We study particle acceleration at the termination shock of a striped pulsar wind by integrating trajectories in a prescribed model of the magnetic field and flow pattern .
Drift motion on the shock surface maintains either electrons or positrons on “ Speiser ” orbits in a ring-shaped region close to the equatorial plane of the pulsar , enabling them to be accelerated to very high energy by the first-order Fermi mechanism .
A power-law spectrum results : dN _ { e } / d \gamma \propto \gamma ^ { \alpha _ { e } } , where \alpha _ { e } lies in the range -1.8 to -2.4 and depends on the downstream turbulence level .
For sufficiently strong turbulence , we find \alpha _ { e } \simeq - 2.2 , and both the photon index and the flux of 1 – 100 keV X-rays from the Crab Nebula , as measured by NuSTAR , can be reproduced .
The particle spectrum hardens to \alpha _ { e } \simeq - 1.8 at lower turbulence levels , which may explain the hard photon index observed by the Chandra X-ray Observatory in the central regions of the Nebula .