ED3305 Magnetohydrodynamics, Advanced Course 6.0 credits

Magnetohydrodynamik, avancerad kurs

A deeper insight is here provided in MHD theory and MHD waves; confinement of plasmas in a three-dimensional magnetic field; effect of resistivity on the stability of plasmas; the appearance of weakly damped global Alfvén eigenmodes in inhomogeneous plasmas and the non-linear evolution of common MHD instabilities .

  • Education cycle

    Third cycle
  • Main field of study

  • Grading scale

    P, F

Course offerings

Autumn 18 for programme students

  • Periods

    Autumn 18 P2 (6.0 credits)

  • Application code


  • Start date


  • End date


  • Language of instruction


  • Campus

    KTH Campus

  • Tutoring time


  • Form of study


  • Number of places

    No limitation

Information for research students about course offerings

The course is given when there is sufficient demand. Please contact the examiner if you are interested in taking the course.

Intended learning outcomes

When completing the course, the student should be able to:
• describe the MHD spectrum and characterise the MHD waves in a cylinder and the basic modifications in a toroidal geometry
• describe the basic structure of magnetic field lines in a three dimensional geometry and magnetic confinement.
• describe the basic MHD instabilities and how they limit magnetic confinement
• describe how resistivity modifies the MHD theory and the implication on stability.
• describe the non-linear evolution of common MHD instabilities in plasmas.

Course main content

Individually adapted from the following areas:

The MHD spectrum in a cylinder; interpretation of the continua, global Alfvén and slow waves, condition for existence of discrete spectrum with cluster points (Suydam criterion and criterion for existence of global Alfvén eigenmodes). MHD stability of a cylindrical plasma. Structure of 3D magnetic fields; magnetic island and regions with ergodic field lines. Toroidal equilibria; the Grad-Shafranov equation. MHD stability of toroidal plasma; Mercier criterion and ballooning modes. Tearing modes. Alfvén eigenmodes in toroidal plasmas. Non-linear MHD; sawtooth, fishbones, disruptions.

In agreement with the examiner topics outside these areas can be included. 


Seminars or discussion meetings.



Lecture notes and articles adapted to individual needs.
R.B. White Theory of Toroidal Confined Plasmas 2001 imperial College Press
A. H. Boozer Physics of Magnetically Confined Plasmas, Reviews of Modern Physics,  Vol. 76, Oct 2004 p.1071-1140.
J. Wesson, Tokamaks, Clarendon Press, Oxford, 1997.
R. D Hazeltine and J. D. Meiss, Plasma Confinement, Dover Publication, INC. Mineola, New York 2003.


  • EXA1 - Examination, 6.0, grading scale: P, F

Requirements for final grade

Written exam and final oral exam.

Offered by

EECS/Fusion Plasma Physics


Jan Scheffel


Jan Scheffel <jan.scheffel@ee.kth.se>


Course syllabus valid from: Spring 2012.
Examination information valid from: Spring 2019.