The relativistic electro-vortical field—revisiting magneto-genesis and allied problems

TLDR: Mahajan et al. as mentioned in this paper proposed a very general Electro-Vortical (EV) field to describe the dynamics of a perfect relativistic fluid, similar to the electromagnetic field Fμν, which unified the macroscopic forces into a single grand force that is the weighted sum of the electromagnetic and the inertial/thermal forces.

Abstract: Following the idea of MagnetoFluid unification [S. M. Mahajan, Phys. Rev. Lett. 90, 035001 (2003)], a very general Electro-Vortical (EV) field is constructed to describe the dynamics of a perfect relativistic fluid. Structurally similar to the electromagnetic field Fμν, the Electro-Vortical field Mνμ unifies the macroscopic forces into a single grand force that is the weighted sum of the electromagnetic and the inertial/thermal forces. The new effective force may be viewed either as a vortico-thermal generalization of the electromagnetic force or as the electromagnetic generalization of the vortico-thermal forces that a fluid element experiences in course of its evolution. Two fundamental consequences follow from this grand unification: (1) emergences of a new helicity that is conserved for arbitrary thermodynamics and (2) the entire dynamics is formally expressible as an MHD (magnetohydrodynamics) like ideal Ohm's law in which the “electric” and “magnetic” components of the EV field replace the standard electric and magnetic fields. In the light of these more and more encompassing conserved helicities, the “scope and significance” of the classical problem of magneto-genesis (need for a seed field to get a dynamo started) is reexamined. It is shown that in models more advanced than MHD, looking for exotic seed-generation mechanisms (like the baroclinic thermodynamics) should not constitute a fundamental pursuit; the totally ideal dynamics is perfectly capable of generating and sustaining magnetic fields entirely within its own devices. For a specified thermodynamics, a variety of exact and semi exact self-consistent analytical solutions for equilibrium magnetic and flow fields are derived for a single species charged fluid. The scale lengths of the fields are determined by two natural scale lengths: the skin depth and the gradient length of the thermodynamic quantities. Generally, the skin depth, being the shorter (even much shorter) than the gradient length, will characterize the kinetic-magnetic reservoir of short scale energy that will drive the dynamo as well as reverse dynamo action—the creation of large scale magnetic and flow fields.