Higher-order dissipative anisotropic magnetohydrodynamics from the Boltzmann-Vlasov equation

TL;DR

This paper derives advanced models of relativistic magnetohydrodynamics incorporating higher-order dissipative effects and anisotropy, using the method of moments applied to the Boltzmann-Vlasov equation, revealing new theoretical frameworks.

Contribution

It introduces a systematic derivation of higher-order dissipative anisotropic magnetohydrodynamics from the Boltzmann-Vlasov equation, extending previous isotropic models.

Findings

Derived a theory of relativistic higher-order dissipative resistive magnetohydrodynamics.

Developed a novel anisotropic magnetohydrodynamics model with independent momentum anisotropy.

Provided a systematic closure scheme for the moment equations.

Abstract

We apply the method of moments to the relativistic Boltzmann-Vlasov equation and derive the equations of motion for the irreducible moments of arbitrary tensor-rank of the invariant single-particle distribution function. We study two cases, in the first of which the moments are taken to be irreducible with respect to the little group associated with the time-like fluid four-velocity, while in the second case they are assumed to be also irreducible with respect to a space-like four-vector orthogonal to the fluid four-velocity, which breaks the spatial isotropy to a rotational symmetry in the plane transverse to this vector. A systematic truncation and closure of the general moment equations leads, in the first case, to a theory of relativistic higher-order dissipative resistive magnetohydrodynamics. In the second case, we obtain a novel theory of dissipative resistive anisotropic magnetohydrodynamics, where the momentum anisotropy is in principle independent from that introduced by the external magnetic field.