Non Linear Compton Scattering of Strong Laser Radiation on Channeled Particles in a Crystal

A version for intense $\gamma $-ray radiation based on the multiphoton scattering of strong laser radiation on relativistic particle beam channeled in a crystal is proposed. The scheme is considered when the incident laser beam and charged paricles beam are counter-propagating and the laser radiation is resonant to the energy levels of transversal motion of channeled particles.