skip to main content

Title: Turbulent Energy Transfer and Proton–Electron Heating in Collisionless Plasmas

Despite decades of study of high-temperature weakly collisional plasmas, a complete understanding of how energy is transferred between particles and fields in turbulent plasmas remains elusive. Two major questions in this regard are how fluid-scale energy transfer rates, associated with turbulence, connect with kinetic-scale dissipation, and what controls the fraction of dissipation on different charged species. Although the rate of cascade has long been recognized as a limiting factor in the heating rate at kinetic scales, there has not been direct evidence correlating the heating rate with MHD-scale cascade rates. Using kinetic simulations and in situ spacecraft data, we show that the fluid-scale energy flux indeed accounts for the total energy dissipated at kinetic scales. A phenomenology, based on disruption of proton gyromotion by fluctuating electric fields that are produced in turbulence at proton scales, argues that the proton versus electron heating is controlled by the ratio of the nonlinear timescale to the proton cyclotron time and by the plasma beta. The proposed scalings are supported by the simulations and observations.

more » « less
Author(s) / Creator(s):
; ; ; ; ; ; ; ; ; ; ;
Publisher / Repository:
DOI PREFIX: 10.3847
Date Published:
Journal Name:
The Astrophysical Journal
Medium: X Size: Article No. 137
["Article No. 137"]
Sponsoring Org:
National Science Foundation
More Like this

    We investigate the spectral properties of the electromagnetic fluctuations of sub-ion scale turbulence in weakly collisional, low-beta plasmas using a two-field isothermal gyrofluid model. The numerical results strongly support a description of the turbulence as a critically balanced Kolmogorov-like cascade of kinetic Alfvén wave fluctuations, as amended by previous studies to include intermittency effects. The measured universal index of the energy spectra from systems with different flux-unfreezing mechanisms excludes the role of tearing mediation in determining the spectra. The fluctuations remain isotropic in the plane perpendicular to the strong background magnetic fields as they cascade to smaller scales, which explains the absence of tearing mediation. The calculation of high-order, multipoint structure functions of magnetic fluctuations suggests that the intermittent structures have a quasi-2D, sheet-type morphology. These results are useful for explaining recent observations of the spectrum and structure of magnetic and density fluctuations in the solar wind at sub-proton scales, and are relevant for modelling the energy dissipation in a broad range of astrophysical systems.

    more » « less
  2. Abstract

    We investigate the local proton energization at magnetic discontinuities/intermittent structures and the corresponding kinetic signatures in velocity phase space in Alfvénic (high cross helicity) and non-Alfvénic (low cross helicity) wind streams observed by Parker Solar Probe. By means of the partial variance of increments method, we find that the hottest proton populations are localized around compressible, coherent magnetic structures in both types of wind. Analysis of parallel and perpendicular temperature distributions suggest that the Alfvénic wind undergoes preferential enhancements ofTat such structures, whereas the non-Alfvénic wind experiences preferentialTenhancements. Although proton beams are present in both types of wind, the proton velocity distribution function displays distinct features. Hot beams, i.e., beams with beam-to-core perpendicular temperatureT⊥,b/T⊥,cup to three times larger than the total distribution anisotropy, are found in the non-Alfvénic wind, whereas colder beams are in the Alfvénic wind. Our data analysis is complemented by 2.5D hybrid simulations in different geometrical setups, which support the idea that proton beams in Alfvénic and non-Alfvénic wind have different kinetic properties and different origins. The development of a perpendicular nonlinear cascade, favored in balanced turbulence, allows a preferential relative enhancement of the perpendicular plasma temperature and the formation of hot beams. Cold field-aligned beams are instead favored by Alfvén wave steepening. Non-Maxwellian distribution functions are found near discontinuities and intermittent structures, pointing to the fact that the nonlinear formation of small-scale structures is intrinsically related to the development of highly nonthermal features in collisionless plasmas. Our results contribute to understanding the role of different coherent structures in proton energization and their implication in collisionless energy dissipation processes in space plasmas.

