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A general formalism for quasi-local correction of multipole distortions in periodic transport systems

Description: We generalize a new concept of local correction of nonlinearities due to multipole content by giving it a mathematical description. We present a general method which allows for a general reduction of all the distortions produced by a given set of multipole errors. The method can be applied to correct an arbitrary distribution of the errors in any transport system, such as transport lines, linacs, synchrotrons and storage rings. 11 refs., 3 figs., 2 tabs.
Date: June 1, 1988
Creator: Neuffer, D. & Forest, E.
Partner: UNT Libraries Government Documents Department

Canonical integration and analysis of periodic maps using non-standard analysis and life methods

Description: We describe a method and a way of thinking which is ideally suited for the study of systems represented by canonical integrators. Starting with the continuous description provided by the Hamiltonians, we replace it by a succession of preferably canonical maps. The power series representation of these maps can be extracted with a computer implementation of the tools of Non-Standard Analysis and analyzed by the same tools. For a nearly integrable system, we can define a Floquet ring in a way consistent with our needs. Using the finite time maps, the Floquet ring is defined only at the locations s/sub i/ where one perturbs or observes the phase space. At most the total number of locations is equal to the total number of steps of our integrator. We can also produce pseudo-Hamiltonians which describe the motion induced by these maps. 15 refs., 1 fig.
Date: June 1, 1988
Creator: Forest, E. & Berz, M.
Partner: UNT Libraries Government Documents Department

Vertically integrated simulation tools for self-consistent tracking and analysis

Description: A modeling, simulation and analysis code complex, the Gemini Package, was developed for the study of single-particle dynamics in the Advanced Light Source (ALS), a 1--2 GeV synchrotron radiation source now being built at Lawrence Berkeley Laboratory. The purpose of this paper is to describe the philosophy behind the package, with special emphasis on our vertical approach. 8 refs., 2 figs.
Date: March 1, 1989
Creator: Forest, E. & Nishimura, H.
Partner: UNT Libraries Government Documents Department

Simulation of synchrotron motion with rf noise

Description: The theoretical formulation is described that is behind an algorithm for synchrotron phase-space tracking with rf noise and some preliminary simulation results of bunch diffusion under rf noise obtained by actual tracking.
Date: August 1, 1986
Creator: Leemann, B.T.; Forest, E. & Chattopadhyay, S.
Partner: UNT Libraries Government Documents Department

Symplectic methods in circular accelerators

Description: By now symplectic integration has been applied to many problems in classical mechanics. It is my conviction that the field of particle simulation in circular rings is ideally suited for the application of symplectic integration. In this paper, I present a short description symplectic tools in circular storage rings.
Date: January 13, 1994
Creator: Forest, E.
Partner: UNT Libraries Government Documents Department

Calculation of aberration coefficients up to sixth order of multipole focusing elements

Description: A method and a computer code have been developed to calculate the aberration coefficients, up to sixth order, for a focusing device consisting of magnetic or electric multipoles. The method is based on the calculation of the ray coordinates at the exit of a focusing device using the RAYTRACE code which provides the magnetic and electric multipole fields necessary for the integration of the equation of motion of the charged particles moving into the focusing device. Subsequently, the exit ray coordinates are considered as a Taylor series expansion, about the origin, in terms of the ray coordinates at the entrance. The coefficients of expansion are the aberration coefficients. The method to calculate the aberration coefficients is discussed further in the text. 5 refs., 1 fig., 1 tab.
Date: 1988~
Creator: Tsoupas, N.; Enge, H. A. & Forest, E.
Partner: UNT Libraries Government Documents Department

Sixth-Order Lie Group Integrators

Description: In this paper we present the coefficients of several 6th order symplectic integrator of the type developed by R. Ruth. To get these results we fully exploit the connection with Lie groups. This integrator, as well as all the explicit integrators of Ruth, may be used in any equation where some sort of Lie bracket is preserved. In fact, if the Lie operator governing the equation of motion is separable into two solvable parts, the Ruth integrators can be used.
Date: March 1, 1990
Creator: Forest, E.
Partner: UNT Libraries Government Documents Department

A Hamiltonian-Free Description of Single Particle Dynamics for Hopelessly Complex Periodic Systems

