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