Simulation of Transverse Multi-Bunch Instabilities of Proton Beams in LHC

The CERN Large Hadron Collider (LHC) is designed for highest luminosity and therefore requires operation with a large number of bunches and high intensities. Its performance could be limited by the electromagnetic interaction between the charged particle beam and its surroundings which cause collective instabilities. This thesis describes methods of simulating and analyzing multi-bunch instabilities in circular accelerators and storage rings. The simulation models as well as analyzing tools presented here, also facilitate the interpretation of measurements in multi-bunch machines. The 3-dimensional, multi-bunch tracking program MultiTRISIM was developed, based on its single-bunch predecessor TRISIM3D. It allows the exploration of longrange effects in round or flat vacuum chambers for equidistant or uneven filling schemes. Previous computer simulations of collective effects concentrated mainly on instabilities of single or few bunches in electron storage rings. There, the strong radiation damping reduces the required simulation time to a few thousand turns at most. For multi-bunch proton beams, however, where radiation damping is weak, much longer computation times are needed. Also the modelling of long-range wakes due to higher order modes and other impedances is computationally quite challenging. Therefore approximations have been investigated carefully. A method has been implemented allowing fast wake summation, which is based on the convolution theorem and the discrete FFT. The resistive wall instability is a major concern for the LHC, in particular since collimators made of graphite are installed. Well-known and recently developed resistive wall impedance models have been compared, and the wake function required for time domain simulation has been obtained in analytical form for one of the models. The simulation program has been verified by making predictions for the effects of impedances on proton beams in the CERN SPS and comparing them with measurements. The results of multi-bunch and/or multi-turn simulations of LHC are presented. Various performance issues related to the resistive wall effect of the collimators have been simulated and analyzed. The partial filling scheme of the LHC beam has been taken into account. The simulation shows that the proposed octupole strengths are adequate to stabilize the LHC beam at top energy.