Kinetic Description of a Low-Gain Free-Electron Laser using the Einstein Coefficient Method

The theory of a low-gain free-electron laser in the Raman regime has been studied using the Einstein coefficient method. Particle trajectories are chosen that are suited for perfect and imperfect injections of a beam in a circularly polarized, static, periodic helical-wiggler, and axial-guide magnetic fields. The spontaneous emission and gain per unit length were determined by the Einstein coefficient method. The expressions are general and are suited for higher harmonics also. The expressions obtained are compared with available expressions from earlier studies. The numerical results obtained for the Raman regime in the microwave and infrared regions are discussed. The results indicate that it is easier to achieve free-electron laser action in the infrared region than in the microwave region