L. Teng

Effects of errors on the dynamic aperture of the Advanced Photon Source storage ring

The individual tolerance limits for alignment errors and magnet fabrication errors in the 7-GeV Advanced Photon Source storage ring are determined by computer-simulated tracking. Limits are established for dipole strength and roll errors, quadrupole strength and alignment errors, sextupole strength and alignment errors, as well as higher-order multipole strengths in dipole and quadrupole magnets. The effects of girder misalignments on the dynamic aperture are also studied. Computer simulations are obtained with the tracking program RACETRACK, with errors introduced from a user-defined Gaussian distribution, truncated at +or-5 standard deviation units.<<ETX>>

Nonlinear resonance studies at the synchrotron radiation center, Stoughton, Wisconsin

A single bunch is stored in ALADDIN at 800 MeV. The coherent oscillations produced by a fast kicker are recorded for each turn at two horizontal position detectors separated by pi /2 in phase. Displaying the recorded positions on horizontal and vertical axes produces a phase plot of the coherent motion. Resonances are produced by adding a controlled amount of sextupole field. The results are compared with computer simulations. To adequately describe the behavior near unstable fixed points the finite size of the beam must be taken into account.<<ETX>>

Effects of construction and alignment errors on the orbit functions of the Advanced Photon Source Storage Ring

The orbit functions for the Advanced Photon Source storage ring have been studied using the simulation code RACETRACK. Nonlinear elements are substituted into the storage ring lattice to simulate the effects of construction and alignment errors in the quadrupole, dipole, and sextupole magnets. The effects of these errors on the orbit distortion, dispersion, and beta functions are then graphically analyzed to show the RMS spread of the functions across several machines. The studies show that the most significant error is displacement of the quadrupole magnets. Further studies using a three-bump correction routine show that these errors can be corrected to acceptable levels.<<ETX>>

Paraxial expansion of a static magnetic field in a ring accelerator

In the paraxial approximation, trajectories of beam particles in a ring accelerator are computed expanded in powers of lateral displacements and slopes from a closed reference orbit. To do this, one needs first the expanded expressions of the magnetic field and potentials producing the particle motion. This is derived here in a most general form.

Particle diffusion from resonance islands in ALADDIN at SRC

The dynamics of the beam in the resonance islands was studied on the electron storage ring ALADDIN at the Synchrotron Radiation Center (SRC). We especially studied the horizontal third- and fourth-integral resonances driven by sextupole fields in the first and second order. A fast kicker was fired to kick the beam into one of the outboard stable islands. The beam took on a quasi-Gaussian distribution and slowly diffused out of the island. The diffusion rate and its dependence on the strengths of the driving sextupoles and the chromaticity sextupoles were measured by tracing the resonance peak of the betatron oscillation on the spectrum analyzer. Beam positions were also recorded through the data acquisition device which was clocked by a pulse-delay circuitry. Interesting results are shown and compared with numerical calculations.<<ETX>>

Study of loss factor for slots in the vacuum chamber

Using the 3-D wakefield calculation program MAFIA, the longitudinal loss factor (energy lost by the beam) and the transverse loss factor (transverse kick experienced by the beam) are systematically studied with the depth and the length of a slot as parameter values. When the bunch is longer than the slot, it is found that simulation results agree with the early theoretical prediction by M. Sands (1977). The loss factor decreases exponentially as the slot gets deeper. However, when the bunch is shorter than the slot, it is found that the longitudinal loss factor decreases but the transverse loss factor does not change very much as the slot gets longer.<<ETX>>

Global coupling and decoupling of the APS storage ring

This paper describes a study of controlling the coupling between the horizontal and the vertical betatron oscillations in the 7-GeV Advanced Photon Source (APS) storage ring. First, we investigate the strengthening of coupling using two families of skew quadrupoles. Twenty skew quadrupoles are arranged in the 40 sectors of the storage ring and powered in such a way so as to generate both quadrature components of the required 21/sup st/ harmonic. The numerical results from tracking a single particle are presented for the various configurations of skew quadrupoles. Second, we describe the global decoupling procedure to minimize the unwanted coupling effects. These are mainly due to the random roll errors of normal quadrupoles. It is shown that even with the rather large RMS roll error of 2 mrad, the coupling effects can be compensated for with 20 skew quadrupoles each having maximum strength one order of magnitude lower than the typical normal quadrupole strength.<<ETX>>

Establishment of a tolerance budget for the Advanced Photon Source storage ring

The limitations on the dynamic aperture of the Advanced Photon Source storage ring due to magnet misalignments and fabrication errors are presented. The reduction of the dynamic aperture is analyzed first for each error considered individually, and then for combined error multipole fields in dipole, quadrupole, and sextupole magnets, excluding and including magnet misalignments. Since misalignments of the strong quadrupoles in the ring induce large orbit distortions, the effects on the dynamic aperture are investigated before and after orbit correction. Effects of off-momentum particles and the tune dependence with momentum are also presented. This extensive analysis leads to the establishment of a tolerance budget. With all the errors set at the tolerance level, and with the orbit distortions corrected, the dynamic aperture reduction is no greater than 50% of that of the ideal machine.<<ETX>>

First turn beam correction for the Advanced Photon Source storage ring

A procedure was developed for precise realignment of the quadrupoles in a synchrotron radiation storage ring which can substantially ease the required precision of the initial survey. The procedure consists of first using the injected beam to obtain a closed orbit which is centered on the beam position monitors by the correction dipoles. The strengths of the correction dipoles then give the required fine-adjustment of the quadrupole positions. The authors discuss only the algorithm for obtaining the closed orbit.<<ETX>>