  The growth rate of the non-linear ablative Rayleigh-Taylor (RT) instability
is enhanced by magnetic fields self-generated by the Biermann battery
mechanism; a scaling for this effect with perturbation height and wavelength is
proposed and validated with extended-magnetohydrodynamic simulations. The
magnetic flux generation rate around a single RT spike is found to scale with
the spike height. The Hall Parameter, which quantifies electron magnetization,
is found to be strongly enhanced for short wavelength spikes due to Nernst
compression of the magnetic field at the spike tip. The impact of the magnetic
field on spike growth is through both the suppressed thermal conduction into
the unstable spike and the Righi-Leduc heat-flow deflecting heat from the spike
tip to the base. Righi-Leduc is found to be the dominant effect for small Hall
Parameters, while suppressed thermal conduction dominates for large Hall
Parameters. These results demonstrate the importance of considering magnetic
fields in all perturbed inertial confinement fusion hot-spots.
