SUMMARY OF THE SINGLE-BEAM COLLECTIVE EFFECTS IN THE LHCBerg, J.S.; Bruening, O.; Caspers, F.; D'yachkov, M.*; Morvillo, M.; Ruggiero, F.Single beam collective effects can limit the performance of the LHC and, together with parasitic losses, impose constraints on the design of the components of the LHC vacuum system. Because of the large number of bunches in the LHC, coherent losses and multibunch instability rise times generated by the impedance items can be rather large. For example, the vacuum chambers of the main experiments can lead to large parasitic losses and a continuous feedback from the impedance calculations during their design process is desirable. We first summarise the current status of the impedance model for the LHC and estimate rise times and threshold currents for different instabilities. In a second step, we discuss possibilities of controlling these instabilities, using feedback systems and Landau damping. Abstract Single beam collective effects can limit the performance of the LHC and, together with parasitic losses, impose constraints on the design of the components of the LHC vacuum system. Because of the large number of bunches in the LHC, coherent losses and multibunch instability rise times generated by the impedance items can be rather large. For example, the vacuum chambers of the main experiments can lead to large parasitic losses and a continuous feedback from the impedance calculations during their design process is desirable. We first summarise the current status of the impedance model for the LHC and estimate rise times and threshold currents for different instabilities. In a second step, we discuss possibilities of controlling these instabilities, using feedback systems and Landau damping.

Coherent modes which are present when there is no incoherent tune spread may be absent when such a spread exists. Such modes are``Landau damped.'' There is instead an incoherent spectrum, a continuum of an infinite number of frequencies, which will decohere (filament), thus not leading to collective instabilities. A stability diagram indicates when Landau damping will be effective. It divides the effective impedance plane, or equivalently the plane of coherent frequency in the absence of tune spread, into regions. The region which contains +i/infinity corresponds to instability. Thus, one can substitute a simpler computation (finding discrete eigenvalues) for a more complex computation (solving an eigenvalue system with both a discrete and a continuous eigenvalue spectrum). We present stability diagrams assuming a linear tune shift with amplitude, allowing tune spread in two transverse planes or in the longitudinal plane alone. When there is longitudinal tune spread, this can not be done exactly, and we describe approximations which make the computation tractable.

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This paper describes how to use the code vlasov, which implements the computation of multibunch frequencies and growth rates when the effects of multibunch mode coupling are included. The theory behind this code is described in [BR95a, BR95b, Ber961. This paper also describes the algorithm used to compute the modes, and the approximations made.