TRAPPED MODES STUDY IN A ROTATABLE COLLIMATOR DESIGN FOR THE LHC UPGRADE*

1
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.
Transverse Modes
Simulation Model
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
¼ meshed models for Omega3P calculations
Solid models (Courtesy of Steven Lundgren)
Simulation models
Longitudinal Modes
Cause beam energy loss and power dissipation on
vacuum chamber wall
Ferrite-Loaded Collimator
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
Lowest longitudinal trapped mode
Transient heating
B-field
TEM-like mode, lower Q
Cavity mode, higher Q
Trapped modes damped to Q lt 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.