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

Abstract

The first complete estimation of the compressible energy cascade rate jεCj 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, jεCj identifies well with its incompressible analog jεIj at MHD scales but becomes much larger than jεIj at subion scales. For larger density fluctuations, jεCj is larger than jεIj 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 jεCj at subion scales comes from the compressible Hall flux.