Possibility of obtaining coherent radiation from a solid state undulator

The idea of using a crystal lattice or a superlattice as an undulator for a free electron laser is explored. A purely classical treatment of relativistic positrons channeling through the proposed structure is performed in a self-consistent fashion involving the wave equation for the radiating electromagnetic field and the kinetic equation for the positron distribution function. The (positive) gain coefficient for a forward radiating field is obtained in closed form. Matching the Kumakhov channeling resonance to the undulator frequency further enhances the gain. This result, combined with a feedback mechanism arising from Bragg diffraction within the basic crystal lattice, leads to an instability of the radiation inside the crystal. A simple threshold condition involving the atomic scattering factor and the net gain is formulated. Finally, a numerical estimate of the Kumakhov-enhanced gain coefficient is made for the (110) planar channeling in a strain-modulated Si superlattice.