Abstract
We discuss VHE gamma-ray generation through inverse Compton scattering of relativistic electrons on the soft thermal and non-thermal emission of the Crab pulsar. In the model of pulsar wind acceleration on the Alfvén surface, the interaction of particles with non-thermal emission is negligible. Inverse Compton scattering of relativistic electrons and positrons on the thermal emission of the neutron star surface makes a significant contribution to the pulsating TeV gamma-rays. Comparison with observations shows that the Crab pulsar can make a contribution to the observed emission. Weak pulsations may be unresolved at the present level of statistics on the background of TeV emission from the Crab nebula. It is shown that, in any model of VHE gamma-ray generation through inverse Compton scattering on non-therma soft emission, primary electrons or positrons ejected by the Crab pulsar will initiate an electromagnetic cascade. A dozen generations of secondary particles are produced in the cascade. The energy of the secondary particles is a factor of 200 less than the energy of the primary particles. Under these conditions, this mechanism cannot make a contribution to the observed TeV emission from the Crab
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