Electron Acceleration at Pulsar Wind Termination Shocks

We study the acceleration of electrons and positrons at an electromagnetically modified, ultrarelativistic shock in the context of pulsar wind nebulae. We simulate the outflow produced by an obliquely rotating pulsar in proximity of its termination shock with a two-fluid code that uses a magnetic shear wave to mimic the properties of the wind. We integrate electron trajectories in the test-particle limit in the resulting background electromagnetic fields to analyze the injection mechanism. We find that the shock-precursor structure energizes and reflects a sizable fraction of particles, which becomes available for further acceleration. We investigate the subsequent first-order Fermi process sustained by small-scale magnetic fluctuations with a Monte Carlo code. We find that the acceleration proceeds in two distinct regimes: when the gyroradius $r_g$ exceeds the wavelength of the shear λ, the process is remarkably similar to first-order Fermi acceleration at relativistic, parallel shocks. This regime corresponds to a low-density wind that allows the propagation of superluminal waves. When $r_g<\lambda ,$ which corresponds to the scenario of driven reconnection, the spectrum is softer.