Quantum model of the free‐electron laser in a uniform magnetic field

摘要

A quantum model of the single particle free‐electron laser in a uniform magnetic field is given. Here the classical electron current due to electrons in helical orbits (caused by a uniform magnetic field) interacts with a quantized radiation in the interaction volume of finite extent. The description of this free‐electron laser is through the S matrix which incorporates the quantum recoil completely and yields directly the full ‘‘quantum mechanical’’ gain. Taking the relativistic electron factor γ to be approximately equal to 2.4 and the magnitude of the magnetic field in the range of 0.6–1.6 T, this free‐electron laser should be capable of generating radiation in the far infrared‐microwave spectral region. From the analysis of the asymptotic (classical limit) gain (a gain due to the ‘‘infinite’’ number of photons in the interaction volume V), we conclude that it is generally easier to generate radiation in the forward, rather than backward, direction. We also discuss the dependence of the gain on the electron velocity in the z direction, the strength of the uniform magnetic field, and the fact that our (asymptotic) gain scales as L3, which is similar to the gain of the usual (wiggler) free‐electron laser.