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Title: Chromaticity effects on head-tail instabilities for broadband impedance using two particle model, Vlasov analysis, and simulations

Abstract

Effects of the chromaticity on head-tail instabilities for broadband impedances are comprehensively studied, using the two particle model, the Vlasov analysis and computer simulations. We show both in the two particle model and the Vlasov analysis with the trapezoidal (semiconstant) wake model that we can derive universal contour plots for the growth factor as a function of the two dimensionless parameters: the wakefield strength, Υ, and the difference of the betatron phase advances between the head and the tail, χ. They reveal how the chromaticity affects strong head-tail instabilities and excites head-tail instabilities. We also apply the LEP (Large Electron-Positron Collider) broadband resonator model to the Vlasov approach and find that the results are in very good agreement with those of the trapezoidal wake model. The theoretical findings are also reinforced by the simulation results. In conclusion, the trapezoidal wake model turns out to be a very useful tool since it significantly simplifies the time domain analysis and provides well-behaved impedance at the same time.

Authors:
 [1];  [2];  [3];  [4]
  1. High Energy Accelerator Research Organization (KEK), Ibaraki-ken (Japan)
  2. SLAC National Accelerator Lab., Menlo Park, CA (United States)
  3. Brookhaven National Lab. (BNL), Upton, NY (United States)
  4. Japan Atomic Energy Agency (JAEA), Ibaraki (Japan)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States); Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1373322
Report Number(s):
BNL-114341-2017-JA
Journal ID: ISSN 2469-9888; PRABCJ; TRN: US1702704
Grant/Contract Number:
AC02-76SF00515; SC0012704; DEAC02-76SF00515
Resource Type:
Journal Article: Published Article
Journal Name:
Physical Review Accelerators and Beams
Additional Journal Information:
Journal Volume: 20; Journal Issue: 7; Journal ID: ISSN 2469-9888
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS

Citation Formats

Chin, Yong Ho, Chao, Alexander Wu, Blaskiewicz, Michael M., and Shobuda, Yoshihiro. Chromaticity effects on head-tail instabilities for broadband impedance using two particle model, Vlasov analysis, and simulations. United States: N. p., 2017. Web. doi:10.1103/PhysRevAccelBeams.20.071003.
Chin, Yong Ho, Chao, Alexander Wu, Blaskiewicz, Michael M., & Shobuda, Yoshihiro. Chromaticity effects on head-tail instabilities for broadband impedance using two particle model, Vlasov analysis, and simulations. United States. doi:10.1103/PhysRevAccelBeams.20.071003.
Chin, Yong Ho, Chao, Alexander Wu, Blaskiewicz, Michael M., and Shobuda, Yoshihiro. 2017. "Chromaticity effects on head-tail instabilities for broadband impedance using two particle model, Vlasov analysis, and simulations". United States. doi:10.1103/PhysRevAccelBeams.20.071003.
@article{osti_1373322,
title = {Chromaticity effects on head-tail instabilities for broadband impedance using two particle model, Vlasov analysis, and simulations},
author = {Chin, Yong Ho and Chao, Alexander Wu and Blaskiewicz, Michael M. and Shobuda, Yoshihiro},
abstractNote = {Effects of the chromaticity on head-tail instabilities for broadband impedances are comprehensively studied, using the two particle model, the Vlasov analysis and computer simulations. We show both in the two particle model and the Vlasov analysis with the trapezoidal (semiconstant) wake model that we can derive universal contour plots for the growth factor as a function of the two dimensionless parameters: the wakefield strength, Υ, and the difference of the betatron phase advances between the head and the tail, χ. They reveal how the chromaticity affects strong head-tail instabilities and excites head-tail instabilities. We also apply the LEP (Large Electron-Positron Collider) broadband resonator model to the Vlasov approach and find that the results are in very good agreement with those of the trapezoidal wake model. The theoretical findings are also reinforced by the simulation results. In conclusion, the trapezoidal wake model turns out to be a very useful tool since it significantly simplifies the time domain analysis and provides well-behaved impedance at the same time.},
doi = {10.1103/PhysRevAccelBeams.20.071003},
journal = {Physical Review Accelerators and Beams},
number = 7,
volume = 20,
place = {United States},
year = 2017,
month = 7
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevAccelBeams.20.071003

