Computation and consequences of high order amplitude- and parameter-dependent tune shifts in storage rings for high precision measurements

Weisskopf, Adrian; Tarazona, David; Berz, Martin

doi:10.1142/S0217751X19420119

Title: Computation and consequences of high order amplitude- and parameter-dependent tune shifts in storage rings for high precision measurements

Abstract

Nonlinear effects of the various electric field and magnetic field components of storage rings to confine the particles and bend their trajectory can cause substantial amplitude-dependent tune shifts within the beam. Furthermore, tune shifts are often sensitive to variations of system parameters, e.g. total particle momentum offsets $δp$. Such amplitude- and parameter-dependent tune shifts influence the dynamics and stability of a beam in particle storage rings. Thus, it is critical for high precision measurements to analyze and understand these influences. On this basis, we present in this paper normal form methods for the calculation of high order amplitude and system parameter dependencies of the horizontal and vertical tunes in storage rings using the differential algebra (DA) framework within COSY INFINITY. A storage ring is simulated using COSY INFINITY to generate a DA Poincaré return map describing the transverse phase space behavior after each revolution in the storage ring. The map is expanded around the parameter-dependent closed orbit of the system before transforming the resulting map into normal form coordinates to extract the high order tune dependencies on the phase space amplitude and variation in the system parameters. As a specific example, a storage ring similar to the Storage Ring ofmore »« less

Authors:

^[1]; Tarazona, David ^[1]; Berz, Martin ^[1]

Michigan State Univ., East Lansing, MI (United States)

Publication Date:: Fri Dec 20 00:00:00 EST 2019

Research Org.:: Michigan State Univ., East Lansing, MI (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); Studienstiftung des deutschen Volkes

OSTI Identifier:: 1661862

Grant/Contract Number:: SC0018636; AC02-07CH11359

Resource Type:: Accepted Manuscript

Journal Name:: International Journal of Modern Physics A

Additional Journal Information:: Journal Volume: 34; Journal Issue: 36; Journal ID: ISSN 0217-751X

Publisher:: World Scientific

Country of Publication:: United States

Language:: English

Subject:: 43 PARTICLE ACCELERATORS; Betatron tune shifts; high order transfer maps; nonlinear effects; normal form methods; storage ring

Citation Formats


                    Weisskopf, Adrian, Tarazona, David, and Berz, Martin. Computation and consequences of high order amplitude- and parameter-dependent tune shifts in storage rings for high precision measurements.  United States: N. p., 2019. 
Web.  doi:10.1142/S0217751X19420119.

Copy to clipboard


                    Weisskopf, Adrian, Tarazona, David, & Berz, Martin. Computation and consequences of high order amplitude- and parameter-dependent tune shifts in storage rings for high precision measurements.  United States.  https://doi.org/10.1142/S0217751X19420119

Copy to clipboard


                    Weisskopf, Adrian, Tarazona, David, and Berz, Martin. Fri .  
"Computation and consequences of high order amplitude- and parameter-dependent tune shifts in storage rings for high precision measurements".  United States.  https://doi.org/10.1142/S0217751X19420119.  https://www.osti.gov/servlets/purl/1661862.

Copy to clipboard


                    
@article{osti_1661862,

  title        = {Computation and consequences of high order amplitude- and parameter-dependent tune shifts in storage rings for high precision measurements},

  author       = {Weisskopf, Adrian and Tarazona, David and Berz, Martin},

  abstractNote = {Nonlinear effects of the various electric field and magnetic field components of storage rings to confine the particles and bend their trajectory can cause substantial amplitude-dependent tune shifts within the beam. Furthermore, tune shifts are often sensitive to variations of system parameters, e.g. total particle momentum offsets $δp$. Such amplitude- and parameter-dependent tune shifts influence the dynamics and stability of a beam in particle storage rings. Thus, it is critical for high precision measurements to analyze and understand these influences. On this basis, we present in this paper normal form methods for the calculation of high order amplitude and system parameter dependencies of the horizontal and vertical tunes in storage rings using the differential algebra (DA) framework within COSY INFINITY. A storage ring is simulated using COSY INFINITY to generate a DA Poincaré return map describing the transverse phase space behavior after each revolution in the storage ring. The map is expanded around the parameter-dependent closed orbit of the system before transforming the resulting map into normal form coordinates to extract the high order tune dependencies on the phase space amplitude and variation in the system parameters. As a specific example, a storage ring similar to the Storage Ring of the Muon g-2 Experiment at Fermilab (E989) is investigated.},

  doi          = {10.1142/S0217751X19420119},

  journal      = {International Journal of Modern Physics A},

  number       = 36,

  volume       = 34,

  place        = {United States},

  year         = {Fri Dec 20 00:00:00 EST 2019},

  month        = {Fri Dec 20 00:00:00 EST 2019}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1142/S0217751X19420119

