Oxford Master Course in Mathematical and Theoretical Physics
Centre for Postgraduate Training in Plasma Physics and High Energy Density Science

  Lecturer: Felix I. Parra
Teaching Assistant: Michael Hardman

This is an MMathPhys course which we expect to be of interest to graduate students specialising in the physics (or applied mathematics) of gases and plasmas, and astrophysics.

Trinity Term 2017
Fisher Room (Denys Wilkinson Building)
Mondays 14:00-16:00 weekly
Seminar Room (Denys Wilkinson Building)
Tue 24 April and Tue 1 May 16:30-17:30


Time and place TBD

Course materials, reading suggestions, scheduling notices,
problem sets to appear below shortly.

Syllabus currently given below is subject to revision.

This is a new course, with a new set of notes and problems. There will be typos,
muddy points... Any feedback is welcome!

Lecture I (Mon 23-April-18) Boltzmann collision operator. Coulomb collisions.

Lecture II (Tue 24-April-18) Fokker-Planck collision operator.

Lecture III (Mon 30-April-18) Conservation properties and H-theorem of the Fokker-Planck collision operator. Electron-ion collisions.

Lecture IV (Tue 1-May-18) Effect on ions of electron-ion collisions. Linearized collision operator.

Lecture V (Mon 7-May-18) Properties of the linearized collision operator. Spitzer-Harm problem.

Notes about the Fokker-Planck collision operator
1. Fokker-Planck collision operator
2. Collisions between electrons and ions
3. The linearized Fokker-Planck collision operator and the Spitzer-Harm problem
Lecture VI (Mon 14-May-18) Derivation of plasma fluid equations.

Lecture VII (Mon 21-May-18) Derivation of Braginskii closure for electrons.

Notes about Braginskii equations
Braginskii fluid equations
Lecture VIII (Mon 28-May-18) Braginskii closure for ions. MHD and resistive MHD.

Lecture IX (Mon 4-June-18) Resistive tearing modes.

Notes about resistive MHD
Resistive MHD, reconnection and resistive tearing modes
TOKAMAK PHYSICS> Lecture X (Mon 11-June-18) Introduction to tokamaks. Pfirsch-Schlueter transport for electrons.
Notes about tokamak physics
Pfirsch-Schlueter transport for electrons
Problem Set I (Due Tue 15-May-18)
Problem Set II (Due Tue 12-June-18)


  1. P. Helander & D. J. Sigmar, Collisional Transport in Magnetized Plasmas (Cambridge University Press 2002) (Amazon)
  2. R. D. Hazeltine & F. L. Waelbroeck, The Framework of Plasma Physics (Westview Press 2004) (Amazon)
  3. R. D. Hazeltine & J. D. Meiss, Plasma Confinement (Dover Publications 2003) (Amazon)
  4. R. Fitzpatrick, Plasma Physics: An Introduction (CRC Press 2014) (Amazon)
  5. R. J. Goldston & P. H. Rutherford, Introduction to Plasma Physics (CRC Press 1995) (Amazon)