Revisiting the Longitudinal 90° Limit in High Intensity Linear Accelerators

Parametric envelope and sum envelope resonances are analyzed to revisit the validity of an assumed stop band and design limit of high intensity linear accelerators at a longitudinal phase advance of 90° per focusing lattice period. While the 90° limit is unquestioned in the transverse plane, we show here that it can be dropped as longitudinal limit for lattices with two or more rf gaps per focusing period. A new limit arises, however, from a novel transverse-longitudinal parametric sum envelope instability. The resulting sum instability rule allows the phase advance to exceed 90° longitudinally provided that transversely it remains correspondingly under 90°. We suggest that the additional design freedom opens the possibility for larger accelerating gradients and stronger longitudinal focusing with potential length and cost saving in the design of advanced superconducting linear accelerator concepts-as long as technological cavity limits are not reached.