Abstract
We propose a novel algorithm to deal with the interaction of beam-cavity, which is convenient to be implemented on the platform of matlab supporting graphics process unit operations and can significantly improve the computational efficiency. Actually, this algorithm has been implemented and the corresponding code is named stable, which can be used to study the longitudinal beam dynamics of arbitrary filled bunches in electron storage rings. In this paper, the stable code is mainly used to evaluate the bunch lengthening produced by the passive higher harmonic cavity. We first carry out efficiency tests for stable and the results are satisfactory. We then benchmark the stable code against the semianalytical approach and elegant tracking for equilibrium and nonequilibrium cases, respectively, and the results are in good agreement. Furthermore, the stable code is applied to the case of Advanced Light Source upgrade (ALS-U) with distributed gaps, and the results firstly reveal a regular and periodic transient beam loading effect and thus show a nonequilibrium state for the overstretching case. As a second example, the stable code is also applied to the case of the Hefei advanced light facility (HALF) storage ring with uniformly distributed gaps, and the results show that the passive normal conducting harmonic cavities with a total $R/Q$ of $\ensuremath{\sim}200\text{ }\text{ }\mathrm{\ensuremath{\Omega}}$ will cause severe transient effects, thus being not suitable for Hefei advanced light facility.
Highlights
In an electron storage ring with main parameters roughly fixed, the longitudinal beam dynamics mainly depend on the fundamental and higher order modes (HOMs) of rf cavities, trapped modes of cavity-like components, as well as the short-range wakes
For the fourth-generation storage ring light source, it is necessary to evaluate the influence of HOMs and the beam loading related to the fundamental mode on the beam, in order to provide a reference for the design of rf cavities, especially higher harmonic cavities (HHCs), since HHCs are widely employed for bunch lengthening to improve
The fill pattern with uniformly distributed gaps will be preferred by the Hefei advanced light facility (HALF) storage ring, as it can effectively mitigate the influence of the transient beam loading on bunch lengthening and ensure that the bunches are stretched by a factor of 4 [5]
Summary
In an electron storage ring with main parameters roughly fixed, the longitudinal beam dynamics mainly depend on the fundamental and higher order modes (HOMs) of rf cavities, trapped modes of cavity-like components, as well as the short-range wakes. There are two types of methods that can be used for related assessments—analysis-based and tracking-based methods For the former, there are several recently developed semianalytical methods that can calculate the equilibrium bunch profiles for arbitrary fill patterns [3,4,5,6], as well as a method that can further calculate the instability growth rate induced by HOMs on the basis of the equilibrium solution [7]. This voltage phasor can be updated particle by particle, so that there is no need to keep in memory the long history of previous bunch interactions This algorithm has already been implemented into MBTRACK [9] and ELEGANT [10] and is equivalent to the so-called “wakefield matrix” employed by MUSIC [11].
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