Excitation of the σ_{l}_{l} = 90° Resonance by the Cavity RF Accelerating Fields

International audienceIn RF linacs the longitudinal focusing is done by nonlinear forces and at high accelerating fields the zero-current longitudinal phase advance per longitudinal focusing period σ₀l_{l} can be high. The nonlinear components of the RF field (sextupolar, octupolar and higher order components) can then excite parametric resonances, including the 4th-order resonance (σ_{l}_{l} = 90°) when σ₀l_{l} is higher than 90°, inducing strong longitudinal emittance growths and acceptance reductions. The longitudinal beam dynamics is therefore complex, even when the nonlinear space-charge forces are ignored. The parametric resonance excitation by the RF field is analyzed before discussing the additional effect of the nonlinear space-charge forces, in particular to explain why the zero-current longitudinal phase advance per transverse focusing period σ₀l_{t} is not a relevant parameter. Examples are given in the SPIRAL2 linac case