Applied Plasma Physics: Large Vortices (Zonal Flows and Other Structures) in Fusion Reactors, Jupiter, Climate and Astrophysics

Module PH2233

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.

Basic Information

PH2233 is a semester module in English or German language at Master’s level which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

  • General catalogue of special courses
  • Specific catalogue of special courses for Applied and Engineering Physics
  • Specific catalogue of special courses for nuclear, particle, and astrophysics

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 50 h 5 CP

Responsible coordinator of the module PH2233 is Klaus Hallatschek.

Content, Learning Outcome and Preconditions


The module discusses structure formation in turbulence systems on the basis of the example of the zonal flows.

The strong temperature contrast between fusion plasmas and the environment drives convective turbulent vortices. At first hard to explain and different from everyday experience, these eddies interact and create flows spanning the whole plasma, so called "zonal flows". These flows in turn are a vital factor reigning in the convective heat losses, thereby aiding to approach the ignition condition for a reactor. This occurs, e.g., in the "low/high-confinement" transition in all current fusion experiments, and is an essential requirement for ITER, the first device which will meet the ignition condition. The zonal flows are currently a topic of intense research and a promising possibility to make it easier to fulfill the partially contradictory requirements for a working fusion device.

Zonal flows also are responsible for the cloud bands on the large gas planets, occur on the newly discovered exoplanets (presumably), as well as in many cases of atmospheric turbulence on earth. They are presently strongly researched for their influence on the atmospheric heat transport.

Starting with the plasma zonal flows, the lecture delivers the equipment for their description and the application of the plasma physical know-how to a geo- and astro-physics context.

Learning Outcome

After successful completion of this module, the student is able to

  • describe current experimental methods and results on the zonal flows and other phenomena of self organization in plasma and astro-physical systems.
  • understand and describe the fundamental magnetohydrodynamic, drift- and gyro-kinetic equations for the description of turbulence and zonal flows in magnetized high-temperature plasmas.
  • derive and describe the anelastic equations for the turbulence in rotating planetary and stellar atmospheres
  • describe the different types of global flows in fusion plasmas and planetary/stellar atmospheres, and characterize their various properties
  • regarding the spin-up of zonal flows:
    • derive the conserved quantities in two- and three-dimensional hydrodynamic and magneto-hydrodynamic turbulence
    • apply the principle of the cascades and the various conserved quantities to arrive at predictions on the collective phenomena
    • explain the fundamental waves in the above systems as well as their influence on momentum and energy transport
  • derive examples for the main variants of convective turbulence (e.g., drift waves, Rayleigh-Taylor instabilities, Rossby waves) in the treated systems, and estimate their influence on the formation of zonal flows.
  • understand methods and problems of the computer simulation of the discussed systems.


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Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

Lecture using blackboard and transparencies, demonstration experiments, exercises.


Transparencies in the web.


  • R.J. Goldston, P.H. Rutherford, "Introduction to Plasma Physics", IOP Publishing Ltd 1995
  • J. Wesson, "Tokamaks", Oxford University Press 2011
  • U. Frisch, "Turbulence", Cambridge University Press 1996
  • Hazeltine, Waelbroeck, "The Framework of Plasma Physics", Westview Press 2004
  • D. Biskamp, "Magnetohydrodynamic Turbulence", Cambridge University Press 2008
  • F.F. Chen, "Introduction to Plasma Physics and Controlled Fusion", Springer 2016
  • A. Majda, "Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows", Cambridge University Press 2006
  • Applied Plasma Physics: Large Vortices, (Zonal Flows and Other Structures) in Fusion Reactors, Jupiter, Climate and Astrophysics

Module Exam

Description of exams and course work

In a written exam of 60 minutes the learning outcome is tested using comprehension questions and sample problems.

In accordance with §12 (8) APSO the exam can be done as an oral exam. In this case the time duration is 25 minutes.

Exam Repetition

There is a possibility to take the exam at the end of the semester.

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