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

Cascade-Dissipation Balance in Astrophysical Plasmas: Insights from the Terrestrial Magnetosheath

The differential heating of electrons and ions by turbulence in weakly collisional magnetized plasmas and the scales at which such energy dissipation is most effective are still debated. Using a large data sample measured in Earth's magnetosheath by the magnetospheric multiscale mission and the coarse-grained energy equations derived from the Vlasov-Maxwell system, we find evidence of a balance over two decades in scales between the energy cascade and dissipation rates. The decline of the cascade rate at kinetic scales (in contrast with a constant one in the inertial range), is balanced by an increasing ion and electron heating rates, estimated via the pressure strain. Ion scales are found to contribute most effectively to ion heating, while electron heating originates from both ion and electron scales. These results can potentially impact the current understanding of particle heating in turbulent magnetized plasmas as well as their theoretical and numerical modeling.

Turbulence in Magnetic Reconnection Jets from Injection to Sub-Ion Scales

We investigate turbulence in magnetic reconnection jets in the Earth's magnetotail using data from the Magnetospheric Multiscale spacecraft. We show that signatures of a limited inertial range are observed in many reconnection jets. The observed turbulence develops on the timescale of a few ion gyroperiods, resulting in intermittent multifractal energy cascade from the characteristic scale of the jet down to the ion scales. We show that at sub-ion scales, the fluctuations are close to monofractal and predominantly kinetic Alfvén waves. The observed energy transfer rate across the inertial range is ∼10^{8}  J kg^{-1} s^{-1}, which is the largest reported for space plasmas so far.

Three-Dimensional Energy Transfer in Space Plasma Turbulence from Multipoint Measurement

A novel multispacecraft technique applied to Magnetospheric Multiscale Mission data in the Earth's magnetosheath enables evaluation of the energy cascade rate from the full Yaglom's equation. The method differs from existing approaches in that it (i) is inherently three-dimensional, (ii) provides a statistically significant number of estimates from a single data stream, and (iii) allows visualization of energy flux in turbulent plasmas. This new "lag polyhedral derivative ensemble" technique exploits ensembles of tetrahedra in lag space and established curlometerlike algorithms.

Local energy transfer and dissipation in incompressible Hall magnetohydrodynamic turbulence: The coarse-graining approach

We derive the coarse-graining (CG) equations of incompressible Hall magnetohydrodynamic (HMHD) turbulence to investigate the local (in space) energy transfer rate as a function of the filtering scale ℓ. First, the CG equations are space averaged to obtain the analytical expression of the mean cascade rate. Its application to three-dimensional simulations of (weakly compressible) HMHD shows a cascade rate consistent with the value of the mean dissipation rate in the simulations and with the classical estimates based on the "third-order" law. Furthermore, we developed an anisotropic version of CG that allows us to study the magnitude of the cascade rate along different directions with respect to the mean magnetic field. Its implementation on the numerical data with moderate background magnetic field shows a weaker cascade along the magnetic field than in the perpendicular plane, while an isotropic cascade is recovered in the absence of a background field. The strength of the CG approach is further revealed when considering the local-in-space energy transfer, which is shown theoretically and numerically to match at a given position x, when locally averaged over a neighboring region, the (quasi-)local dissipation. Prospects of exploiting this model to investigate local dissipation in spacecraft data are discussed.

Exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence: Toward linking energy cascade and instabilities

We derive an exact law for compressible pressure-anisotropic magnetohydrodynamic turbulence. For a gyrotropic pressure tensor, we study the double-adiabatic case and show the presence of new flux and source terms in the exact law, reminiscent of the plasma instability conditions due to pressure anisotropy. The Hall term is shown to bring ion-scale corrections to the exact law without affecting explicitly the pressure terms. In the pressure isotropy limit we recover all known results obtained for isothermal and polytropic closures. The incompressible limit of the gyrotropic system leads to a generalization of the Politano and Pouquet's law where a new incompressible source term is revealed and reflects exchanges of the magnetic and kinetic energies with the no-longer-conserved internal energy. We highlight the possibilities offered by the new laws to investigate potential links between turbulence cascade and instabilities widely observed in laboratory and astrophysical plasmas.

Energy transfer in reconnection and turbulence

Reconnection and turbulence are two of the most commonly observed dynamical processes in plasmas, but their relationship is still not fully understood. Using 2.5D kinetic particle-in-cell simulations of both strong turbulence and reconnection, we compare the cross-scale transfer of energy in the two systems by analyzing the generalization of the von Kármán Howarth equations for Hall magnetohydrodynamics, a formulation that subsumes the third-order law for steady energy transfer rates. Even though the large scale features are quite different, the finding is that the decomposition of the energy transfer is structurally very similar in the two cases. In the reconnection case, the time evolution of the energy transfer also exhibits a correlation with the reconnection rate. These results provide explicit evidence that reconnection dynamics fundamentally involves turbulence-like energy transfer.

Proof of the zeroth law of turbulence in one-dimensional compressible magnetohydrodynamics and shock heating

The zeroth law is one of the oldest conjectures in turbulence that is still unproven. Here, we consider weak solutions of one-dimensional compressible magnetohydrodynamics and demonstrate that the lack of smoothness of the fields introduces a dissipative term, named inertial dissipation, into the expression of energy conservation that is neither viscous nor resistive in nature. We propose exact solutions assuming that the kinematic viscosity and the magnetic diffusivity are equal, and we demonstrate that the associated inertial dissipation is positive and equal on average to the mean viscous dissipation rate in the limit of small viscosity, proving the conjecture of the zeroth law of turbulence and the existence of an anomalous dissipation. As an illustration, we evaluate the shock heating produced by discontinuities detected by Voyager in the solar wind around 5 AU. We deduce a heating rate of ∼10^{-18}Jm^{-3}s^{-1}, which is significantly higher than the value obtained from the turbulent fluctuations. This suggests that collisionless shocks can be a dominant source of heating in the outer solar wind.

