Determining the hot-spot temperature profile in inertial confinement fusion implosions with an applied magnetic field

Inertial confinement fusion (ICF) involves the spherical compression of a target capsule using lasers to sufficient pressure and temperature conditions for fusion. Imposing an external magnetic field to these implosions suppresses heat losses perpendicular to field lines, which increases hot-spot temperature and fusion yield. An ongoing campaign at the National Ignition Facility (NIF) creates implosions which compress the 26 T imposed magnetic field to magnitudes of around 5 kT. These strong fields magnetize the fusion fuel, increasing temperature by 40% and yield by 3.2x over the unmagnetized implosions [J.D. Moody et al., Phys. Rev. Lett. 2022, B. Lahmann et al., APS DPP 2022]. To better interpret and analyze these experimental results, we develop a 1-D analytic model of the change in temperature profile due to the magnetized suppression to heat conduction. The analytic model is extended to show that the change to the temperature profile predicts a overall hot-spot temperature amplification different than previous analytic models. This work explains both the observed temperature profile and temperature amplification as measured in magnetized hohlraum experiments on the NIF.