¼ meshed models for Omega3P calculations TRAPPED MODES STUDY IN A ROTATABLE COLLIMATOR DESIGN FOR THE LHC UPGRADE* Liling Xiao, Cho-Kuen Ng, Jeffery Claiborne Smith, SLAC; Fritz Caspers, CERN ABSTRACT: A rotatable collimator is proposed for the LHC phase II collimation upgrade. When the beam crosses the collimator, it will excite trapped modes that can contribute to the beam energy loss and power dissipation on the vacuum chamber wall. Transverse trapped modes can also generate transverse kicks on the beam and may thus affect the beam quality. In this paper, the parallel eigensolver code Omega3P is used to search for all the trapped modes below 2 GHz in two collimator designs, one with rectangular and the other with circular vacuum chamber. It is found that the longitudinal trapped modes in the circular vacuum chamber design may cause excessive heating. Adding ferrite tiles on the circular vacuum chamber wall can strongly damp these trapped modes. We will present and discuss the simulation results. Simulation Model Transverse Modes y Rectangular chamber Cause transverse kicks in the y-direction and power dissipation on vacuum chamber wall Retractable and rotatable jaws When the jaws are fully inserted with a 42mm gap, the kick factors of the transverse trapped modes are the largest. y x Circular chamber Circular chamber for easier fabrication The loss factors depend on the beam offset. x Solid models (Courtesy of Steven Lundgren) Simulation models ¼ meshed models for Omega3P calculations Longitudinal Modes Cause beam energy loss and power dissipation on vacuum chamber wall Ferrite-Loaded Collimator E-field 2mm thin ferrite tiles Jaws will move in and out with a 2mm to 42mm gap. When the jaws are fully retracted with a 42mm gap, the loss factors of the longitudinal trapped modes are the largest. Stainless steel vacuum chamber wall and copper jaws are used for Q calculation Transient heating Lowest longitudinal trapped mode B-field TEM-like mode, lower Q Cavity mode, higher Q Trapped modes damped to Q < 100 Resonant heating Summary All trapped modes below 2GHz in the SLAC rotatable collimator design are calculated using Omega3P, and their RF heating effects are evaluated. The longitudinal trapped modes in the circular vacuum chamber design have higher Q-values. In the worst case, they may cause excessive heating if they all interact with the beam in resonance. The heating due to the transverse trapped modes are negligible. The beam instability due to the transverse kicks on the beam will be evaluated. Adding ferrite tiles in the circular vacuum chamber collimator can strongly damp the trapped modes. Need effort on design and analysis of the tiles that include thermal and mechanical effects. Using the amplitude ratio of the longitudinal and transverse modes to determine the position of the beam is underway. Rectangular chamber Circular chamber Trapped Mode Heating * Work supported by US Department of Energy under contract DE-AC02-76SF00515.