arXiv:2610.26110v1 Announce Type: new Abstract: We study the full-horizon control of a two-dimensional Vlasov--Poisson system through an externally imposed magnetic field. The control is represented by time-dependent coefficients associated with smooth, spatially localized basis functions, and is designed to steer selected position and velocity moments of the distribution function while limiting particle dispersion and the control effort. Starting from the kinetic constrained optimization problem, we derive the continuous first-order optimality conditions, including a backward Vlasov equation, an elliptic adjoint equation, and the variational inequality associated with bounded controls. We then project this system onto a particle--grid representation and identify the resulting particle adjoints and control gradient. The full-horizon field is then computed on a reduced particle ensemble, initialized by an instantaneous control, and subsequently applied to a larger set of particles. Numerical experiments indicate that the instantaneous control field already provides an effective baseline, while the full-horizon correction can further reduce the relative thermal energy near the boundaries and improve confinement over the prescribed time interval.