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We introduce an extension of the particle-in-cell (PIC) method that capturesthe Landau collisional effects in the Vlasov-Maxwell-Landau equations. Themethod arises from a regularisation of the variational formulation of theLandau equation, leading to a discretisation of the operator that conservesmass, charge, momentum, and energy, while dissipating the (regularised)entropy. The collisional effects appear as a fully deterministic effectiveforce, thus the method does not require any transport-collision splitting. Thescheme can be used in arbitrary dimension, and for a general interaction,including the Coulomb case. We validate the scheme on scenarios such as theLandau damping, the two-stream instability, and the Weibel instability,demonstrating its effectiveness in the numerical simulation of plasma.

The Collisional Particle-In-Cell Method for the Vlasov-Maxwell-Landau Equations