Description: We develop a picture of periodic systems which does not rely on the Hamiltonian of the system but on maps between a finite number of time locations. Moser or Deprit-like normalizations are done directly on the maps thereby avoiding the complex time-dependent theory. We redefine linear and nonlinear Floquet variables entirely in terms of maps. This approach relies heavily on the Lie representation of maps introduced by Dragt and Finn. One might say that although we do not use the Hamiltonian in the normalization transformation, we are using Lie operators which are themselves, in some sense, pseudo-Hamiltonians for the maps they represent. Our techniques find application in accelerator dynamics or in any field where the Hamiltonian is periodic but hopelessly complex, such as magnetic field design in stellarators.
Date: January 1, 1990
Creator: Forest, E.
Partner: UNT Libraries Government Documents Department

Compendation of SSC lattice optics in the presence of dipole field errors: Report of the Correction Element Working Group

Description: The assignment of the Correction Element Working Group (CEWG) is to advance the designs of various candidate correction schemes to a point where they can be compared and distilled down to a single plan. Choosing among, the options often involves consideration of incommensurate factors such as cost, practicality, and theoretical performance. Except for minor issues, the CEWG purpose is to gather and array the facts in a form from which these decisions can be rationally made, but not to make the decisions. The present report analyses various schemes for compensating nonlinear multipole errors in the main arc dipoles of the Superconducting Super Collider. Emphasis is on comparing lumped and distributed compensation, on minimizing the total number of correction elements, and on reducing the sensitivity to closed-orbit errors.
Date: February 1, 1989
Creator: Bintinger, D.; Chao, A. & Forest, E.
Partner: UNT Libraries Government Documents Department

Semi-parameterization of Dragt-Finn factorization map and its application to Irwin kick factorization

Description: This note is based on the work we did in August, 1989 for parameterizing Irwin factorization kick map. A semi-parameterization method was employed in which the linear part of the map is three-dimensional (six-dimensional in phase space) while the nonlinear part of the map is two-and-one-half-dimensional. The one-half dimension can be eliminated once the parameter (off-momentum) is updated at the beginning of each turn of the kick map.
Date: November 1, 1990
Creator: Yan, Yiton & Forest, E.
Partner: UNT Libraries Government Documents Department

The effects of insertion devices on beam dynamics in the ALS (Advanced Light Source)

Description: Third generation synchrotron radiation sources, such as the Advanced Light Source (ALS), are specifically designed to operate with long undulators that produce very high brightness beams of synchrotron radiation. Including such devices in the storage ring magnet lattice introduced extra linear and nonlinear fields that are intrinsic to the undulator. These fields break the symmetry of the lattice and provide driving forces for nonlinear resonances, thereby perturbing the dynamics of the electron motion, particularly at large amplitudes. The main impact of these perturbations is on the beam lifetime, arising out of a reduction of both the transverse acceptance and the momentum acceptance. In this paper, we present the results of an ongoing study of these effects as they relate to the performance of the ALS. 7 refs., 7 figs., 2 tabs.
Date: March 1, 1989
Creator: Jackson, A.; Forest, E.; Nishimura, H. & Zisman, M.S.
Partner: UNT Libraries Government Documents Department

Application of the Yoshida-Ruth Techniques to Implicit Integration and Multi-Map Explicit Integration

Description: The full power of Yoshida's technique is exploited to produce an arbitrary order implicit symplectic integrator and multi-map explicit integrator. This implicit integrator uses a characteristic function involving the force term alone. Also we point out the usefulness of the plain Ruth algorithm in computing Taylor series map using the techniques first introduced by Berz in his 'COSY-INFINITY' code.
Date: April 1, 1991
Creator: Forest, E.; Bengtsson, J. & Reusch, M.F.
Partner: UNT Libraries Government Documents Department

A formula for the integration of radiation using Yoshida's Lie methods

Description: We present our earlier formula and show how the nonsymplectic operator for the classical radiation can be imported in a generalized Yoshida's formula. The challenge is to break the force into exactly solvable parts. Then the entire machinery of Lie integrators takes over.
Date: October 1, 1998
Creator: Forest, E., Parsa, Z.
Partner: UNT Libraries Government Documents Department

