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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.

Module version of SS 2021 (current)

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
SS 2021SS 2020SS 2019SS 2018SS 2017SS 2016

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.

  • Specific catalogue of special courses for nuclear, particle, and astrophysics
  • Specific catalogue of special courses for Applied and Engineering Physics
  • Complementary catalogue of special courses for condensed matter physics
  • Complementary catalogue of special courses for Biophysics

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 30 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 module 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.
  • 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.

Regarding the spin-up of zonal flows the students are especially able to

  • 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.


No preconditions in addition to the requirements for the Master’s program in Physics.

Courses, Learning and Teaching Methods and Literature

Courses and Schedule

Learning and Teaching Methods

In the thematically structured lecture the learning content is presented. With cross references between different topics the universal concepts in physics are shown. In scientific discussions the students are involved to stimulate their analytic-physics intellectual power.

In exercises the learning content is deepened and exercised using problem examples and calculations. Thus the students are able to explain and apply the learned physics knowledge independently.

To motivate and for visualization demonstration experiments are shown.


Transparencies, black board work, exercises, question catalogue, movies, etc.


  • 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

There will be an oral exam of 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions and sample calculations.

For example an assignment in the exam might be:

  • Where do Jupiter’s stripes come from?
  • What is the relation between pressure and wind speed on Jupiter?
  • What is enstrophy?

In the exam no learning aids are permitted.

Exam Repetition

The exam may be repeated at the end of the semester.

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