Semi-Implicit Gyrokinetic Ion–Fluid Electron Simulations of Tokamak Edge Plasmas with the COGENT Code

We report on the development of implicit numerical capabilities that enable hybrid kinetic ion–fluid electron simulations of cross-separatrix edge plasma transport using the continuum gyrokinetic code COGENT. Implicit time integration for the low-dimensional electron fluid system allows stepping over fast electron time scales, achieving significant speed-up over fully kinetic models. While ion parallel transit and collisional time scales must be retained for accurate modeling of 5D ion-scale turbulence, axisymmetric (4D) simulations that primarily focus on quasi-stationary transport can further benefit from stepping over these time scales. To that end, our recent studies have focused on developing implicit capabilities for solving the axisymmetric full-F gyrokinetic Vlasov equation for the ion species coupled to the nonlinear Fokker–Planck operator. To facilitate implicit simulations, advanced preconditioning of individual physics operators has been developed, and a global multi-physics preconditioner is constructed by adapting an operator-splitting methodology. Notably, the preconditioning of the gyrokinetic Vlasov operator is enhanced by using algebraic multigrid solvers based on the recently developed Approximate Ideal Restriction approach. Significant speed-up is demonstrated in both 4D and 5D edge plasma simulations of the DIII-D and LTX-beta tokamak systems, including studies of main ion and impurity species transport.