Verification of a Fully Implicit Particle-in-Cell Method for the $v_{\parallel }$ Formalism of Electromagnetic Gyrokinetics in the XGC Code

Abstract

A fully implicit particle-in-cell method for handling the $v_{\parallel }$-formalism of electromagnetic gyrokinetics has been implemented in XGC. By choosing the $v_{\parallel }$-formalism, we avoid introducing the non-physical skin terms in Ampère's law, which are responsible for the well-known ``cancellation problem" in the $p_{\parallel }$-formalism. The $v_{\parallel }$-formalism, however, is known to suffer from a numerical instability when explicit time integration schemes are used due to the appearance of a time derivative in the particle equations of motion from the inductive component of the electric field. Here, using the conventional $\delta f$ scheme, we demonstrate that our implicitly discretized algorithm can provide numerically stable simulation results with accurate dispersive properties. We verify the algorithm using a test case for shear Alfvén wave propagation in addition to a case demonstrating the ITG-KBM transition. The ITG-KBM transition case is compared to results obtained from other $\delta f$ gyrokinetic codes/schemes, whose verification has already been archived in the literature.

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Cited by in corpus (2)

• Electromagnetic total-f algorithm for gyrokinetic particle-in-cell simulations of boundary plasma in XGC
• An E & B Gyrokinetic Simulation Model for Kinetic Alfvén Waves inTokamak Plasmas