Fast calculation of the resistive wall wake sum for multi bunch beams

For the numerical study of the beam injection process into the LHC, several technical and beam dynamical effects have to be taken into account, e.g. closed orbit variations of the pre-accelerator SPS, ripples on extraction and injection kickers, optics of the LHC itself and the behaviour of its transverse feedback system. Prominent beam dynamical effects are coupled bunch instabilities caused for example by the vacuum chamber resistance. This paper describes a fast approximate calculation of the beam deflection due to the wake field which is built up by the vacuum chamber resistance and caused by a large number of previous bunches and/or bunch passages. The code has been implemented into the framework of the CNGS extraction simulations [1] and the results are compared with measurements [2].