Intermittency in Collisionless Large-Amplitude Turbulence

TL;DR

This work demonstrates that collisionless, large-amplitude turbulence exhibits intermittency patterns closely related to MHD expectations but strongly modulated by pressure anisotropy. Using fully kinetic 3D simulations across a wide range of δB/B0 and driving-scale separations, the authors show that pressure anisotropy steepens the B–K_parallel relation to B ∝ K_parallel^{-3/4} and triggers mirror and firehose instabilities, which increase small-scale fluctuations and affect field-line dynamics. The resulting K_parallel and K_perp statistics reveal extended power-law tails and non-MHD features, with implications for particle transport via resonant curvature scattering and for particle acceleration through curvature-drift and magnetic pumping mechanisms. These findings have direct relevance for cosmic-ray transport in the hot ISM and the ICM, suggesting that kinetic effects must be accounted for in models of turbulence-driven transport and acceleration in astrophysical plasmas.

Abstract

Large-amplitude turbulence -- characterized by a fluctuating magnetic field component, $δB$, that is stronger than the mean component, $B_0$ -- is generically intermittent, populated with intense localized structures such as sharp field-line bends and rapid field reversals. Recent MHD simulations suggest that these structures play an important role in particle transport and acceleration; however, MHD is inapplicable in most of our Universe, where the plasma is so hot or diffuse that Coulomb collisions are negligible. Therefore, in this paper, we analyze the intermittent properties of collisionless large-amplitude turbulence in electron-positron plasmas via fully kinetic 3D simulations, exploring a wide range of $δB / B_0$ and scale separations between the turbulence driving scale, $L$, and kinetic scales, $c/ω_{\rm p}$. The steady-state collisionless turbulence in our simulations broadly resembles that of MHD, but the development of pressure anisotropy steepens the scaling between magnetic field strength, $B$, and scalar field-line curvature, $K_\parallel$ -- yielding $B \propto K_\parallel^{-3/4}$ -- and consequently modifies the power-law slope of the probability density function of $K_\parallel$; this slope hardens from $K_\parallel^{-2.5}$ to $K_\parallel^{-2.0}$ as $δB / B_0$ increases from 4 to 140. Pressure anisotropy also triggers mirror and firehose instabilities, with the volume-filling fractions of these fluctuations increasing with $δB / B_0$; for our largest $δB / B_0$, $20\%$ of the volume is mirror-unstable and $6\%$ is firehose-unstable. Both the curvature and the Larmor-scale fluctuations in collisionless large-amplitude turbulence are expected to significantly influence cosmic ray transport and acceleration in the interstellar medium of our Galaxy and the intracluster medium of galaxy clusters.

Figures (17)

• Figure 1: Time evolution of the magnetic energy (top panel) and the kinetic energy (bottom panel) for each of our simulations with $L/(c/\omega_{\rm p}) = 2000$; the unmagnetized dynamo case, $\delta B/B_0 \rightarrow \infty$, is depicted with a dotted curve to distinguish it from the rest of the cases. The magnetic energy is normalized to give $1/\beta$ at fixed temperature (Equation \ref{['eq:beta']}) and the kinetic energy is normalized to give the square of the sonic Mach number at fixed temperature (Equation \ref{['eq:mach2']}). Each simulation reaches a steady state within a few tens of eddy turnover times, $t_{\rm L} \equiv L/2\pi u_{\rm rms,0}$.
• Figure 2: Isotropic magnetic (top panel) and kinetic (bottom panel) power spectra for each of our simulations with $L/(c/\omega_{\rm p}) = 2000$. The normalization of each spectrum is multiplied by the radial wavenumber, $k$, to show the energy in log-spaced bins; the integral over the magnetic spectrum yields $1/\beta$ (Equation \ref{['eq:beta']}) and the integral over the kinetic spectrum yields the square of the sonic Mach number (Equation \ref{['eq:mach2']}). The red dotted lines in each panel indicate the Kolmogorov scaling ${\rm M}(k) \propto {\rm K}(k) \propto k^{-5/3}$kolmogorov. The magnetic power spectrum becomes noise-dominated at wavenumbers $k \, c/\omega_{\rm p} \gtrsim 0.7$, or physical scales below $\sim 9 \, c/\omega_{\rm p}$.
• Figure 3: 2D slices (in the $xy$-plane) of $B/B_{\rm rms}$ -- the local magnetic field strength normalized by the global rms magnetic field strength -- at late times for our simulations with $\delta B/B_0 \approx 1$ (upper left), $4$ (upper right), $10$ (lower left), and $140$ (lower right) and $L/(c/\omega_{\rm p}) = 2000$; brighter colors represent regions of stronger field.
• Figure 4: Renormalized probability density functions (PDFs) of increments of the $x$-component of the magnetic field (Equation \ref{['eq:increment']}) for our simulations with $\delta B/B_0 = 1$ (upper left), $4$ (upper right), $10$ (lower left), and $140$ (lower right) and $L/(c/\omega_{\rm p})=2000$. By subtracting the mean of the raw PDF, $\overline{\Delta B_x}$, and dividing by the standard deviation of the raw PDF, $\Sigma_{\Delta B_x}$, these renormalized PDFs have a mean of zero and a standard deviation of unity; the equivalent Gaussian distribution is shown as a dotted curve in each panel. For each $\delta B/B_0$, we show the renormalized PDF of field increments at five different separations, $r/(c/\omega_{\rm p}) = 15$, $45$, $129$, $357$, and $999$, with lighter shades for larger separations.
• Figure 5: 2D PDFs of the local magnetic field strength, $B/B_{\rm rms}$, vs. the local field-line curvature, $K_\parallel$, for each of our simulations with $L/(c/\omega_{\rm p})=2000$ (see panel labels). The red dotted line in each panel shows the scaling $B \propto K_\parallel^{-1/2}$ (expected in MHD, e.g., schek_dynamo), while the blue dotted line shows $B \propto K_\parallel^{-3/4}$. To increase the contrast in the high-$K_\parallel$ tails of these PDFs, we normalize the PDFs such that the integral over the 1D PDF of $B/B_{\rm rms}$ at each $K_\parallel$ is unity.