Analysis of OK SR FEL devices

We discuss a simple model for the evolution of a Storage-Ring (SR) FEL operating in the optical-klystron (OK) configuration. We analyze the OK gain formula and introduce the parametrizations which account for the inhomogeneous broadening and saturation effects. We also derive a parametrization for the induced energy spread. The OK SR FEL evolution is then described by two coupled rate equations which accounts for the evolution of the intracavity power and the associated e-beam heating and damping. The model allows the derivation of the stationary output and intracavity power and is also a flexible tool for the system optimization. The analytical results are confronted with the available experimental data and the agreement is found more than satisfactory.