Trapped Mode Study in the LHC Rotatable Collimator

A rotatable collimator is proposed for the LHC phase II collimation upgrade. When the beam crosses the collimator, trapped modes will be excited that result in beam energy loss and collimator power dissipation. Some of the trapped modes can also generate transverse kick on the beam and affect the beam operation. In this paper the parallel eigensolver code Omega3P is used to search for all the trapped modes below 2GHz in the collimator, including longitudinal modes and transverse modes. The loss factors and kick factors of the trapped modes are calculated as function of the jaw positions. The amplitude ratio between transverse and longitudinal trapped mode intensity can be used as a direct measure of the position of the beam. We present simulation results and discuss the results.