Biermann battery

In astrophysics, the Biermann battery is a process by which a weak seed magnetic field can be generated from zero initial conditions. The relative motion between electrons and ions is driven by rotation. The process was discovered by Ludwig Biermann in 1950.

A simple derivation of the effect starts with the momentum equation for the free electron fluid, keeping only the electric field and pressure force:

${\displaystyle m_{e}{d{\vec {v}}_{e} \over dt}=-e{\vec {E}}-{\nabla p_{e} \over n_{e}}}$.

For phenomena on sufficiently slow time scales, we can neglect the left-hand side, and arrive at an Ohm's law for the electric field:

${\displaystyle {\vec {E}}=-{\nabla p_{e} \over en_{e}}}$.

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