Transverse beam coupling impedance of the CERN Proton Synchrotron

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Starting from the electric fields produced by a point charge and a dipole traveling inside a circular vacuum chamber, in this paper we derive a formalism for a complete set of equations that describe the electromagnetic fields and the longitudinal and transverse coupling impedances arising by the interaction of a beam with a perfectly conducting pipe in the case of elliptic geometry. The expressions, which are valid for any frequency and beam energy, are written in terms of expansions of Mathieu functions, allow to range from a circular geometry to the parallel plates, and show an interesting parallelism with the well-known expressions for a circular pipe. We also obtain that, under the approximation of low frequency, the formalism allows us to derive the Laslett coefficients for parallel plates, circular and elliptic beam pipe.

Section: Longitudinal Space Charge Impedancementioning

confidence: 99%

Space charge impedance and electromagnetic fields in elliptical vacuum chambers

Migliorati

Biancacci

Masullo

et al. 2018

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“…Among several geometries, the elliptic cross section is of particular interest because it can be found in circular machines [11][12][13] as well as in undulators for free electron lasers [14].…”

Section: Introductionmentioning

confidence: 99%

Resistive wall impedance in elliptical multilayer vacuum chambers

Migliorati

Palumbo

Zannini

et al. 2019

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The resistive wall impedance of a vacuum chamber with elliptic cross section is of particular interest for circular particle accelerators as well as for undulators in free electron lasers. By using the electric field of a point charge and of a small dipole moving at arbitrary speed in an elliptical vacuum chamber, expressed in terms of Mathieu functions, in this paper we take into account the finite conductivity of the beam pipe walls by means of the surface impedance, and evaluate the longitudinal and transverse driving and detuning impedances for any beam velocity. We also extend the definition of the Yokoya form factors, valid in the thick wall regime, at any beam energy, and show that, in the ultra-relativistic limit, they coincide with the ones that are found in literature. The method is also extended to the multilayer vacuum chamber case. Under conditions generally satisfied with particle accelerator beam pipes, the classical transmission line theory can be used to modelling the impedance seen by a bunch in a vacuum chamber with several layers as an equivalent circuit with the same number of load impedances, giving, as result, a surface impedance that can be used in combination with the fields of the elliptic geometry to obtain the resistive wall impedance in an elliptical multilayer vacuum chamber. The results are also compared with a more time consuming 3D electromagnetic code and with solutions for known cases of circular and flat beam pipe.

“…In parallel with the machine measurements, a new coupling impedance model of the PS has been developed in both longitudinal [11] and transverse planes [12]. The effects of the wakefields on the transverse beam dynamics have been evaluated using the PyHEADTAIL [13] macroparticle tracking code, and are discussed in Sec.…”

Section: Introductionmentioning

confidence: 99%

Instability studies at the CERN Proton Synchrotron during transition crossing

Migliorati¹,

Aumon

Koukovini-Platia

et al. 2018

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The CERN Proton Synchrotron (PS) routinely crosses transition energy at around 6 GeV in order to accelerate protons that are injected in the Super Proton Synchrotron (SPS) or transferred to users of fixed target experiments. Depending on the beam parameters and intensity, a fast vertical coherent instability occurs during transition crossing. The instability, characterized by beam losses and a frequency spectrum in the range of 500-900 MHz, represents an important intensity limitation for the neutron time-of-flight (nTOF) beam, and in general could represent a bottleneck for future high intensity beams. In order to better understand the nature and the source of the instability and to find possible mitigations, a dedicated measurement campaign took place. Parallel to the measurements, beam dynamics simulations have been performed to study the observed instability. In particular, single bunch effects have been simulated using the PS transverse beam coupling impedance model developed over recent years. In this paper we present the measurements results along with the obtained instability thresholds. Different beam configurations and stabilizing effects, such as the gamma jump scheme and the octupole-induced tune spread, are also considered. The measurements results are compared with simulations.