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

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

6. Conventional Definition of Wave Vector x y z

7. General Dispersion Equation (cold)

8. Alfven and Magnetosonic Waves Alfven waves Magnetosonic waves

9. Conventional Definition of Wave Vector x y z

10. Wave-energy spectral density General expression Unmagnetized plasma

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

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

13. 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.

14. “Collisions” and Fluctuations

15. 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.

16. Landau’s Collision Integral (1937)

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

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

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

20. 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.

21. Thermal Fluctuations The physical origin Spontaneous emission Induced emission

22. Particles can emit waves via resonance