An energy and momentum conserving collisional bracket for the guiding-centre Vlasov-Maxwell-Landau model

This paper proposes a metric bracket for representing Coulomb collisions in the so-called guiding-centre Vlasov-Maxwell-Landau model. The bracket is manufactured to preserve the same energy and momentum functionals as does the Vlasov-Maxwell part and to simultaneously satisfy a revised version of the H-theorem, where the equilibrium distributions with respect to collisional dynamics are identified as Maxwellians. This is achieved by exploiting the special projective nature of the Landau collision operator and the simple form of the system's momentum functional. A discussion regarding a possible extension of the results to electromagnetic drift-kinetic and gyrokinetic systems is included. We anticipate that energy conservation and entropy dissipation can always be manufactured whereas guaranteeing momentum conservation is a delicate matter yet to be resolved.