Longitudinal stability in multiharmonic standing wave linacs

Accelerating cavities that excite multiple modes at integer harmonics of the fundamental frequency have the potential to be used to suppress the onset of rf breakdown and reduce the pulsed surface heating at high accelerating gradients. Understanding the effect of an additional harmonic cavity mode on the longitudinal beam dynamics is important to their development and use. A Hamiltonian that describes the longitudinal motion of a particle as it traverses a chain of multiharmonic cavities has been derived and is applied to the case of a second harmonic cavity. The Hamiltonian is based upon formalisms found in literature for the fundamental harmonic and is extended to include different longitudinal field distributions and harmonic frequencies. The study initially explores the longitudinal motion for moderate accelerating gradients with high-beta protons, as this will allow fundamental properties of the stable region (acceptance and shape of the rf bucket) to be determined. High accelerating gradients are also investigated but the focus will be on phase stability throughout. This work concludes by considering the longitudinal dynamics of a modified European Spallation Source accelerator, comprised of multiharmonic cavities that has specifications broadly consistent with the accelerator.