Biermann battery
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 components, and was first identified by Ludwig Biermann in 1950.
Physics
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.
It is also important in laser-produced plasmas, where perpendicular temperature gradients may arise from laser-imposed temperature profiles. See also cosmological simulations demonstrating Biermann battery field generation in protostellar disks.