Numerical Algorithms for Solving the Gyrokinetic Equation for Plasma Turbulence

Emily Belli

Astrophysical Sciences, Program in Plasma Physics, Princeton University

In this talk, I will describe various numerical methods and computational tricks that have been used to solve the 5-D integro-differential nonlinear gyrokinetic equation. The gyrokinetic equation is the fundamental equation describing drift-like microinstability-driven turbulence in magnetized plasmas. Presently, gyrokinetic simulations of plasma turbulence and transport are one of the primary tools used by physicists to design the next generation of experimental nuclear fusion devices with optimal neoclassical confinement and stability properties. However, solving the full nonlinear, electromagnetic, multiple-species gyrokinetic equation in realistic geometry can be computationally intensive, requiring hundreds of hours of computing time on massively parallel machines. Thus, all numerical schemes must be designed to optimize accuracy and efficiency for rapid convergence with grid refinement.

This talk will focus on various schemes for continuum or Eulerian gyrokinetic solvers, as opposed to particle-in-cell types of algorithms. I will also discuss a unique fast approximate iterative implicit method which we are developing based on analytic physics-based Pade approximations of species-dependent response functions. This method would eliminate the long time needed to set-up implicit arrays, yet still have the same larger time-step advantages of an implicit method over the traditional explicit Runge-Kutta and Adams-Bashforth methods.