Polytropic representation of non-isotropic kinetic pressure tensor for non-ideal plasma fluids in relativistic jets

Abstract

Non-ideal fluids are likely to be affected by the occurrence of pressure anisotropy effects, whose understanding for relativistic systems requires knowledge of the energy-momentum tensor. In this paper the case of magnetized jet plasmas at equilibrium is considered, in which both microscopic velocities of constituent particles as well as the continuum fluid flow are treated as relativistic ones. A theoretical framework based on covariant statistical kinetic approach is implemented, which permits the proper treatment of single-particle and phase-space kinetic constraints and, ultimately, the calculation of the system continuum fluid fields associated with physical observables. A Gaussian-like solution for the kinetic distribution function (KDF) is constructed, in which the physical mechanism responsible for the generation of temperature anisotropy is identified with magnetic moment conservation. A Chapman-Enskog representation of the same KDF is then obtained in terms of expansion around an equilibrium isotropic Juttner distribution. This permits the analytical calculation of the fluid 4-flow and stress-energy tensor and the consequent proof that the corresponding kinetic pressure tensor is non-isotropic. As a notable result, the validity of a polytropic representation for the perturbative non-isotropic pressure contributions is established, whereby directional pressures exhibit specific power-law functional dependences on fluid density.

20 pages

References in corpus (17)

• Energy exchange between relativistic fluids: the polytropic case
• Short Gamma Ray Bursts: a bimodal origin?
• Generalized Magnetofluid Connections in Relativistic Magnetohydrodynamics
• Relationship between polytropic index and temperature anisotropy in space plasmas
• Spontaneous generation of a temperature anisotropy in a strongly coupled magnetized plasma
• Numerical modelling of imposed magnetohydrodynamic effects in hypersonic flows
• Synchrotron-Self-Compton radiation from magnetically-dominated turbulent plasmas in relativistic jets
• Constraints on the merging binary neutron star mass distribution and equation of state based on the incidence of jets in the population
• Theory of spatially non-symmetric kinetic equilibria for collisionless plasmas
• Kinetic equilibria of relativistic collisionless plasmas in the presence of non-stationary electromagnetic fields
• Covariant formulation of spatially non-symmetric kinetic equilibria in magnetized astrophysical plasmas
• Carter-constant induced mechanism for generation of anisotropic kinetic equilibria in collisionless N-body systems
• Radiation reaction effects in relativistic plasmas -- the electrostatic limit
• Kinetic formulation of Tolman-Ehrenfest effect: Non-ideal fluids in Schwarzschild and Kerr space-times
• Linear Stability of an Impulsively Accelerated Density Interface in an Ideal Two-Fluid Plasma
• Realizability conditions for relativistic gases with a non-zero heat flux
• Polytropic representation of the kinetic pressure tensor of non-ideal magnetized fluids in equilibrium toroidal structures