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

Abstract

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 $F_{\mathrm{gc}}$ and the electromagnetic fields $({\mathbf{D}}_{\mathrm{gc}},\mathbf{B})$, where the guiding-center displacement vector ${\mathbf{D}}_{\mathrm{gc}}\equiv \mathbf{E}+4\pi {\mathsf{P}}_{\mathrm{gc}}$ is expressed in terms of the electric field $\mathbf{E}$ and the guiding-center polarization ${\mathsf{P}}_{\mathrm{gc}}$. This dissipative Landau bracket conserves guiding-center energy-momentum and angular momentum, as well as satisfying a guiding-center H-theorem.

32 pages