The controlling parameters and the laser expression for a wiggler-free free-electron laser

Using the canonical transformations in Bambini–Renieri frame, the basic equations governing a wiggler-free free-electron laser are presented. It is found that the evolution of the system is determined by two controlling parameters. The condition, under which the exponentially growing exists, is obtained. Furthermore, starting from an arbitrary initial state of the system, the laser expression is derived. Finally, the possibility of employing this kind of system to give 300 (or 400) μm radiation is discussed using the Free Electron Laser for Infrared eXperiments (FELIX) parameters [P. W. van Amersfoort et al., Nucl. Instrum. Methods Phys. Res. A 318, 42 (1992)].