Jan Bartsch (University of Würzburg): Optimal Control of Vlasov-Poisson Models Using the Jensen-Shannon Distance

The Vlasov-Poisson equation describes the evolution of plasmas in the so-called collisionless regime while taking the self-consistent fields into account. The investigation of plasma that is influenced by an exterior magnetic field is a significant aspect in various research fields, ranging from hot to cold plasmas. One of them is the cooling of plasmas. The adiabatic cooling of non-neutral plasma can be achieved by slowly decreasing the trapping frequency and letting the plasma occupy a larger volume. In this talk, we propose an optimal control approach for non-adiabatic cooling for plasma trapped in a one-dimensional well. In this approach, the governing model is the Vlasov-Poisson equation and a functional containing the Jensen-Shannon divergence has to be minimized subject to this model constraint and the action of a varying trapping frequency. A particle method and a gradient-based technique are developed to solve the resulting kinetic optimal control problem. We present results of numerical experiments that successfully validate the proposed optimal cooling framework with comparing it to the adiabatic cooling.