Magnetospheric Multiscale Observation of Plasma Velocity-Space Cascade: Hermite Representation and Theory

Abstract

Plasma turbulence is investigated using high-resolution ion velocity distributions measured by the Magnetospheric Multiscale Mission (MMS) in the Earth's magnetosheath. The particle distribution is highly structured, suggesting a cascade-like process in velocity space. This complex velocity space structure is investigated using a three-dimensional Hermite transform that reveals a power law distribution of moments. In analogy to hydrodynamics, a Kolmogorov approach leads directly to a range of predictions for this phase-space cascade. The scaling theory is in agreement with observations, suggesting a new path for the study of plasma turbulence in weakly collisional space and astrophysical plasmas.Turbulence in fluids is characterized by nonlinear interactions that transfer energy from large to small scales, eventually producing heat. For a collisional medium, whether an ordinary gas or a plasma, turbulence leads to complex real space structure, but the velocity space, constrained by collisions, remains smooth and close to local thermodynamic equilibrium (as, e.g., in ChapmanEnskog theory [1].) However, in a weakly collisional plasma, spatial fluctuations are accompanied by fluctuations in velocity space, representing another essential facet of plasma dynamics. The characterization of the velocity space is challenging in computations and in experiments, although Vlasov simulation has revealed complexity in the velocity space, often near coherent magnetic and flow structures [2][3][4]. Here we make use of powerful new spacecraft observations in the terrestrial magnetosheath that reveal this structure with sufficient accuracy to quantify the velocity cascade for the first time in a space plasma.The observations reported here are enabled by the Magnetospheric Multiscale Mission (MMS), launched in 2015 to explore magnetic reconnection. The MMS/FPI instrument measures ion and electron velocity distributions (VDFs) at high time cadence, and with high resolution in angle and energy. High resolution magnetic field measurements are available and four-point observation is available for all instruments. MMS provides characterization of plasma turbulence with unprecedented resolution and accuracy. The spacecraft orbit repeatedly crosses the Earth's magnetosheath, enabling new and important characterizations of plasma dynamics (see e.g. Burch et al. [5]). Here we focus on one traversal of the magnetosheath, and specifically on a quantitative description of the ion velocity space cascade.

Statistical Analysis of Ions in Two-Dimensional Plasma Turbulence

“…This non-Maxwellian state of plasmas suggests that self-consistent, weakly-collisional models need to be adopted [Servidio et al, 2015, Schekochihin et al, 2016, Howes, 2017. Recent observations reveal that particles are strongly modulated by the presence of turbulence, which leads to the formation of temperature anisotropies, heat fluxes, particle beams and a wide variety of other features [Servidio et al, 2017]. These features are associated with the stochastic dynamics of particles, that cannot be observed from in situ measurements and have to be investigated with the support of kinetic models.…”

Sign Singularity of the Local Energy Transfer in Space Plasma Turbulence

“…The increasing performance of numerical simulations has also allowed processes on several scales to be examined, and therefore to highlight their relationship [15][16][17][18][19][20][21][22][23][24]. Theoretical efforts are also being carried out in order to highlight the specific processes governing the energy exchange between ranges associated to different regimes [25][26][27]. In this framework, the local, finescale details of the turbulent energy cascade acquire new importance, as the specific characteristics of the fluctuations carrying energy to the kinetic scales can be associated with different plasma processes [11,28,29].…”

On the deviation from Maxwellian of the ion velocity distribution functions in the turbulent magnetosheath

“…Thus, ǫ i = 0 indicates Maxwellian VDF, while any ǫ i = 0 suggests a deviation from the equilibrium. As pointed out in Servidio et al (2017), ǫ 2 i is related to the phasespace enstrophy. We are comparing the real ion VDFs in the magnetosheath with a Maxwellian distribution as a quantitative measure of distortion of the distributions.…”

“…This represents a sample of turbulent plasma where three thin current sheets encounters have been analyzed in previous studies Yordanova et al 2016;Vörös et al 2017) and are highlighted with colored boxes in figure 1. Thus, in such a turbulent environment the ion VDFs can be highly distorted and modified as observed in numerical simulations Perrone et al 2013) and in in situ data (Vörös et al 2017;Servidio et al 2017;Sorriso-Valvo et al 2019). An example of one-dimensional VDF cut as a function of energy is shown in figure 2 (symbols), where a clear departure from a Maxwellian distribution (solid line) is observed.…”