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Explanatory Notes
Instructions
Web page:
www.aldebaran.cz/studium/tpla/
Anotation:
The first part of the lecture will be devoted to the individual particles motion in Lagrange and Hamilton formalism for both relativistic and non-relativistic behavior. The particle drifts will be solved in the frame of adiabatic approach. The second part of the lecture will be devoted to magnetohydrodynamics, especially such phenomena as helicity and helical structures, magnetic field-lines reconnection, MHD dynamo and others.
Study targets:
Honourable
Content:
Students will become familiar with plasma theory: charged particle motion, magntetohydrodynamics, waves and instabilities, and statistical description of the plasma.
Course outlines:
| 1. | | Charged particles motion, Lagrange function for the charged particle in electric and magnetic fields; |
| 2. | | Relativistic motion, relativistic Lagrange and Hamilton functions, electric field acceleration; |
| 3. | | Examples. Gyration, cyclotron frequency and Larmor radius, particle motion through the interface od two media; |
| 4. | | Adiabatic approach, gyration center equation, basic drift motion; |
| 5. | | Motion in magnetic dipole field, magnetic mirror, motion in tokamak vessel; |
| 6. | | Adiabatic invariants, first invariant and charged particle magnetic moment, second and third invariants, Fermi mechanism; |
| 7. | | Magnetohydrodynamics and its variants, one-fluid and multi-fluid models, minimal MHD variant; |
| 8. | | Frozen fields, magnetic field diffusion, Reynolds magnetic number; |
| 9. | | Simple MHD tasks: Hartmann solution, finite amplitude waves, Alfven velocity; |
| 10. | | Helicity, helicity conservation law, Beltrami field, helical structures in plasmas; |
| 11. | | Force-free configuration, helical pinch, reverse pinch, Bennett equilibrium; |
| 12. | | Magnetic field reconnection, Sweet-Parker model, Petschek model, 2D and 3D reconnection; |
| 13. | | MHD dynamo, alpha effect, omega effect, transformation of fluctuations into macroscopic magnetic field; |
| 14. | | Shock waves, double-layer, shock wave Rankin-Hugoniot conditions; |
Exercises outline:
corresponds with the outline of the lecture
Literature:
Key references:
| [1] | | Richard E. Fitzpatrick, Mitchel Goldman: Plasma Physics, An introduction; Taylor & Francis Inc 2014, |
ISBN: 9781466594265
Recommended references:
| [2] | | D.R.Nicholson:IntroductiontoPlasmaTheory,JohnWileyandSonsInc,1992 |
| [3] | | T. J. M. Boyd, J. J. Sanderson: The Physics of Plasmas, Cambridge University Press, 2003 |
Requirements:
Knowledge of basic course of physics
02TEF1,2 Theoretical physics 1,2
Keywords:
Plasma physics, Lagrange formulation, Hamilton formulation, magnetohydrodynamics, reconnection, helicity, MHD dynamo, shock wave, magnetic dipole, magnetic mirrors.
Subject is included into these academic programs:
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| Page updated 20.4.2024 11:50:56, semester: L/2023-4, Z/2024-5, Z/2023-4, Send comments about the content to the Administrators of the Academic Programs |
Proposal and Realization: I. Halaška (K336), J. Novák (K336) |