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NSLS-II: Nonlinear Model Calibration for Synchrotrons

Description: This tech note is essentially a summary of a lecture we delivered to the Acc. Phys. Journal Club Apr, 2010. However, since the estimated accuracy of these methods has been naive and misleading in the field of particle accelerators, i.e., ignores the impact of noise, we will elaborate on this in some detail. A prerequisite for a calibration of the nonlinear Hamiltonian is that the quadratic part has been understood, i.e., that the linear optics for the real accelerator has been calibrated. For synchrotron light source operations, this problem has been solved by the interactive LOCO technique/tool (Linear Optics from Closed Orbits). Before that, in the context of hadron accelerators, it has been done by signal processing of turn-by-turn BPM data. We have outlined how to make a basic calibration of the nonlinear model for synchrotrons. In particular, we have shown how this was done for LEAR, CERN (antiprotons) in the mid-80s. Specifically, our accuracy for frequency estimation was {approx} 1 x 10{sup -5} for 1024 turns (to calibrate the linear optics) and {approx} 1 x 10{sup -4} for 256 turns for tune footprint and betatron spectrum. For a comparison, the estimated tune footprint for stable beam for NSLS-II is {approx}0.1. Since the transverse damping time is {approx}20 msec, i.e., {approx}4,000 turns. There is no fundamental difference for: antiprotons, protons, and electrons in this case. Because the estimated accuracy for these methods in the field of particle accelerators has been naive, i.e., ignoring the impact of noise, we have also derived explicit formula, from first principles, for a quantitative statement. For e.g. N = 256 and 5% noise we obtain {delta}{nu} {approx} 1 x 10{sup -5}. A comparison with the state-of-the-arts in e.g. telecomm and electrical engineering since the 60s is quite revealing. For example, Kalman filter (1960), crucial for ...
Date: October 8, 2010
Creator: Bengtsson, J.
Partner: UNT Libraries Government Documents Department

NSLS-II Control of Dynamic Aperture

Description: We have outlined how, by an intuitive approach, the on- and off-momentum dynamic aperture for a synchrotron light source can be estimated from a nonlinear system of algebraic equations for the sextupole/multipole strengths. The approach has only two free parameters: the relative weight for resonance vs. tune shift terms and the tune footprint for stable trajectories in a modern third generation synchrotron light source. In other words, we have established a control theory approach for the medium term (10{sup 3} turns) stability for a dynamic system described by a nonlinear system of ordinary differential equations. Equipped with a predictive, quantitative model for stability, we have then evaluated how to improve the control of the dynamics by analyzing and modifying the properties of the corresponding algebraic system. In particular, by changing the number- and characteristics of the parameters, i.e., we have not evaluated how the underlying (linear) optics could be improved. We have also validated our conjectures by numerical simulations with a realistic model. Presumably, our conclusions, summarized in Section 1.0, are a direct result of the presented analysis and observations.
Date: October 31, 2008
Creator: Bengtsson,J.
Partner: UNT Libraries Government Documents Department

Ultra Low Emittance Light Sources

Description: This paper outlines the special issues for reaching sub-nm emittance in a storage ring. Effects of damping wigglers, intra-beam scattering and lifetime issues, dynamic aperture optimization, control of optics, and their interrelations are covered in some detail. The unique choices for the NSLS-II are given as one example.
Date: June 23, 2008
Creator: Bengtsson,J.
Partner: UNT Libraries Government Documents Department

THE POINCARE MAP, LIE GENERATOR, NONLINEAR INVARIANT, PARAMETER DEPENDANCE, AND DYNAMIC APERTURE FOR RINGS.

