Alfven and magnetosonic wave • Langmuir wave • Physical implication is important.

  12. 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.

  13. “Collisions” and Fluctuations

  14. 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.

  15. Landau’s Collision Integral (1937)

  16. Balescu-Lenard Collision Integral • It was derived in 1960 independently by R. Balescu and A. Lenard.

  17. Vlasov Equations Kinetic equation neglecting fluctuations The neglected term is

  18. Klimontovich Formalism • According to Klimontovich (1967) the “collision integral” may be simply written as

  19. 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.

  20. Thermal Fluctuations • The physical origin • Spontaneous emission • Induced emission

  21. Particles can emit waves via resonance

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