We address here the problem of the transverse coupled-bunch instabilities created by the Large Hadron Collider (LHC) beam-coupling impedance, that can possibly limit the machine operation. A rather complete vision of the problem is proposed, going from the calculation of the impedances and wake functions of individual machine elements, to the beam dynamics study. New results are obtained in the theory of the beam-coupling impedance for an axisymmetric two-dimensional structure, generalizing Zotter's theories, and a new general theory is derived for the impedance of an infinite flat two-dimensional structure. Then, a new approach is found to compute the wake functions from such analytically obtained beam-coupling impedances, overcoming limitations that could be met with standard discrete Fourier transform procedures. Those results are used to obtain an impedance and wake function model of the LHC, based on the (resistive-) wall impedances of various contributors (collimators, beam screens and vacuum pipe) and additional estimations of the geometrical impedance contributions. Finally, the existing code HEADTAIL is improved to make possible the simulation of multibunch trains. All those theories and tools are used to obtain new results concerning the LHC transverse coupled-bunch instabilities, comparing them with actual measurements in the LHC, providing a very good agreement at injection energy and a correct order of magnitude at 3.5 TeV/c.
Organisers: H. Burkhardt (BE), S. Sgobba (EN), G. deRijk (TE)