Electron heating by filamentary instability

It is widely believed that relativistic low magnetized shocks are mediated by filamentary (Weibel) instability. Numerical simulations show that the developing filamentation results in the shock formation accompanied by ion deceleration and efficient electron heating. Similar heating efficiency was found in periodic numerical simulations which indicates similar mechanisms for both systems. Yet, the mechanism of the electron energization has not been identified so far. Here a new simple model of electron acceleration in filamentary relativistic shocks is presented. We suggest that the large-scale inductive electric field, generated in the course of the filamentary instability, is responsible for ion deceleration and electron energization within the filaments. Acceleration of electrons along the filaments is due to the electric field alignment with the filaments, while isotropization is due to the magnetic scattering, broadband nature of the instability and continuous growth of the dominant scale of the magnetic field. This electron heating is a nonstationary effect and occurs as long as the filaments keep growing.