Self-consistent simulations and analysis of the coupled-bunch instability for arbitrary multibunch configurations

Bassi, Gabriele; Blednykh, Alexei; Smaluk, Victor

doi:10.1103/physrevaccelbeams.19.024401

Cited by 16 publications

(9 citation statements)

References 14 publications

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“…The second equality comes from replacing the summation indices n and l with k as suggested by [38]. Then, we separate the sum over μ 0 to find that…”

Section: Discussionmentioning

confidence: 99%

“…Here, we use methods developed in Ref. [38] to show that a rather simple generalization to the dispersion relation (21) is possible if the ring is filled with two or more essentially identical trains of bunches. Within each bunch train the backgroundF n ðIÞ can vary according to bunch number, but the approximate periodicity permits analytic calculation of the matrix eigenvalues λ.…”

Section: Appendix A: Extension To Certain Nonuniform Fillsmentioning

confidence: 99%

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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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“…The second equality comes from replacing the summation indices n and l with k as suggested by [38]. Then, we separate the sum over μ 0 to find that…”

Section: Discussionmentioning

confidence: 99%

Section: Appendix A: Extension To Certain Nonuniform Fillsmentioning

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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“…Although the instability has been seen with a non-uniform bunch filling pattern, in our analysis we assume that the average current is distributed evenly in 1320 bunches. A justification of this assumption is discussed in [15]. In our interpretation of the measurements, we assume that the onset of the instability is observed when the growth time induced by the HOMs is of the same order of the radiation damping time τ s = 27ms.…”

Section: Commissioning Studiesmentioning

confidence: 99%

“…A justification of this assumption is based on the work of Prabhakar [13] and Kohaupt [14]. A detailed analysis of the coupled-bunch instability driven by non-uniform fillings is discussed in a separate paper [15], where a derivation of the analytical formula for the complex frequency shift induced by arbitrary fillings is given and benchmarked against numerical simulations and measurements in the 15 NSLS-II storage ring. For the instability threshold calculations based on the HOMs of the 7-cell PETRA-III cavity structure we rely on the numerical data computed by R. Wanzenberg [16], complemented by measurements aimed to determine the dependence of the HOM frequencies on the cavity temperature [17].…”

mentioning

confidence: 99%

Analysis of coupled-bunch instabilities for the NSLS-II storage ring with a 500 MHz 7-cell PETRA-III cavity

Bassi

Blednykh

Cheng

et al. 2016

Nuclear Instruments and Methods in Physics Research Section A:

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The NSLS-II storage ring is designed to operate with superconducting RF-cavities with the aim to store an average current of 500mA distributed in 1080 bunches, with a gap in the uniform filling for ion clearing. At the early stage of the commissioning (phase 1), characterized by a bare lattice without damping wigglers and without Landau cavities, a normal conducting 7-cell PETRA-III RF-cavity structure has been installed with the goal to store an average current of 25mA. In this paper we discuss our analysis of coupled-bunch instabilities driven by the Higher Order Modes (HOMs) of the 7-cell PETRA-III RF-cavity. As a cure of the instabilities, we apply a well-known scheme based on a proper detuning of the HOMs frequencies based upon cavity temperature change, and the use of the beneficial effect of the slow head-tail damping at positive chromaticity to increase the transverse coupled-bunch instability thresholds. In addition, we discuss measurements of coupled-bunch instabilities observed during the phase 1 commissioning of the NSLS-II storage ring. In our analysis we rely, in the longitudinal case, on the theory of coupled-bunch instability for uniform fillings, while in the transverse case we complement our studies with numerical simulations with OASIS, a novel parallel particle tracking code for self-consistent simulations of collective effects driven by short and long-range wakefields.the coupled-bunch instability for uniform fillings. A justification of this assumption is based on the work of Prabhakar [13] and Kohaupt [14]. A detailed analysis of the coupled-bunch instability driven by non-uniform fillings is discussed in a separate paper [15], where a derivation of the analytical formula for the complex frequency shift induced by arbitrary fillings is given and benchmarked against numerical simulations and measurements in the 15 NSLS-II storage ring. For the instability threshold calculations based on the HOMs of the 7-cell PETRA-III cavity structure we rely on the numerical data computed by R. Wanzenberg [16], complemented by measurements aimed to determine the dependence of the HOM frequencies on the cavity temperature [17]. In the longitudinal case, since in the NSLS-II storage ring the cut-off frequency of the PETRA-III cavity is higher than the case considered by R. Wanzenberg, we computed HOMs up to 1390 MHz [18], as shown in Table 2, with the GdfidL code [19]. 20 The beam dynamics simulation results discussed in this paper have been obtained with OASIS [20], a parallel code for self-consistent simulations of single and multi-bunch effects. For single-bunch effects, the code uses the same physical model of the TRANFT code developed by M. Blaskiewicz [21], [22], while in the case of multi-bunch effects the code implements a novel self-consistent algorithm to take into account long-range effects [23]. The novelty of the algorithm consists of the capability to simulate efficiently the self-consistent coupled-bunch interaction of 25 bunches with finite length distributed in arbitrary filling patterns, v...

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“…III we derive the complex frequency shift induced by the dipole and quadrupole impedance using the method applied in Ref. [18]. In Sec.…”

Section: Introductionmentioning

confidence: 99%

Low-frequency quadrupole impedance of undulators and wigglers

Blednykh¹,

Bassi²,

Hidaka³

et al. 2016

Phys. Rev. Accel. Beams

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An analytical expression of the low-frequency quadrupole impedance for undulators and wigglers is derived and benchmarked against beam-based impedance measurements done at the 3 GeV NSLS-II storage ring. The adopted theoretical model, valid for an arbitrary number of electromagnetic layers with parallel geometry, allows to calculate the quadrupole impedance for arbitrary values of the magnetic permeability μ r. In the comparison of the analytical results with the measurements for variable magnet gaps, two limit cases of the permeability have been studied: the case of perfect magnets (μ r → ∞), and the case in which the magnets are fully saturated (μ r ¼ 1).

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Self-consistent simulations and analysis of the coupled-bunch instability for arbitrary multibunch configurations

Cited by 16 publications

References 14 publications

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

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

Analysis of coupled-bunch instabilities for the NSLS-II storage ring with a 500 MHz 7-cell PETRA-III cavity

Low-frequency quadrupole impedance of undulators and wigglers

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