Exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence: toward linking energy cascade and instabilities

TL;DR

This paper derives an exact law for compressible pressure-anisotropic MHD turbulence, revealing new flux and source terms that connect energy cascade processes with plasma instabilities, applicable across various plasma conditions.

Contribution

It introduces a novel exact law for pressure-anisotropic compressible MHD turbulence, incorporating Hall effects and generalizing existing turbulence laws to include pressure anisotropy and instability considerations.

Findings

New flux and source terms identified in the exact law.

Hall effects introduce ion-scale corrections without altering pressure terms.

Generalization of turbulence laws to include pressure anisotropy and internal energy exchanges.

Abstract

We derive a first exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence. For a gyrotropic pressure tensor, we study the double-adiabatic case and show the presence of new flux and source terms in the exact law, reminiscent of the plasma instability conditions due to pressure anisotropy. The Hall term is shown to bring ion-scale corrections to the exact law without affecting explicitly the pressure terms. In the pressure isotropy limit we recover all known results obtained for isothermal and polytropic closures. The incompressible limit of the gyrotropic system leads to a generalization of the Politano and Pouquet's law where a new {\it incompressible} source term is revealed and reflects exchanges of the magnetic and kinetic energies with the no-longer-conserved internal energy. We highlight the possibilities offered by the new laws to investigate potential links between turbulence cascade and instabilities widely observed in laboratory and astrophysical plasmas.