Analytical Study Of Multimode Competition

A theoretical analysis of the multimode competition problem in a FEL is presented. For the three-mode problem the system is mathematically described by a set of three coupled differential equations. The coupling coefficients in the equations are obtained from a perturbation expansion of the current driving the FEL. The only asymptotically stable solutions are single-mode. Then a system of any number of modes is studied. In this case also only single-mode solutions are asymptotically stable.