Full f and δf gyrokinetic particle simulations of Alfvén waves and energetic particle physics
Zhixin Lu, G. Meng, R. Hatzky, M. Hoelzl, P. Lauber
Abstract
Abstract In this work, we focus on the development of the particle-in-cell scheme and its application to the studies of Alfvén waves and energetic particle (EP) physics in tokamak plasmas. The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>δ</mml:mi> <mml:mi>f</mml:mi> </mml:math> 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 2021 J. Comput. Phys. 440 110384) has been upgraded using cubic spline finite elements and full f and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>δ</mml:mi> <mml:mi>f</mml:mi> </mml:math> schemes. The toroidal Alfvén eigenmode (TAE) driven by EPs has been simulated for the International Tokamak Physics activity (ITPA)-TAE case featured by a small electron skin depth <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo>∼</mml:mo> </mml:mrow> <mml:mn>1.18</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:msup> <mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:mrow> </mml:math> , which is a challenging parameter regime for electromagnetic simulations, especially for the full f model. The simulation results using the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>δ</mml:mi> <mml:mi>f</mml:mi> </mml:math> scheme are in good agreement with previous work. Excellent performance of the mixed variable/pullback scheme has been observed for both full f and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>δ</mml:mi> <mml:mi>f</mml:mi> </mml:math> schemes. Simulations with mixed full f EPs and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>δ</mml:mi> <mml:mi>f</mml:mi> </mml:math> 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 for large variations 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.