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.

翻译：等离子体不稳定性是等离子体科学中的核心问题，其应用范围涵盖从粒子加速器到核聚变反应堆的多个领域。本研究探讨了通过在Vlasov-Poisson方程中引入外部电场来控制此类不稳定性的可能性。我们通过对方程组进行线性分析来确定外部电场的配置。研究表明，当平衡分布函数和扰动已知时，可以选择能够完全抑制系统中等离子体不稳定性的外部电场。事实上，所提出的控制策略能使等离子体以快于指数衰减的速率恢复平衡状态。我们进一步对非线性双流不稳定性和尾峰不稳定性进行了数值模拟，以验证理论结果并比较本文提出的不同控制策略。