Plasma Theory 2

Lecturer:

Petr Kulhánek (gar.)

Tutor:

Petr Kulhánek (gar.)

Supervisor:

Department of Physics

Synopsis:

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), magnetic field arrangement, solitons in plasma, and some typical plasma configurations.

Requirements:

Knowledge of basic course of physics

02TEF1,2 Theoretical physics 1,2

Syllabus of lectures:

1.Basics of the wave phenomena description. Angular frequency, wave vector. Dispersion relations, linearization of the equations, Fourier transform, nonlinear waves, soliton.

2.Plasma oscillations and waves. Dispersion relation derivation. Plasma oscillations of the electrons and ions. Plasma waves. Phenomena influencing plasma waves.

3.Low frequency wave complex, magnetoacoustic waves and individual modes. Magnetoacoustic wavefront shape and direction of individual vectors.

4.High frequency wave complex. X, O, R, and L waves. Whistlers. Resonant and cutoff frequencies. Permittivity tensor of electromagnetic waves propagating through plasma.

5.Electromagnetic waves absorption in plasma. Microwave heating of the plasma.

6.MHD plasma instabilities. Bunemann, Rayleigh-Taylor, Kelvin-Helmholtz, diocotron instabilities.

7.Instabilities of current filament and individual modes, plasma behavior on free and fixed boundary. Boundary conditions. Runkine-Hugoniot shock wave jump conditions.

8.Other instabilities. Interchange instability; drift instabilities, ion acoustic instabilities.

9.Magnetic field structures. Helicity, Beltram condition, turbulence, alpha effect, MHD dynamo.

10.Magnetic reconnection. Stationary and non-stationary reconnection. Resistive tearing modes. Fan, spine and separator reconnection.

11.Nonlinear and finite amplitude phenomena. Hartman solution, Landau damping and its importance. Rules for nonlinear terms manipulation.

12.Some soliton solutions. Langmuir soliton. KdV equation, Sacharov-Kuznetsov equations, NLS equation.

13.Quasiparticles, phonons, magnons, plasmons, excitons, polarons, polaritons, bound states.

14.Some typical plasma configurations. Plasma in the magnetic dipole and in the Earth magnetic field.. Pinch. Magnetic mirrors, tokamaks, stelarators.

Syllabus of tutorials:

Calculations of examples on:

basics of the wave phenomena description; plasma oscillations and waves. Dispersion relation derivation; low frequency wave complex; high frequency wave complex; electromagnetic waves absorption in plasma; MHD plasma instabilities; instabilities of current filament and individual modes, boundary conditions; magnetic field structures; magnetic reconnection; nonlinear and finite amplitude phenomena; some soliton solutions; quasiparticles; some typical plasma configurations

Study Objective:

Knowledge: basic wave phenomena will be introduced in the first part of the lecture

Skills: application of the above mentioned knowledge

Study materials:

Key references:

[1] Kulhánek P.: Theoretical physics - in czech: Teoretická fyzika (Teoretická mechanika, Statistická fyzika, Vlny a nestability v plazmatu). Studijní texty pro PhD studenty FEL ČVUT, 2004, http://www.aldebaran.cz/studium/tf.pdf

[2] J. P. Freidberg: Ideal Magnetohydrodynamics, Springer, 1987, ISBN: 0306425122.

Recommended references:

[3] T. H. Stix: Waves in Plasmas Springer, 2006, ISBN: 0883188597.

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: