On the spectrum of the pulsed gamma-ray emission from 10MeV to 400GeV of   the Crab pulsar
  In the present paper a self-consistent theory, interpreting the VERITAS observations of the very high energy pulsed emission from the Crab pulsar is considered. The photon spectrum between 10MeV and 400GeV can be described by two power-law functions with the spectral indexes equal to 2 and 3.8. The source of the pulsed emission above 10MeV is assumed to be the synchrotron radiation, which is generated near the light cylinder during the quasi-linear stage of the cyclotron instability. The emitting particles are the primary beam electrons with the Lorentz factors up to $10^{9}$. Such high energies by beam particles is supposed to be reached due to Landau damping of the centrifugally induced Langmuir waves. This mechanism provides simultaneous generation of low (radio) and high energy (10MeV-400GeV) emission on the light cylinder scales, in one location of the pulsar magnetosphere. 
Nino Chkheidze, George Machabeli and Zaza Osmanov
astro-ph.HE