Plasma Theory 1
Code  Completion  Credits  Range  Language 

02TPLA1  Z,ZK  5  2+2  Czech 
 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.Nonequilibrium statistics, Boltzmann equation and its variants (FokkerPlanck, 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.Onefluid and twofluid 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 nonrelativistic 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 (PeaseBraginski solution).
 Syllabus of tutorials:

Calculations of examples on:
many particle ensembles and statistical description; LHO, vibrational a rotational spectra of the molecules; nonequilibrium statistics, Boltzmann equation and its variants; magnetohydrodynamics; onefluid and twofluid 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:
 Timetable for winter semester 2019/2020:
 Timetable is not available yet
 Timetable for summer semester 2019/2020:
 Timetable is not available yet
 The course is a part of the following study plans:

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