Controlling instability in the Vlasov-Poisson system through moment-based optimization

TL;DR

This paper develops a moment-based control method to suppress plasma instability caused by kinetic effects, offering a computationally efficient and data-accessible alternative to full kinetic modeling.

Contribution

The work introduces a novel moment-based control framework for the Vlasov-Poisson system, reducing computational costs and enhancing practicality in plasma instability suppression.

Findings

Moment-based control effectively suppresses instability.

Compared favorably to full kinetic control in simulations.

Reduces computational complexity significantly.

Abstract

Controlling instability in plasma is one of the central challenges in fusion energy research. Among the various sources of instability, kinetic effects play a significant role. In this work, we aim to suppress the instability induced by kinetic effects by designing an external electric field. However, rather than directly solving the full kinetic Vlasov-Poisson system, we focus on a reduced-order model, specifically the moment-based system, to capture the underlying dynamics. This approach is motivated by the desire to reduce the computational cost associated with repeatedly solving the high-dimensional kinetic equations during the optimization of the electric field. Additionally, moment-based data is more readily accessible in practice, making a moment-based control framework more adaptable to data-driven scenarios. We investigate the effectiveness of moment-based control both analytically and numerically, by comparing it to control based on the full kinetic model.