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 vertical bar epsilon(C)vertical bar 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 multispwecraft 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,vertical bar epsilon(C)vertical bar identifies well with its incompressible analog vertical bar epsilon(I)vertical bar ; at MHD scales but becomes much larger than led at subion scales. For larger density fluctuations, vertical bar epsilon(C)vertical bar is larger than vertical bar epsilon(I)vertical bar 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 vertical bar epsilon(C)vertical bar at subion scales comes from the compressible Hall flux.