Geometric Methods for Physics of Magnetized Plasmas

What it is about

You will learn to apply geometric methods (Hamiltonian and Lagrangian formalism) for the systematic reduction of complex multi-scale dynamical systems based on magnetized plasmas. You understand perturbative Lie-Transform methods, the derivation of field and kinetic equations from variational principles as well as the associated conservation laws; in addition you will see how continuous variational descriptions can be transferred to discrete formulations and implemented numerically, e.g. in Particle-In-Cell Monte-Carlo simulations.

What you will be able to do

• Knowledge of perturbative geometric methods for the dynamic reduction of multi-scale systems
• Mastery of variational calculations and Noether methods for deriving conservation laws
• Application of variational methods in continuous and discretized (Monte-Carlo/FEM) form
• Understanding the derivation of Ampère, Poisson and kinetic equations from variational principles
• Foundations for implementing discretized dynamic systems, e.g. in Particle-In-Cell simulations

What the module consists of

• VorlesungIntroduction of the relevant models and theoretical principles; development of illustrative examples
• ÜbungApplication of the methods to concrete examples and implementation in Python (two hours every two weeks)

Teaching method

• VorlesungConveying models and theory and working through examples
• Übungsstunden mit Implementierung in PythonPractical application of the methods to examples and implementation in code
• TafelarbeitPresentation and derivation of formulas and arguments