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  • Effects of the chromaticity on head-tail instabilities for broadband impedances are comprehensively studied, using the two particle model, the Vlasov analysis and computer simulations. We show both in the two particle model and the Vlasov analysis with the trapezoidal (semiconstant) wake model that we can derive universal contour plots for the growth factor as a function of the two dimensionless parameters: the wakefield strength, Υ, and the difference of the betatron phase advances between the head and the tail, χ. They reveal how the chromaticity affects strong head-tail instabilities and excites head-tail instabilities. We also apply the LEP (Large Electron-Positronmore » Collider) broadband resonator model to the Vlasov approach and find that the results are in very good agreement with those of the trapezoidal wake model. The theoretical findings are also reinforced by the simulation results. In conclusion, the trapezoidal wake model turns out to be a very useful tool since it significantly simplifies the time domain analysis and provides well-behaved impedance at the same time.« less
  • In this paper, we present a new two particle model for studying the strong head-tail instabilities in the presence of the space-charge force. It is a simple expansion of the well-known two particle model for strong head-tail instability and is still analytically solvable. No chromaticity effect is included. It leads to a formula for the growth rate as a function of the two dimensionless parameters: the space-charge tune shift parameter (normalized by the synchrotron tune) and the wakefield strength, Upsilon. The three-dimensional contour plot of the growth rate as a function of those two dimensionless parameters reveals stopband structures. Manymore » simulation results generally indicate that a strong head-tail instability can be damped by a weak space-charge force, but the beam becomes unstable again when the space-charge force is further increased. The new two particle model indicates a similar behavior. In weak space-charge regions, additional tune shifts by the space-charge force dissolve the mode coupling. As the space-charge force is increased, they conversely restore the mode coupling, but then a further increase of the space-charge force decouples the modes again. Lastly, this mode coupling/decoupling behavior creates the stopband structures.« less
  • In our paper, we present a new two particle model for studying the strong head-tail instabilities in the presence of the space-charge force. It is a simple expansion of the well-known two particle model for strong head-tail instability and is still analytically solvable. No chromaticity effect is included. It leads to a formula for the growth rate as a function of the two dimensionless parameters: the space-charge tune shift parameter (normalized by the synchrotron tune) and the wakefield strength, Υ. The three-dimensional contour plot of the growth rate as a function of those two dimensionless parameters reveals stopband structures. Manymore » simulation results generally indicate that a strong head-tail instability can be damped by a weak space-charge force, but the beam becomes unstable again when the space-charge force is further increased. Moreover, the new two particle model indicates a similar behavior. In weak space-charge regions, additional tune shifts by the space-charge force dissolve the mode coupling. As the space-charge force is increased, they conversely restore the mode coupling, but then a further increase of the space-charge force decouples the modes again. This mode coupling/decoupling behavior creates the stopband structures.« less
  • In this report, we present a new two particle model for studying the strong head-tail instabilities in the presence of the space-charge force. It is a simple expansion of the well-known two particle model for strong head-tail instability and is still analytically solvable. No chromaticity effect is included. It leads to a formula for the growth rate as a function of the two dimensionless parameters: the space-charge tune shift parameter (normalized by the synchrotron tune) and the wakefield strength, Υ. The three-dimensional contour plot of the growth rate as a function of those two dimensionless parameters reveals stopband structures. Manymore » simulation results generally indicate that a strong head-tail instability can be damped by a weak space-charge force, but the beam becomes unstable again when the space-charge force is further increased. The new two particle model indicates a similar behavior. In weak space-charge regions, additional tune shifts by the space-charge force dissolve the mode coupling. As the space-charge force is increased, they conversely restore the mode coupling, but then a further increase of the space-charge force decouples the modes again. This mode coupling/decoupling behavior creates the stopband structures.« less