We show that the mysterious, rapidly variable emission at similar to 400 MeV observed from the Crab Nebula by the AGILE and Fermi satellites could be the result of a sudden drop in the mass loading of the pulsar wind. The current required to maintain wave activity in the wind is then carried by very few particles of a high Lorentz factor. On impacting the nebula, these particles produce a tightly beamed, high-luminosity burst of hard gamma rays, similar to those observed. This implies that (i) the emission is synchrotron radiation in the toroidal field of the nebula and, therefore, linearly polarized and (ii) this mechanism potentially contributes to the gamma-ray emission from other powerful pulsars, such as the Magellanic Cloud objects J0...
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