Energy partition in collisionless counterstreaming plasmas

Abstract

Fast, counter-streaming plasma outflows drive magnetic field amplification, plasma heating, and particle acceleration in numerous astrophysical environments, from supernova remnant shocks to active galactic nuclei jets. Understanding how, in the absence of Coulomb collisions, energy is redistributed between the different plasma species remains a fundamental open question. We use 3D fully-kinetic simulations to investigate energy partition in weakly magnetized counter-propagating plasmas. Our results reveal a complex interplay between different processes, where at early times the Weibel instability drives a first stage of magnetic field amplification and at late times the kinking of current filaments drives a second amplification stage via a dynamo-type mechanism. Electrons are heated primarily during the latter phase through magnetic pumping. By the time the flows thermalize, we observe that the final temperature ratio $T_e/T_i$ and energy partition depend on the ion-to-electron mass ratio. For electron-proton flows, the electron thermal energy only reaches up to a few percent of the initial ion kinetic energy.

Figures (6)

• Figure 1: Evolution of the ion drift kinetic energy $\mathcal{E}_i=(\gamma_i-1)m_ic^2$ (orange), magnetic field energy $\mathcal{E}_B=B^2/(8\pi n_0)$ (black), electron temperature $T_e$ (blue) and ion temperature $T_i$ (red) for the early (a) and late (b) times, normalized to the initial ion kinetic energy $\mathcal{E}_{i0}$.
• Figure 2: Ion density ($x-y$) slice for the ion population propagating initially toward the positive $x$ direction in the (a) full box and (b) shortened box cases, taken at $t=50.9\omega_{pi}^{-1}$ during the drift-kink instability phase. (c) Temporal evolution of filament radius $R$ (red) and comparison with the size of the transverse perturbation amplitude of the filaments $a$ (blue) and with the scaled electron gyroradius extracted from particle tracking data $r_{Le}(\pi/2)$ (gray) for the full box case. The dashed vertical line indicates the time when the electrons become magnetized $r_{Le}(\pi/2)\leq R$. (d) Similar to (c) but for the shortened box case $L_x=2c/\omega_{pi}<\lambda_{kink}$. The black line indicates the electron gyroradius $r_{Le}$. (e) Evolution of the ion drift kinetic energy $\mathcal{E}_i$, (f) electron temperature $T_e$, (g) total magnetic field $B$ (solid line) and longitudinal component $B_x$ (dashed line), in the full box (red line, kink) and shortened box (black line, no kink) cases.
• Figure 3: (a) Evolution of the magnetic field amplification rate $dB/dt$ from the simulation (orange) and from Eq. \ref{['eq:dBdt_theory']} (red). (b) Evolution of the electron heating rate $d T_e/d t$ from the simulation (blue) and from Eq. \ref{['eq:dTedt_theory']} (black). The dashed vertical lines indicate the electron magnetization ($r_{Le}(\pi/2)\leq R$, $t\approx70\omega_{pi}^{-1}$) and drift-kink instability saturation (Eq. \ref{['eq:bsat_v']}, $t\approx190\omega_{pi}^{-1}$), with the theoretical predictions valid only within this time window and shown with reduced opacity beyond it.
• Figure 4: (a) Magnetic field amplification $B$ as a function of mass ratio $m_i/m_e$ in the shortened box (noted 'no kink', black dot markers) and full box (noted 'kink', black cross markers) cases. The magnetic field observed in the full box simulations at the time Eq. \ref{['eq:bsat_v']} is verified is shown with red circles. The case $M_A=50$ is shown with green square markers. (b) Electron temperature (blue) and ion temperature (red) in the full box case (noted 'kink', cross markers). The results for the case $M_A=50$ are shown with green triangles (electrons) and squares (ions).
• Figure 5: Evolution of the ion drift kinetic energy $\mathcal{E}_i$ (orange), magnetic field energy $\mathcal{E}_B$ (black), electron temperature $T_e$ (blue) and ion temperature $T_i$ (red) for the early (a) and late (b) times, normalized to the initial ion kinetic energy $\mathcal{E}_{i0}$ in a 2D simulation with $L_xL_y=40\times20(c/\omega_{pi})^2$ and $m_i/m_e=64$.