Detector solenoid compensation in the PEP-II B-Factory

Description: The PEP-II experimental detector includes a strong 1.5 T solenoid field in the interaction region (IR). With the fringe fields, the solenoid extends over a range of 6 m. Additional complications are that (1) it is displaced longitudinally from the interaction point (IP) by about 40 cm, (2) neither beam is parallel to the solenoid axis, and (3) the solenoid overlaps a dipole and a quadrupole on either side of the IP. In each half IR the correction system includes a set of skew quadrupoles, dipole correctors and normal quadrupoles to independently compensate the coupling, orbit perturbation, dispersion and focusing effect produced by the solenoid. The correction schemes for the Low Energy Ring (LER) and for the High Energy Ring (HER) are described, and the impact on the dynamic aperture is evaluated.
Date: June 1, 1995
Creator: Nosochkov, Y.; Cai, Y.; Irwin, J.; Sullivan, M. & Forest, E.
Partner: UNT Libraries Government Documents Department

Fast symplectic mapping and quasi-invariants for the Large Hadron Collider

Description: Beginning with a tracking code for the LHC, we construct the canonical generator of the full-turn map in polar coordinates. For very fast mapping we adopt a model in which the momentum is modulated sinusoidally with a period of 130 turns (very close to the synchrotron period). We achieve symplectic mapping of 10{sup 7} turns in 3.6 hours on a workstation. Quasi-invariant tori are constructed on the Poincare section corresponding to multiples of the synchrotron period. The possible use of quasi-invariants in derivin, long-term bounds on the motion is discussed.
Date: May 1, 1995
Creator: Warnock, R.L.; Berg, J.S. & Forest, E.
Partner: UNT Libraries Government Documents Department

Modeling in control of the Advanced Light Source

Description: A software system for control of accelerator physics parameters of the Advanced Light Source (ALS) is being designed and implemented at LBL. Some of the parameters we wish to control are tunes, chromaticities, and closed orbit distortions as well as linear lattice distortions and, possibly, amplitude- and momentum-dependent tune shifts. In all our applications, the goal is to allow the user to adjust physics parameters of the machine, instead of turning knobs that control magnets directly. This control will take place via a highly graphical user interface, with both a model appropriate to the application and any correction algorithm running alongside as separate processes. Many of these applications will run on a Unix workstation, separate from the controls system, but communicating with the hardware database via Remote Procedure Calls (RPCs).
Date: May 1, 1991
Creator: Bengtsson, J.; Forest, E.; Nishimura, H. & Schachinger, L.
Partner: UNT Libraries Government Documents Department

Study of a relaxed'' ALS storage ring lattice

Description: The lattice of the Advanced Light Source (ALS) 1--1.9 GeV electron storage ring was reexamined, introducing an additional family of focusing quadrupoles and looking for a working point with larger dynamic aperture. In the first part of this study, the ideal lattice was investigated to confirm the anticipated behavior, and indeed conditions with increased dynamic aperture were found. In the second part, realistic magnet errors and an undulator in one of the straight sections were taken into account. Under these conditions the dynamic aperture could not be significantly improved over the nominal configuration. Further studies included investigation of the Touschek momentum acceptance of the lattice. In this case too, no net benefit was obtained from the additional quadrupoles. 6 refs., 5 figs. , 2 tabs.
Date: June 1, 1990
Creator: Keller, R.; Forest, E.; Nishimura, H. & Zisman, M.S.
Partner: UNT Libraries Government Documents Department

Localized chromaticity correction of low-beta insertions in storage rings

Description: The correction of the chromaticity of low-beta insertions in the storage rings is usually made with sextupole lenses in the ring`s arcs. When decreasing the beta functions at the insertion point (IP), this technique becomes fairly ineffective, since it fails to properly correct the higher order chromatic aberrations. Here we consider the approach where the chromatic effects of the quadrupole lenses generating low beta functions at the IP are corrected locally with two families of sextupoles, one family for each plane. Each family has two pairs of sextupoles which are located symmetrically on both sides of the IP. The sextupole-like aberrations of individual sextupoles are eliminated by utilizing optics forming a -I transformation between sextupoles in the pair. The optics also includes bending magnets which preserve equal dispersion functions at the two sextupoles in each pair. At sextupoles in one family, the vertical beta function is made large and the horizontal is made small. The situation is reversed in the sextupoles of the other family. The betatron phase advances from the IP to the sextupoles are chosen to eliminate a second order chromatic aberration. The application of the localized chromatic correction is demonstrated using as an example the lattice design for the Low Energy Ring of the SLAC/LBL/LLNL PEP-II B Factory.
Date: April 1, 1993
Creator: Donald, M.; Helm, R.; Irwin, J.; Moshammer, H.; Sullivan, M.; Forest, E. et al.
Partner: UNT Libraries Government Documents Department

