  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.

Plasma Physics