Theoretical study of FEL active guiding in the small signal regime

Abstract We use a self-consistent small signal FEL field equation to study active guiding. We show that self-similar mode propagation is possible only in the exponential regime. These modes must be either growing or decaying; the purely oscillatory self-similar mode is not confined. By a Gaussian approximation, we investigate the eigenvalue structure of the fundamental mode analytically, and derive a cubic equation for the complex growth rate, the laser mode size, and the radius of the phase front curvature.