Turbulence versus Fire-hose Instabilities: 3D Hybrid Expanding Box Simulations

The relationship between a decaying plasma turbulence and proton fire hose instabilities in a slowly expanding plasma is investigated using three-dimensional hybrid expanding box simulations. We impose an initial ambient magnetic field along the radial direction, and we start with an isotropic spectrum of large-scale, linearly polarized, random-phase Alfvénic fluctuations with zero cross-helicity. A turbulent cascade rapidly develops and leads to a weak proton heating that is not sufficient to overcome the expansion-driven perpendicular cooling. The plasma system eventually drives the parallel and oblique fire hose instabilities that generate quasi-monochromatic wave packets that reduce the proton temperature anisotropy. The fire hose wave activity has a low amplitude with wave vectors quasi-parallel/oblique with respect to the ambient magnetic field outside of the region dominated by the turbulent cascade and is discernible in one-dimensional power spectra taken only in the direction quasi-parallel/ oblique with respect to the ambient magnetic field; at quasi-perpendicular angles the wave activity is hidden by the turbulent background. These waves are partly reabsorbed by protons and partly couple to and participate in the turbulent cascade. Their presence reduces kurtosis, a measure of intermittency, and the Shannon entropy, but increases the Jensen–Shannon complexity of magnetic fluctuations; these changes are weak and anisotropic with respect to the ambient magnetic field and it is not clear if they can be used to indirectly discern the presence of instability-driven waves.