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

Magnetic fields spontaneously grow at unstable interfaces around hot-spot asymmetries during inertial confinement fusion implosions. The predicted field strengths exceed 5 kT (50 MG) in current National Ignition Facility experiments. We demonstrate this via magnetic post-processing of two-dimensional xRAGE radiation-hydrodynamic simulation data for HDC shot N170601. Although the resulting magnetic pressure is too small to significantly affect hydrodynamics, magnetic fields can also have an indirect effect by reducing and deflecting the heat flux. The rate of hot-spot heat loss is reduced by > 5% in the post-processed data. We derive a model for the self-magnetization, finding that it varies with the square of the hot-spot temperature and inversely with the hot-spot areal density. The self-magnetized Lawson analysis then gives a slightly reduced static ignition threshold, perhaps by ~200eV for typical hot-spot parameters. Time dependent self-magnetized hot-spot energy balance models corroborate this finding, with the magnetic field quadrupling the fusion yield for near threshold parameters. The model shows that self-magnetization effects should increase with yield, becoming a key consideration in recent burning plasma experiments. We also discuss the implications and caveats with these findings. A key caveat is the unknown self-consistent evolution of asymmetries with magnetized heat flux. A future ignition parameter scan with extended-magnetohydrodynamics simulations should address this.