Physics of Tokamaks

Course guarantor:

Igor Jex

Lecturer:

Ondřej Ficker

Tutor:

Ondřej Ficker, Petr Mácha

Supervisor:

Department of Physics

Synopsis:

Advanced course on physics of thermonuclear fusion in the magnetic confinement of tokamaks. The course is focused on

the physics context, terminology and phenomenology of the subject so that students can substantially improve their understanding of physics background as well as their capacity to search for information and to work independently with scientific literature.

Requirements:

Requirements for successful completion:

Assessment:

1) maximum 2 absences from exercises (out of a total of 6-7 exercises), more only with a good reason/after agreement with the teacher

2) a short assessment test (a few simple examples) with the teacher of the exercises organized towards the end of the semester. At least 50% correct for awarding the assessment. One retake term organized if necessary.

Exam:

The student will be assigned two randomly selected topics from a total of 11 covering the content of the lecture. From these two, the student can choose „primary“ - the student will answer all sub-questions and additional questions with preparation, and „secondary“ - the student will answer at least half of the sub-questions on the topic of their own choice.

Syllabus of lectures:

1) Purpose and contents of the course. Magnetic fields in tokamaks.

2) Plasma equilibrium in tokamaks: derivation of the Grad-Shafranov equation

3) Plasma equilibrium in tokamaks: Solutions and interpretation

4) Shafranov shift, vertical field in the tokamak, magnetic islands

5) Electric fields and electric current in tokamaks, bootstrap current

6) Plasma radiation

7) Transport in tokamaks I : Classical and neoclassical diffusion

8)Transport in tokamaks II: Anomalous transport, scaling

9) Plasma heating and fuelling

10) Physics of the plasma edge, plasma-wall interaction

11) Tokamak instabilities I

12) Tokamak Instabilities II.

13) Present status of the research, the ITER project, participation of the Czech Republic

Syllabus of tutorials:

Calculations of examples on:

1)Purpose and contents of the course. Magnetic fields in tokamaks. Plasma equilibrium in tokamaks: Grad-Shafranov equation

2)Plasma equilibrium in tokamaks: Solutions and interpretation. Electric fields and electric current in tokamaks

3)Plasma radiation, Transport in tokamaks I : Neoclassical diffusion

4)Transport in tokamaks II: Empirical approach, Plasma heating and fuelling

5)Physics of the plasma edge. Plasma-wall interaction

6)Tokamak instabilities.

7)Plasma stability, operational diagrams, ITER

Study Objective:

Knowledge:

introducing in detail to physics of tokamak experiments

Skills:

the course will be focused on the physics context, terminology and phenomenology of the subject so that the participants can substantially improve their capacity to search for information and to work independently with scientific literature.

Study materials:

Key references:

[1] J Wesson, Tokamaks 4th ed., Oxford University Press 2011, chapters 11-13, ISBN: 9780199592234

[2] H. Zohm, Magnetohydrodynamic Stability of Tokamaks, Wiley 2014 ISBN 978-3-527-41232-7

Recommended references:

[3] J.P. Freidberg: Ideal Magnetohydrodynamics, Cambridge University Press, 2014

[4] C. Stangeby: The Plasma Boundary of Magnetic Fusion Devices, IOP Press, 2000 (úvodní kapitoly).

Note:

Time-table for winter semester 2025/2026:

Time-table is not available yet

Time-table for summer semester 2025/2026:

Time-table is not available yet

The course is a part of the following study plans: