Kinetic Simulations of Particle Acceleration in Relativistic Perpendicular Electron-positron Shocks with Proton Admixture

TL;DR

The paper investigates how a small proton fraction affects particle acceleration in relativistic perpendicular shocks using 2D PIC simulations with $\gamma_0=10$ and $\sigma=2.0\times10^{-2}$. It finds that positrons are efficiently accelerated to nonthermal energies with a spectrum $N(E)\propto E^{-\alpha}$ with $\alpha\approx2$, reaching energies comparable to protons, while electrons remain largely thermal. The acceleration arises from proton-driven instabilities that emit left-handed waves resonantly energizing positrons, and the process saturates when proton-emitted waves are depleted. These results underscore the critical role of plasma composition in shaping nonthermal emission and have implications for astrophysical sources such as PWNe and GRBs.

Abstract

Particle acceleration in relativistic shocks of electron-positron plasmas with proton admixture is investigated through two-dimensional (2D) particle-in-cell (PIC) simulations. The upstream plasma, with a bulk Lorentz factor of $10$ and a magnetization parameter of 0.02, includes a small fraction of protons ($\sim 5\%$ by number). A relativistic perpendicular shock is formed by reflecting the flow off a conducting wall. The shock structure, electromagnetic fields, and particle energy spectra are analyzed. The particle density and the magnetic field have fluctuations. In the far-downstream region of the shock, positrons are accelerated to energies comparable to protons and develop a hard nonthermal component with a spectral index of $\sim 2$ in their energy spectrum, while electrons remain confined to lower energies. This asymmetry is attributed to the polarization properties of proton-driven electromagnetic waves, which favor positron acceleration. The results highlight the importance of plasma composition in shaping particle acceleration and nonthermal emission in relativistic shocks. These findings provide new insights into the microphysics of particle acceleration in astrophysical sources containing relativistic shocks.

Figures (10)

• Figure 1: Particle number density normalized to $n_0$ as a function of $x$ at $t=6.25\times10^3 \omega_{\mathrm{pe}}^{-1}$.
• Figure 2: 2D density distribution of electrons (top panel), positrons (middle panel), and protons (bottom panel) obtained from the simulation at $t=6.25\times10^3 \omega_{\mathrm{pe}}^{-1}$. The color scale indicates the relative density.
• Figure 3: Spatial distribution of $B_z$, $E_x$ and $E_y$ at $t=6.25\times10^3 \omega_{\mathrm{pe}}^{-1}$. The magnetic field is amplified at the shock front and decays downstream.
• Figure 4: Longitudinal phase space plots $x - p_x$ of electrons, positrons, and protons at $t=6.25\times10^3 \omega_{\mathrm{pe}}^{-1}$.
• Figure 5: Energy spectra of the electrons, positrons, and protons downstream of the shock ($800\ c/\omega_{\mathrm{pe}}\leq x \leq 1600 \ c/\omega_{\mathrm{pe}}$) at $t=6.25\times10^3 \omega_{\mathrm{pe}}^{-1}$. The spectra consist of a thermal component at low energies and a nonthermal tail at high energies. The thermal distribution with a temperature of $T =5 m_e c^2/k_{\mathrm{B}}$ (dotted line) is also illustrated.