Analysis on the stop band of fourth-order resonance in high-intensity linear accelerators

Abstract

The earlier study of [Jeon et al., Phys. Rev. Spec. Top.--Accel. Beams 12, 054204 (2009)] discovered 4 sigma = 360 degrees fourth-order particle resonance in linear accelerators (linacs) for any non-KV distributions (such as Gaussian and waterbag) and found that this particle resonance was predominantly manifested over the envelope instability. Several experiments have since been performed and demonstrated that fourth-order resonance indeed occurred for sigma < 90 <degrees>. Nonetheless, the lower bound of the particle resonance stop band and detailed parametric studies (e.g., scanning with various beam currents and zero-current phase advances sigma (0)) on the emittance growth from the fourth-order resonance have been somewhat limited. This paper presents analytical and numerical investigations to observe the fourth-order resonance under several focusing field types (e.g., solenoid and quadrupole) with a wide range of parameters. From these studies, the general stop band for the 4 sigma = 360 degrees fourth-order particle resonance is established to be sigma 0 > 90 degrees and sigma < 90 <degrees>. Self-consistent multi-particle simulations using TraceWin and PARMILA codes are performed with initially well-matched Gaussian beams to observe the emittance growth originating from the fourth-order particle resonance. It is found that the emittance growth rate varies depending on sigma (0) and tune depression (or equivalently beam current). It transpires that the region in which the envelope instability develops is consistent with the envelope instability stop band. The fourth-order particle resonance stop band is wider than the envelope instability stop band, and the envelope instability is induced following fourth-order particle resonance only within the envelope instability stop band in the tune-depression space.