Full f and δf gyrokinetic particle simulations of Alfvén waves and energetic particle physics

Abstract

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.

Nonlinear equilibria and transport processes in burning plasmas

“…This point will be further discussed in section 2.2. The approach proposed in the present analysis could be considered a 'full-F' description [28,29] of the nonlinear evolving equilibrium, and a 'delta-F' approach [30] for the (toroidal) symmetry breaking perturbations (see [31] for a general review for gyrokinetic simulations of turbulent transport).…”

Energetic particles transport in constants of motion space due to collisions in tokamak plasmas

“…The CoM variables provide an appropriate way to describe the EP dynamics. Specifically, in full f simulations the adoption of the CoM space is necessary to initialize a steady state distribution with the finite orbit width effects taken into account [2]. A parametric equilibrium distribution function in the CoM space is applicable to gyrokinetic studies investigating the behavior of guiding centers with finite orbit width in axisymmetric tokamak plasmas, as discussed in [3].…”

Nonlinear drift-wave and energetic particle long-time behaviour in stellarators: solution of the kinetic problem

“…We are starting to see the first numerical results on the behaviour of energetic particles embedded into turbulence (Biancalani et al 2021;Di Siena et al 2021;Carlevaro et al 2022;Lu et al 2023), but, to date, the aforementioned fundamental theoretical aspects have only been covered in the context of tokamak physics (Zonca et al 2015;Chen & Zonca 2016Falessi & Zonca 2019). A generalisation to stellarators is not straightforward mainly for two reasons.…”

“…2022; Lu et al. 2023), but, to date, the aforementioned fundamental theoretical aspects have only been covered in the context of tokamak physics (Zonca et al. 2015; Chen & Zonca 2016, 2019; Falessi & Zonca 2019).…”