Computational plasma physics

The lecture will provide an introduction to scientific computing with application to plasma physics and magnetic fusion. We well introduce spectral (FFT based) numerical methods as well as Finite Differences and Finite Elements highlighting the essential concepts of consistency and stability. The classical kinetic and fluid descriptions of plasmas will be introduced and the numerical methods will be applied to the computation of MHD equilibria in a Tokamak with the Grad-Shafranov equation and then to the linear MHD stability problem. Finally an introduction to kinetic simulation based on spectral and PIC methods will be proposed and applied to the 1D Landau damping and bump-on-tail problems. An exercise class will be associated to the lecture where the methods introduced in the lecture will be coded in MATLAB.

Prerequisites are basic analysis and linear algebra. The lecture is accessible to students with a bachelor in mathematics, in physics or a related field.

News

Literature

• J.P. Freidberg, Plasma physics and fusion energy, Cambridge University Press (2007)
• R.D. Hazeltine, J.D. Meiss, Plasma Confinement, Courier Dover Publications (2003)
• R. Gruber and J. Rappaz Finite Element Methods in Linear Ideal Magnetohydrodynamics, Springer (2012)
• C.K. Birdsall and A.B. Langdon: Plasma Physics via Computer Simulation, Taylor & Francis (2005)

Lecturers

• Lectures: Prof. Dr. Eric Sonnendrücker. Monday 10:15-11:45 MI 03.08.011
• Exercises: Dr. Stefan Possanner. Monday 12:00-12:45 MI 03.04.011

Lecture notes

• lecture notes

Exercise sheets

• Exercise sheet 1 (April 9): 1D Poisson solver with finite differences
• Exercise sheet 2 (April 30): 1D-1V Vlasov-Poisson
• Exercise sheet 3 (May 28): 1D elliptic probelm with Galerkin FEM
• Notes on cardinal B-splines
• Exercise sheet 4 (June 25): Particle-in-cell discretization of Vlasov-Poisson

Examination

As a bonus mechanism in order to improve your grade at the final examination, an assessment of the programming exercises in MATLAB will be offered at the end of the course. In order to be able to participate in the programming assessment, active participation during the exercises is required since the assessment will be based on the code written in the exercise classes. Your result in the programming assessment will be one third of your final grade but only if it improves the grade.

-- StefanPossanner - 20 Mar 2018