• Svenska

# FED3230 Magnetohydrodynamics 8.0 credits

This is an introductory course to magnetohydrodynamics (MHD), an essential theory for modelling plasmas on earth and in space.
The course covers:
• theoretical basis
• properties of the MHD plasma
• MHD equilibrium
• stability and waves
• MHD in nature

Picture: Orszag-Tang vortex.

Course offerings are missing for current or upcoming semesters.
Headings with content from the Course syllabus FED3230 (Spring 2019–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

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.

### 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

## Literature and preparations

### Specific prerequisites

No information inserted

### Recommended prerequisites

No information inserted

### Equipment

No information inserted

### Literature

No information inserted

## Examination and completion

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

P, F

### Examination

• EXA1 - Examination, 8.0 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.

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.

### Main field of study

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

Third cycle