A Case for Electron-Astrophysics

The smallest characteristic scales, at which electron dynamics determines the plasma behaviour, are the next frontier in space and astrophysical plasma research. The analysis of astrophysical processes at these scales lies at the heart of the research theme of electron-astrophysics. Electron scales are the ultimate bottleneck for dissipation of plasma turbulence, which is a fundamental process not understood in the electron-kinetic regime. In addition, plasma electrons often play an important role for the spatial transfer of thermal energy due to the high heat flux associated with their velocity distribution. The regulation of this electron heat flux is likewise not understood. By focussing on these and other fundamental electron processes, the research theme of electron-astrophysics links outstanding science questions of great importance to the fields of space physics, astrophysics, and laboratory plasma physics. In this White Paper, submitted to ESA in response to the Voyage 2050 call, we review a selection of these outstanding questions, discuss their importance, and present a roadmap for answering them through novel space-mission concepts.

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

NASA’s Magnetospheric Multi-Scale (MMS) mission is designed to explore the proton- and electron-gyroscale kinetics of plasma turbulence where the bulk of particle acceleration and heating takes place. Understanding the nature of cross-scale structures ubiquitous as magnetic cavities is important to assess the energy partition, cascade and conversion in the plasma universe. Here, we present theoretical insight into magnetic cavities by deriving a self-consistent, kinetic theory of these coherent structures. By taking advantage of the multipoint measurements from the MMS constellation, we demonstrate that our kinetic model can utilize magnetic cavity observations by one MMS spacecraft to predict measurements from a second/third spacecraft. The methodology of “observe and predict” validates the theory we have derived, and confirms that nested magnetic cavities are self-organized plasma structures supported by trapped proton and electron populations in analogous to the classical theta-pinches in laboratory plasmas.

Magnetic cavities play important roles in the energy cascade, conversion and dissipation in turbulent plasmas. Here, the authors show a theoretical insight into magnetic cavities by deriving a self-consistent, kinetic theory of these coherent structures.

In Situ Observation of Hall Magnetohydrodynamic Cascade in Space Plasma

We present estimates of the turbulent energy-cascade rate derived from a Hall-magnetohydrodynamic (MHD) third-order law. We compute the contribution from the Hall term and the MHD term to the energy flux. Magnetospheric Multiscale (MMS) data accumulated in the magnetosheath and the solar wind are compared with previously established simulation results. Consistent with the simulations, we find that at large (MHD) scales, the MMS observations exhibit a clear inertial range dominated by the MHD flux. In the subion range, the cascade continues at a diminished level via the Hall term, and the change becomes more pronounced as the plasma beta increases. Additionally, the MHD contribution to interscale energy transfer remains important at smaller scales than previously thought. Possible reasons are offered for this unanticipated result.

Scale-to-scale energy transfer rate in compressible two-fluid plasma turbulence

We derive the exact relation for the energy transfer in three-dimensional compressible two-fluid plasma turbulence. In the long-time limit, we obtain an exact law which expresses the scale-to-scale average energy flux rate in terms of two point increments of the fluid variables of each species, electric and magnetic field and current density, and puts a strong constraint on the turbulent dynamics. The incompressible single fluid and two-fluid limits and the compressible single fluid limit are recovered under appropriate assumption. In the single fluid limits, analyses are done with and without neglecting the electron mass thereby making the exact relation suitable for a broader range of application. In the compressible two-fluid regime, the total energy flux rate, unlike the single fluid case, is found to be unaltered by the presence of a background magnetic field. The exact relation provides a way to test whether a range of scales in a plasma is inertial or dissipative and is essential to understand the nonlinear nature of both space and dilute astrophysical plasmas.

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.

Evidence for electron Landau damping in space plasma turbulence

How turbulent energy is dissipated in weakly collisional space and astrophysical plasmas is a major open question. Here, we present the application of a field-particle correlation technique to directly measure the transfer of energy between the turbulent electromagnetic field and electrons in the Earth's magnetosheath, the region of solar wind downstream of the Earth's bow shock. The measurement of the secular energy transfer from the parallel electric field as a function of electron velocity shows a signature consistent with Landau damping. This signature is coherent over time, close to the predicted resonant velocity, similar to that seen in kinetic Alfven turbulence simulations, and disappears under phase randomisation. This suggests that electron Landau damping could play a significant role in turbulent plasma heating, and that the technique is a valuable tool for determining the particle energisation processes operating in space and astrophysical plasmas.

Turbulence-Driven Ion Beams in the Magnetospheric Kelvin-Helmholtz Instability

The description of the local turbulent energy transfer and the high-resolution ion distributions measured by the Magnetospheric Multiscale mission together provide a formidable tool to explore the cross-scale connection between the fluid-scale energy cascade and plasma processes at subion scales. When the small-scale energy transfer is dominated by Alfvénic, correlated velocity, and magnetic field fluctuations, beams of accelerated particles are more likely observed. Here, for the first time, we report observations suggesting the nonlinear wave-particle interaction as one possible mechanism for the energy dissipation in space plasmas.