Comparison between laboratory measurements, simulations, and analytical predictions of the transverse wall impedance at low frequencies

Abstract

The prediction of the transverse wall beam impedance at the first unstable betatron line (8kHz) of the CERN Large Hadron Collider (LHC) is of paramount importance for understanding and controlling the related coupled-bunch instabilities. Until now only novel analytical formulas were available at this frequency. Recently, laboratory measurements and numerical simulations were performed to cross-check the analytical predictions. The experimental results based on the measurement of the variation of a probe coil inductance in the presence of (i)sample graphite plates, (ii)stand-alone LHC collimator jaws, and (iii)a full LHC collimator assembly are presented in detail. The measurement results are compared to both analytical theories and simulations. In addition, the consequences for the understanding of the LHC impedance are discussed

Matrix solution for the wall impedance of infinitely long multilayer circular beam tubes

“…Also plotted is the absolute impedance value for the classic thick wall approximations, with dashed black for an uncoated ceramic collimator, and blue for a copper collimator. The present numerical results are consistent with those recently published by the CERN team [20], but a detailed comparison with the experimental data for very low frequencies, which would involve extending to the radial model, is beyond the scope of this paper.…”

“…The results for the PETRA III beam tube and the LHC uncoated collimator exhibit similar low-frequency behavior, although the results below 1 kHz are problematic. Notwithstanding the recent collimator paper [20], there is as yet not enough experimental data available to select either model.…”

“…In addition to the standard references on im-pedance problems [4,13], this paper rests on and has profited from the various publications at GSI [14], FNAL [15], DESY [8,16], and primarily the experimental and theoretical work at CERN for the LHC collimator [17][18][19]. The analytic treatments of both the transverse and longitudinal beam tube impedances suffered from a tenuous agreement with experimental data in the low-frequency regime; this issue was addressed successfully in a recent comprehensive paper [20], although, seemingly, further work may be needed.…”

“…As to the terminology used later on and following Ref. [20], the total coupling impedance affecting the beam is obtained as the sum of the (incoherent) spacecharge impedance plus the resistive wall impedance, thus avoiding the traditional use of ''resistive wall impedance'' for the total beam impedance. Note that the matrix method applies strictly only to the derivation of the wall (surface) impedance.…”

Beam Instabilities in Hadron Synchrotrons

“…The resistive impedance is about two orders of magnitude lower at this frequency, which was a very good news for the LHC. A number of papers have been published on this subject in the last few years using the field matching technique starting from the Maxwell equations and assuming a circular geometry [18][19][20][21][22]. Recently, new results have been also obtained for flat chambers, extending the (constant) Yokoya factors to frequency and material dependent ones [23] (see later), as was already found with some simplified kicker impedance models [24,25].…”