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Title: Equilibrium of an arbitrary bunch train in presence of a passive harmonic cavity: Solution through coupled Haïssinski equations

Abstract

We study the effect of a passive harmonic cavity, introduced to cause bunch lengthening, in an electron storage ring. We derive a formula for the induced voltage from such a cavity with high Q, excited by a sequence of bunches, allowing for arbitrary gaps in the sequence and arbitrary currents. Except for a minor term that can be determined iteratively, the voltage is given in terms of a single mode of the Fourier transforms of the bunch forms, namely, the mode at the resonant frequency of the cavity. Supposing that the only wakefield is from the harmonic cavity, we derive a system of coupled Haïssinski equations which determine the bunch positions and profiles in the equilibrium state. The number of unknowns in the system is only twice the number of bunches, and it can be solved quickly by a Newton iteration, starting with a guess determined by path following from a solution at a weak current. We explore the effect of the fill pattern on the bunch lengthening and also the dependence on the shunt impedance and detuning of the cavity away from the third harmonic of the main accelerating cavity. We consider two measures to reduce the effects ofmore » gaps: (i) distribution of the gaps around the ring to the greatest extent allowed and (ii) “guard bunches” with higher charges adjacent to the gaps, compensating for the charge missing in gaps. Results for parameters of the forthcoming Advanced Light Source upgrade are presented.« less

Authors:
ORCiD logo;
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1635048
Alternate Identifier(s):
OSTI ID: 1647236
Grant/Contract Number:  
AC03-76SF00515; AC02-05CH11231; AC02-76SF00515
Resource Type:
Published Article
Journal Name:
Physical Review Accelerators and Beams
Additional Journal Information:
Journal Name: Physical Review Accelerators and Beams Journal Volume: 23 Journal Issue: 6; Journal ID: ISSN 2469-9888
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; Beam code development & simulation techniques; Beam dynamics; Relativistic multiple-particle dynamics

Citation Formats

Warnock, Robert, and Venturini, Marco. Equilibrium of an arbitrary bunch train in presence of a passive harmonic cavity: Solution through coupled Haïssinski equations. United States: N. p., 2020. Web. doi:10.1103/PhysRevAccelBeams.23.064403.
Warnock, Robert, & Venturini, Marco. Equilibrium of an arbitrary bunch train in presence of a passive harmonic cavity: Solution through coupled Haïssinski equations. United States. doi:https://doi.org/10.1103/PhysRevAccelBeams.23.064403
Warnock, Robert, and Venturini, Marco. Wed . "Equilibrium of an arbitrary bunch train in presence of a passive harmonic cavity: Solution through coupled Haïssinski equations". United States. doi:https://doi.org/10.1103/PhysRevAccelBeams.23.064403.
@article{osti_1635048,
title = {Equilibrium of an arbitrary bunch train in presence of a passive harmonic cavity: Solution through coupled Haïssinski equations},
author = {Warnock, Robert and Venturini, Marco},
abstractNote = {We study the effect of a passive harmonic cavity, introduced to cause bunch lengthening, in an electron storage ring. We derive a formula for the induced voltage from such a cavity with high Q, excited by a sequence of bunches, allowing for arbitrary gaps in the sequence and arbitrary currents. Except for a minor term that can be determined iteratively, the voltage is given in terms of a single mode of the Fourier transforms of the bunch forms, namely, the mode at the resonant frequency of the cavity. Supposing that the only wakefield is from the harmonic cavity, we derive a system of coupled Haïssinski equations which determine the bunch positions and profiles in the equilibrium state. The number of unknowns in the system is only twice the number of bunches, and it can be solved quickly by a Newton iteration, starting with a guess determined by path following from a solution at a weak current. We explore the effect of the fill pattern on the bunch lengthening and also the dependence on the shunt impedance and detuning of the cavity away from the third harmonic of the main accelerating cavity. We consider two measures to reduce the effects of gaps: (i) distribution of the gaps around the ring to the greatest extent allowed and (ii) “guard bunches” with higher charges adjacent to the gaps, compensating for the charge missing in gaps. Results for parameters of the forthcoming Advanced Light Source upgrade are presented.},
doi = {10.1103/PhysRevAccelBeams.23.064403},
journal = {Physical Review Accelerators and Beams},
number = 6,
volume = 23,
place = {United States},
year = {2020},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: https://doi.org/10.1103/PhysRevAccelBeams.23.064403

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Works referenced in this record:

Harmonic cavities and the transverse mode-coupling instability driven by a resistive wall
journal, February 2018


Study of bunch instabilities by the nonlinear Vlasov–Fokker–Planck equation
journal, June 2006

  • Warnock, Robert L.
  • Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 561, Issue 2
  • DOI: 10.1016/j.nima.2006.01.041

Instabilities driven by higher-order modes in a radio frequency system with a passive higher-harmonic cavity
journal, August 2005


Equilibrium bunch density distribution with passive harmonic cavities in a storage ring
journal, June 2014

  • Tavares, Pedro F.; Andersson, Åke; Hansson, Anders
  • Physical Review Special Topics - Accelerators and Beams, Vol. 17, Issue 6
  • DOI: 10.1103/PhysRevSTAB.17.064401

Bunch length manipulation in a diffraction-limited storage ring
journal, December 2015


Longitudinal beam dynamics with a higher-harmonic cavity for bunch lengthening
journal, December 2019


Lifetime increase using passive harmonic cavities in synchrotron light sources
journal, March 2001


PETRA IV: the ultralow-emittance source project at DESY
journal, August 2018

  • Schroer, Christian G.; Agapov, Ilya; Brefeld, Werner
  • Journal of Synchrotron Radiation, Vol. 25, Issue 5
  • DOI: 10.1107/S1600577518008858

SLS-2 – the upgrade of the Swiss Light Source
journal, April 2018

  • Streun, Andreas; Garvey, Terence; Rivkin, Lenny
  • Journal of Synchrotron Radiation, Vol. 25, Issue 3
  • DOI: 10.1107/S1600577518002722

Self-consistent calculation of transient beam loading in electron storage rings with passive harmonic cavities
journal, December 2018


Commissioning of a higher harmonic RF system for the Advanced Light Source
journal, December 2000

  • Byrd, J. M.; Santis, S. De; Georgsson, M.
  • Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 455, Issue 2
  • DOI: 10.1016/S0168-9002(00)00504-0

Theory of coupled-bunch longitudinal instabilities in a storage ring for arbitrary rf potentials
journal, December 2018


Numerical solution of the Haïssinski equation for the equilibrium state of a stored electron beam
journal, December 2018


Passive higher-harmonic rf cavities with general settings and multibunch instabilities in electron storage rings
journal, November 2018


Transient beam loading effects in harmonic rf systems for light sources
journal, September 2002

  • Byrd, J. M.; De Santis, S.; Jacob, J.
  • Physical Review Special Topics - Accelerators and Beams, Vol. 5, Issue 9
  • DOI: 10.1103/PhysRevSTAB.5.092001

Landau cavities at MAX II
journal, November 1998

  • Georgsson, M.; Andersson, Å.; Eriksson, M.
  • Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 416, Issue 2-3
  • DOI: 10.1016/S0168-9002(98)00667-6

Longitudinal simulations and measurements of stretched bunches
journal, November 2001


Reduction and compensation of the transient beam loading effect in a double rf system of synchrotron light sources
journal, January 2018