Role of self-generated magnetic fields in the inertial fusion ignition threshold

Abstract: Magnetic fields spontaneously grow at unstable interfaces around hot-spot asymmetries during inertial confinement fusion implosions. Although difficult to measure, theoretical considerations and numerical simulations predict field strengths exceeding 5kT in current national ignition facility experiments. Magnetic confinement of electrons then reduces the hot-spot heat loss by >5%. We demonstrate this via magnetic post-processing of two-dimensional xRAGE hydrodynamic simulation data at bang time. We then derive a model for the self-magnetization, finding that it varies with the square of the stagnation temperature and inversely with the areal density. The self-magnetized Lawson analysis then gives a slightly reduced ignition threshold. Time dependent hot-spot energy balance models corroborate this finding, with the magnetic field quadrupling the fusion yield for near threshold parameters. The inclusion of magnetized multi-dimensional fluid instabilities could further alter the ignition threshold, and will be the subject of future work.