### Applicant

Prof. Dr. Eric Sonnendrücker

Numerische Methoden der Plasmaphysik (M16)

TU München

### Project Overview

Computational plasma physics plays a key role in the effort of the plasma physics community to design tokamak or stellarator devices for harnessing the energy released by nuclear fusion. Many of the computational models are extremely demanding, for instance due to the high dimensionality of the model, the multiscale nature of the underlying physics, or the complexity of the geometry. Therefore, plasma physics is a big consumer of computing resources which motivates the development of robust, flexible, and scalable numerical algorithms for the next generation of plasma physics codes. Models of various level of details are used in the community to understand different phenomena. The most comprehensive model that is still computationally feasible is a kinetic description of the plasma by a distribution function of each particle species in phase space. Kinetic effects play a fundamental role in the development of plasma turbulence and pure fluid models are therefore often insufficient. A kinetic description of plasma in its self-consistent and external electromagnetic fields is given by the Vlasov–Maxwell equations.

In magnetic confinement fusion, the plasma is confined by strong external magnetic fields and the particles perform a fast gyro-motion perpendicular to the field lines. In the gyrokinetic theory, this fast gyro-motion is systematically removed from the description of the dynamics, resulting in a transport equation in a phase space including three spatial dimensions, the velocity parallel to the external field as well as the magnetic moment.

It is our goal with this project to provide HPC implementations of new solvers for the kinetic Vlasov– Maxwell equations in the full six-dimensional phase space rather than the gyrokinetic equations underlying state-of-the-art plasma turbulence simulators. The interest in fully kinetic simulations is twofold: On the one hand, kinetic simulations are the only accurate model in regions where assumptions of the gyrokinetic model are not valid or at least questionable, like the edge and scrape-off layer region of fusion devices. On the other hand, the underlying modeling leading to the gyrokinetic equations is sophisticated and the structure of the resulting equations is more complicated than the pure kinetic equations. A numerical treatment of the multi-scale physics in magnetized plasmas can thus be an alternative way to design efficient algorithms and complement existing toolsets. These activities are embedded into the chair “Numerical Methods for Plasma Physics” at the department of mathematics and the division of “Numerical Methods in Plasma Physics” (NMPP) at the Max Planck Institute for Plasma Physics (IPP) that develop numerical algorithms and implementation models for plasma physics applications.