The LEP impedance model

The bunch current in LEP is limited by collective effects slightly below its design value. To understand this limitation, a set of experiments has been carried out to obtain a model of the impedance seen by the circulating beam. From measurements of the current dependance of the synchrotron and betatron frequencies information about the longitudinal and transverse reactive impedance has been obtained. The growth rate of the m=1 head-tail instability has been observed to gain some knowledge of the resistive transverse impedance. The dependence of the transverse mode-coupling threshold on bunch length has been measured. The energy loss per turn of a stable bunch is given by the longitudinal resistive impedance and has been measured by recording the change of the synchronous phase angle with current. All these quantities represent integrals over products of bunch mode spectra and impedances. By measuring them for different bunch lengths the frequency dependence of the impedances can be estimated. From these results a model of the LEP impedance has been obtained which can be used to estimate the current limitation under different operating conditions.<
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