Description: In earlier work related to the NSLS-II project we have outlined a control theory approach for the dynamic aperture problem. In particular, an algorithm for the joint optimization of the Lie generator and the working point for the Poincare map. This time we report on how the Lie generator provides guidelines on acceptable magnitudes for e.g. the intrinsic nonlinear effects from insertion devices, and the nonlinear pseudo-invariant from the map normal form can be used to optimize the dynamic aperture. We also show how a polymorphic beam line class can be used to study the parameter dependence and rank conditions for control of optics and dynamic aperture.
Date: June 25, 2007
Creator: BENGTSSON,J.
Partner: UNT Libraries Government Documents Department

Achromatic and isochronous electron beam transport for tunable free electron lasers

Description: We have continued the study of a suitable electron beam transport line, which is both isochronous and achromatic, for the free electron laser being designed at Lawrence Berkeley Laboratory. A refined version of the beam transport optics is discussed that accommodates two different modes of FEL wavelength tuning. For the fine tuning involving a small change of the electron beam energy, sextupoles are added to cancel the leading nonlinear dispersion. For the main tuning involving the change of the undulator gap, a practical solution of maintaining the beam matching condition is presented. Calculation of the higher order aberrations is facilitated by a newly developed code. 11 refs., 4 figs., 3 tabs.
Date: September 1, 1991
Creator: Bengtsson, J. & Kim, K.J.
Partner: UNT Libraries Government Documents Department

Achromatic and Isochronous Electron Beam Transport for Tunable Free Electron Lasers

Description: We have continued the study of a suitable electron beam transport line, which is both isochronous and achromatic, for the free electron laser being designed at Lawrence Berkeley Laboratory. A refined version of the beam transport optics is discussed that accommodates two different modes of FEL wavelength tuning. For the fine tuning involving a small change of the electron beam energy, sextupoles are added to cancel the leading nonlinear dispersion. For the main tuning involving the change of the undulator gap, a practical solution of maintaining the beam matching condition is presented. Calculation of the higher order aberrations is facilitated by a newly developed code. 11 refs., 4 figs., 3 tabs.
Date: September 1991
Creator: Bengtsson, J. & Kim, K. J.
Partner: UNT Libraries Government Documents Department

Modeling of beam dynamics and comparison with measurements for the advanced light source (ALS)

Description: The data collected during the April 1993 ALS commissioning period includes the measured closed orbit as a function of either dipole corrector strength or RF frequency, in addition to turn by turn data for the betatron motion as a function of RF frequency. The sensitivity matrix and dispersion function are extracted from this data by taking differences between orbits, whereas lattice functions and chromaticity are obtained using Fourier analysis and interpolation techniques. Lattice functions are also derived from the sensitivity matrix using a nonlinear least squares fit. The results are then compared with numerical simulations and analytical formulas derived using maps and a Lie product normal form approach. The Lie method is preferred to traditional Hamiltonian perturbation theory because it is easily generalized to the nonlinear case and also leads to a significantly reduced amount of algebra. The computer modeling uses state of the art single particle beam dynamics tools including: Tracy-2, DA-pascal, DA-Library and Lie-Lib. In particular, DA-Pascal allows for a straightforward implementation of a Krakpot style code, based on the {open_quote}exact{close_quotes} single particle local Hamiltonian and a symplectic integrator, necessary for correct modeling of the nonlinear chromaticity.
Date: June 1, 1994
Creator: Bengtsson, J. & Meddahi, M.
Partner: UNT Libraries Government Documents Department

Six-dimensional modeling of coherent bunch instabilities and related freedback systems in storage rings with power-series maps for the lattice

Description: The authors have developed 6-dimensional phase-space code that tracks macroparticles for the study of coherent bunch instabilities and related feedback systems. The model is based on power-series maps to represent the lattice, and allows for straightforward inclusion of effects such as amplitude dependent tune shift, chromaticity, synchrotron oscillations, and synchrotron radiation. It simulates long range wake fields such as resistive-wall effects as well as the higher order modes in cavities. The model has served to study the dynamics relevant to the transverse feedback system currently being commissioned for the Advanced Light Source (ALS). Current work integrates earlier versions into a modular system that includes models for transverse and longitudinal feedback systems. It is designed to provide a modular approach to the dynamics and diagnostics, allowing a user to modify the model of a storage ring at run-time without recompilation.
Date: June 1, 1994
Creator: Bengtsson, J.; Briggs, D. & Meddahi, M.
Partner: UNT Libraries Government Documents Department