Explicit higher order symplectic integrator for s-dependent magnetic field

Description: We derive second and higher order explicit symplectic integrators for the charged particle motion in an s-dependent magnetic field with the paraxial approximation. The Hamiltonian of such a system takes the form of H {summation}{sub k}(p{sub k} - a{sub k} {rvec q}, s){sup 2} + V({rvec q}, s). This work solves a long-standing problem for modeling s-dependent magnetic elements. Important applications of this work include the studies of the charged particle dynamics in a storage ring with strong field wigglers, arbitrarily polarized insertion devices,and super-conducting magnets with strong fringe fields. Consequently, this work will have a significant impact on the optimal use of the above magnetic devices in the light source rings as well as in next generation linear collider damping rings.
Date: June 1, 2001
Creator: Wu, Y.; Forest, E. & Robin, D.S.
Partner: UNT Libraries Government Documents Department

Initial lattice studies for the Berkeley Femtosecond X-ray Light Source

Description: We present lattice studies for a proposed femtosecond synchrotron radiation X-ray source based on a recirculating accelerator. After a general description, we cover specific aspects of the lattice that are relevant to this type of machine and show preliminary results of particle tracking and briefly describe a new code developed for a comprehensive particle tracking in recirculating accelerators.
Date: May 30, 2002
Creator: Zholents, A.; Reichel, I.; Robin, D.; Tanabe, J.; Wan, W.; Forest, E. et al.
Partner: UNT Libraries Government Documents Department

Single resonance theory with maps

Description: We describe how one can perform a single resonance calculation using the single resonance map and the co-moving map. Again we emphasize that all the concepts of this paper have been implemented for the most complicated situations using the Differential Algebra Package of Berz. In theory, it is possible and desirable to do similar calculations on fitted maps (a la Warnock) with fitted canonical transformations, unfortunately the tools based on fitted maps are not yet as versatile as DA-based tools. 5 refs.
Date: April 1, 1990
Creator: Forest, E. (Lawrence Berkeley Lab., CA (USA)) & Irwin, J. (Stanford Linear Accelerator Center, Menlo Park, CA (USA))
Partner: UNT Libraries Government Documents Department

Local chromatic correction scheme for LER of PEP-II

Description: The correction of the chromaticity of low-beta insertions in storage rings is usually made with sextupole lenses in the ring arcs. When decreasing the beta functions at the interaction point (IP), this technique becomes fairly ineffective, since it fails to properly correct the higher-order chromatic aberrations. Here we consider the approach for PEP-II B Factory low energy ring (LER) where the chromatic effects of the quadrupole lenses generating low beta functions at the IP are corrected locally with two families of sextupoles, one family for each plane. For the IP straight section the lattice is designed in such a way that the chromatic aberrations are made small and sextupole-like aberrations are eliminated. The results of dimensional tracking simulations are presented.
Date: 1992-23~
Creator: Forest, E.; Robin, D.; Zholents, A.; Donald, M.; Helm, R.; Irwin, J. et al.
Partner: UNT Libraries Government Documents Department

Local chromatic correction scheme for LER of PEP-II

Description: The correction of the chromaticity of low-beta insertions in storage rings is usually made with sextupole lenses in the ring arcs. When decreasing the beta functions at the interaction point (IP), this technique becomes fairly ineffective, since it fails to properly correct the higher-order chromatic aberrations. Here we consider the approach for & PEP-II B Factory low energy ring (LER) where the chromatic effects of the quadrupole lenses generating low beta functions at the IP are corrected locally with two families of sextupoles, one family for each plane. For the IP straight section the lattice is designed in such a way that the chromatic aberrations are made small and sextupole-like aberrations are eliminated. The results of dimensional tracking simulations are presented.
Date: January 1, 1993
Creator: Forest, E.; Robin, D.; Zholents, A.; Donald, M.; Helm, R.; Irwin, J. et al.
Partner: UNT Libraries Government Documents Department