Bounce-Averaged Theories for Multi-Well Plasmas

In both mirror and toroidal plasmas, bounce-averaged theories provide a framework for simulating relatively slow processes, such as collisional transport and quasilinear diffusion, by averaging these processes over the fast periodic motions of a particle on a closed orbit. This procedure dramatically increases the characteristic timescale and reduces the dimensionality of the modeled system. The natural coordinates for such calculations are the constants of motion (COM) of the fast particle motion, which by definition do not change during an orbit. However, for sufficiently complicated fields---particularly, but not exclusively, in the presence of local maxima of the electric potential and magnetic field---the COM are not sufficient to specify the particle trajectory. In such cases, multiple domains in COM space must be used to solve the problem, with boundary conditions enforced between the domains to ensure continuity and particle conservation. Here, we show how to solve for these domains under quite general conditions, and how to generate the directed graph encoding the domain connections [1]. This framework allows for the simulation of multi-region plasmas self-consistently using bounce-averaged theories, even when the fields change over the course of a simulation. We also present current results integrating this multi-region physics into the R3FP (Radiation and Reabsorption in Relativistic Fokker-Planck) code [2-4], which natively handles relativistic collisions, bremsstrahlung, and synchrotron emission and reabsorption in a mirror-focused geometry.