Commissioning Experience from PEP-II HER Longitudinal Feedback

The DSP-based bunch-by-bunch feedback system installed in the PEPII high-energy ring (HER) has been used to damp instabilities induced by unwanted higher-order modes (HOMs) at beam currents up to 605 mA during commissioning. Beam pseudospectra calculated from feedback system data indicate the presence of coupled-bunch modes that coincide with a previously observed cavity mode (0-M-2). Bunch current and synchronous phase measurements are also extracted from the data. These measurements reveal the impedance seen by the beam at revolution harmonics. The impedance peak at 3 frev indicates incorrect parking of the idle cavities, and explains the observed instability of mode 3. Bunch synchrotron tunes are calculated from lorentzian ts to the data. Bunch-to-bunch tune variation due to the cavity transient is shown to be large enough to result in Landau damping of coupled-bunch modes. INTRODUCTION The PEP-II high-energy ring (HER) electron beam has a design current of 1A. Beam currents up to 750 mA have been achieved so far. During commissioning, a variety of longitudinal and transverse beam dynamics experiments have been performed [1{3] with the help of the PEP-II longitudinal feedback (LFB) system [4]. The most useful diagnostic characteristic of this system is its ability to record the oscillations of each bunch over a 27 ms time window. The recorded data can then be archived and analyzed o line to extract detailed information about beam dynamics and beam conditions. The two main sources of longitudinal motion identi ed in PEP-II are cavity impedance induced coupled-bunch instabilities and noise from the klystron. Coupled-bunch instabilities are usually caused by unwanted higher-order modes (HOMs) in the rf cavities, or by impedance sources elsewhere in the beam surroundings. At PEP-II however, the large beam current and small revolution frequency combine to produce low-mode instabilities within the bandwidth of the detuned rf 1: Work supported by DOE contract No. DE-AC03-76SF00515. cavity fundamental mode [3]. The HOM-induced instabilities have been successfully damped by the above-mentioned longitudinal feedback system. Low-mode motion is damped by a combination of rf feedback loops acting through the klystron. In this paper we demonstrate the ability of the broadband LFB system to drive coupled-bunch motion with positive feedback, and damp it with negative feedback. We also present a novel beam-based method for measuring the longitudinal impedance spectrum [2]. This method involves calculation of the transfer function from ll shape (bunch current versus bunch number) to synchronous phase of a multibunch beam, which is shown to yield the longitudinal impedance seen by the beam at revolution harmonics. This technique has been used to measure the impedance of parked cavities at PEP-II, and explain the occasional instability of low-order coupled-bunch modes at unexpectedly low total currents. Multibunch synchronous phases and bunch currents are extracted from data stored by the LFB system. In addition to providing impedance information, multibunch synchronous phase measurements are useful in themselves, since HER and LER phase transients need to be matched to achieve high luminosity. The synchronous phase transients are also an indicator of the amount of Landau damping a orded by bunch-to-bunch tune shifts. Lorentzian ts to bunch motion spectra yield a bunch tune versus bunch number graph that correlates well with the synchronous phase transients. We examine the interesting features of one such graph in the nal section, and demonstrate the decoupling of bunch oscillations at the ends of the bunch tune range.