Generalized electron beam matching in the free-electron laser

Three matching schemes are presented for Gaussian profile electron beams in free-electron lasers (FELs). The three different classes of matching or symmetry conditions are (1) electron beams with separate betatron matching in each plane, (2) those with aspect ratio matching, and (3) cross-matched beams. The new schemes are distinct generalizations of well-known betatron matching and include ribbon profiles. The corresponding effective energy distributions and their Fourier transforms are obtained in analytical form. An analytical kernel produces the key Fredholm integral equation that solves the initial value problem.<
>