1. Chapter 4 Waves in Plasmas 4.1 Representation of Waves 4.2 Group velocity 4.3 Plasma Oscillations 4.4 Electron Plasma Waves 4.5 Sound Waves 4.6 Ion Waves 4.7 Validity of the Plasma Approximation 4.8 Comparison of Ion and Electron Waves 4.9 Electrostatic Electron Oscillations Perpendicular to

2. 4.10 Electrostatic Ion Waves Perpendicular to 4.11 The Lower Hybrid Frequency : 4.12 Electromagnetic Waves with 4.13 Experimental Applications of the EM waves in plasmas 4.14 Electromagnetic Waves Perpendicular to ; 4.15 Cutoffs and Resonances 4.16 Electromagnetic Waves Parallel to 4.17 Experimental Consequences of EM Waves in Magnetized Plasma 4.18 Hydromagnetic (low-frequency ion) waves along ; T=0

3. 4.19 Magnetosonic (low-frequency ion) waves across ; T=0 4.20 Summary of elementary plasma waves 4.21 The CMA diagram

4. 4.1 Representation of Waves density in Cartesian coordinates. in 1D, The density of the sinusoidal oscillation to be measured is phase

5. in x coordinate 4.1(2) one moves with the phase At an observation phase

6. In a media, there may be many waves and each has it own phase, that is, 4.1(3) real in general complex Why use complex amplitude? Where is complex function.

7. 4.2 Group velocity For Beating

8. 4.2(2) < C

9. 4.2(3) Dominated by

10. 4.3 Plasma Oscillations neutral + + + + shifted causes the plasma oscillating with the plasma frequency. conditions B = 0 uniform and infinite plasma KT = 0 (cold plasma, p = 0) ion fixed 1 D in

11. 4.3(2) so, 1 D electrostatic oscillation functions to be found: egs :

12. 4.3(3) Perturbation theory, linearization 1st order 2nd order differential eq. zero order: 0

13. 4.3(4) algebraic eqs. 0

14. 4.3(4) plasma frequency.

15. 4.4 Electron Plasma Waves Conditions:

16. 4.4(2)

17. 4.4(3)

18. 4.5 Sound waves In ordinary air, the Navier-Stokes e.q. the equation of continuity (two eqs for two variable: and ) For a stationary equilibrium with and, the first order parts of the above eqs in Fourier transformed form are

19. 4.5(2) Sound speed in a neutral gas The waves are pressure waves propagating by collision.

20. 4.6 Ion waves In plasma, there is no ordinary sound waves because of the absence of collisions. The perturbation on ions can propagate through electric field. ion fluid equation :

21. 4.6(2) the balance of forces on electron requires ion equation of continuity ion acoustic wave

22. 4.7 Validity of the plasma approximation The approximation was used while is finite. The error is going to be evaluated.

23. 4.7(2)

24. 4.8 Comparison of Ion and Electron Waves

25. 4.8(2)

26. 4.9 Electrostatic Electron Oscillation Perpendicular to (nonrelativistic) terminology: perpendicular parallel mixed mode transverse, electromagnetic longitudinal, electrostatic

27. 4.9(2) For a longitudinal waves, the governing e.q.s for the motion of electron and the waves are

28. 4.9(3)

29. 4.9(4) upper hybrid frequency electron orbitPlanes of constant density

30. 4.9(5)

31. 4.10 Electrostatic Ion Waves Perpendicular to (almost)

32. 4.10(2) the dispersion relation for electrostatic ion cyclotron waves

33. 4.11 The Lower Hybrid Frequency:

34. 4.11(2) lower hybrid frequency 2 pi ceci 2 LH 1e1i 111,nnofinsteadusedwas.qes'PoissonIf      

35. 4.12 Electromagnetic Waves with Light waves in vacuum 0 1 2 2 1

36. 4.12(2)

37. In a plasma with 4.12(3) for 0 1 3 3

38. 4.12(4) Self - consistent 4

39. 4.12(5) cutoff condition skin depth

40. 4.13 Experimental Applications of the EM waves in plasmas Measurement of plasma density with the cutoff phenomenon by applying waves of varying frequency. Microwave measurement of plasma density by the cutoff of the transmitted signal. plasma

41. Microwave interferometer for plasma density measurement index of refraction 4.13(2) A microwave interferometer for plasma density measurement.

42. 4.13(3) The observed signal from interferometer (right) as plasma density is increased, and the corresponding wave patterns in the plasma (left).

43. plasma lens for EM waves 4.13(4) A plasma lens has unusual optical properties, since the index of refraction is less than unity. A plasma confined in a long, linear, solenoid will trap the laser light used to heat it only if the plasma has a density minimum on axis. The vacuum chamber has been omitted for clarity.

44. 4.13(5) the effect of plasma on radio communications. plasma induced by friction that causes a plasma cutoff for a communication blackout. ionosphere Exaggerated view of the earth’s ionosphere, illustrating the effect of plasma on radio communications.