  Engineering features are known to cause jets of ablator material to enter the
fuel hot-spot in inertial confinement fusion implosions. The Biermann battery
mechanism wraps them in self-generated magnetic field. We show that higher-Z
jets have an additional thermoelectric magnetic source term that is not present
for hydrogen jets, verified here through a kinetic simulation. It has similar
magnitude to the Biermann term. We then include this in an extended
magneto-hydrodynamics approach to post-process an xRAGE radiation-hydrodynamic
implosion simulation. The simulation includes an accurate model for the capsule
fill tube, producing a dense carbon jet that becomes wrapped in a 4000T
magnetic field. A simple spherical carbon mix model shows that this insulates
the electron heat conduction enough to cause contraction of the jet to an
optically thick equilibrium. The denser magnetized jet hydrodynamics could
change its core penetration and therefore the final mix mass, which is known to
be well correlated with fusion yield degradation. Fully exploring this will
require self-consistent magneto-hydrodynamic simulations. Experimental
signatures of this self-magnetization may emerge in the high energy neutron
spectrum.
