1. 6. Wave Phenomena 6.1 General Wave Properties(1) Following Schunk’s notation, we use index 1 to indicate the electric and magnetic wave fields, E 1 and B 1, and the plasma charge variations,  1c, caused by the waves.The direction of the propagating wave is given by the propagation constant K. To find the plasma waves we must solve Maxwell’s differential equations in the plasma environment.

2. 6.1 General Wave Properties(2) We solve Maxwell’s equations by taking the curl of (3):

3. 6.1 General Wave Properties(3)

4. 6.1 General Wave Properties(4) B E SkSk =0 in vacuum

5. 6.2 Plasma Dynamics(1) The propagation of waves in a plasma is governed by Maxwell’s equations and the transport equations. We assume that the 5-moment simplified continuity, momentum, and energy equations (5.22a-c) can describe the plasma dynamics in the presence of waves. If we neglect gravity and collisions these equations become (Euler equations):

6. 6.2 Plasma Dynamics (2)

7. 6.2 Plasma Dynamics (3)

8. 6.2 Plasma Dynamics (3a)

9. 6.2 Plasma Dynamics (4)

10. 6.2 Plasma Dynamics (4a)

11. 6.2 Plasma Dynamics (5)

12. 6.2 Plasma Dynamics (5a)

13. Electrostatic Waves: B 1 = 0 6.3 Electron Plasma Waves (1)

14. 6.3 Electron Plasma Waves (1a) (B 1 =0)

15. 6.3 Electron Plasma Waves (2) (B 1 =0)

16. 6.4 Ion-Acoustic Waves (1) (B 1 =0)

17. 6.4 Ion-Acoustic Waves (2) (B 1 =0)

18. 6.4 Ion-Acoustic Waves (2a) (B 1 =0)

19. 6.4 Ion-Acoustic Waves (2b) (B 1 =0)

20. 6.5 Upper Hybrid Oscillations

21. 6.6 Lower Hybrid Oscillations

22. 6.7 Ion-Cyclotron Waves

23. 6.8 Electromagnetic Waves in a Plasma (1) Now we consider the case where E 1 and B 1 are non-zero. We start with the general wave equation (6.20) assuming again a plane wave solution:

24. 6.8 Electromagnetic Waves in a Plasma (2)

25. 6.8 Electromagnetic Waves in a Plasma (2a)

26. 6.8 Electromagnetic Waves in a Plasma (3)

27. 6.8 Electromagnetic Waves in a Plasma (4)

28. 6.9 Ordinary and Extraordinary Waves (1) K BoBo

29. 6.9 Ordinary and Extraordinary Waves (2) We can use the following equations: K BoBo

30. 6.9 Ordinary and Extraordinary Waves (2a) K BoBo

31. 6.10 L and R Waves (1) z x y K B0B0 ELEL ERER

32. 6.10 L and R Waves (2) x y K B0B0 ELEL ERER

33. 6.11 Alfvén and Magnetosonic Waves Low frequency transverse (i.e. ) electromagnetic waves are called: Alfvén waves, if magnetosonic waves, if The dispersion relations are, respectively:

34. EM waves in arbitrary direction K B0B0 