Excitation of the σl_l = 90° resonance by the cavity rf accelerating fields

Abstract

In rf linacs the longitudinal focalization is done by si-nusoidal forces and at high accelerating fields the zero-current longitudinal phase advance per longitudinal fo-cusing period σ0l_l can be high. The nonlinear compo-nents of the sinusoidal rf field (sextupolar, octupolar and higher order components) can then excite parametric resonances, including the 4th-order resonance (σl_l = 90°) when σ0l_l is higher than 90°, inducing strong longitudinal emittance growths and acceptance reductions. As pointed out in previous papers, the longitudinal beam dynamics is therefore complex, even when the space-charge forces are ignored. The parametric resonance excitation by the rf field is analyzed before discussing the additional effect of the space-charge forces, in particular to explain why the zero-current longitudinal phase advance per trans-verse focusing period σ0l_t is not a relevant parameter. Examples are given in the SPIRAL2 linac case.