A Geometric Transfer Matrix Method Model for Neutral Transport Through the Vacuum Region of Tokamak Magnetic Fusion Devices

A geometric vacuum transport model is applied to numerical simulations of tokamak devices to assess the effect of vacuum-region neutral transport on the recycling boundary conditions in the multi-fluid edge-plasma code UEDGE. For a given magnetic equilibrium, plasma grid, and limiter geometry, the model calculates the neutral transport from the numerical plasma grid boundary to the material wall, including transport between all surfaces. The model considers thermal reflections from wall to plasma surfaces and uses a geometric representation of integration of the recycled particles’ angular distribution and the of line of sight between individual surfaces. The Transfer Matrix Method is used to derive a matrix describing reflections and transport between plasma and wall surfaces in the vacuum region. This is compared to its counterpart calculated using the DEGAS2 kinetic Monte Carlo neutral code, which considers fast reflections off wall surfaces and nonlinear scattering processes. By assuming vacuum between the numerical plasma grid and walls, the transport is linear, allowing it to be precomputed for a given simulation setup and to provide boundary conditions for the continuity equation in UEDGE, compatible with its implicit solver. Tokamaks are primarily fueled through the recycling of neutral particles, which are not bound by magnetic field lines in the device. Thus, neutral transport and their ionization profiles are crucial to accurately model edge plasma conditions in tokamak devices.