Acceleration of ultrarelativistic electrons in the Crab Nebula

Ultrarelativistic electrons must be being accelerated in the Crab Nebula to maintain the synchrotron spectrum. Sufficient power to maintain the synchrotron spectrum is supplied by an observed damping of compressional motions in the central region of the nebula (the wisps of Baade). An acceleration mechanism which involves compressional motions, the gyrorelaxation effect and the removal of pitch angle anisotropies by the generation of hydromagnetic waves is formulated and applied to a model of the Crab Nebula with acceleration confined to a central region. This can account for the power supplied to the electrons, the overall shape of the spectrum and allows acceleration up to energies corresponding to the synchrotron emission of hard X-rays. The acceleration process tends to flatten an initial energy spectrum.