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 2 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Muon ( g − 2): experiment and theory
journal, April 2007

Miller, James P.; Rafael, Eduardo de; Roberts, B. Lee
Reports on Progress in Physics, Vol. 70, Issue 5
DOI: 10.1088/0034-4885/70/5/R03

Computation of the main and fringe fields for the electrostatic quadrupoles of the muon g − 2 storage ring
journal, December 2019

Valetov, Eremey; Berz, Martin; Makino, Kyoko
International Journal of Modern Physics A, Vol. 34, Issue 36
DOI: 10.1142/S0217751X19420417

Differential Equations from the Algebraic Standpoint.
journal, April 1933

Carmichael, R. D.; Ritt, J. F.
The American Mathematical Monthly, Vol. 40, Issue 4
DOI: 10.2307/2302181

Effects of kinematic correction on the dynamics in muon rings
conference, January 2000

Makino, Kyoko
Studies on colliders and collider physics at the highest energies, AIP Conference Proceedings
DOI: 10.1063/1.1361680

Muon loss rates from betatron resonances at the Muon g − 2 Storage Ring at Fermilab
journal, November 2019

Tarazona, D. A.; Berz, M.; Makino, K.
International Journal of Modern Physics A, Vol. 34, Issue 36
DOI: 10.1142/S0217751X19420089

The method of power series tracking for the mathematical description of beam dynamics
journal, August 1987

Berz, M.
Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 258, Issue 3
DOI: 10.1016/0168-9002(87)90927-2

Integration in Finite Terms
journal, November 1972

Rosenlicht, Maxwell
The American Mathematical Monthly, Vol. 79, Issue 9
DOI: 10.2307/2318066

COSY INFINITY Version 9
journal, March 2006

Makino, Kyoko; Berz, Martin
Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 558, Issue 1
DOI: 10.1016/j.nima.2005.11.109

Integration in finite terms
journal, May 1984

Davenport, James
ACM SIGSAM Bulletin, Vol. 18, Issue 2
DOI: 10.1145/1089369.1089378

High-order representation of Poincaré maps
journal, March 2006

Grote, Johannes; Berz, Martin; Makino, Kyoko
Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 558, Issue 1
DOI: 10.1016/j.nima.2006.01.001

Similar Records in DOE PAGES and OSTI.GOV collections:

Dynamical simulations of the Muon Campus at Fermilab

Journal Article Tarazona, D. A. ; Berz, M. ; Makino, K. ; ... - International Journal of Modern Physics A

The Muon Campus at Fermilab is a system through which muons are delivered to the storage ring of the Muon [Formula: see text] Experiment (E989). It consists of a set of 1 km beamlines that transport and prepare a highly polarized muon beam out of secondaries produced downstream a target station. Realistic simulations of this beam delivery system (BDS) using COSY INFINITY, and presented here, contribute to the understanding and characterization of the muon beam production in relation to the statistical and systematic uncertainties of the E989 measurement, intended to be smaller than 0.14 parts per million to achieve the goalsmore »« less
Cited by 2
https://doi.org/10.1142/S0217751X19420338

Full Text Available
Optimization of accelerator parameters using normal form methods on high-order transfer maps

Thesis/Dissertation Snopok, Pavel

Methods of analysis of the dynamics of ensembles of charged particles in collider rings are developed. The following problems are posed and solved using normal form transformations and other methods of perturbative nonlinear dynamics: (1) Optimization of the Tevatron dynamics: (a) Skew quadrupole correction of the dynamics of particles in the Tevatron in the presence of the systematic skew quadrupole errors in dipoles; (b) Calculation of the nonlinear tune shift with amplitude based on the results of measurements and the linear lattice information; (2) Optimization of the Muon Collider storage ring: (a) Computation and optimization of the dynamic aperture ofmore »« less
https://doi.org/10.2172/924531

