1. References

In astrophysics, the Biermann battery is a process by which a weak seed magnetic field can be generated from zero initial conditions.^[1] The relative motion between electrons and ions is driven by rotation. The process was discovered by Ludwig Biermann in 1950.^[2][3]

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

.

For phenomena on sufficiently slow time scales, the left-hand side of the above equation can be neglected. That leads to the Ohm's law for the electric field:

.

The other terms in the general Ohm's law are neglected here since they typically vanish for zero magnetic field and do not spontaneously generate field. Inserting the above electric field into Faraday's law of induction gives an equation for the magnetic field:

This shows that magnetic fields develop "spontaneously", that is, from initially being zero, when there are non-parallel gradients in electron temperature and density.

References

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