JD3300 Kinetic Plasma Theory 6.0 credits

Kinetisk plasmateori

With a foundation in particle distribution functions, the course provides the basic theory for equilibrium and dynamics of many-particle systems. Both kinetic gas theory and kinetic plasma theory are treated. Comparisons with fluid plasma models are made. Fundamental plasma phenomena where kinetic models are essential are studied.

  • Education cycle

    Third cycle
  • Main field of study

  • Grading scale

    P, F

Course offerings

Autumn 18 for programme students

  • Periods

    Autumn 18 P2 (6.0 credits)

  • Application code

    51758

  • Start date

    29/10/2018

  • End date

    14/01/2019

  • Language of instruction

    English

  • Campus

    KTH Campus

  • Tutoring time

    Daytime

  • Form of study

    Normal

  • Number of places

    No limitation

Information for research students about course offerings

The course is given every second year or more frequently when required.

Intended learning outcomes

When completing the course, the student should be able to

  • Derive the basic plasma kinetic equation from first principles
  • Discuss applications and validity of the Vlasov and Boltzmann equations
  • Describe and explain Landau damping and the two-stream instability
  • Describe basic kinetic properties of hot magnetised plasmas
  • Derive and explain the Fokker-Planck equation
  • Describe basic relaxation processes and collision times
  • Distinguish between fully kinetic, drift kinetic, hybrid and gyrofluid models

Course main content

Liouvilles theorem. BBGKY hierarchy. Vlasov and Boltzmann equations. Plasma dispersion function. Landau damping. The bump-on-tail instability. Criteria of Nyquist and Penrose. Bernstein modes. The Fokker-Planck equation. Relaxation times. Resistivity. Chapman and Enskog expansions. Drift-kinetic model. Gyrokinetic model. Gyrofluid model. Vlasov-Fluid hybrid model. Two-stream instability. Inverse Landau damping. Collisionless drift waves. Electron and ion temperature gradient instabilities. Loss-cone instability.

Disposition

Students and teacher meet for four course sessions. These two hour-sessions start with a short introductory lecture by the teacher on the corresponding part of the course. Remaining time is used for discussion on topics that the students bring up. The students should, before each course meeting, study the literature and bring five relevant questions for group discussion.

At the end of the course the student should complete a home assignment in the form of written answers to a set of detailed questions on each part of the course. Having done this satisfactorily, the student should pass an oral exam related to the written assignment.

Eligibility

Master in Electrical Engineering or Engineering Physics or similar.

Recommended prerequisites

Master in Electrical Engineering or Engineering Physics or similar.    

Literature

Selected pages from the following books (for details see separate ”Contents” document):

• T. J. M. Boyd and J. J. Sanderson, The Physics of Plasmas, Cambridge University Press, 2007.

• F. Chen, Plasma Physics and Controlled Fusion, Plenum Press, 1985.

• R. O. Dendy, Plasma Dynamics, Clarendon Press, 1994.

• R. J. Goldston and P. H. Rutherford, Introduction to Plasma Physics, IOP Publishing Ltd, 1995.

• P. Helander and D. J. Sigmar, Collisional Transport in Magnetized Plasmas, Cambridge University Press, 2002.

• S. Ichimaru, Statistical Plasma Physics, Volume I: Basic principles, Westview Press, 2004.

• D. G. Swanson, Plasma Kinetic Theory, CRC Press, 2008.

• W. Stacey, Fusion Plasma Physics, Wiley, 2012.

• J. Wesson, Tokamaks, Clarendon Press, Oxford, 1997.

 Journal articles on topics not covered in books will be added.

Examination

  • EXA1 - Examination, 6.0, grading scale: P, F

Requirements for final grade

Participation in group discussions, completion of home assignments and oral exam.

Offered by

EECS/Fusion Plasma Physics

Contact

Jan Scheffel

Examiner

Jan Scheffel <jan.scheffel@ee.kth.se>

Supplementary information

Course main content: 

Liouvilles theorem. BBGKY hierarchy. Vlasov and Boltzmann equations. Plasma dispersion function. Landau damping. The bump-on-tail instability. Criteria of Nyquist and Penrose. Bernstein modes. The Fokker-Planck equation. Relaxation times. Resistivity. Chapman and Enskog expansions. Drift-kinetic model. Gyrokinetic model. Gyrofluid model. Vlasov-Fluid hybrid model. Two-stream instability. Inverse Landau damping. Collisionless drift waves. Electron and ion temperature gradient instabilities. Loss-cone instability.

Learning outcomes:

When completing the course, the student should be able to

  • Derive the basic plasma kinetic equation from first principles
  • Discuss applications and validity of the Vlasov and Boltzmann equations
  • Describe and explain Landau damping and the two-stream instability
  • Describe basic kinetic properties of hot magnetised plasmas
  • Derive and explain the Fokker-Planck equation
  • Describe basic relaxation processes and collision times
  • Distinguish between fully kinetic, drift kinetic, hybrid and gyrofluid models

Version

Course syllabus valid from: Autumn 2018.
Examination information valid from: Spring 2019.