Abstract
The recent discovery of PeV electrons from the Crab nebula, produced on rapid time scales of one day or less with a sharply peaked gamma-ray spectrum without hard X-rays, challenges traditional models of diffusive shock acceleration followed by synchrotron radiation. Here we outline an accleration model involving a DC electric field parallel to the magnetic field in a twisted toroidal field around the pulsar. Sudden developments of resistivity in localized regions of the twisted field are thought to drive the particle acceleration, up to PeV energies, resulting in flares. This model can reproduce the observed time scales of $T \approx 1$ day, the peak photon energies of $U_{\Phi,rr} \approx 1$ MeV, maximum electron energies of $U_{e,rr} \approx 1$ PeV, and luminosities of $L \approx 10^{36}$ erg s$^{-1}$.
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