Studies of transverse coherent bunch instabilities for the Advanced Light Source (ALS)

Description: We have studied the transverse coherent bunch instabilities for the Advanced Light Source (ALS). We have in particular applied a Hamiltonian formalism to obtain the linearized averaged equations of motion (i.e. the one turn map) for the resistive wall effect to obtain the corresponding localized kick when the beta function is varying along the lattice. We have also included a 2-dimensional model for the transverse higher order cavity modes. In addition, we have used power series maps to represent the lattice which enabled us to include non-linear effects. These models have been implemented in a computer code and numerical simulations have been carried out for ALS. The model was successfully verified against analytical calculations in cases where they overlap. The non-linear effects from the lattice proved to be important, since they led to a qualitative change of the dynamics for the stored beam. We also studied the injection process in some detail and found that the non-linear effects also fundamentally change the injection dynamics.
Date: May 31, 1994
Creator: Meddahi, M. & Bengtsson, J.
Partner: UNT Libraries Government Documents Department

Study of possible energy upgrade for the ALS and modeling of the ``Real Lattice`` for the diagnosis of lattice problems

Description: We have studied change of expected performance of the Advanced Light Source storage ring at LBL for the (design) nominal and maximum energy of 1.5 and 1.9 GeV respectively. Furthermore, we have also studied a possible increase to 2.3 GeV by modeling the change of dynamical aperture caused by saturation of the magnets. Independently, we have also modeled the beam`s trajectory at injection. Comparison with bpm data from early storage ring commissioning led to the diagnosis of a major lattice error due to a short in a quadrupole, which was rectified leading to stored beam of 60 turns.
Date: May 1, 1993
Creator: Meddahi, M. & Bengtsson, J.
Partner: UNT Libraries Government Documents Department

Study of transverse coupled bunch instabilities by using non-linear Taylor maps for the Advanced Light Source (ALS)

Description: To study coherent bunch instabilities for the third generation light source, ALS, it is insufficient to rely on a linear map with radiation damping for the lattice to obtain the correct dynamics. We have implemented a code for transverse bunch instabilities, using a 4-dimensional map for the lattice and wake field expansions for cavities and resistive wall effects. This model has been used to study the injection process and to determine the needed performance of the proposed feedback system for the storage ring.
Date: May 1, 1993
Creator: Meddahi, M. & Bengtsson, J.
Partner: UNT Libraries Government Documents Department

Emittance measurement and modeling of the ALS 50 MeV linac to booster line

Description: The Twiss parameters and emittance have been measured for the ALS LINAC through non-linear {chi}{sup 2} fitting of the measured beam size (fixed location) vs. focal strength of a quadrupole triplet. The obtained values have been used to calculate the expected beam size and dispersion along the linac-to-booster transport line giving good agreement with measurements. The efforts resulted in superior injection into the booster.
Date: May 1, 1993
Creator: Bengtsson, J.; Leemans, W. & Byrne, T.
Partner: UNT Libraries Government Documents Department

A closed-loop photon beam control study for the Advanced Light Source

Description: The third generation Advanced Light Source (ALS) will produce extremely bright photon beams using undulators and wigglers. In order to position the photon beams accurate to the micron level, a closed-loop feedback system is being developed. Using photon position monitors and dipole corrector magnets, a closed-loop system can automatically compensate for modeling uncertainties and exogenous disturbances. The following paper will present a dynamics model for the perturbations of the closed orbit of the electron beam in the ALS storage ring including the vacuum chamber magnetic field penetration effects. Using this reference model, two closed-loop feedback algorithms will be compared -- a classical PI controller and a two degree-of-freedom approach. The two degree-of-freedom method provides superior disturbance rejection while maintaining the desired performance goals. Both methods will address the need to gain schedule the controller due to the time varying dynamics introduced by changing field strengths when scanning the insertion devices.
Date: May 1, 1993
Creator: Portmann, G. & Bengtsson, J.
Partner: UNT Libraries Government Documents Department

