Alpha heating enhancement in MagLIF targets: A simple analytic model

In this article, a dynamic ignition criterion for magnetized cylindrical implosions is derived. The analysis of the hot spot dynamics after stagnation performed by Christopherson et al. [Phys. Plasmas 25, 012703 (2018)] for spherical implosions is extended to cylindrical geometry with the addition of an external magnetic field. The hot spot dynamics have been consistently solved with a kinetic model for the alpha particle motion. The magnetic field confines the alpha particles and enhances their energy deposition inside the fuel. The ignition criterion is based on the identification of ignited solutions, where pressure exhibits a singularity in finite time and neutron yield diverges. It is formulated in terms of a normalized Lawson parameter and the magnetization of the alpha particles at stagnation. The beneficial effect of magnetizing the fuel to increase the neutron yield is asserted by the analysis.