# ED3230 Magnetohydrodynamics8.0 credits

## Magnetohydrodynamik

In this course, the theoretical basis for and regime of validity of ideal and resistive magnetohydrodynamics (MHD) is presented. The student should be able to account for the theory for plasma equilibrium, MHD waves, stability, energy methods and MHD phenomena in nature.

Third cycle

P, F

## 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

• Provide the details of the derivation of ideal and resistive MHD equations
• Describe and explain the domains of validity of one-fluid MHD
• Demonstrate the basic properties of ideal MHD
• Give detailed examples of MHD equilibria and their properties
• Discuss MHD waves
• Derive the Energy principle
• Apply the Energy principle to the Rayleigh-Taylor instability

Characteristics of a fluid. Derivation of the fluid equations from Boltzmann’s equation. The equations of continuity, momentum and energy transport. Ideal and resistive MHD. Ohm’s law. The Lundquist number. Simplifications and domains of validity. Conservation laws. Fluid drifts. Magnetic pressure. Boundary conditions. The virial theorem. Shear and magnetic well. Equilibrium in cylinder geometry. Flux and surface quantities. Pinches. The reversed-field pinch. Toroidicity, the Grad-Shafranov equation. Resistive diffusion. MHD waves and spectra. Stabilising and destabilising forces. Nondimensionalisation of equations. Linearisation. Normal modes. Eigenvalue problems in MHD. The energy principle. Rayleigh-Taylor instability. Resistive instabilities. The magnetosphere. MHD processes in the Sun.

## Disposition

Discussion meetings.

## Literature

Parts of the following, or similar, literature:

D. Schnack, University of Wisconsin,Lecture notes,

J. P. Freidberg,Ideal Magnetohydrodynamics, Plenum Press, New York (1987).

J. P. Freidberg,Plasma Physics and Fusion Energy, Cambridge University Press 2007.

## Examination

• EXA1 - Examination, 8.0, grading scale: P, F

Final oral exam.

## Offered by

EECS/Fusion Plasma Physics

Jan Scheffel

## Examiner

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

## Version

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