Turbulence and Magnetic Reconnection in Relativistic Multispecies Plasmas

TL;DR

The study tackles how relativistic turbulence and magnetic reconnection operate in multispecies plasmas containing electrons, positrons, and protons with realistic mass ratios. It employs two-dimensional PIC simulations and derives a novel generalized Ohm's law for a three-species plasma to interpret reconnection dynamics, current sheets, and energy dissipation. By varying the positron fraction $\chi$, the work shows that protons suppress small-scale turbulence and elevate dissipation and reconnection energy, while pair-dominated plasmas exhibit more frequent but weaker reconnection and preserved power-law spectra. These findings have implications for particle acceleration and high-energy emission in astrophysical environments near compact objects, and the generalized Ohm's law provides a framework for analyzing kinetic dissipation in relativistic multispecies plasmas.

Abstract

Simulations of relativistic plasmas traditionally focus on the dynamics of two-species mixtures of charged particles under the influence of external magnetic fields and those generated by particle currents. However, the extreme conditions of astrophysical plasmas near compact objects such as black holes and neutron stars are often characterized by mixtures of electrons, protons, and positrons, whose dynamics can differ significantly because of the considerable mass contrast. We present the first two-dimensional particle-in-cell simulations of relativistic turbulence and magnetic reconnection in a three-species plasma, varying the relative abundance of electrons, protons, and positrons while employing realistic mass ratios to achieve unprecedented accuracy. We find that turbulence leads to the formation of magnetic islands, current sheets, and plasmoids. Reconnection occurs between these structures, with plasma composition playing a key role in determining the number of reconnection sites and their energy-conversion efficiency. In particular, as the proton fraction increases, very small-scale features of the turbulence are washed out, while global dissipative effects are amplified. Finally, using a novel generalization of Ohm's law for a relativistic multi-species plasma, we find that the reconnection rate is primarily governed by the electric fields associated to the divergence of the positron and electron pressure tensors. These results provide new insights into dissipation and particle acceleration in turbulent relativistic plasmas, such as those near black holes and neutron stars, and can be used to interpret their high-energy emission and phenomenology.

Figures (7)

• Figure 1: Upper row: Snapshots of the (normalized) total number density $n/\langle n \rangle_{\mathrm{rms}}$ at time $t = 3 \, t_{\text{A}}$ for $\chi = 0.1$ (a), $\chi = 0.5$ (b), and $\chi = 0.9$ (c). Lower row: Panel (d) shows the evolution of the rms of the out-of-plane component of the current density for different concentration ratios; (e) shows the power spectrum of the magnetic field when turbulence is fully developed at $t = 3\, t_{\text{A}}$, with the corresponding slopes; (f) shows the same as in (e), but for the electric field. The power spectra are normalized to the rms of the in-plane magnetic field. Thin solid lines mark the spectral slope breaks in the inertial range.
• Figure 2: PDFs of the reconnection rates (symbols) for $\chi = 0.1$ (blue), $\chi = 0.5$ (red), and $\chi = 0.9$ (green), with corresponding linear fits shown as solid lines in matching colors. Dashed vertical lines indicate the median reconnection rates for each distribution, while the inset shows the evolution of the number of X-points (${\rm \#XP}$) for each configuration.
• Figure 3: Top panel: PDFs of the various contributions to the electric field in the $z$-direction, as given in Eq. \ref{['eq:Ohm']}, for $\chi = 0.5$ and at $t = 3\,t_\text{A}$. Bottom panel: Power spectra of the dominant contributions reported in the top panel. Marked with the gray vertical line is the typical proton scale.
• Figure 4: Left panel: colormap of the current density in the $z$-direction at $t = 3 \, t_{\text{A}}$ for the simulation with $\chi = 0.5$. Bright green lines indicate isocontours of the out-of-plane component of the vector potential $A^z$. Several strong X-points are marked with an $\bm{\times}$ and serve as origin for the normal and tangent unit vectors $\bm{\hat{n}}$ (red arrows) and $\bm{\hat{t}}$ (blue arrows), respectively. Right panels: the left column shows the average profiles of the magnetic-field components parallel (blue lines) and perpendicular (gray lines) to the current sheet, plotted along the $n$-direction, for $\chi = 0.1$ (top row), $\chi = 0.5$ (middle row), and $\chi = 0.9$ (bottom row). The right column displays the average profiles of the various contributions to Ohm's law, including the total electric field (black lines), the positron pressure-gradient contribution (purple lines), the electron pressure-gradient contribution (red lines), and the electron-positron electromotive contribution (orange lines), also along the $n$-direction. As before, each row correspond to a different value of $\chi$.
• Figure A1: Consistency study showing the particle kinetic-energy distributions expressed as a function of the Lorentz factor for electrons (left panel), positrons (middle panel), and protons (right panel). The simulations refer to the case with $\chi = 0.5$ and show the different setups listed in \ref{['eq:num_setups']} at $t = t_{\text{A}}$