Noether theorem for magnetised plasmas.
Hamiltonian systems, from topology to applications through analysis I October 08, 2018 - October 12, 2018
Location: MSRI: Simons Auditorium
How the fundamental mathematical tools such as Noether's Theorem can be implemented for practical purposes, such as control of quality of prediction of fusion plasmas discharges? In this talk I will try to respond on this intricate question. Below are some motivations. In fusion plasmas the strong magnetic field allows the fast gyro motion to be systematically removed from the description of the dynamics, resulting in a considerable model simplification and gain of computational time. The dynamically reduced kinetic model obtained in the given setup is called gyrokinetic model. Performing dynamical reduction in the framework of Lagrangian formalism allows one to control the exactness of reduction procedure and derive robust models for numerical implementations. In their turn, specific results of gyrokinetic (GK) simulations performed prior to consideralby costly fusion plasma experiments allows to predict and optimise experimental setup. In particular, numerical simulations of fusion plasma discharges can impact our predictions of the plasma behavior in ITER and future fusion reactors. Confidence in these predictions requires a rigorous and systematic verification of the underlying model, which should be regarded as an indispensable step before any validation of the numerical results against experiments can be considered meaningful. A new and generic theoretical framework and specific numerical applications to test the validity and the domain of applicability of existing GK codes will be presented. In particular the role of the energy invariants issued from the Noether theorem will be explicitly highlighted throughout the analysis of energy balance and generic plasma instabilities mechanisms providing the ultimate connection between the fundamental mathematical tools and practical implementations.