Simulations of Kinetic Electrostatic Electron Nonlinear (KEEN) Waves with Variable Velocity Resolution Grids and High-Order Time-Splitting

TL;DR

This paper introduces a novel semi-Lagrangian Vlasov-Poisson solver with adaptive velocity resolution and high-order time-splitting, enabling efficient simulation of nonlinear KEEN waves across different amplitudes and dimensions.

Contribution

The authors develop a new numerical method combining non-uniform cubic splines and high-order time-splitting to improve KEEN wave simulations, especially for weakly driven cases.

Findings

Enhanced velocity resolution captures weak KEEN wave dynamics.

Longer simulation times are feasible with the new high-order scheme.

Performance improvements over uniform grid methods are demonstrated.

Abstract

KEEN waves are nonlinear, non-stationary, self-organized asymptotic states in Vlasov plasmas outside the scope or purview of linear theory constructs such as electron plasma waves or ion acoustic waves. Nonlinear stationary mode theories such as those leading to BGK modes also do not apply. The range in velocity that is strongly perturbed by KEEN waves depends on the amplitude and duration of the ponderomotive force used to drive them. Smaller amplitude drives create highly localized structures attempting to coalesce into KEEN waves. These cases have much more chaotic and intricate time histories than strongly driven ones. The narrow range in which one must maintain adequate velocity resolution in the weakly driven cases challenges xed grid numerical schemes. What is missing there is the capability of resolving locally in velocity while maintaining a coarse grid outside the highly perturbed region of phase space. We here report on a new Semi-Lagrangian Vlasov-Poisson solver based on conservative non-uniform cubic splines in velocity that tackles this problem head on. An additional feature of our approach is the use of a new high-order time-splitting scheme which allows much longer simulations per computational e ort. This is needed for low amplitude runs which take a long time to set up KEEN waves, if they are able to do so at all. The new code's performance is compared to uniform grid simulations and the advantages quanti ed. The birth pains associated with KEEN waves which are weakly driven is captured in these simulations. These techniques allow the e cient simulation of KEEN waves in multiple dimensions which will be tackled next as well as generalizations to Vlasov-Maxwell codes which are essential to understanding the impact of KEEN waves in practice.