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

TL;DR

This paper introduces a geometric framework for understanding matter-radiation interactions via kinetic and moment systems, highlighting Hamiltonian structures and moment closure techniques with applications to radiation hydrodynamics.

Contribution

It presents a novel geometric and Hamiltonian perspective on kinetic matter-radiation systems and develops new Hamiltonian moment closures for radiation transport.

Findings

Geometric interpretation of moment closure problem.

Hamiltonian structure for kinetic matter-radiation systems.

New Hamiltonian moment closures for radiation transport.

Abstract

We provide a geometric perspective on the kinetic interaction of matter and radiation, based on a pair bracket 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 an application, we discuss in detail diffusion radiation hydrodynamics as an example of a pair bracket formulation on a space of moments corresponding to kinetic matter-radiation interaction. Additionally, using the variable moment closure framework of Burby (2023), we show how to construct Hamiltonian moment closures for kinetic transport equations with arbitrary Hamiltonian. Using this general construction, we derive novel Hamiltonian moment closures for pure radiation transport.