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

2. 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

3. 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

4. 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

5. 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

6. 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
0.5mm
0.5mm
Gap=2mm
Gap=60mm
There are strong Ey fields between the two jaws for fully inserted jaws.
L. Xiao 6

7. 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 74MHz
(CERN Design: Max. R = GHz)
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 63MHz
(CERN Design: Max. R/Q ~ 10e5 ohm/collimator) Problem!!!
L. Xiao 7

8. 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

9. 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 RF
L. Xiao

10. 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

11. 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

12. 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

13. 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