Formulation and verification of multiscale gyrokinetic simulation of kinetic-MHD processes in toroidal plasmas

TL;DR

The paper develops a comprehensive nonlinear electromagnetic gyrokinetic model in the global GTC code to simulate multiscale kinetic–MHD processes in toroidal plasmas. It introduces a unified electron dynamics framework based on solving the drift-kinetic electron equation with analytic/non-analytic separation, while retaining the equilibrium parallel current and compressible magnetic perturbations that drive current-driven instabilities. The model includes fluid–kinetic hybrid and conservative schemes for electrons, a reduction path to electrostatic and ultimately to ideal MHD in appropriate limits, and robust tools for constructing Boozer coordinates in realistic geometry. It validates kink-mode physics against DIII-D geometry, generates a large kink-mode database for surrogate modeling, and uncovers key parameters—such as the location of the $q=1$ surface and the poloidal/β profiles—that correlate with kink stability and growth rates, highlighting the framework’s potential for predictive, cross-scale plasma control.

Abstract

A comprehensive gyrokinetic simulation model has been implemented in the global toroidal gyrokinetic code (GTC) and verified for studying low-frequency waves and turbulence in magnetic fusion plasmas by treating all kinetic-MHD processes on an equal footing. A theoretical framework has been formulated to unify various methods for efficiently solving the electron drift kinetic equation in multiscale simulations by separating electron responses into analytic and non-analytic parts based on the smallness parameter of electron-to-ion mass ratio. The model can be reduced to the ideal MHD model with both the linear dispersion relation and the nonlinear ponderomotive force in theory and simulation. The model is used for the verification and validation of simulating internal kink modes in the DIII-D tokamak with accurate calculations of equilibrium parallel current and compressible magnetic perturbation. A large simulation database has been generated to train a surrogate model to predict the kink instability. Statistical analysis shows that the radial location of safety factor q=1 flux-surface and the plasma beta inside the q=1 surface are the most important parameters for predicting the kink instability.

Figures (7)

• Figure 1: Verification of two fluid model (TF) and single fluid (SF) model using gyrokinetic ion model with $T_i\approx0$
• Figure 2: $\hat{\delta}$ current. Normalized by $1/R_0$, where $R_0$ is the major radius.
• Figure 3: Parallel current term $\mu_0 J_{\parallel0}/B_0$. Normalized by $1/R_0$.
• Figure 4: Parallel current term from different methods implemented for Boozer coordinate (See Appendix \ref{['sec:Jpara']}). The reference value shown is calculated from $\nabla\times \mathbf{B}_0$ in cylindrical coordinates. The poloidal angle $\theta=0$. The value is normalized by $1/R_0$.
• Figure 5: Poloidal harmonics of $\delta B_\parallel$ and $\delta B_\perp$ for $n=1$ kink mode