Control plasma instabilities via an external magnetic field in a Vlasov-Poisson system.
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The study of the problem of plasma con finement in huge devices, such as for example the tokamak, has attracted a lot of attention in recent years. The presence of strong magnetic fi elds can give rise to instabilities, leading to vortex formation. The approach involves examining a plasma composed of numerous particles and studying its evolution through the Vlasov-Poisson equations. The particles dynamics is simulated by means of Particle-in-Cells schemes, which are able to capture the individual particles behavior. In this talk an instantaneous feedback control will be derived by minimizing a specific functional with the aim to force the plasma density to assume a desired distribution. Various numerical experiments will be conducted to validate the results, with a specific focus on the analysis of the Kelvin-Helmholtz instability problem.
