Fermi-type particle acceleration from magnetic reconnection at the termination shock of a relativistic striped wind

An oblique-rotating pulsar generates a relativistic striped wind in a pulsar wind nebula (PWN). The termination shock of the PWN compresses the Poynting-flux-dominated flow and drives magnetic reconnection. By carrying out particle-in-cell (PIC) simulations of the termination shock of the PWN, we study the shock structure as well as the energy conversion processes and particle acceleration mechanisms. With the recent advances in the numerical methods, we extend the simulations to the ultra-relativistic regime with bulk Lorentz factor up to \gamma_{0}=10^{6}. Magnetic reconnection at the termination shock is highly efficient at converting magnetic energy to particle kinetic energy and accelerating particles to high energies. We find that the resulting energy spectra crucially depend on \lambda/d_{e}. When \lambda/d_{e} is large (\lambda\gtrsim40d_{e}) , the downstream particle spectra form a power-law distribution in the magnetically dominated relativistic wind regime with upstream magnetization parameter \sigma_{0}=10. By analyzing particle trajectories and statistical quantities relevant to particle energization, we find that Fermi-type mechanism dominates the particle acceleration and power-law formation. We find that the results for particle acceleration are scalable as \gamma_{0} and \sigma_{0} increase to large values. The maximum energy for electrons and positrons can reach hundreds of TeV if the wind has a bulk Lorentz factor \gamma_{0}\approx10^{6} and magnetization parameter \sigma_{0}=10, which can explain the recent observations of high-energy gamma-rays from pulsar wind nebulae (PWNe).