QUANTUM-FIELD THEORETICAL RELATIONSHIP BETWEEN THE AXIAL SPONTANEOUS EMISSION AND THE LASER GAIN, AND ITS APPLICATION TO THE FREE-ELECTRON 2-QUANTUM STARK-EMISSION LASER

The relationship between the axial spontaneous emission and the laser gain is obtained by means of quantum field theory. Using the relationship, the spontaneous two-quantum Stark emission in the beam direction by a relativistic electron beam and in an electrostatic wave propagating in the antiparallel direction of the electron beam (<<electric wiggler>>) is derived from the laser gain by the stimulated free-electron two-quantum Stark emission. It is found that the spontaneous-emission power per unit solid angle in the axial direction scales as E(b)6E(o)2-lambda(W)0, where E(b) is the beam energy and E(o) and lambda(W) are the field amplitude and wiggler wavelength of the electric wiggler, respectively.