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Possible Methods for Reducing the Trapped Mode Effect in the SLAC Rotatable Collimator for the LHC Phase II Upgrade. Liling Xiao. 1. Current Model. Courtesy Steven Lundgren. R_beampipe=30.5mm. Jaw’s opening=2mm / 60mm. 2. Two Jaw Gaps – Longitudinal Modes. Current Design.
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Possible Methods for Reducing the Trapped Mode Effect in the SLAC Rotatable Collimator for the LHC Phase II Upgrade Liling Xiao 1
Current Model 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 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