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.
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.
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.
Content and learning outcomes
Course contents
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
Recommended prerequisites
Equipment
Literature
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
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.
Other requirements for final grade
Final oral exam.
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
Examiner
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.