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 »
- Authors:
- Publication Date:
- Research Org.:
- SLAC National Accelerator Laboratory (SLAC), 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. 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. 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 = {Wed Jun 24 00:00:00 EDT 2020},
month = {Wed Jun 24 00:00:00 EDT 2020}
}
https://doi.org/10.1103/PhysRevAccelBeams.23.064403
Web of Science
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