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Introduction to Magneto Hydrodynamics: Ideal Plasma Effects

Module PH2037

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

Module version of WS 2010/1

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
WS 2022/3WS 2021/2WS 2019/20WS 2017/8WS 2016/7WS 2010/1

Basic Information

PH2037 is a semester module in German or English language at Master’s level which is offered in winter semester.

This module description is valid to SS 2016.

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

Total workloadContact hoursCredits (ECTS)
150 h 40 h 5 CP

Responsible coordinator of the module PH2037 in the version of WS 2010/1 was Klaus Hallatschek.

Content, Learning Outcome and Preconditions


Selected, accessible phenomena in fluid dynamics, magnetohydrodynamics and plasma physics are discussed. Applications include vortex rings, Van Allen Belts, plasma confinement in fusion, accretion disks of newborn solar system, galactic magnetic fields, belts and wind flow on Jupiter. Except for plasma and astrophysics interested listeners the lecture  should also be suited to consolidate and illustrate basic knowledge of fluid mechanics, electrodynamics, theoretical mechanics and classical thermodynamics. The lecture is thus the first part of an introduction to the theoretical plasma physics and presents the topics:

  • Vortex
  • dynamo effect
  • magnetic forces
  • magnetic levitation
  • plasma equilibrium
  • single particle picture / collective movement
  • instabilities
  • turbulence
  • 2D/3D turbulence
  • turbulent convection 
  • conservation laws
  • cascades
  • Zonal Flows

Learning Outcome

After successful completion of this module, the students are able to understand and to explain

  1. the magneto hydrodynamic (MHD) equations, the main consequences, and its scope of application
  2. the single particle movements the MHD equations are based on
  3. the conditions for stable magnetic equilibria plasmas 
  4. the MHD instability mechanisms
  5. conservation laws in different scenarios and the turbulence Richardson cascade 


No special knowledge exceeding the admissibility conditions for the master studies required.

Courses, Learning and Teaching Methods and Literature

Learning and Teaching Methods

Lecture, Transparencies, Blackboard presentation, Discussion, Exercises.


no info


  • F. F. Chen: "Introduction to Plasma Physics and Controlled Fusion", Plenum Press, NY 1984
  • R. J. Goldstone, P. H. Rutherford: "Introduction to Plasma Physics", IOP Publishing Ltd 1995
  • Wesson: "Tokamaks"
  • U. Frisch: "Turbulence''
  • Hazeltine, Waelbroeck: "The Framework of Plasma Physics"
  • Biskamp: "Nonlinear Magnetohydrodynamics''
  • Landau Lifshitz X: "Physical Kinetics''

Module Exam

Description of exams and course work

In an oral exam the learning outcome is tested using comprehension questions and sample problems.

In accordance with §12 (8) APSO the exam can be done as a written test. In this case the time duration is 60 minutes.

Exam Repetition

The exam may be repeated at the end of the semester. There is a possibility to take the exam in the following semester.

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