Impact of the resistive wall impedance on beam dynamics in the Future Circulare+e−Collider

Abstract

The Future Circular Collider study, which aims at designing post-LHC particle accelerator options, is entering in the final stage, which foresees a conceptual design report containing the basic requirements for a hadron and a lepton collider, as well as options for an electron-proton machine. Due to the high beam intensities of these accelerators, collective effects have to be carefully analyzed. Among them, the finite conductivity of the beam vacuum chamber represents a major source of impedance for the electron-positron collider. By using numerical and analytical tools, a parametric study of longitudinal and transverse instabilities caused by the resistive wall is performed in this paper for the case of the Future Circular Collider lepton machine, by taking into account also the effects of coating, used to fight the electron cloud build up. It will be proved that under certain assumptions the coupling impedance of a two layer system does not depend on the conductivity of the coating and this property represents an important characteristic for the choice of the material itself. The results and findings of this study have an impact on the machine design in several aspects. In particular the quite low threshold of single bunch instabilities with respect to the nominal beam current and the not negligible power losses due to the resistive wall are shown, together with the necessity of a new feedback system to counteract the fast transverse coupled bunch instability. The importance of a round vacuum chamber to avoid the quadrupolar tune shift is also discussed. Finally the crucial importance of the beam pipe material coating and thickness choice for the above results is underlined.

Study of collective effects in the FCC-ee collider

“…As it can be seen, for the above assumptions, the real part of the impedance does not depend on the coating thickness and conductivity. The performed numerical studies [13] have confirmed that the resulting RF power losses due to the RW impedance remain almost unchanged for the coating conductivity and thickness varying in a very wide range. In turn, since the perturbation of the imaginary part due to the coating is proportional to its thickness and to the term (1 − 1 2 ), if the coating conductivity is much smaller than the beam pipe material conductivity the impedance depends only on the thickness of the coating layer.…”

“…As it has been shown in [13], for the 100 km long collider, the finite conductivity of the beam vacuum chamber represents a major source of the beam coupling impedance, and wake fields strongly affect the beam dynamics and, respectively, collider design solutions and parameters choice. This fact has been taking into account while choosing the vacuum chamber shape and its dimensions.…”

“…Analyzing the multi-bunch beam dynamics it has been found that the coupled bunch instability due to the transverse RW long range wake fields is another critical issue for the collider [13]. The growth rate of the fastest coupled bunch mode is estimated to be 435 s -1 , corresponding to about 7 revolution turns.…”

Resistive wall impedance in elliptical multilayer vacuum chambers

“…The coupling impedance [1][2][3][4][5] due to the finite resistivity of the beam vacuum chamber, generally called resistive wall impedance, can represent an important source of impedance, as, for example, in LCLS undulator [6], or even the main contributor, as in the case of the Future Circular Collider project [7][8][9][10].…”

Space charge impedance and electromagnetic fields in elliptical vacuum chambers

“…Collective effects due to self-induced electromagnetic fields in a particle accelerator are generally studied by introducing the concepts of wakefield and coupling impedance [1][2][3], which represent, in time and frequency domain respectively, the response of the environment to a point charge traveling inside the beam vacuum chamber or in any of the accelerator devices. These effects can be very important [4], and in some cases they could compromise the machine performance leading to partial or total beam losses [5]. For low energy accelerators with nonrelativistic beams, a not negligible contribution to the total impedance is given by the so-called space charge effects [6,7], which are generated directly by the charge distribution and indirectly by the image charges on the pipe wall.…”