Abstract
We propose a novel scheme for the calculation of bunch profiles and synchronous phase shifts for arbitrary fill patterns in electron storage rings considering both the effects of the passive harmonic cavity and the short range wakefield. This scheme treats the bunch as a charge distribution rather than a point charge with a bunch form factor, and divides the voltage induced in the cavity into two groups: that induced by the previous passages and that by the present passage, where the latter is integrated with the short range wakefield from all the other vacuum components. An iteration loop for computing the bunch profiles, including a subloop using Newton iteration for calculating the synchronous phase deviations, is built and implemented into a matlab-based code. Using this code, we study the bunch lengthening and centroid transient effects for several possible fill patterns in the Hefei Advanced Light Facility storage ring under design. We find the method is very efficient, and the CPU time for the whole calculation on a regular personal computer is less than 30 seconds for each case even with more than 700 bunches. Using the case of a long gap fill as a benchmark example, both the results given by our code and the multiparticle tracking simulation with elegant are in very good agreement.
Highlights
In the ongoing fourth generation storage rings, the higher harmonic cavity (HHC) is an essential component to attain the machine performance, which can, by elongating the bunch, mitigate the intrabeam scattering, increase the Touschek lifetime, and reduce the beam-induced vacuum components heating [1]
To benchmark our MATLAB-based code, we study the case of a long gap fill pattern with 720 identical bunches by parallel ELEGANT tracking [27], with and without a broadband resonator (BBR)
We have presented a semianalytical self-consistent scheme for quickly computing the centroid shifts and bunch profiles of arbitrary filled bunches in the presence of a passive harmonic cavity and the short range wakefield
Summary
In the ongoing fourth generation storage rings ( called diffraction-limited storage rings), the higher harmonic cavity (HHC) is an essential component to attain the machine performance, which can, by elongating the bunch, mitigate the intrabeam scattering, increase the Touschek lifetime, and reduce the beam-induced vacuum components heating [1]. Two types of approaches can be used to study the bunch lengthening for the case of nonuniform fill pattern: semianalytical calculation and multiparticle tracking simulation The former can be traced back to [18], where the bunch was treated as a point charge, and the induced voltage seen by every bunch was determined by the single particle tracking, so the effect of the bunch profile was ignored. We propose an alternative novel semianalytical scheme to calculate the longitudinal equilibrium density distribution for arbitrary fill patterns and HHC settings This scheme uses the matrix formulation to form the induced voltage as done in [14], but treats the bunch as a charge density distribution rather than a macroparticle with a bunch form factor. The phasor plot for the main cavity is presented in Appendix A, and the corresponding Newton iteration method for the synchronous phase deviation is described in Appendix B
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