Metriplectic bracket for guiding-center Vlasov–Maxwell–Landau theory

The metriplectic formulation of collisional guiding-center Vlasov–Maxwell–Landau theory is presented. The guiding-center Landau collision operator, which describes collisions involving test-particle and field-particle guiding-center orbits, is represented in terms of a symmetric dissipative bracket involving functional derivatives of the guiding-center Vlasov phase-space density Fgc and the electromagnetic fields (Dgc,B), where the guiding-center displacement vector Dgc≡E+4π Pgc is expressed in terms of the electric field E and the guiding-center polarization Pgc. This dissipative Landau bracket not only conserves guiding-center energy–momentum and angular momentum, but it also satisfies a guiding-center H-theorem.