Plasma Waves and Instabilities

B232 - Summer 23/24

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XP02VNP

Plasma Waves and Instabilities - XP02VNP

Credits	4
Semesters	Winter
Completion	Assessment + Examination
Language of teaching	undefined
Extent of teaching	3P+1C

Annotation

Basic wave phenomena will be introduced in the first part of the lecture (dispersion relation, phase and group velocities, Fourier analysis). Fundamental plasma dispersion relations will be derived from the linearized MHD equations (magnetoacoustic waves - Alfven, F and S wave; electromagnetic waves in plasma - O, X, R, L wave, CMA diagram). The second part of the lecture will be devoted to final size waves, nonlinear phenomena (Landau damping) and solitons in plasma.

Study targets

Basics of plasma physics and linear wave theory.

Course outlines

1. Sound in hydrodynamics.
2. MHD equations.
3. Low frequency wave complex, megnetoacoustic waves
4. High frequency wave complex. Plasma oscillations and waves
5. Resonant and cutoff frequencies.
6. CMA diagram
7. Finit amplitude phenomena, Hartman solution.
8. Basic instabilities in plasma.
9. Instabilities of current filament.
10. Other instabilities
11. Magnetic reconnection, alpha effect.
12. Nonlinear phenomena
13. Landau damping
14. Solitons

Exercises outlines

dimensional analysis
linearization of equations
Fourier transformation
disperse relation
phase and group velocity calculation
cutoff and resonant frequency calculation
instabilities in dispersion relation
boundary condotions
KdV equation
nonlinear phenomena

Literature

1. P. Kulhánek: Úvod do teorie plazmatu; AGA 2011
2. P. Kulhánek: Vybrané kapitoly z teoretické fyziky, AGA 2017
3. P. Kulhánek: Teorie elektromagnetického pole, online www.aldebaran.cz/studium/elmg.pdf, 2020

Requirements

Theoretical Physics 1