Full ff and δf\delta f gyrokinetic particle simulations of Alfv\'en waves and energetic particle physics

In this work, we focus on the development of the particle-in-cell scheme and the application to the studies of Alfv\'en waves and energetic particle physics in tokamak plasmas. The $\delta f$ and full $f$ schemes are formulated on the same footing adopting mixed variables and the pullback scheme for electromagnetic problems. The TRIMEG-GKX code [Lu et al. J. Comput. Phys. 440 (2021) 110384] has been upgraded using cubic spline finite elements and full $f$ and $\delta f$ schemes. The EP-driven TAE has been simulated for the ITPA-TAE case featured by a small electron skin depth $\sim 1.18\times10^{-3}\;{\rm m}$, which is a challenging parameter regime of electromagnetic simulations, especially for the full $f$ model. The simulation results using the $\delta f$ scheme are in good agreement with previous work. Excellent performance of the mixed variable/pullback scheme has been observed for both full $f$ and $\delta f$ schemes. Simulations with mixed full $f$ EPs and $\delta f$ electrons and thermal ions demonstrate the good features of this novel scheme in mitigating the noise level. The full $f$ scheme is a natural choice for EP physics studies which allows a large variation of EP profiles and distributions in velocity space, providing a powerful tool for kinetic studies using realistic experimental distributions related to intermittent and transient plasma activities.Comment: 27 pages, 8 figure

Benchmark of gyrokinetic, kinetic MHD and gyrofluid codes for the linear calculation of fast particle driven TAE dynamics

Fast particles in fusion plasmas may drive Alfvén modes unstable leading to fluctuations of the internal electromagnetic fields and potential loss of particles. Such instabilities can have an impact on the performance and the wall-load of machines with burning plasmas such as ITER. A linear benchmark for a toroidal Alfvén eigenmode (TAE) is done with 11 participating codes with a broad variation in the physical as well as the numerical models. A reasonable agreement of around 20% has been found for the growth rates. Also, the agreement of the eigenfunctions and mode frequencies is satisfying. However, they are found to depend strongly on the complexity of the used model

Global simulations of tokamak microturbulence: finite beta effects and collisions

In this paper, we present global nonlinear gyrokinetic simulations including finite beta effects and collisions in tokamak geometry. Global electromagnetic simulations using conventional delta-f particle in cell methods are very demanding, with respect to numerical resources, in order to correctly describe the evolution of the non-adiabatic part of the electron distribution function. This difficulty has been overcome using an appropriate adjustable control variate method in the conventional delta-f scheme. Linearized inter-species and like-species collision operators have also been introduced in the model. The inclusion of the collisional dynamics makes it possible to carry out simulations of microturbulence starting from a global neoclassical equilibrium and to study the effect of collisions on the transport induced by electrostatic microinstabilities