How the pressure tensor both generates and dissipates magnetic fields in collisionless plasmas through the canonical battery effect

The bearing of the pressure tensor on two important plasma processes—magnetogenesis and magnetic reconnection—that violate magnetic flux conservation in ideal magnetohydrodynamics is demonstrated by examining the canonical battery effect. Taking the curl of the first moment of the Vlasov equation yields the generalized canonical induction equation for each plasma species. This equation describes the time evolution of canonical vorticity determined by two terms: the convective term and the canonical battery term, the latter of which is due to the finite pressure tensor. This battery term not only generates magnetic fields during magnetogenesis but also dissipates them during magnetic reconnection. The relevance of this term to previously known mechanisms is demonstrated; canonical battery is effectively a generalization of the individual mechanisms. Possible extensions to this framework and analysis are also presented.