skip to main content

Title: Statistics of pressure fluctuations in turbulent kinetic plasmas

In this study, we explore the statistics of pressure fluctuations in kinetic collisionless turbulence. A 2.5D kinetic particle-in-cell simulation of decaying turbulence is used to investigate pressure balance via the evolution of thermal and magnetic pressure in a plasma with β of order unity. We also discuss the behaviour of thermal, magnetic, and total pressure structure functions and their corresponding wavenumber spectra. The total pressure spectrum exhibits a slope of −7/3 extending for about a decade in the ion-inertial range. In contrast, shallower −5/3 spectra are characteristic of the magnetic pressure and thermal pressure. The steeper total pressure spectrum is a consequence of cancellation caused by density-magnetic field magnitude anti-correlation. Further, we evaluate higher order total pressure structure functions in an effort to discuss intermittency and compare the power exponents with higher order structure functions of velocity and magnetic fluctuations. Finally, applications to astrophysical systems are also discussed.

more » « less
Author(s) / Creator(s):
; ; ; ;
Publisher / Repository:
Oxford University Press
Date Published:
Journal Name:
Monthly Notices of the Royal Astronomical Society
Medium: X Size: p. 4067-4078
["p. 4067-4078"]
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

    The Parker Solar Probe (PSP) entered a region of sub-Alfvénic solar wind during encounter 8, and we present the first detailed analysis of low-frequency turbulence properties in this novel region. The magnetic field and flow velocity vectors were highly aligned during this interval. By constructing spectrograms of the normalized magnetic helicity, cross-helicity, and residual energy, we find that PSP observed primarily Alfvénic fluctuations, a consequence of the highly field-aligned flow that renders quasi-2D fluctuations unobservable to PSP. We extend Taylor’s hypothesis to sub- and super-Alfvénic flows. Spectra for the fluctuating forward and backward Elsässer variables (z±, respectively) are presented, showing thatz+modes dominatezby an order of magnitude or more, and thez+spectrum is a power law in frequency (parallel wavenumber)f−3/2(k3/2) compared to the convexzspectrum withf−3/2(k3/2) at low frequencies, flattening around a transition frequency (at which the nonlinear and Alfvén timescales are balanced) tof−1.25at higher frequencies. The observed spectra are well fitted using a spectral theory for nearly incompressible magnetohydrodynamics assuming a wavenumber anisotropykk3/4, that thez+fluctuations experience primarily nonlinear interactions, and that the minorityzfluctuations experience both nonlinear and Alfvénic interactions withz+fluctuations. The density spectrum is a power law that resembles neither thez±spectra nor the compressible magnetic field spectrum, suggesting that these are advected entropic rather than magnetosonic modes and not due to the parametric decay instability. Spectra in the neighboring modestly super-Alfvénic intervals are similar.

    more » « less

    The coupling state between ions and neutrals in the interstellar medium plays a key role in the dynamics of magnetohydrodynamic (MHD) turbulence, but is challenging to study numerically. In this work, we investigate the damping of MHD turbulence in a partially ionized medium using 3D two-fluid (ions + neutrals) simulations generated with the athenak code. Specifically, we examine the velocity, density, and magnetic field statistics of the two-fluid MHD turbulence in different regimes of neutral-ion coupling. Our results demonstrate that when ions and neutrals are strongly coupled, the velocity statistics resemble those of single-fluid MHD turbulence. Both the velocity structures and kinetic energy spectra of ions and neutrals are similar, while their density structures can be significantly different. With an excess of small-scale sharp density fluctuations in ions, the density spectrum in ions is shallower than that of neutrals. When ions and neutrals are weakly coupled, the turbulence in ions is more severely damped due to the ion-neutral collisional friction than that in neutrals, resulting in a steep kinetic energy spectrum and density spectrum in ions compared to the Kolmogorov spectrum. We also find that the magnetic energy spectrum basically follows the shape of the kinetic energy spectrum of ions, irrespective of the coupling regime. In addition, we find large density fluctuations in ions and neutrals and thus spatially inhomogeneous ionization fractions. As a result, the neutral-ion decoupling and damping of MHD turbulence take place over a range of length-scales.

    more » « less
  4. Abstract We investigate the interaction of turbulence with shock waves by performing 2D hybrid kinetic simulations. We inject force-free magnetic fields upstream that are unstable to the tearing-mode instability. The magnetic fields evolve into turbulence and interact with a shock wave whose sonic Mach number is 2.4. Turbulence properties, the total and normalized residual energy and the normalized cross helicity, change across the shock wave. While the energy of velocity and magnetic fluctuations is mostly distributed equally upstream, the velocity fluctuations are amplified dominantly downstream of the shock wave. The amplitude of turbulence spectra for magnetic, velocity, and density fluctuations are also increased at the shock wave while their spectral index remains unchanged. We compare our results with the Zank et al. model of turbulence transmission across a shock, and find that it provides a reasonable explanation for the spectral change across the shock wave. We find that particles are efficiently accelerated at the shock front, and a power-law spectrum forms downstream. This can be explained by diffusive shock acceleration, in which particles gain energy by being scattered upstream and downstream of a shock wave. The trajectory of an accelerated particle suggests that upstream turbulence plays a role scattering of particles. 
    more » « less
  5. Abstract

    We investigate a secondary proton beam instability coexisting with the ambient solar wind turbulence at 50R. Three-dimensional hybrid numerical simulations (particle ions and a quasi-neutralizing electron fluid) are carried out with the plasma parameters in the observed range. In the turbulent background, the particle distribution function, in particular the slope of the “bump-on-tail” responsible for the instability, is time-dependent and inhomogeneous. The presence of the turbulence substantially reduces the growth rate and saturation level of the instability. We derive magnetic power spectra from the observational data and perform a statistical analysis to evaluate the average turbulence intensity at 50R. This information is used to link the observed frequency spectrum to the wavenumber spectrum in the simulations. We verify that Taylor’s frozen-in hypothesis is valid for this purpose to a sufficient extent. To reproduce the typical magnetic power spectrum of the instability observed concurrently with the background turbulence, an artificial spacecraft probe is run through the simulation box. The thermal-ion instabilities are often seen as power elevations in the kinetic range of scales above an extrapolation of the turbulence spectrum from larger scales. We show that the elevated power in the simulations is much higher than the background level. Therefore, the turbulence at the average intensity does not obscure the secondary proton beam instability, as opposed to the solar wind at 1 au, in which the ambient turbulence typically obscures thermal-ion instabilities.

    more » « less