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FED3305 Magnetohydrodynamics, Advanced Course 6.0 credits

This is an advanced course in magnetohydrodynamics (MHD), with particular focus on fusion plasma physics.
The course covers:
• MHD spectrum and stability
• resistive MHD stability
• toroidal MHD equilibrium and stability
• linear and nonlinear toroidal MHD instabilities

Course offerings are missing for current or upcoming semesters.
Headings with content from the Course syllabus FED3305 (Spring 2019–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

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. 

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.

Literature and preparations

Specific prerequisites

No information inserted

Recommended prerequisites

No information inserted


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No information inserted

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

P, F


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

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Other requirements for final grade

Written exam and final oral exam.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted


Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

Main field of study

This course does not belong to any Main field of study.

Education cycle

Third cycle

Add-on studies

No information inserted


Jan Scheffel

Postgraduate course

Postgraduate courses at EECS/Fusion Plasma Physics