The three-dimensional wake potentials of the APS storage ring have been reconstructed according to the impedance database concept. Every wakefield-generating component in the ring was considered including small-gap insertion device (ID) chambers, rf cavities, shielded bellows, beam position monitors, synchrotron radiation absorbers, scrapers, flags, various chamber transitions, septum chambers, and pulsed kickers. In this paper the result for the longitudinal wake potentials and its impedance are presented. The total impedance is not model-based but the direct sum of numerical functions. The fit parameters for the broadband resonator model are also included as a convenient representation. We used this impedance model to investigate the observed microwave instability, namely bunch lengthening, anomalous energy spread, and coherent excitation at high synchrotron sideband.
IMPEDANCE DATABASEThe concept of impedance database is described in the companion paper [1]. We report highlights of building the database for the longitudinal impedance.The horizontal and vertical impedance are reported separately [2,3]. The rf cavities at the APS storage ring provide energy to the beam with 9.5 MV of gap voltage distributed in sixteen cavities in four sectors. One of the rf sectors is shown in Fig. 1.
Rf-Sector (rf-cavities and transition)An rf sector consists of four cavities and the transition of vacuum chamber at both ends. The complexity is simplified in the simulation to axially symmetric geometry. We used the program ABCI in order to calculate wake potential The wake potential of one rf sector for a 5 mm bunch is shown in Fig. 2; the cavityonly wake potential is also included for comparison. We note that there exists significant interference effect between the transition and cavities. The impedance, the Fourier transform of the wake potential divided by the bunch spectrum, is shown in Fig. 3. The graph on the left shows the impedance of shortranged wake over 30 cm, which shows the characteristic cavity-type impedance in the form of. This short-ranged wake potential is included in the total wake potential. Note the imaginary part of the impedance is negative.The impedance of long-ranged wake over 10 m is also shown in Fig. 3 on the right. Higher-order modes (HOMs) as well as the fundamental mode resonating at 352 MHz are clearly shown. The total HOM contribution to Z/n is 0.2 Ω, which was estimated by using the formula ( ) ( )where R s is the shunt impedance, Q is the quality factor, and n is the harmonic number. This (Z/n) HOM is included in the impedance breakdown for Z/n.