SPONTANEOUS EMISSION IN THE UNIFORM MAGNETIC-FIELD FREE-ELECTRON LASER DESCRIBED BY THE ORDINARY AND SCALARIZED PHOTONS

As is the case with the usual free-electron laser with a helical magnetic field, the uniform magnetic-field free-electron laser has both the fundamental and the higher harmonic-frequency (spontaneous and stimulated) emission, where, however, emission with higher harmonic frequencies occurs only off axis. (The z component of the initial electron velocity defines the axis direction, which is also the direction of the uniform magnetic field B.) Here, within the multiphoton formalism, using both the ordinary and scalarized photons, we study only the spontaneous emission, into the fundamental and higher harmonic frequencies. It is proven that the use of the scalarized photons, whose advantage is that they simplify many calculations, is generally equivalent to the use of the ordinary photons. Specifically we find that the radiated energy, either total or partial (for a particular harmonic), scales linearly with L, the interaction length, and quadratically with B. The numerical analysis of the angular distribution of the spontaneously emitted energy indicates that, in addition to dominant on-axis fundamental frequency spontaneous emission, we can have rather significant higher harmonic-frequency spontaneous emission occurring just slightly off axis. So it appears that, at least in principle, not only on axis but also slightly off axis (higher harmonic) spontaneous emission could be used to stimulate emission from electrons further along for sufficiently wide electron beams.