Young Researchers Workshop: Kinetic theory with applications in physical sciences

Numerical computation of the distribution function in a stellarator

Matt Landreman

University of Maryland

The stellarator, exemplified by the $1B W7-X experiment commencing operation this year, is a fusion energy concept in which a plasma is magnetically confined in nonaxisymmetric toroidal geometry. Kinetic effects and Fokker-Planck collisions are crucial in determining the self-generated plasma current and transport of particles and heat in these devices. We will discuss challenges and techniques for numerical computation of these kinetic effects. Challenges include high dimensionality and internal boundary layers in the distribution function. A pseudospectral method based on nonclassical orthogonal polynomials is very efficient for representing velocity space. The method also enables fully implicit treatment of the collision operator. With 5 coupled dimensions, the linear system representing the kinetic equation is relatively dense, and preconditioned iterative methods must be used. We demonstrate effective preconditioning by direct solution of a reduced 3D advection-dominated diffusion problem. These techniques enable us to accurately model many important physics properties of W7-X and other stellarators.