    more » « less
  3. Abstract

    While it is well known that cosmic rays (CRs) can gain energy from turbulence via second-order Fermi acceleration, how this energy transfer affects the turbulent cascade remains largely unexplored. Here, we show that damping and steepening of the compressive turbulent power spectrum are expected once the damping timetdampρv2/ĖCRECR1becomes comparable to the turbulent cascade time. Magnetohydrodynamic simulations of stirred compressive turbulence in a gas-CR fluid with diffusive CR transport show clear imprints of CR-induced damping, saturating atĖCRϵ˜, whereϵ˜is the turbulent energy input rate. In that case, almost all of the energy in large-scale motions is absorbed by CRs and does not cascade down to grid scale. Through a Hodge–Helmholtz decomposition, we confirm that purely compressive forcing can generate significant solenoidal motions, and we find preferential CR damping of the compressive component in simulations with diffusion and streaming, rendering small-scale turbulence largely solenoidal, with implications for thermal instability and proposed resonant scattering ofE≳ 300 GeV CRs by fast modes. When CR transport is streaming dominated, CRs also damp large-scale motions, with kinetic energy reduced by up to 1 order of magnitude in realisticECREgscenarios, but turbulence (with a reduced amplitude) still cascades down to small scales with the same power spectrum. Such large-scale damping implies that turbulent velocities obtained from the observed velocity dispersion may significantly underestimate turbulent forcing rates, i.e.,ϵ˜ρv3/L.

    more » « less
  4. null (Ed.)
    ABSTRACT The physical foundations of the dissipation of energy and the associated heating in weakly collisional plasmas are poorly understood. Here, we compare and contrast several measures that have been used to characterize energy dissipation and kinetic-scale conversion in plasmas by means of a suite of kinetic numerical simulations describing both magnetic reconnection and decaying plasma turbulence. We adopt three different numerical codes that can also include interparticle collisions: the fully kinetic particle-in-cell vpic, the fully kinetic continuum Gkeyll, and the Eulerian Hybrid Vlasov–Maxwell (HVM) code. We differentiate between (i) four energy-based parameters, whose definition is related to energy transfer in a fluid description of a plasma, and (ii) four distribution function-based parameters, requiring knowledge of the particle velocity distribution function. There is an overall agreement between the dissipation measures obtained in the PIC and continuum reconnection simulations, with slight differences due to the presence/absence of secondary islands in the two simulations. There are also many qualitative similarities between the signatures in the reconnection simulations and the self-consistent current sheets that form in turbulence, although the latter exhibits significant variations compared to the reconnection results. All the parameters confirm that dissipation occurs close to regions of intense magnetic stresses, thus exhibiting local correlation. The distribution function-based measures show a broader width compared to energy-based proxies, suggesting that energy transfer is co-localized at coherent structures, but can affect the particle distribution function in wider regions. The effect of interparticle collisions on these parameters is finally discussed. 
    more » « less
  5. Abstract

    Magnetized turbulence is ubiquitous in many astrophysical and terrestrial plasmas but no universal theory exists. Even the detailed energy dynamics in magnetohydrodynamic (MHD) turbulence are still not well understood. We present a suite of subsonic, super-Alfvénic, high plasma beta MHD turbulence simulations that only vary in their dynamical range, i.e., in their separation between the large-scale forcing and dissipation scales, and their dissipation mechanism (implicit large eddy simulation, ILES, and direct numerical simulation (DNS)). Using an energy transfer analysis framework we calculate the effective numerical viscosities and resistivities, and demonstrate that all ILES calculations of MHD turbulence are resolved and correspond to an equivalent visco-resistive MHD turbulence calculation. Increasing the number of grid points used in an ILES corresponds to lowering the dissipation coefficients, i.e., larger (kinetic and magnetic) Reynolds numbers for a constant forcing scale. Independently, we use this same framework to demonstrate that—contrary to hydrodynamic turbulence—the cross-scale energy fluxes are not constant in MHD turbulence. This applies both to different mediators (such as cascade processes or magnetic tension) for a given dynamical range as well as to a dependence on the dynamical range itself, which determines the physical properties of the flow. We do not observe any indication of convergence even at the highest resolution (largest Reynolds numbers) simulation at 20483cells, calling into question whether an asymptotic regime in MHD turbulence exists, and, if so, what it looks like.

    more » « less