Nonlinear theory of the free-electron laser based upon a coaxial hybrid wiggler

Abstract

A three-dimensional nonlinear formulation of a free-electron laser based upon a coaxial hybrid iron (CHI) wiggler is described. The CHI wiggler is created by insertion of a central rod and an outer ring [composed of alternating ferrite and dielectric spacers in which the ferrite (dielectric) spacer on the central rod is opposite to the dielectric (ferrite) spacer on the outer ring] along the axis of a solenoidal. An analytic model of the CHI wiggler is developed which is in good agreement with the Poisson/Superfish group of codes. The free-electron laser (FEL) formulation is a slow-time-scale analysis of the interaction of an annular electron beam with the CHI wiggler in a coaxial waveguide. The electromagnetic field is represented as the superposition of the vacuum transverse electric (TE), transverse magnetic (TM), and transverse electromagnetic (TEM) modes of the waveguide, and a set of nonlinear second-order differential equations is derived for the amplitudes and phases of these modes. These equations are solved simultaneously with the three-dimensional Lorentz force equations for the combined magnetostatic and electromagnetic fields. An adiabatic taper is used to model the injection of the beam, and an amplitude taper is included for efficiency enhancement. Simulations are presented for Ka-, Ku- and W-band operation. Multimode operation is also studied. The results indicate that operation over a wide bandwidth is practical with the CHI wiggler, and that the bandwidth in the tapered-wiggler cases is comparable to that for a uniform wiggler. Therefore, relatively high field strengths can be achieved with the CHI wiggler at shorter wiggler periods than is possible in many other conventional wiggler designs.