Long Time Simulation of LHC Beam Propagation in Electron Clouds

In this report we show the simulation results of single-bunch instabilities caused by interaction of a proton beam with an electron cloud for the Large Hadron Collider (LHC) using the code QuickPIC [1]. We describe three new results: 1) We test the effect of the space charge of the beam on itself; 2) we add the effect of dispersion in the equation of motion in the x direction, and 3) we extend previous modeling by an order of magnitude (from 50ms to 500ms) of beam circulation time. The effect of including space charge is to change the emittance growth by less than a few percent. Including dispersion changes the plane of instability but keeps the total emittance approximately the same. The longer runs indicate that the long term growth of electron cloud instability of the LHC beam cannot be obtained by extrapolating the results of short runs.