Equilibrium phase instability in the double RF system for Landau damping

Miyahara, Yoshikazu; Asaoka, Seiji; Mikuni, Akira; Soda, Kazuo

doi:10.1016/0168-9002(87)90125-2

Cited by 17 publications

(9 citation statements)

References 4 publications

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“…The dipole mode zero-frequency instability criterion may also be obtained as the condition under which the rf generator voltages do not provide a restoring force for slow rigid bunch motions in which the wake fields move with the bunch [19]; the instability is known accordingly as the equilibrium phase instability [3]. When zero-frequency instability is avoided, the Robinson damping rate is given by Equations (13)- (16) may be obtained directly for the dipole mode by assuming a rigid bunch motion in the synchrotron potential produced by two rf cavities [5].…”

Section: Single-mode Robinson Instability Formulasmentioning

confidence: 99%

“…A radio frequency cavity with resonant frequency near a harmonic of the fundamental rf cavity may increase Landau damping of synchrotron oscillations and lengthen the bunch, thereby suppressing coupled-bunch instabilities and increasing the Touschek lifetime [1][2][3][4][5][6][7][8][9]. A Landau cavity may be operated in passive mode, where its voltage is induced by the beam current, or active mode, where its voltage is maintained by an rf power supply and feedback.…”

Section: Introductionmentioning

confidence: 99%

“…A Landau cavity may be operated in passive mode, where its voltage is induced by the beam current, or active mode, where its voltage is maintained by an rf power supply and feedback. In either case, quiet operation requires avoidance of Robinson instabilities [3,5,[10][11][12][13][14][15][16], which are coupled-bunch instabilities where all bunches oscillate in unison.…”

Section: Introductionmentioning

confidence: 99%

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Robinson instabilities with a higher-harmonic cavity

Bosch

Kleman

Bisognano

2001

Phys. Rev. ST Accel. Beams

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A radio frequency system with a fourth-harmonic "Landau" cavity suppresses coupled-bunch instabilities and increases the beam lifetime of the Aladdin electron storage ring. When the storage ring is operated with a small momentum compaction, instabilities limit the utility of the Landau cavity. Analytical modeling of instability frequencies and growth rates, simulations, and experiments suggest that the observed instabilities result from coupling between dipole and quadrupole Robinson modes.

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Section: Single-mode Robinson Instability Formulasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robinson instabilities with a higher-harmonic cavity

Bosch

Kleman

Bisognano

2001

Phys. Rev. ST Accel. Beams

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“…However, these references (and the many cited therein) are typically restricted to simple harmonic motion in all three planes; in particular, most theoretical approaches neglect the effects of Landau damping that arise when the longitudinal motion is nonlinear. While this approximation is valid for short bunches in single rf systems as is often the case, it does not describe multiple rf systems that are used to lengthen the bunch and increase Landau damping [5][6][7][8][9][10][11], and it fails for the extreme stretching and highly nonlinear (possibly quartic) longitudinal potentials planned for many ultralow emittance light sources (see, e.g., [12]).…”

Section: Introductionmentioning

confidence: 99%

Theory of coupled-bunch longitudinal instabilities in a storage ring for arbitrary rf potentials

Lindberg¹

2018

Phys. Rev. Accel. Beams

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We present a theory of coupled-bunch longitudinal instabilities that is based on the coupled set of Vlasov equations governing the particle distribution function, and can be applied to arbitrary longitudinal potentials. We find that the coupled-bunch growth rate is given by a dispersion relation that is parametrized by the eigenvalues of the linear (harmonic) coupled-bunch matrix problem. Our theory therefore treats the wakefield-driven source of the instability and the effect of Landau damping together and on equal footing, and also indicates that the stabilizing effects of Landau damping can approximately be compared to the instability growth rates in a harmonic potential that has the same bunch length. We then apply the theory to a weakly nonlinear oscillator and to a quartic potential that is relevant for ultralow emittance storage rings that employ bunch-lengthening systems. In the latter case we find that the theory compares quite favorably with particle tracking simulations for the parameters of the planned upgrade of the Advanced Photon Source.

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“…Higher harmonic cavities, also known as Landau cavities, have been proposed and tested [1][2][3][4][5] as a means of introducing Landau damping for controlling beam instabilities and/or improving the beam lifetime due to large-angle intrabeam (Touschek) scattering. Touschek scattering is particularly important for storage rings such as the Advanced Light Source (ALS) because of the high density of electrons resulting from the small transverse beam size and the moderately low beam energy of 1.5 to 1.9 GeV.…”

Section: Introductionmentioning

confidence: 99%

Commissioning of a higher harmonic RF system for the Advanced Light Source

Byrd

Santis

Georgsson

et al. 2000

Nuclear Instruments and Methods in Physics Research Section A:

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We report on the commissioning of a higher harmonic RF system designed to improve the Touschek lifetime of the Advanced Light Source. In our best results, we have achieved over a factor of two increase in the beam lifetime. Transient beam loading of the harmonic cavities by unequal fill patterns presents the greatest limitations on lifetime improvement. We also describe several interesting effects of the harmonic cavities on the operation of the longitudinal and transverse multibunch feedback systems.

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Equilibrium phase instability in the double RF system for Landau damping

Cited by 17 publications

References 4 publications

Robinson instabilities with a higher-harmonic cavity

Robinson instabilities with a higher-harmonic cavity

Theory of coupled-bunch longitudinal instabilities in a storage ring for arbitrary rf potentials

Commissioning of a higher harmonic RF system for the Advanced Light Source

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