Abstract

The idea of using a strain modulated superlattice¹ as an undulator for a free electron laser is explored. A purely classical treatment of an infinite array of macroscopic currents of relativistic positrons channeling through the proposed structure and the radiated elctromagnetic field is performed in a self-consistent fashion involving the wave equation and the kinetic equation² for the positron density distribution function. The resulting linear gain coefficient for the forward radiating elctromagnetic field combined with a feedback mechanism arising from Bragg diffraction within the basic crystal lattice, leads to an instability of the radiaton inside the crystal. The gain coefficient is studied numerically for a strain modulated Si crystal. Assuming a strain modulation of the superlattice with a period of ℓ=100 a (a=5.43Å is the Si lattice spacing), the energy of the Kumakhov resonance³ corresponds to γ_k=1.25. If the energy of incoming particle beam matches γ_k the linear gain coefficient has a maximum corresponding to an emitted electromagnetic radiation of λ ≃ 100Å. The maximum possible gain combined with intrinsic losses arising from various x-ray attenuation mechanisms gives a net gain in the system.

© 1986 Optical Society of America