Storage Ring Lattice Modeling and Its Applications

Lingyun Yang Storage Ring Lattice Modeling and Its Applications Small amplitude particle motion around its closed orbit in an accelerator can be well approximated by the linear betatron oscillation. This linearized betatron oscillation is simple harmonic motion governed by Hill’s equation. The closed orbit may be distorted by a dipole error or an orbit bump, and the observed distortion divided by the orbit bump strength (dipole error) is the Green’s function. Measurement of Green’s function can uniquely determine the linear part of the dynamical system. The Orbit Response Matrix (ORM) measure the Green’s function at BPM (Beam Position Monitor) location with orbit bumpers at various locations. This measurement has been shown to be a powerful tool in accelerator modeling in finding gradient errors, quadrupole tilt angles, BPM gain factors and the tilt angles. A new orbit code named YAOC (Yet Another Orbit Code) is developed to reconstruct the ring lattice based on the ORM data. The code can be used to model the errors of quadrupoles and BPMs of a running machine, and to restore the symmetry of the linear lattice. Using a powerful optimization algorithm called Scaled Levenberg-Marquardt algorithm, we get a much better convergence in simulations than the earlier code developed at Indiana University. This new code has been used to study the Fermilab Booster, the Taiwan Photon Source (TPS) design lattice and the NSLS VUV ring at BNL. Thousands of accelerator error models were randomly generated and successfully reconstructed. The symmetry of lattice can thus be restored, except for very few cases where the random error distribution accidentally put vi vii the lattice tunes too close to the betatron resonance such that no finite ORM data exists. YAOC uses a similar beam transport matrix as TRANSPORT, MAD and Elegant up to the 3rd order expansion. Users can implement their own elements with the virtual matrix (VMatrix). The operations between transfer matrices are straightforward due to operator overloading. The modeling and optimization algorithm of YAOC is based on the Scaled Levenberg-Marquardt algorithm, which provides better convergence property and is more robust to avoid the betatron resonance in iterative fittings. YAOC is also extensible to include the misalignment errors. We have simulated Fermilab Booster with YAOC. In thousands of random lattice, YAOC reconstructed most of them correctly. We have also simulated different levels of errors, up to 25% of the nominal value. YAOC can reconstruct the lattices even when the ORM elements have noise or only part of the BPMs are used. Besides the proton ring, YAOC was also bench marked on electron storage rings, such as the TPS design lattice and the NSLS VUV ring at BNL. Another application for identifying the source of vertical orbit oscillation is presented. In this dissertation, I will also discuss the beam lifetime of the VUV ring. Both theoretical and experiment results are presented and compared. Some most fundamental beam qualities are measured, and calibrated, such as bunch length, vacuum pressure, lifetime and momentum acceptance. The effect of vacuum chamber dimensions on beam lifetime will be discussed.