An algorithm for the design and tuning of RF accelerating structures with variable cell lengths

Design studies of a continuous-wave normal conducting buncher for European X-ray Free Electron Laser

“…and K(e0) and E(e0) are the complete elliptic integrals of the first and second kind [21]. For an input RF power (Pin), the power coupled to the cavity is given as…”

“…As discussed in Ref [21], for a coupled multi-cell structure, the resonance frequency, field flatness and RF are interdependent which makes the tuning very tedious and time consuming.…”

“…To simplify the RF coupler design, method discussed in Ref [21] is employed to determine the dimensions of the RF coupling slot for desired RF coupling coefficient. As discussed in Ref [22], the presence of an RF coupling slot also breaks the azimuthal symmetry of the coupler cell which leads to generation of multipole modes and may distort the beam trajectory, shape and phase space.…”

“…The optimum waveguide tapering length of 130 mm is selected, which corresponds to a tapering angle of ~11.5 and reduces the critical coupling slot length from 69 mm to 41 mm. As discussed in Ref [21], to compensate the effect of coupling slot opening, coupler cell ID is reduced to 99.77 mm from 99.91 mm. The structure resonates for  mode at 1.3 GHz with RF =1.05 and field flatness of 1.01.…”