Energy Cascade Rate Measured in a Collisionless Space Plasma with MMS Data and Compressible Hall Magnetohydrodynamic Turbulence Theory

The first complete estimation of the compressible energy cascade rate |ϵ_{C}| at magnetohydrodynamic (MHD) and subion scales is obtained in Earth's magnetosheath using Magnetospheric MultiScale spacecraft data and an exact law derived recently for compressible Hall MHD turbulence. A multispacecraft technique is used to compute the velocity and magnetic gradients, and then all the correlation functions involved in the exact relation. It is shown that when the density fluctuations are relatively small, |ϵ_{C}| identifies well with its incompressible analog |ϵ_{I}| at MHD scales but becomes much larger than |ϵ_{I}| at subion scales. For larger density fluctuations, |ϵ_{C}| is larger than |ϵ_{I}| at every scale with a value significantly higher than for smaller density fluctuations. Our study reveals also that for both small and large density fluctuations, the nonflux terms remain always negligible with respect to the flux terms and that the major contribution to |ϵ_{C}| at subion scales comes from the compressible Hall flux.

Compressible Magnetohydrodynamic Turbulence in the Earth's Magnetosheath: Estimation of the Energy Cascade Rate Using in situ Spacecraft Data

The first estimation of the energy cascade rate |ε_{C}| of magnetosheath turbulence is obtained using the Cluster and THEMIS spacecraft data and an exact law of compressible isothermal magnetohydrodynamics turbulence. The mean value of |ε_{C}| is found to be close to 10^{-13}  J m^{-3} s^{-1}, at least 2 orders of magnitude larger than its value in the solar wind (∼10^{-16}  J m^{-3} s^{-1} in the fast wind). Two types of turbulence are evidenced and shown to be dominated either by incompressible Alfvénic or compressible magnetosoniclike fluctuations. Density fluctuations are shown to amplify the cascade rate and its spatial anisotropy in comparison with incompressible Alfvénic turbulence. Furthermore, for compressible magnetosonic fluctuations, large cascade rates are found to lie mostly near the linear kinetic instability of the mirror mode. New empirical power-laws relating |ε_{C}| to the turbulent Mach number and to the internal energy are evidenced. These new findings have potential applications in distant astrophysical plasmas that are not accessible to in situ measurements.