In plasma physics, the Biermann battery is a thermoelectric effect that produces a magnetic field when the electron density and temperature gradients have non-collinear (perpendicular) components, and was first identified by Ludwig Biermann in 1950.^[1]

The Biermann source term may be derived by starting from a single-fluid Ohm’s law that retains the electron pressure term,

Using Faraday’s law,

one obtains the induction equation,

where we used . The first term on the right-hand side describes advection of magnetic field by the bulk flow, and the last term is the Biermann battery source term. Physically, the associated currents are driven by pressure-force-induced rotational motion between electrons and ions. Notably, the Biermann term contains no explicit dependence on , so magnetic fields can be generated from zero initial field provided non-collinear and are present.

In astrophysics, the Biermann battery effect is a candidate mechanism for the source of seed fields in protogalactic environments.^[2] It is also important in laser-produced plasmas, where perpendicular temperature gradients may arise from laser-imposed temperature profiles.^[3] See also cosmological simulations demonstrating Biermann battery field generation in protostellar disks.^[4]