Magnetic field transport in propagating thermonuclear burn

High energy gain in inertial fusion schemes requires the propagation of a thermonuclear burn wave from hot to cold fuel. We consider the problem of burn propagation when a magnetic field is orthogonal to the burn wave. Using an extended-MHD model with a magnetized $\alpha$ energy transport equation we find that the magnetic field can reduce the rate of burn propagation by suppressing electron thermal conduction and $\alpha$ particle flux. Magnetic field transport during burn propagation is subject to competing effects: field can be advected from cold to hot regions by ablation of cold fuel, while the Nernst and $\alpha$ particle flux effects transport field from hot to cold fuel. These effects, combined with the temperature increase due to burn, can cause the electron Hall parameter to grow rapidly at the burn front. This results in the formation of a self-insulating layer between hot and cold fuel that reduces electron thermal conductivity and $\alpha$ transport, increases the temperature gradient and reduces the rate of burn propagation.