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 |εC| at magnetohydrodynamic (MHD) and sub-ion scales is obtained in the Earth's magnetosheath using Magnetospheric MultiScale (MMS) spacecraft data and an exact law derived recently for compressible Hall MHD turbulence. A multi-spacecraft 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, |εC| identifies well with its incompressible analogue |εI| at MHD scales but becomes much larger than |εI| at sub-ion scales. For larger density fluctuations, |εC| is larger than |εI| 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 non-flux terms remain always negligible with respect to the flux terms and that the major contribution to |εC| at sub-ion scales comes from the compressible Hall flux.Introduction. Turbulence is a universal phenomenon observed from quantum to astrophysical scales [see e.g., 1-3]. It is mainly characterized by a nonlinear transfer (or cascade) of energy from a source to a sink. In astrophysical plasmas, fully developed turbulence plays a major role in several physical processes such as accretion flows around massive objects, star formation, solar wind heating or energy transport in planetary magnetospheres [e.g., 4-7]. In particular, the Earth's magnetosheath (MS) -the region of the solar wind downstream of the bow shock [8] -provides a unique laboratory to investigate compressible plasma turbulence. Indeed, a key feature of the MS plasma is the high level of density fluctuations in it, which can reach up to 100% of the background density [9][10][11], in contrast to the solar wind where it is ∼ 20% [12,13]. Thanks to the high time resolution data provided by the Magnetospheric Multi-Scale (MMS) mission in the Earth's MS [14], we are now able for the first time to measure the compressible energy cascade rate ε C from the magnetohydrodynamic (MHD) inertial range down to the sub-ion scales.

Energy budget in decaying compressible MHD turbulence

“…(2017, 2018) and Andrés et al. (2019) employ the cascade model and evaluate contributions to the total cascade rate due to both compressive and incompressive channels. While these theories are of great interest, the experimental implementation is hampered by inability of measuring all quantities involved with single spacecraft, as well as limitation of applicability due to the additional approximations adopted (such as constant plasma beta).…”

“…2018; Andrés et al. 2019). In the nonlinear regime, different scaling relations emerge (Lithwick & Goldreich 2001; Beresnyak, Lazarian & Cho 2005; Kowal & Lazarian 2007; Benzi et al.…”

Self-consistent kinetic model of nested electron- and ion-scale magnetic cavities in space plasmas

“…These magnetic cavities, traveling with the plasma flows over a macrotime scale, can transport the hot trapped electrons away from the energy release source and shape the spectrum of compressional fluctuations on scales as small as the electron thermal gyroradius. In fact, the reported magnetic cavities were observed in the terrestrial magnetosheath, a location where compressional turbulence has been proposed and observed to be more important than in the solar wind plasmas 60 – 62 . Given the complicated dynamics of energy cascade and dissipation 63 , 64 indicated by the presence of distinct breakpoints in the turbulent magnetic spectrum at electron gyroscales 65 , 66 , the analyzed magnetic cavities may also be considered intermittent structures produced by the inhomogeneity of electron-scale turbulence cascade.…”

Local and global properties of energy transfer in models of plasma turbulence

“…2018) and measurements in a collisionless space plasma using Magnetospheric Multiscale data in comparison with simulations of compressible HMHD turbulence (Andrés et al. 2019) indicate that neglecting the contribution of compressibility to the exact laws results in an underestimation of the total energy flux and dissipation rate, especially near the ion scale. However, in Andrés et al.…”

“…This effect was explicitly shown for two-dimensional simulations, for instance, in . Direct numerical simulations of compressible MHD turbulence (Andrés et al 2018) and measurements in a collisionless space plasma using Magnetospheric Multiscale data in comparison with simulations of compressible HMHD turbulence (Andrés et al 2019) indicate that neglecting the contribution of compressibility to the exact laws results in an underestimation of the total energy flux and dissipation rate, especially near the ion scale. However, in Andrés et al (2018) it was also found that except in cases in which the largest scales already On the other hand, a heuristic proxy has been recently introduced.…”