Full Text Available
Beam-Based Diagnostics of Electric Guide Fields and Lattice Parameters for Run-1 of the Muon g-2 Storage Ring at Fermilab

Conference Tarazona, David ; Berz, Martin ; Crnkovic, Jason ; ... - JACoW

A portion of the Muon g-2 Storage Ring electric system, which provides vertical beam focusing, exhibited an unexpected time dependence that produced a characteristic evolution of the stored beam during Run-1 of the Muon g-2 Experiment at Fermilab (E989). A method to reconstruct the Run-1 electric guide fields has been developed, which is based on a numerical model of the muon storage ring and optimization algorithms supported by COSY INFINITY. This method takes beam profile measurements from the Muon g-2 straw tracking detectors as input, and it produces a full reconstruction of the time-dependent fields. The fields can then bemore »« less
https://doi.org/10.18429/JACoW-IPAC2022-MOPOTK035

Full Text Available
Validation of transfer map calculation for electrostatic deflectors in the code COSY INFINITY

Journal Article Valetov, Eremey ; Berz, Martin ; Makino, Kyoko - International Journal of Modern Physics A

The code COSY INFINITY uses a beamline coordinate system with a Frenet–Serret frame relative to the reference particle, and calculates differential algebra-valued transfer maps by integrating the ODEs of motion in the respective vector space over a differential algebra (DA). In our work, we described and performed computation of the DA transfer map of an electrostatic spherical deflector in a laboratory coordinate system using two conventional methods: (1) by integrating the ODEs of motion using a numerical integrator and (2) by computing analytically and in closed form the properties of the respective elliptical orbits from Kepler theory. We compared themore »« less
https://doi.org/10.1142/S0217751X19420107

Full Text Available
Realistic Modeling of the Muon g-2 Experiment Beamlines at Fermilab

Conference Tarazona, David ; Berz, Martin ; Makino, Kyoko ; ...

The main goal of the Muon g-2 Experiment at Fermilab (E989) is to measure the muon anomalous magnetic moment (a, also dubbed as the "anomaly’’) to unprecedented precision. This new measurement will allow to test the completeness of the Standard Model (SM) and to validate other theoretical models beyond the SM. Simulations of the beamlines from the pion production target to the entrance of the g-2 Storage Ring using COSY INFINITY contribute to the understanding and characterization of the muon beam production in relation to the statistical and systematics uncertainties of the E989 measurement. The effect of nonlinearites from fringemore »« less
https://doi.org/10.18429/JACoW-ICAP2018-MOPAF02

Full Text Available

Similar Records

Title: Computation and consequences of high order amplitude- and parameter-dependent tune shifts in storage rings for high precision measurements

Abstract

Citation Formats

Muon ( g − 2): experiment and theory journal, April 2007

Computation of the main and fringe fields for the electrostatic quadrupoles of the muon g − 2 storage ring journal, December 2019

Differential Equations from the Algebraic Standpoint. journal, April 1933

Effects of kinematic correction on the dynamics in muon rings conference, January 2000

Muon loss rates from betatron resonances at the Muon g − 2 Storage Ring at Fermilab journal, November 2019

The method of power series tracking for the mathematical description of beam dynamics journal, August 1987

Integration in Finite Terms journal, November 1972

COSY INFINITY Version 9 journal, March 2006

Integration in finite terms journal, May 1984

High-order representation of Poincaré maps journal, March 2006

Muon ( g − 2): experiment and theory
journal, April 2007

Computation of the main and fringe fields for the electrostatic quadrupoles of the muon g − 2 storage ring
journal, December 2019

Differential Equations from the Algebraic Standpoint.
journal, April 1933

Effects of kinematic correction on the dynamics in muon rings
conference, January 2000

Muon loss rates from betatron resonances at the Muon g − 2 Storage Ring at Fermilab
journal, November 2019

The method of power series tracking for the mathematical description of beam dynamics
journal, August 1987

Integration in Finite Terms
journal, November 1972

COSY INFINITY Version 9
journal, March 2006

Integration in finite terms
journal, May 1984

High-order representation of Poincaré maps
journal, March 2006