Continuum electromagnetic gyrokinetic simulations of turbulence in the tokamak scrape-off layer and laboratory devices

Abstract

We present algorithms and results from Gkeyll, a full-f continuum, electromagnetic gyrokinetic code, designed to study turbulence in the edge region of fusion devices. The edge is computationally very challenging, requiring robust algorithms that can handle large-amplitude fluctuations and stable interactions with plasma sheaths. We present an energy-conserving high-order discontinuous Galerkin scheme that solves gyrokinetic equations in Hamiltonian form. Efficiency is improved by a careful choice of basis functions and automatically generated computation kernels. Previous verification tests were performed in the straight-field-line large plasma device [Shi et al., J. Plasma Phys. 83, 905830304 (2017)] and the Texas Helimak, a simple magnetized torus [Bernard et al., Phys. Plasmas 26, 042301 (2019)], including the effect of end-plate biasing on turbulence. Results for the scrape-off layer for NSTX parameters with a model helical magnetic geometry with bad curvature have been obtained [Shi et al., Phys. Plasmas 26, 012307 (2019)]. In this paper, we present algorithms for the two formulations of electromagnetic gyrokinetics: the Hamiltonian and the symplectic. We describe each formulation and show results of benchmark tests. Although our scheme works for the Hamiltonian formulation, the presence of spurious numerical modes for high-β and large k⊥2ρs2 regimes shows that the symplectic formulation is more robust. We then review our recent algorithm for the symplectic formulation [Mandell et al., J. Plasma Phys. 86, 905860109 (2020)], along with example application of this new capability. Maintaining positivity of the distribution function can be challenging, and we describe a new and novel exponential recovery based algorithm to address this.

A gyrokinetic model for the plasma periphery of tokamak devices

“…2007; Cohen & Xu 2008; Ku, Chang & Diamond 2009; Shi, Hakim & Hammett 2015; Hakim et al. 2016; Pan, Told & Jenko 2016; Chang et al. 2017; Pan et al.…”

Kinetic modeling of neutral transport for a continuum gyrokinetic code

“…Thus, in this work we present a continuum kinetic model of neutral transport coupled to a continuum gyrokinetic solver within the computational plasma physics framework Gkeyll, 35 which has previously been used to model plasma turbulence on open field lines. 25,31,[36][37][38][39] The collisionless Vlasov solver in Gkeyll 40,41 facilitated the implementation of this model. A continuum kinetic neutral model avoids the statistical noise issues that are associated with MC codes and the shortcomings of fluid neutral transport models.…”

Drift reduced Landau fluid model for magnetized plasma turbulence simulations in BOUT++ framework

“…In recent years, a large effort has been devoted to tokamak edge modelling and significant progress has been made. Several fluid (e.g., GBS [2], TOKAM3X [3], GDB [4], GRILLIX [5]), gyro-fluid (e.g., GEMR [6] BOUT++-GLF [7]) and gyrokinetic (e.g., XGC [8], Gkeyll [9],COGENT [10]) codes have been developed to investigate different aspects of the plentiful edge related problems. However, the extremely demanding computational requirement of these high-fidelity multi-scale gyrokinetic models limits their applications in the routine global edge simulations.…”