Correspondence principle in free-electron lasers

Multiphoton interaction in free-electron lasers is studied using the correspondence principle. The developed theory is applicable to both quantum-mechanical and classical regimes of operation of the laser. The suggested formalism simplifies the traditional calculation of the small-signal, single-particle gain in the system. As an example, the theory is applied to the case of the free-electron laser operating in combined transverse helical and axial guide magnetic fields.