A Geometric Perspective on Kinetic Matter-Radiation Interaction and Moment Systems

We provide a geometric perspective on the kinetic interaction of matter and radiation, based on a metriplectic approach. We discuss the interaction of kinetic theories via dissipative brackets, with our fundamental example being the coupling of matter, described by the Boltzmann equation, and radiation, described by the radiation transport equation. We explore the transition from kinetic systems to their corresponding moment systems, provide a Hamiltonian description of such moment systems, and give a geometric interpretation of the moment closure problem for kinetic theories. As applications, we discuss in detail diffusion radiation hydrodynamics as an example of a geometric moment closure of kinetic matter-radiation interaction and additionally, we apply the variable moment closure framework of Burby (2023) to derive novel Hamiltonian moment closures for pure radiation transport and discuss an interesting connection to the Hamiltonian fluid closures derived by Burby (2023).