Mathematics Colloquium

The Vlasov-Maxwell-Landau equation is often regarded as the first-principle physics model for plasmas. In this talk, we introduce a novel particle method for this equation that collectively models particle transport, electromagnetic field effects, and Coulomb collisions. The method arises from a regularization of the variational formulation of the Landau collision operator, leading to a discretization of the operator that conserves mass, momentum, and energy, as well as dissipates the entropy. The collisional effects appear as a fully deterministic effective force, which can be naturally coupled with the classical particle-in-cell (PIC) method. We validate the method on several plasma benchmark tests, including collisional Landau damping, two-stream instability, and Weibel instability.