Modified jump conditions for parallel collisionless shocks

TL;DR

This paper extends a theoretical model for parallel collisionless shocks in electron/positron plasmas, deriving key thermodynamic jumps and revealing a transition between 3D and 1D downstream states.

Contribution

It introduces modified jump conditions for collisionless shocks, accounting for magnetic field effects on downstream anisotropy, expanding upon previous models.

Findings

Derived entropy, pressure, and temperature jumps from the model.

Identified a transition between 3D and 1D downstream states.

Provided a theoretical framework linking magnetic field strength to shock properties.

Abstract

Within the context of Magnetohydrodynamics (MHD), the properties of a parallel shock do not depend on the field strength, as the field and the fluid are disconnected for such a geometry. However, in the collisionless case, the field can sustain a stable anisotropy in the downstream, triggering a departure from the expected MHD behavior. In a recent work [A. Bret and R. Narayan, J. Plasma Phys. \textbf{84}, 905840604 (2018)], a theoretical model was presented allowing to derive the density ratio of a non-relativistic parallel collisionless shock in an electron/positron plasma, as a function of the field. Here we derive the entropy, pressure and temperature jumps stemming from this model. It is found to offer a transition between a 3D and a 1D downstream for the jumps in density, entropy, parallel temperature and parallel pressure.