The inadequacy of a magnetohydrodynamic approach to the Biermann battery

C. P. Ridgers, C. Arran, J. J. Bissell, R. J. Kingham

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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)'.

Original languageEnglish
Article number20200017
Number of pages13
JournalPhilosophical transactions. Series A, Mathematical, physical, and engineering sciences
Issue number2189
Early online date7 Dec 2020
Publication statusPublished - 25 Jan 2021


  • high intensity laser
  • inertial confinement fusion
  • magnetic field
  • plasma

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