Simulation of Longitudinal and Transverse Impedances of Trapped Modes in LHC Secondary Collimator

The results of simulation of trapped modes in LHC (phase 1) secondary collimators are presented. Both monopole and dipole modes have been analyzed giving estimates of the longitudinal and transverse impedances for different values of the collimator gap. The comparison with available measurement data shows good agreement. It has been found that a monopole mode at 1.25 GHz gives the main contribution to the longitudinal impedance resulting mainly in heat deposition in the region of sliding RF finger. Estimated maximum losses are 65 mW per finger for nominal LHC beam intensity. Several dipole modes which give non-negligible contribution to the transverse impedance at frequencies below 2 GHz have been found and analyzed.