Abstract
Refractive guiding in the FEL is investigated with a new approach, the beam phase space model, in which the optical beam is regarded as a bundle of rays which is assumed to be an ellipse in optical phase. In this nonwave optical model the area of the ellipse acts like the wavelength resulting from wave theory. A beam envelope equation is deduced from the model to describe the propagation behavior of a Gaussian beam through free space and various optical devices. This equation is applied to an FEL with the effective refractive index derived from 1-D FEL theory to study the refractive guiding effect in the FEL. As an example the effect in an FEL oscillator is modeled by means of the theory.
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