TOUSCHEK LIFETIME CALCULATIONS AND SIMULATIONS FOR NSLS-II

Description: The beam lifetime in most medium energy synchrotron radiation sources is limited by the Touschek effect, which describes the momentum transfer from the transverse into the longitudinal direction due to binary collisions between electrons. While an analytical formula exists to calculate the resulting lifetime, the actual momentum acceptance necessary to perform this calculation can only be determined by tracking. This is especially the case in the presence of small vertical apertures at insertion devices. In this case, nonlinear betatron coupling leads to beam losses at these vertical aperture restrictions. In addition, a realistic model of the storage ring is necessary for calculation of equilibrium beam sizes (particularly in the vertical direction) which are important for a self-consistent lifetime calculation.
Date: June 25, 2007
Creator: MONTAG,C.; BENGTSSON, J. & NASH, B.
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

OPTIMIZING THE DYNAMIC APERTURE FOR TRIPLE BEND ACHROMATIC LATTICES.

Description: The Triple Bend Achromatic (TBA) lattice has the potential for lower natural emittance per period than the Double Bend Achromatic (DBA) lattice for high brightness light sources. However, the DBA has been chosen for 3rd generation light sources more often due to the higher number of undulator straight section available for a comparable emittance. The TBA has considerable flexibility in linear optics tuning while maintaining this emittance advantage. We have used the tune and chromaticity flexibility of a TBA lattice to minimize the lowest order nonlinearities to implement a 3rd order achromatic tune, while maintaining a constant emittance. This frees the geometric sextupoles to counter the higher order nonlinearities. This procedure is being used to improve the nonlinear dynamics of the TBA as a proposed lattice for NSLS-II facility. The flexibility of the TBA lattice will also provide for future upgrade capabilities of the beam parameters.
Date: June 26, 2006
Creator: KRAMER, S.L. & BENGTSSON, J.
Partner: UNT Libraries Government Documents Department

COMPARISON OF DOUBLE BEND AND TRIPLE BEND ACHROMATIC LATTICE STRUCTURES AND NSLS-II.

Description: The Double Bend Achromatic (DBA) and the Triple Bend Achromatic (TBA) lattice have been studied rather extensively for use for the NSLS-II storage ring. The advantage of the TBA compared to the DBA in terms of emittance per period is well known. However, the DBA has the advantage of greater number of ID straight sections for the users and maybe easier to tune the dispersive section for reduced chromatic sextupole strength. We present a comparison of these lattices based on optimization of the non-linear driving terms using high order achromatic cancellation of driving terms of the nonlinear lattice.
Date: June 26, 2006
Creator: KRAMER, S.L.; KRINSKY, S. & BENGTSSON, J.
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

ADDITIONAL QUADRUPOLES AT CENTER OF LONG STRAIGHTS IN THE NSLS-II LATTICE

Description: The NSLS-II storage ring lattice is comprised of 30 DBA cells arranged in 15 superperiods. There are 15 long straight sections (9.3m) for injection, RF and insertion devices and 15 shorter straights (6.6m) for insertion devices. In the baseline lattice, the short straights have small horizontal and vertical beta functions but the long straights have large horizontal beta function optimized for injection. In this paper, we explore the possibility of installing additional quadrupoles at the center of selected long straight sections in order to provide two low-beta source locations for undulators in the same straight. The required modification to the linear lattice is discussed as well as the preservation of adequate dynamic aperture required for good injection efficiency and adequate Touschek lifetime. This paper discusses the possibility of producing two low-beta source locations for optimum brightness of undulators in the long straights of NSLS-II lattice by installing additional quadrupoles at the center. The linear optics is optimized to satisfy the requirements of lattice function and properties. Nonlinear optimization for a lattice with working point at (37.16, 17.22) is performed. Considering the magnets misalignment errors and physical apertures, we calculate the frequency maps and plot the tune footprint. The results show that the modified high-low beta function lattice can achieve a modest dynamic aperture in this preliminary study. Further work will continue to expand the dynamic aperture to meet the requirement of good injection efficiency and sufficient Touschek lifetime.
Date: March 28, 2011
Creator: Lin, F.; Bengtsson, J.; Guo, W.; Krinsky, S.; Li, Y. & Yang, L.
Partner: UNT Libraries Government Documents Department

