Compression of an applied magnetic field in inertial confinement fusion

Applying an external magnetic field to inertial confinement fusion is a proposed candidate for enhancing fusion yield in capsule implosions. The field is compressed along with the plasma, producing a magnetized hot-spot which suppresses thermal losses and increases the fraction of alpha particle energy deposited into the hot-spot. The degree of thermal insulation and alpha heating enhancement are sensitive to the topology and magnitude of the compressed magnetic field. In this work, we derive the exact field under spherical compression, and apply perturbative corrections due to magnetic tension, resistive diffusion, and Nernst advection. These results are compared against 2D HYDRA extended-magnetohydrodynamics simulations of a magnetized N210808 showing strong agreement. We then discuss how the resulting field-line topology affects thermal conduction, alpha heating, and the magnetized ignition threshold.