Transverse beam coupling impedance of the CERN Proton Synchrotron

Beam coupling impedance is a fundamental parameter to characterize the electromagnetic interaction of a particle beam with the surrounding environment. Synchrotron machine performances are critically affected by instabilities and collective effects triggered by beam coupling impedance. In particular, transverse beam coupling impedance is expected to impact beam dynamics of the CERN Proton Synchrotron (PS), since a significant increase in beam intensity is foreseen within the framework of the LHC Injectors Upgrade (LIU) project. In this paper we describe the study of the transverse beam coupling impedance of the PS, taking into account the main sources of geometrical impedance and the contribution of indirect space charge at different energies. The total machine impedance budget, determined from beam-based dedicated machine measurement sessions, is also discussed and compared with the theoretical model.

Figure 1

Magnetic field as a function of time of the 25.48 GeV beam cycle.

Figure 2

Horizontal tune shifts with beam intensity measured at 25.48 GeV.

Figure 3

Vertical tune shifts with beam intensity measured at different energies and the vertical chromaticity set to a value as close as possible to zero.

Figure 4

Transverse section view of a ferrite-loaded delay line kicker model used for CST simulations of KFA13. The kicker is made of three identical modules. In each module the ferrite (in green) is split longitudinally in nine cells. Each cell is 24 mm long: 19 mm of ferrite and 5 mm of aluminium (in yellow). In each module there are two conducting cables, modeled in CST with PEC (perfectly conducting boundaries, in grey). Vacuum is represented in light blue. This model has been discretized in CST with 7,588,152 mesh cells and simulated with a wake length of 25 m.

Figure 5

Transverse section view of lumped kicker models used for CST simulations of PS kicker KFA28 (left) and BFA09S-21S (right). The kickers are made of a single ferrite yoke (in green). A brick of aluminium is inserted in the yoke in order to reduce the impedance seen by the beam. Kickers with the prefix KFA are designed with two conducting cables, while kickers with the prefix BFA are designed with four conducting cables, modeled in CST as aluminium (in yellow). Vacuum is represented in light blue.

Figure 6

Total horizontal and vertical impedance of the PS kickers (sum of dipolar and quadrupolar components), weighted for the $\beta$-function, computed with CST Particle Studio.

Figure 7

3D model of a PS flange used for CST Particle Studio simulations (left); 3D model of a PS sector valve used for CST Particle Studio simulations (right).

Figure 8

3D model of a PS vacuum pump used for CST Particle Studio simulations (left); 3D model of a PS bellow used for CST Particle Studio simulations (right).

Figure 9

Comparison between measured and reconstructed phase advance slope as a function of the BPM position along the machine circumference. The horizontal unit represents the straight section number in the PS ring.

Figure 10

Comparison between the localized measured and simulated effective vertical impedance, as a function of the impedance reconstruction location along the machine circumference. Considering the noise level in the BPM and the achieved signal amplitude, a threshold for the lowest localizable impedance is deduced.

Figure 11

Imaginary part of the effective vertical impedance computed from tune shift measurements and from the impedance model, as a function of energy.

Figure 12

Horizontal and vertical total PS impedance model (sum of dipolar and quadrupolar components) a 2 GeV. The curves are obtained summing the contributions of space charge, resistive wall, kickers, rf, and vacuum equipments.

Figure 13

Imaginary part of the vertical effective impedance as a function of vertical chromaticity at different energies. At injection energy (below transition) the machine operates at negative chromaticity.