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.
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