Cavitation instability in unmagnetized relativistic pair shocks

TL;DR

This work identifies a cavitation instability in unmagnetized relativistic pair shocks as a nonlinear consequence of asymmetric Weibel filamentation. By combining homogeneous PIC simulations with a minimal two-fluid toy model, it shows how magnetic walls and low-field cavities form self-consistently, and derives a criterion for cavity onset tied to the Weibel-frame velocity. The results reveal two regimes—magnetized and non-magnetized cores—whose wall dynamics can produce long-lived, intermittently strong magnetic fields, offering a potential link between kinetic turbulence and macroscopic magnetization relevant to GRB afterglows. This mechanism thus bridges kinetic-scale Weibel turbulence and large-scale magnetic structure, contributing to resolving the GRB magnetization paradox and informing shock-accelerated particle dynamics.

Abstract

We investigate the formation of plasma cavities in unmagnetized relativistic pair shocks and demonstrate that these cavities emerge naturally as a nonlinear consequence of asymmetric Weibel instability. We provide an intuitive physical picture and a minimal fluid model that captures the essential features of this cavitation instability and compare them with PIC results. This mechanism may provide the missing link between kinetic Weibel turbulence and macroscopic magnetic fields in astrophysical shocks.

Figures (16)

• Figure 1: Distribution of total plasma density and magnetic field $B_z$ in a PIC simulation of a relativistic shock propagating into an unmagnetized pair plasma. The shock precursor exhibits a cellular pattern, with plasma collecting in dense walls where the $B$-field is the strongest. The simulation is in the downstream frame, where the upstream plasma Lorentz factor is $\Gamma_0=10$. The shock transition at the presented time, $4000\omega_p^{-1}$, is located at $\sim 1800(c/\omega_p)$ and moves to the right with velocity $v_\text{sh}\sim c/2$. All simulation parameters are listed in Appendix \ref{['sec:numerical']}.
• Figure 2: Reference run distributions of total plasma density, total charge density, and magnetic field $B_z$ in the lab frame $S$ at different simulation times: a) just before cavity formation; b) when cavities are formed as magnetic fields and plasma gather into thin walls at the edges of the filament. The figure shows only the part of the simulation box, $y<20(c/\omega_p)$, where the cavity walls are the strongest.
• Figure 3: Reference run distributions of total plasma density, total charge density, and magnetic field $B_z$ in the lab frame $S$ at $t=200\omega_p^{-1}$. Top panel -- same as Fig. \ref{['fig:lab2']}; bottom panel -- profiles of $N_+/N_0$ (positrons), $N_-/N_0$ (electrons), and $B_z/\sqrt{16\pi N_0\Gamma_0 mc^2}$ averaged over the $x$-coordinate (for clarity, the magnetic field is scaled by a factor of $\Gamma_0$).
• Figure 4: Sketch of a plasma positron-dominated Weibel filament. Black arrows show the longitudinal component of velocities; $F_e$ and $F_m$ denote the transverse electric and magnetic forces, respectively.
• Figure 5: Sketch of total Lorentz force acting on positrons in the plasma positron filament: a) during the linear Weibel stage; b) during cavity formation. The arrows show the direction of positron acceleration under the action of force $F_{+y}$.