Control Plasma in a uniform magnetic field with an external electric potential

The stability of plasmas is a challenging topic. We study a control problem for plasma living in a uniform external magnetic field. Linear analysis for any equilibrium $\mu$ is investigated through the Laplace-Fourier transform approach. Moreover, the Penrose condition, which characterizes the stability of equilibrium, is derived for Bernstein modes and verified numerically. Based on the linear analysis, a general control strategy is introduced, with recovering the free-streaming solution as a specific example. We finally present several examples to control instabilities, including Gaussian equilibria and Dory-Guest-Harris instability.