Magnetized ICF: Field Topology Evolution Under Spherical Compression

Applying an external magnetic field to inertial confinement fusion is a proposed candidate for enhancing fusion yield in capsule implosions. In both NIF and OMEGA experiments, magnetization of the central hot-spot inhibits thermal losses causing temperature increases up to 40% and yield enhancement of 2-3x. During the implosion, the initial axial magnetic field is spherically compressed, causing a change in the field topology. This field evolution is conventionally modeled using 2D or 3D extended-magnetohydrodynamics (XMHD) simulations which are costly and not straightforwardly integrated with simple models of magnetized implosions. In this work, we derive a closed-form exact solution to the ideal MHD field evolution under spherical compression. This field topology is compared against XMHD simulations, demonstrating good agreement, although alterations due to resistive diffusion, the Lorentz force (JxB), and the Nernst effect are discussed. A perturbative solution is found for field-line straightening by resistive diffusion and magnetic tension. We describe how this model can be used in analysis and modeling of NIF and OMEGA experiments, including measuring the compressed field strength and estimating yield enhancement in magnetized implosions.