ANL, Argonne, Illinois, USA
We analyze single bunch transverse instabilities due to wakefields using a Fokker-Planck model. We expand on the work of Suzuki*, writing out the linear matrix equation including chromaticity, both dipolar and quadrupolar transverse wakefields, and the effects of damping and diffusion due to the synchrotron radiation. The eigenvalues and eigenvectors determine the collective stability of the beam, and we show that the predicted threshold current for transverse instability and the profile of the unstable agree well with tracking simulations. In particular, we find that predicting collective stability for high energy electron beams at moderate to large values of chromaticity requires the full Fokker-Planck analysis to properly account for the effects of damping and diffusion due to synchrotron radiation.
* T. Suzuki, Particle Accel., 12, 237 (1982)
Fermilab, Batavia, Illinois, USA
The Fermilab Booster accelerates bunches and accelerates proton beams from 400 MeV to 8 GeV. During the acceleration the Radio Frequency (RF) cavities are swept from 38MHz to 52.8MHz and requires crossing through transition where accelerating phase is shifted 90 degrees. In order to keep the beam stable and minimize losses and emittance growth a longitudinal damping system is required. This has traditionally been done by dedicated analog electronics designed to operate on specific beam modes for frequencies of instabilities. A complete digital implementation has been developed for this same purpose. The new digital system features and performance are detailed.
Cornell University (CLASSE), Cornell Laboratory for Accelerator-Based Sciences and Education, Ithaca, New York, USA
CalPoly, San Luis Obispo, California, USA
University of Notre Dame, Indiana, USA
BNL, Upton, Long Island, New York, USA
Auburn University, Auburn, USA
A model to simulate the effect of a transverse feedback system is implemented in SPACE, a parallel, self-consistent code for collective effects. As an application, we discuss single bunch instability thresholds in the NSLS-II storage ring and compare the numerical results with measurements.
Fermilab, Batavia, Illinois, USA
Using Synergia accelerator modeling package and Dynamic Mode Decomposition technique, the properties of the first transverse dipole mode in Gaussian bunches with space charge are compared at transverse coupling resonance and off-resonance. The Landau damping at coupling resonance and in the strong space charge regime is a factor of two larger, while the mode's tune and shape are nearly the same. While the damping mechanism in the off-resonance case fits well with the classical Landau damping paradigm, the enhancement at coupling resonance is due to a higher order mode-particle coupling term which is modulated by the amplitude oscillation of the resonance trapped particles.
ANL, Argonne, Illinois, USA
he Advanced Photon Source (APS) is pursuing an upgrade to the storage ring to a hybrid seven-bend-achromat design*. The nominal design provides a natural emittance of 67 pm. By adding reverse dipole fields to several quadrupoles**, we can reduce the natural emittance to 41 pm while simultaneously providing more optimal beta functions in the insertion devices. The improved emittance results from a combination of increased energy loss per turn and a change in the damping partition. At the same time, the nonlinear dynamics performance is very similar, thanks in part to increased dispersion in the sextupoles. This paper describes the properties, optimization, and performance of the new lattice.
* L. Farvacque et al., IPAC13, 79 (2013).
** J.P. Delahaye \em et al., PAC89, 1611 (1990); A. Streun, NIM A 737, 148 (2014).