Rugged magneto-hydrodynamic invariants in weakly collisional plasma turbulence: Two-dimensional hybrid simulation results

TL;DR

This study uses two-dimensional hybrid simulations to analyze the behavior of magneto-hydrodynamic invariants in weakly collisional plasma turbulence, revealing scale-dependent cascades and dissipation mechanisms relevant to solar wind dynamics.

Contribution

It provides new insights into the scale-dependent evolution and dissipation of MHD invariants, especially the role of Hall effects in plasma turbulence.

Findings

Energy cascades from large to small scales via MHD and Hall non-linearities.

Cross helicity exhibits a cascade and dissipation similar to energy, with Hall effects influencing its behavior.

Magnetic helicity shows minimal generation and no cascade in the simulation.

Abstract

Aims. We investigated plasma turbulence in the context of solar wind. We concentrated on properties of ideal second-order magneto-hydrodynamic (MHD) and Hall MHD invariants. Methods. We studied the results of a two-dimensional hybrid simulation of decaying plasma turbulence with an initial large cross helicity and a negligible magnetic helicity. We investigated the evolution of the combined energy and the cross, kinetic, mixed, and magnetic helicities. For the combined energy and the cross, kinetic, and mixed helicities, we analysed the corresponding K\'arm\'an-Howarth-Monin (KHM) equation in the hybrid (kinetic proton and fluid electron) approximation. Results. The KHM analysis shows that the combined energy decays at large scales. At intermediate scales, this energy cascades (from large to small scales) via the MHD non-linearity and this cascade partly continues via Hall coupling to sub-ion scales. The cascading combined energy is transferred (dissipated) to the internal energy at small scales via the resistive dissipation and the pressure-strain effect. The Hall term couples the cross helicity with the kinetic one, suggesting that the coupled invariant, referred to here as the mixed helicity, is a relevant turbulence quantity. However, when analysed using the KHM equations, the kinetic and mixed helicities exhibit very dissimilar behaviours to that of the combined energy. On the other hand, the cross helicity, in analogy to the energy, decays at large scales, cascades from large to small scales via the MHD+Hall non-linearity, and is dissipated at small scales via the resistive dissipation and the cross-helicity equivalent of the pressure-strain effect. In contrast to the combined energy, the Hall term is important for the cross helicity over a wide range of scales. The magnetic helicity is scantily generated through the resistive term and does not exhibit any cascade.