Asymptotic preserving schemes for highly oscillatory kinetic equation
This work addresses the computational challenge of simulating kinetic equations with rapid oscillations, offering a unified numerical approach for plasma physics and beam dynamics.
The paper develops an Asymptotic Preserving numerical scheme for the Vlasov-Poisson model of charged particle beams under rapidly oscillating external fields, enabling efficient simulation without time step refinement across both oscillatory and non-oscillatory regimes.
This work is devoted to the numerical simulation of a Vlasov-Poisson model describing a charged particle beam under the action of a rapidly oscillating external electric field. We construct an Asymptotic Preserving numerical scheme for this kinetic equation in the highly oscillatory limit. This scheme enables to simulate the problem without using any time step refinement technique. Moreover, since our numerical method is not based on the derivation of the simulation of asymptotic models, it works in the regime where the solution does not oscillate rapidly, and in the highly oscillatory regime as well. Our method is based on a "double-scale" reformulation of the initial equation, with the introduction of an additional periodic variable.