Towards hybrid kinetic/drift-kinetic simulations in 6d Vlasov codes

TL;DR

This paper introduces an implicit hybrid kinetic/drift-kinetic simulation method for 6D Vlasov codes, effectively capturing multiscale plasma dynamics with improved accuracy and computational efficiency.

Contribution

It presents a novel implicit approach for self-consistent electric field calculation in hybrid kinetic models, including error balancing and convergence analysis.

Findings

Successfully captures ion-scale zonal flows.

Demonstrates second-order convergence of the time-splitting scheme.

Provides error analysis for semi-Lagrangian interpolation in steep gradient regimes.

Abstract

Simulating fully kinetic, two-species plasmas is computationally challenging due to the stiff multiscale dynamics of electrons and ions. While enforcing a quasi-neutral time evolution mitigates this stiffness, it requires an electric potential that consistently maintains this constraint. In this work, we present an implicit approach to determine this electric field self-consistently within the semi-Lagrangian, fully kinetic BSL6D code. We employ a hybrid two-species model that couples kinetic ions with massless, drift-kinetic electrons, enabling an implicit treatment of the latter. Notably, the model captures the generation of ion-scale zonal flows. Beyond the algorithmic description, we provide a proof of second-order time-splitting error convergence under specific regularity assumptions. A key feature of our approach is an error-balancing mechanism: we demonstrate that the field solver achieves the required accuracy of the electric field by automatically adjusting the error of certain moments of the distribution function. Furthermore, we provide a comprehensive analysis of semi-Lagrangian interpolation errors to ensure robustness against the steep density and temperature gradients characteristic of tokamak edge plasmas.