  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$^{-1}$.
