Possible Methods for Reducing the Trapped Mode Effect in the SLAC Rotatable Collimator for the LHC Phase II Upgrade Liling Xiao 1

Current Model R_beampipe=30.5mm Jaw’s opening=2mm / 60mm Courtesy Steven Lundgren R_beampipe=30.5mm Jaw’s opening=2mm / 60mm L. Xiao 2

Two Jaw Gaps – Longitudinal Modes Current Design The longitudinal modes have similar R/Q for the fully inserted jaws and the fully retracted jaws in the current design. L. Xiao 3

Lowest Longitudinal Modes E-field Gap=2mm: F=87.4MHz, R/Q=2.10e-1ohm/collimator Gap=60mm: F=73.6MHz, R/Q=3.65e-1ohm/collimator In the current design, the narrow EM foils can only perturb the Ez fields along the beam path without changing it significantly when the jaw gap varies. L. Xiao 4

Two Jaw Gaps – Transverse Modes Current Design The transverse modes have strong R/Q_T for fully inserted jaws than for fully retracted jaws. The transverse modes are gap modes between the two jaws . L. Xiao 5

Lowest Transverse Modes E-field Gap=2mm, F=62.9MHz, R/Q_T=5.5e6ohm/collimator Gap=60mm, F=75.4MHz, R/Q_T=3.3e2ohm/collimator 150 6 yoffset@ 0.5mm yoffset@ 0.5mm Gap=2mm Gap=60mm There are strong Ey fields between the two jaws for fully inserted jaws. L. Xiao 6

Current Design The longitudinal modes have similar R/Qs for the fully inserted jaws and for the fully retracted jaws, and the longitudinal modes R/Q depend on the geometry in transition region. Max. R/Q < 3.65e-1 ohm/structure @ 74MHz (CERN Design: Max. R =2380 ohm @ 1.25GHz) The transverse modes have higher R/Qs for the fully inserted jaws than for the fully retracted jaws. The most dangerous transverse modes are gap modes that exist in the straight section. Max. R/Q_T ~ 5.5e+6 ohm/collimator @ 63MHz (CERN Design: Max. R/Q ~ 10e5 ohm/collimator) Problem!!! L. Xiao 7

Modified Transition Part VS. Longitudinal Modes fully inserted jaws fully retracted jaws Modified EM Foils Increasing the height of the EM foils can reduce the lower longitudinal modes R/Q effectively, thus reduce the beam heating. L. Xiao 8

Transverse Modes in CERN Collimator CERN Collimator I A=140mm Beam in rectangular waveguide with Fc=c/(2*a)=1.07GHz Gap Modes: F>Fc A. Grudiev: AB-Note-2005-042 RF L. Xiao

Transverse Modes in SLAC Collimator F=63MHz F=190MHz Beam in parallel plats waveguide with Fc=0 Gap Modes: F=f(Length of jaw) F=346MHz L. Xiao

Modified Straight Part VS. Transverse Modes Modified SLAC Collimator fully inserted jaws fully retracted jaws h Adding two plates on the top and bottom to form a closed waveguide for the fully inserted jaws, thus suppressing the dangerous gap modes. Beam in double-ridge waveguide with Fc~c/(2*h)=2.5GHz for fully inserted jaws No gap Modes < 2GHz Beam in two pairs of the parallel plates with larger gaps. Strong fields locate between the jaw surface and the base plates. L. Xiao

Lowest Transverse Modes Without Plates E-field Gap=2mm, F=62.9MHz, R/Q_T=5.5e6ohm/collimator Gap=60mm, F=75.4MHz, R/Q_T=3.3e2ohm/collimator With Plates Gap=2mm, F=332MHz Gap=60mm, F=160MHz, The strong gap modes are eliminated by adding the two plates both for fully inserted jaws and fully retracted jaws. L. Xiao 12

Summary Modifying the transition part can reduce the longitudinal modes R/Q_z. Closed the volume around the two cylinder jaws can eliminate the gap modes below 2 GHz for the fully inserted jaws. The gap modes for fully retracted jaws will be reevaluated . L. Xiao, March 15, 2010 13