Control of Instability in a Vlasov-Poisson System Through an External Electric Field

TL;DR

This paper proposes a method to suppress plasma instabilities in a Vlasov-Poisson system by designing external electric fields based on linear analysis, effectively restoring equilibrium faster than exponential time.

Contribution

It introduces a novel control strategy for plasma instabilities using externally applied electric fields derived from linear stability analysis.

Findings

External electric fields can fully suppress plasma instabilities.

The control strategy restores equilibrium faster than exponential.

Numerical simulations confirm the effectiveness of the proposed method.

Abstract

Plasma instabilities are a major concern in plasma science, for applications ranging from particle accelerators to nuclear fusion reactors. In this work, we consider the possibility of controlling such instabilities by adding an external electric field to the Vlasov--Poisson equations. Our approach to determining the external electric field is based on conducting a linear analysis of the resulting equations. We show that it is possible to select external electric fields that completely suppress the plasma instabilities present in the system when the equilibrium distribution and the perturbation are known. In fact, the proposed strategy returns the plasma to its equilibrium with a rate that is faster than exponential in time. We further perform numerical simulations of the nonlinear two-stream and bump-on-tail instabilities to verify our theory and to compare the different strategies that we propose in this work.