γ-rays from pair recombination in a travelling wave structure

To obtain stimulated annihilation of pairs, two photon beams arriving from opposite directions are made to impinge with a region where e- - e+ pairs are interacting, thus stimulating their recombination. At the exit of the interaction region photons are amplified by a factor β. The change in photon density is studied as a function of the length of the interaction region. The pair density needed to have a given gain is calculated and results to be proportional to log β2/(1+β)