Semi-Implicit Methods for the GX Gyrokinetics Code

Gyrokinetics is one of the main models used for understanding turbulent transport in tokamak and stellarator plasmas that ultimately limit total fusion power output. Unfortunately, transport simulations are often limited by the large computational cost of gyrokinetic codes. Although the GX gyrokinetics code [1], [2] has demonstrated dramatic improvements in speed resulting from its GPU implementation and pseudo spectral representation in velocity space, it employs explicit time-integration schemes that suffer from a greatly reduced time-step when kinetically evolving both ions and electrons. In this work, we address the stiff electron terms in the gyrokinetic equation using third-order implicit-explicit additive Runge-Kutta methods from [3]. The ion and non-stiff electron terms are treated explicitly. These methods have the advantage of pairing the implicit advance with well-known explicit strong-stability preserving methods, ensuring high-order accuracy. Our scheme takes advantage of the sparsity of the GX equations, which allows us to efficiently invert the stiff electron terms at each implicit step using standard GPU CUDA linear algebra libraries. We demonstrate our new integration scheme for both linear (electrostatic and electromagnetic) and nonlinear (electrostatic) simulations in general toroidal geometry.

[1] N. R. Mandel et al., J. Plasma Phys 2018

[2] N.R Mandell et al., 2022

[3] S. Conde et al. J. Sci. Comp 2017