Stabilization of kinetic plasma instabilities via instantaneous external field control

Abstract

We propose an instantaneous control framework for the stabilization of kinetic plasma instabilities using external fields. The control problem is formulated as a PDE-constrained optimization that accounts for nonlinear plasma dynamics, while the control is determined at each time step to avoid global-in-time optimization. The Discretize-then-Optimize (DtO) approach is adopted, with the forward equations first discretized using a particle-in-cell (PIC) method. The subsequent control computation is derived from the discrete particle update, ensuring consistency with the forward solver. The control objective is formulated in terms of electromagnetic field energy and low-order moments rather than the full distribution function, making the optimization more amenable to practical implementation. The framework is applied to both electrostatic and electromagnetic settings and evaluated on several benchmark problems, including the two-stream, bump-on-tail, Dory--Guest--Harris, and Weibel instabilities. Across these tests, the control successfully suppresses field energy growth and keeps the distribution function close to its initial state. These results demonstrate the effectiveness of the proposed strategy in suppressing kinetic plasma instabilities.