The inadequacy of a magnetohydrodynamic approach to the Biermann battery

Abstract

Magnetic fields can be generated in plasmas by the Biermann battery when the electric field produced by the electron pressure gradient has a curl. The commonly employed magnetohydrodynamic (MHD) model of the Biermann battery breaks down when the electron distribution function is distorted away from Maxwellian. Using both MHD and kinetic simulations of a laser-plasma interaction relevant to inertial confinement fusion we have shown that this distortion can reduce the Biermann-producing electric field by around 50%. More importantly, the use of a flux limiter in an MHD treatment to deal with the effect of the non-Maxwellian electron distribution on electron thermal transport leads to a completely unphysical prediction of the Biermann-producing electric field and so results in erroneous predictions for the generated magnetic field. This article is part of a discussion meeting issue ‘Prospects for high gain inertial fusion energy (part 2)’.

Role of self-generated magnetic fields in the inertial fusion ignition threshold

“…A further consideration is the applicability of the XMHD model itself. Kinetic studies suggest that Biermann magnetic field generation is strongly reduced for conditions with non-local heat flux 37 . Our model also needs a more rigorous assessment against a database of various XMHD simulations, preferably including burn and perturbations in three-dimensions.…”

“…Additional uncertainty arises from the validity of the XMHD and Biermann models themselves. For steep temperature gradients, Biermann generation is heavily reduced 37,38 . This kinetic reduction could be important in ICF, especially earlier on in the implosion and at the higher temperatures typical of ignition.…”

Momentum Conservation in Current Drive and Alpha-Channeling-Mediated Rotation Drive

“…tend to produces ion-acoustic waves in their wake [76][77][78] . Thus, the same shocked systems that are predicted to produce magnetic fields in astrophysics via the Biermann battery [79][80][81][82][83][84][85][86] , such as those around super-nova remnants 82,83 , could produce magnetic fields via IAWdriven currents, providing an alternate possible mechanism for the origin of cosmological seed magnetic fields.…”

Diagnosing Magnetic Fields in Cylindrical Implosions with Oblique Proton Radiography

“…This asymmetry does not significantly affect the results presented here, but 3-D simulations are required to reproduce the measured neutron yields, and are therefore used for these analysis as well. Simulations of the unmagnetized shot were run with different flux limiters (f = 0.15 and f = 0.05, commonly used values for high and low heat flux, respectively [15]) to test the extent to which the flux limiter affects the Biermann battery mechanism by modifying the electron temperature gradients [16]. All other simulations were run with a flux limiter of f = 0.15.…”