Designing a grating based free electron laser

A compact far-infrared free electron laser (FEL) driven by a moderate energy beam would have many applications in academic and industrial research. Our goal is to find the optimal operating parameters producing the highest gain for a grating FEL with either a SASE or oscillator configuration. The basic structure consists of a grating bounded above by a roof extending over a portion of its length. The dispersion relation for such a system can be found by expanding the electromagnetic fields in a series of resonant modes. When the fields and the beam have near-synchronous velocities, the fields grow at a rate determined by the imaginary component of ω (k for spatial growth) and group velocity. Relations between gain and beam energy, roof height, tooth depth and angle of curve intersection have been investigated