Plasma Theory 1

Lecturer:

Petr Kulhánek (guarantor)

Tutor:

Petr Kulhánek (guarantor)

Supervisor:

Department of Physics

Synopsis:

The first part of the lecture will be devoted to the theoretical plasma behavior description in statistical and MHD approaches. One and two fluid models will be discussed as well as the basic set of MHD equations in curvilinear coordinates. The second part of the lecture will be devoted to the individual particles motion, especially the drift theory, and radiation of the charged particles.

Requirements:

Knowledge of basic course of physics

02TEF1,2 Theoretical physics 1,2

Syllabus of lectures:

1.Many particle ensembles and statistical description. Liouvill theorem, potentials, canonical and grandcanonical partition function.

2.Harmonic oscillator, vibrational a rotational spectra of the molecules - illustration of the statistical approach.

3.Non-equilibrium statistics, Boltzmann equation and its variants (Fokker-Planck, Landau, Krook and Vlasov equations).

4.Boltzmann collision term and its behavior. Momentum equation, transition to continuum.

5.Magnetohydrodynamics. Momentum and energy tensor. Conservation laws of the particles + field system: charge, energy, momentum and angular momentum. Completion of the MHD set of equations.

6.One-fluid and two-fluid models. Diffused and frozen magnetic field lines. Ideal and resistive MHD. Relativistic MHD set of equations.

7.Curvilinear coordinates. Covariant a contravariant tensors, metric tensor, Christofell symbols.

8.Equations and operators in curvilinear coordinates. Spherical and toroidal coordinates. Illustration on MHD set of equations.

9.Transport phenomena. Diffusion, heat transport, entropy flux, entropy wave. Onsager reciprocity relations.

10.Charged particles motion, Lagrange function for the charged particle in electric and magnetic fields. Relativistic and non-relativistic variants.

11.Drift theory, basic drifts, motion in the magnetic dipole. Motion of charged particles in tokamak. Adiabatic invariants.

12.Multipole series for charged particles. Monopole, dipole and quadrupole moment.

13.Charged particles radiation. Retard and advanced potentials. Radiation terms in various approach.

14.Plasma radiation. Bremsstrahlung, synchrotron radiation, recombination spectrum. Radiation scattering on free electron and dust particles. Electromagnetic collapse driven by the radiation (Pease-Braginski solution).

Syllabus of tutorials:

Calculations of examples on:

many particle ensembles and statistical description; LHO, vibrational a rotational spectra of the molecules; non-equilibrium statistics, Boltzmann equation and its variants; magnetohydrodynamics; one-fluid and two-fluid models; curvilinear coordinates; equations and operators in curvilinear coordinates; transport phenomena; charged particles motion; Lagrange function for the charged particle in electric and magnetic fields; drift theory, basic drifts; multipole series for charged particles; charged particles radiation; plasma radiation

Study Objective:

Knowledge:

lecture will be devoted to the theoretical plasma behavior description in statistical and MHD approaches.

Skills:

application of the above mentioned knowledge

Study materials:

Key references:

[1] Kulhánek P.: Theoretical physics - in czech, Kulhánek P.: 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] D. R. Nicholson: Introduction to Plasma Theory, John Wiley and Sons Inc, ISBN: 047109045X

Recommended references:

[3] T. J. M. Boyd, J. J. Sanderson: The Physics of Plasmas, Cambridge University Press, 2003, ISBN: 0521459125.

Note:

Time-table for winter semester 2019/2020:

Time-table is not available yet

Time-table for summer semester 2019/2020:

Time-table is not available yet

The course is a part of the following study plans:

• Fyzika a technika termojaderné fúze (compulsory course of the specialization)