Dissipation and particle acceleration at intermittent structures with velocity and magnetic shear: Interaction of Kelvin-Helmholtz and Drift-Kink instabilities

TL;DR

The paper addresses how energy dissipation and nonthermal particle acceleration arise at intermittent plasma structures featuring both velocity and magnetic shear. It employs 2D PIC simulations of a relativistic pair plasma with KH and DK instabilities, while tearing modes are suppressed, to isolate their nonlinear interplay. The main findings reveal a bent, thickened shear layer with an annihilated core and a KH cocoon, where dissipation peaks at moderate velocity shear, and a novel E_y-driven stochastic acceleration mechanism yields high-energy nonthermal tails with S-shaped particle trajectories; a Hillas-like energy cap suggests substantial acceleration potential in larger systems. These results have implications for dissipation and particle acceleration in astrophysical turbulence, such as AGN jet boundaries, and motivate future 3D kinetic studies and broader instability interactions.

Abstract

We present two-dimensional (2D) particle-in-cell simulations of a magnetized, collisionless, relativistic pair plasma subjected to combined velocity and magnetic-field shear, a scenario typical at intermittent structures in plasma turbulence. We create conditions where only the Kelvin-Helmholtz (KH) and Drift-Kink (DK) instabilities can develop, while tearing modes are forbidden. The interaction of DKI and KHI generates qualitatively new structures, marked by a thickened shear layer with very weak electromagnetic field, modulated by KH vortices. Over a range of moderately strong velocity shears explored, the interaction of DKI and KHI results in a significant enhancement of dissipation over cases with only velocity shear or only magnetic shear. Moreover, we observe a new and efficient way of particle acceleration where particles are stochastically accelerated by the motional electric field exterior to the shear layer as they meander in an S-shaped pattern in and out of it. This process takes advantage of the bent geometry of the shear layer caused by the DK-KHI interaction and is responsible for most of the highest-energy particles produced in our simulations. These results further our understanding of dissipation and particle acceleration at intermittent structures, which are present in plasma turbulence across a wide range of astrophysical contexts such as in AGN jet sheaths, potentially relevant to limb-brightened emission, etc., and highlight the sensitivity of dissipation to multiple interacting instabilities, thus providing a strong motivation for further studies of their nonlinear interaction at the kinetic level.

Figures (15)

• Figure 1: The double shear layer setup used in this study, consisting of two zones, Zone j and Zone w, in equal and opposite motion along the $x$-axis with each other. The magnetic field in Zone j points out of the page ($+z$ direction) while that in Zone w can point either into ($-z$) or out of the page. The plasma quantities $B, E$, etc. are connected smoothly between the two zones by a tanh profile.
• Figure 2: Snapshots of $B_z/B_j$ for simulations with velocity shear only ('VS', upper-top), magnetic shear only ('MS', upper-middle), and both shears ($u_j=0.5,B_w/B_j=-1$, upper-bottom). The lower panel shows snapshots of $B_z, E_x$ in the saturated stage ($tc/L_x=27.3$) for the $u_j=0.5,B_w/B_j=-1$ case, with the 'annihilated core' and 'KH cocoon' annotated.
• Figure 3: Top left: Growth curves of selected modes (indicated by the wavelength $\lambda$) for the control cases (red for VS, blue for MS). Note that the wavelengths of the displayed modes are different for the MS ($\lambda = 33 d_{e,j}$) and VS ($\lambda = 100 d_{e,j}$) case. Top right: Growth curves for selected test cases (red for $u_j=0.05$, blue for $u_j=0.3$, green for $u_j=0.9$). In both panels, dashed lines show fitted linear growth rates as indicated in the legends. The growth curve of the $u_j=0.9$ case is not fitted as no exponential growth phase can be identified. Bottom panel: Fitted linear growth rates for the test cases, with the fastest growing mode displayed in the legend. No fitted growth rate is displayed for the $u_j>0.6$ cases as no exponential growth phase can be identified. Not that the growth rate of the VS case is not displayed in this panel. The black arrow highlights the drop in growth rate for the $u_j=0.5$ case.
• Figure 4: Left: $x$-averaged plots of $B_z/B_j$ for $u_j = 0.05,0.1,0.3,0.8$, $B_w/B_j = -1$, showing how the instabilities thicken the magnetic shear layer. The black dashed line is the $x$-averaged plot of $B_z/B_j$ at $t=0$. The horizontal translucent brown line indicates $B_z=0$. Right: Width of the thickened shear layer as a function of velocity shear, at $tc/L_x=55$.
• Figure 5: Top and bottom left: The total magnetic and bulk kinetic energies within the simulation box $E_B, E_\mathrm{KE}$, normalized by their initial values $E_{B,0}, E_\mathrm{KE,0}$, against time for selected cases ($u_j = 0.05,0.1,0.3,0.8$, $B_w/B_j = -1$ and the VS case). Top and bottom right: brown dotted lines with red triangles show the magnetic and bulk kinetic energy dissipated, measured by $-\Delta E_B/E_{B,0},-\Delta E_\mathrm{KE}/E_\mathrm{KE,0}$, as a function of velocity shear $u_j$, at $tc/L_x=50$. Black dashed lines with blue squares show the width of the thickened shear layer for different $u_j$, same as the bottom right panel of Fig. \ref{['fig:growth']}, superimposed for comparison.