LOW HORIZONTAL BETA FUNCTION IN LONG STRAIGHTS OF THE NSLS-II LATTICE

Description: The NSLS-II storage ring lattice is comprised of 30 DBA cells arranged in 15 superperiods. There are 15 long straight sections (9.3m) for injection, RF and insertion devices and 15 short straights (6.6m) for insertion devices. In the baseline lattice, the short straights have small horizontal and vertical beta functions but the long straights have large horizontal beta function optimized for injection. In this paper, we explore the possibility of maintaining three long straights with large horizontal beta function while providing the other 12 long straights with smaller horizontal beta function to optimize the brightness of insertion devices. Our study considers the possible linear lattice solutions as well as characterizing the nonlinear dynamics. Results are reported on optimization of dynamic aperture required for good injection efficiency and adequate Touschek lifetime. This paper discusses dynamic aperture optimization for the NSLS-II lattice with alternate high and low horizontal beta function in the long straights, which is proposed for the optimization of the brightness of insertion devices. The linear optics is optimized to meet the requirements of lattice function and source properties. Nonlinear optimization for a lattice with working point at (37.18, 16.2) is performed. Considering the realistic magnets errors and physical apertures, we calculate the frequency maps and plot the tune footprint. The results show that the lattice with high-low beta function has adequate dynamic aperture for good injection efficiency and sufficient Touschek lifetime.
Date: March 28, 2011
Creator: Fanglei, L.; Bengtsson, J.; Guo, W.; Krinsky, S.; Li, Y. & Yang, L.
Partner: UNT Libraries Government Documents Department

MEASUREMENT AND CORRECTION OF THIRD RESONANCE DRIVING TERM IN THE RHIC

Description: To further improve the luminosity in polarized proton operation of the Relativistic Heavy Ion Collider, correction of the horizontal two-third resonance at store is desirable. The long-lasting coherent beam oscillations, produced by the AC dipole, are used to measure 3Q,'s resonance driving term h{sub 30000} through the analysis of turn-by-turn beam position data with the algorithm outlined by J. Bengtsson. The resonance driving term h30000 can be compensated with the 12 arc chromatic sextupole families. In this article, we will review the technique of h{sub 30000} resonance driving term's measurement and correction with AC dipole excitation in the RHIC, followed by the preliminary beam experiment results from the RHIC 2006 polarized proton run.
Date: June 25, 2007
Creator: LUO,Y.; BAI, M.; BENGTSSON, J.; CALAGA, R.; FISCHER, W. & AL., ET
Partner: UNT Libraries Government Documents Department

PHILOSOPHY FOR NSLS-II DESIGN WITH SUB-NANOMETER HORIZONTAL EMITTANCE.

Description: NSLS-II at Brookhaven National Laboratory is a new third-generation storage ring light source, whose construction is on the verge of being approved by DOE. When completed, NSLS-II with its ability to provide users with a wide range of spectrum, ranging from IR to ultra-high brightness hard x-ray beams will replace the existing two (20+ years old) NSLS light sources. While presenting an overview of the NSLS-II accelerator system, this paper focuses on the strategy and development of a novel <1 nm emittance light source.
Date: June 25, 2007
Creator: OZAKI,S.; BENGTSSON, J.; KRAMER, S.L.; KRINSKY, S. & LITVINENKO, V.N.
Partner: UNT Libraries Government Documents Department