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 memo Autumn 2021
Recent memos are listed on Course memo.
Course presentation
Headings denoted with an asterisk ( * ) is retrieved from the course syllabus version Spring 2019
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.
Detailed plan
| Learning activities | Content | Preparations |
|---|---|---|
| Discussion meeting 1 | Part 1 of literature | Study text, prepare 5 questions |
| Discussion meeting 2 | Part 2 of literature | Study text, prepare 5 questions |
| Discussion meeting 3 | Part 3 of literature | Study text, prepare 5 questions |
| Discussion meeting 4 | Part 4 of literature | Study text, prepare 5 questions |
| Oral presentation |
A 15 minutes presentation on any topic from the course contents. |
Preparations before course start
Literature
No information insertedSupport for students with disabilities
Students at KTH with a permanent disability can get support during studies from Funka:
Examination and completion
Grading scale
P, F
Examination
- 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.
The section below is not retrieved from the course syllabus:
Examination ( EXA1 )
Participation in discussion meetings.
Hand-in of assignment with questions relating to all four parts of the course.
Individual oral presentation on chosen subject.
Other requirements for final grade
Written exam and final oral exam.
Opportunity to complete the requirements via supplementary examination
Unsatisfactory assignment hand-in can be complemented.
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
No information inserted
Contacts
Round Facts
Start date
30 Aug 2021
Course offering
- Autumn 2021-51655
Language Of Instruction
English