Action principles for relativistic extended magnetohydrodynamics: A unified theory of magnetofluid models

Abstract

Two types of Eulerian action principles for relativistic extended magnetohydrodynamics (MHD) are formulated. With the first, the action is extremized under the constraints of density, entropy, and Lagrangian label conservation, which leads to a Clebsch representation for a generalized momentum and a generalized vector potential. The second action arises upon transformation to physical field variables, giving rise to a covariant bracket action principle, i.e., a variational principle in which constrained variations are generated by a degenerate Poisson bracket. Upon taking appropriate limits, the action principles lead to relativistic Hall MHD and well-known relativistic ideal MHD. For the first time, the Hamiltonian formulation of relativistic Hall MHD with electron thermal inertia (akin to [Comisso et al., Phys. Rev. Lett. 113, 045001 (2014)] for the electron-positron plasma) is introduced. This thermal inertia effect allows for violation of the frozen-in magnetic flux condition in marked contrast to nonrelativistic Hall MHD that does satisfy the frozenin condition. We also find violation of the frozen-in condition is accompanied by freezing-in of an alternative flux determined by a generalized vector potential. Finally, we derive a more general 3+1 Poisson bracket for nonrelativistic extended MHD, one that does not assume smallness of the electron ion mass ratio.

Modification of magnetohydrodynamic waves by the relativistic Hall effect

“…The T 0 dependence is straightforward, i.e., a high temperature induces large effective mass resulting in a long inertial length. This dependence has been pointed out in past studies [21,24,33]. However, the shrink of the inertial length by large B 0 is not trivial.…”

“…Koide's extended version of the relativistic MHD (XMHD), in contrast, takes into account several microscopic effects originating from two-fluid nature [19,20]. This model has been highlighted in recent studies [21][22][23][24] To understand these various MHD models, it is crucial to consider the properties of linear wave propagation. While the linear wave properties for non-relativistic ideal MHD have been widely known (see Refs.…”

Lorentz invariant ‘potential magnetic field’ and magnetic flux conservation in an ideal relativistic plasma

“…Finally we notice that the results obtained in this article can be extended to non ideal plasmas that obey a generalised ideal Ohm's law, including e.g., electron inertia, as discussed explicitly in [10]. A possible extension to more general fluid theories (see e.g., [16] in the non relativistic limit) and in particular to those that involve an antisymmetric tensor that unifies the electromagnetic and the fluid fields, [17,18] should also be investigated. On the contrary a possible extension to an ideal plasma in curved space-time must incude the fact that in General Relativity covariant derivatives do not commute (which would result in a modification of Eq.…”

Collisionless magnetic reconnection in curved spacetime and the effect of black hole rotation

“…(5) are Hall terms. For definiteness, in this work we focus on the investigation of magnetic reconnection in the thermal-inertial regime, which correspond to the situation in which the thermal-inertial terms are larger than the Hall terms [33][34][35][36]. For an electron-ion plasma, assuming that the Hall terms are of the same order, the thermal-inertial regime can be achieved if the condition ∆µJB ξh ne U J…”