Y.T. Yan

LEGO: a modular accelerator design code

An object-oriented accelerator design code has been designed and implemented in a simple and modular fashion. It contains all major features of its predecessors: TRACY and DESPOT. All physics of single-particle dynamics is implemented based on the Hamiltonian in the local frame of the component. Components can be moved arbitrarily in the three dimensional space. Several symplectic integrators are used to approximate the integration of the Hamiltonian. A differential algebra class is introduced to extract a Taylor map up to arbitrary order. Analysis of optics is done in the same way both for the linear and non-linear case. Currently, the code is used to design and simulate the lattices of the PEP-II. It will also be used for the commissioning.

Low Energy Ring lattice of the PEP-II asymmetric B-factory

Developing a lattice that contains a very low beta value at the interaction point (IP) and has adequate dynamic aperture is one of the major challenges in designing the PEP-II asymmetric B-factory. For the Low Energy Ring (LER) we have studied several different chromatic correction schemes since the conceptual design report (CDR). Based on these studies, a hybrid solution with local and semi-local chromatic sextupoles has been selected as the new baseline lattice to replace the local scheme in the CDR. The new design simplifies the interaction region (IR) and reduces the number of sextupoles in the arcs. Arc sextupoles are paired at /spl pi/ phase difference and are not interleaved. In this paper we describe the baseline lattice with the emphasis on the lattice changes made since the CDR.

A fast tracking method using resonance basis Hamiltonians

A resonance basis map is an important way of analyzing lattice properties in circular accelerators. A method is developed to do tracking with resonance basis maps. The speed of this method is faster than other map tracking methods, and can be dramatically increased by dropping insignificant resonance terms. This mapping method enables us to simulate and study the interplay between lattice nonlinearities and other effects such as the beam-beam interaction.

A flexible-variable truncated power series algebra in Zlib

Zlib is a numerical library for truncated power series algebra (TPSA) and Lie algebra for application to nonlinear analysis of single particle dynamics. The first version was developed in 1990 with the use of the one-step index pointers (OSIPs). The OSIPs form the Zlib nerve that offers optimal computation and allow order grading as well as flexible initialization of the global number of variables for the TPSA. While the OSIPs are still kept for minimum index passing to achieve efficient computation, Zlib has been upgraded to allow flexible and gradable local number of variables in each C++ object of the truncated power series class. Possible applications using Zlib are discussed.

Swamp plots for dynamic aperture studies of PEP-II lattices

With a newly developed algorithm using resonance basis Lie generators and their evaluation with action-angle Poisson bracket maps (nPB tracking), we have been able to perform fast tracking for dynamic aperture studies of PEP-II lattices as well as incorporate lattice nonlinearities in beam-beam studies. We have been able to better understand the relationship between dynamic apertures and the tune shift and resonance coefficients in the generators of the one-turn maps. To obtain swamp plots (dynamic aperture vs. working point) of the PEP-II lattices, we first compute a one-turn resonance basis map for a nominal working point and then perform nPB tracking by switching the working point while holding fixed all other terms in the map. Results have been spot-checked by comparing with element-by-element tracking.

ZLIB++: Object Oriented Numerical Library for Differential Algebra

New software engineering tools and object-oriented design have a great impact on the software development process. but in high energy physics all major packages were implemented in FORTRAN and porting of these codes to another language is rather complicated, primarily because of their huge size and heavy use of FORTRAN mathematical libraries. But some intrinsic accelerator concepts, such as nested structure of modern accelerators, look very pretty when implemented with the object-oriented approach. In this paper the authors present the object-oriented version of ZLIB, numerical library for differential algebra, and show how the modern approaches can simplify the development and support of accelerator codes, decrease code size, and allow description of complex mathematical transformations by simple language.

Computational tools and lattice design for the PEP-II B-Factory

Several accelerator codes were used to design the PEP-II lattices, ranging from matrix-based codes, such as MAD and DIMAD, to symplectic-integrator codes, such as TRACY and DESPOT. In addition to element-by-element tracking, we constructed maps to determine aberration strengths. Furthermore, we have developed a fast and reliable method (nPB tracking) to track particles with a one-turn map. This new technique allows us to evaluate performance of the lattices on the entire tune-plane. Recently, we designed and implemented an object-oriented code in C++ called LEGO which integrates and expands upon TRACY and DESPOT.

Nonlinear analyses of storage ring lattices using one-turn maps

Using normalized one-turn resonance-basis Lie generators in conjunction with an action-angle tracking algorithm (nPB tracking), we have been able to better understand the relationship between the dynamic aperture and lattice nonlinearities. Tunes, tune shifts with amplitude and/or energy, and resonance strengths may be freely changed to probe their individual impact on the dynamic aperture. Fast beam-beam simulations can be performed with the inclusion of nonlinear lattice effects. Examples from studies of the PEP-II lattices are given.

Validation of PEP-II resonantly excited turn-by-turn BMP Data

For optics measurement and modeling of the PEP-II electron (HER) and position (LER) storage rings, we have been doing well with MIA which requires analyzing turn-by-turn Beam Position Monitor (BPM) data that are resonantly excited at the horizontal, vertical, and longitudinal tunes. However, in anticipation that certain BPM buttons and even pins in the PEP-II IR region would be missing for the run starting in January 2007, we had been developing a data validation process to reduce the effect due to the reduced BPM data accuracy on PEP-II optics measurement and modeling. Besides the routine process for ranking BPM noise level through data correlation among BPMs with a singular-value decomposition (SVD), we could also check BPM data symplecticity by comparing the invariant ratios. Results from PEP-II measurement will be presented.

Dynamic Aperture Improvement of PEP-II Lattices Using Resonance Basis Lie Generators

To simplify the engineering efforts of implementing the PEP-II lattices, many modifications have been made to these lattices since the conceptual design report. During the development and evolution of the lattices, changes in a lattice would often result in a significant reduction in the dynamic aperture. At such times, we often relied on a non-linear analysis using the one-turn resonance basis Lie generator to identify the cause of the degradation. In this paper, we will present such examples to facilitate the usage of map for diagnosing the problems in lattice design.