SIMPLE APPROXIMATIONS TO TRANSVERSE WIGGLER SPECTRA INTEGRATED OVER FINITE APERTURES IN THE WIGGLE PLANE

Simple approximations to conventional transverse wiggler spectra integ rated over finite apertures in the wiggle plane are derived. Account i s taken of the departure of the wiggler's on-axis field profile from a n idealized sinusoidal shape. By introducing a generalization of the c onventional K parameter, it is shown that the approximations can be fo rmulated from a Fourier decomposition of the wiggler's dominant field profile in the direction of particle motion without explicit reference to the particle beam trajectory. Use of the generalized K parameter f or estimating the first harmonic output energies of undulators and the critical energies of wigglers is examined.