Intrabeam scattering in the LHC

Intrabeam Scattering (IBS) is the process where particles within an accelerator beam elastically scatter off each other. The effect of IBS is not to be confused with the Coulomb repulsion due to the fields generated by the other particles in the beam. The Coulomb repulsion effects are referred to as space-charge effects in Accelerator Physics and become less important than IBS at high energies because of the 1/gamma^2 that occurs in the space-charge equations making IBS one of the most important causes of beam size growth. At high energies (for example at 7 TeV or the LHC nominal operation energy) IBS effects are counteracted by Radiation Damping effects, in some cases leading to decrease in beam sizes instead of beam growth. But at the time of writing the operation energies were still low enough to neglect Radiation Damping Effects in comparison with IBS effects (Radiation Lifetimes were a factor five to ten higher than the IBS Lifetimes in the cases presented at the end of this text). Because of its effect on beam size IBS is an important effect to consider in beam operation. In many cases, especially for heavy ions that have a large charge compared to protons, the IBS effect will be one of the main factors determining the beam lifetime and thus putting constraints on the beam operation. In this aspect it is important to have a good model for IBS to be able to predict what lifetimes can be expected for the beam under different circumstances. In this text we will derive the equations for the IBS growth rates in the different planes that were presented in the article published by Bjorken and Mtingwa [14]. We will also give a short discussion of the other IBS models that were already used to simulate the IBS lifetimes in the LHC. Next to these models the Nagaitsev Model is introduced. Roderik Bruce and myself implemented this model in the simulation software during my internship at CERN. This Nagaitsev Model has the advantage that the calculations of the integrals, necessary for determining the IBS growth rates, can be done fairly quickly and the accuracy can be set in the software. A disadvantage of this model is that it does not take Vertical Dispersion into account. After comparing the different models with each other on a test case we decided to use the Nagaitsev Model to do simulations and compared them with the data from the 2010 LHC operation. The comparison is mainly done for ions because there the IBS effect is the strongest, but in some sections I will deviate from that and also have a look at proton data. Future work is planned to compare simulations with proton data. Simulations were done with a FORTRAN particle tracking code. This particle tracking software (PTS) was developed by Roderik Bruce (CERN/LUND university) and Mike Blaskiewisc (BNL) in collaboration with John Jowett (CERN) and was applied succesfully to RHIC [4, 20] (Relativistic Heavy Ion Collider), it was also used to make predictions for the LHC.