Nonlinear Dynamics of Single Bunch Instability

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A nonlinear equation is derived that governs the evolution of the amplitude of unstable oscillations with account of quantum diffusion effects due to the synchrotron radiation. Numerical solutions to this equation predict a variety of possible scenarios of nonlinear evolution of the instability some of which are in good qualitative agreement with experimental observations. Microwave single bunch instability in circular accelerators has been observed in many machines. The instability usually arises when the number of particles in the bunch exceeds some critical value, Nc, which varies depending on the parameters of the accelerating regime. Recent observations on the SLC damping ... continued below

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3 pages

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Stupakov, G.V.; /SLAC; Breizman, B.N.; Pekker, M.S. & U., /Texas September 9, 2011.

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A nonlinear equation is derived that governs the evolution of the amplitude of unstable oscillations with account of quantum diffusion effects due to the synchrotron radiation. Numerical solutions to this equation predict a variety of possible scenarios of nonlinear evolution of the instability some of which are in good qualitative agreement with experimental observations. Microwave single bunch instability in circular accelerators has been observed in many machines. The instability usually arises when the number of particles in the bunch exceeds some critical value, Nc, which varies depending on the parameters of the accelerating regime. Recent observations on the SLC damping rings at SLAC with a new low-impedance vacuum chamber revealed new interesting features of the instability. In some cases, after initial exponential growth, the instability eventually saturated at a level that remained constant through the accumulation cycle. In other regimes, relaxation-type oscillations were measured in nonlinear phase of the instability. In many cases, the instability was characterized by a frequency close to the second harmonic of the synchrotron oscillations. Several attempts have been made to address the nonlinear stage of the instability based on either computer simulations or some specific assumptions regarding the structure of the unstable mode. An attempt of a more general consideration of the problem is carried out in this paper. We adopt an approach recently developed in plasma physics for analysis of nonlinear behavior of weakly unstable modes in dynamic systems. Assuming that the growth rate of the instability is much smaller than its frequency, we find a time dependent solution to Vlasov equation and derive an equation for the complex amplitude of the oscillations valid in the nonlinear regime. Numerical solutions to this equation predict a variety of possible scenarios of nonlinear evolution of the instability some of which are in good qualitative agreement with experimental observations.

Physical Description

3 pages

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  • Journal Name: Conf.Proc.C970512:1635,1997; Conference: 17th IEEE Particle Accelerator Conference (PAC 97): Accelerator Science, Technology and Applications, 12-16 May 1997, Vancouver, British Columbia, Canada

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  • Report No.: SLAC-PUB-14582
  • Grant Number: AC02-76SF00515
  • Office of Scientific & Technical Information Report Number: 1024174
  • Archival Resource Key: ark:/67531/metadc831536

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  • September 9, 2011

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  • May 19, 2016, 3:16 p.m.

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  • Nov. 30, 2016, 1:07 p.m.

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Stupakov, G.V.; /SLAC; Breizman, B.N.; Pekker, M.S. & U., /Texas. Nonlinear Dynamics of Single Bunch Instability, article, September 9, 2011; United States. (digital.library.unt.edu/ark:/67531/metadc831536/: accessed October 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.