RF Heating in the SLAC Rotatable Collimator Design

1
RF Heating in the SLAC Rotatable Collimator
Design Liling Xiao Advanced Computations
Department SLAC National Accelerator Laboratory
2
Outline

• Simulation Model
• Rectangular vacuum tank, Circular vacuum tank
• Longitudinal Trapped Modes (loss factor, Q0)
• Beam energy loss, Power dissipation
• Transverse Trapped Modes (kick factor, Q0)
• Beam instability, Power dissipation
• Ferrite-Loaded Collimator
• Damped trapped modes in circular vacuum
  collimator
• Summary

3
Beam Frequency Spectrum
F(Hz)
4
Rotatable Collimator
Rectangular Vacuum Tank Design
Circular Vacuum Tank Design
Easier for fabrication
Beampipe R 42mm, Fc(TE11) 2.1GHz, Fc(TM01)
2.7GHz
The collimator jaw will move in and out with a
2mm to 42mm gap.
5
Simulation Model
Circular Design
Rectangular Design
x
z
y
¼ Omega3P Model
6
Finite Element Mesh

• Tetrahedras with 2nd order curved surface
• Denser mesh along beam path plus 3rd order basis
  functions for better accuracy

7
Trapped Mode Excitation
Longitudinal Modes With magnetic boundary
conditions on x and y symmetric planes, modes
with Ez component on z beam axis are excited
resulting in energy loss and collimator power
dissipation.
Transverse Modes With magnetic/electric
boundaries on y/x symmetry planes, modes with Ey
component between the two jaws are excited when
the beam crosses the collimator at an y-offset
generating a transverse kick in the y-direction
as well as beam energy loss. Due to the small gap
of the jaws, this Ey is very strong over the full
length of the collimator.
8
Longitudinal Trapped Modes
Loss Parameters vs. Jaws Opening
Rectangular Tank
Circular Tank
When the two jaws move out, more and more EM
fields will be generated along the beam path. The
loss factors are getting the largest for fully
retracted jaws with gap42mm.
9
Longitudinal Trapped Modes
RF Parameters for fully retracted jaws, gap42mm
Q0
R
Vacuum tank is made of stainless steel,
s0.116e7s/m. Two jaws are made of copper,
s5.8e7s/m
10
Longitudinal Trapped Modes
Lowest Trapped Mode Field Pattern
E-field
B-field
Cir. Tank f193MHz, Q1662 The trapped mode
spreads around the jaws. Q is higher.
Rec. Tank f182MHz, Q279 The trapped mode
locates between the jaw and chamber wall. Q is
lower.
11
Longitudinal Trapped Modes
Transient Heating Effects
Transient beam energy losses is total energy left
by the passage of the bunch train through the
collimator.
The transient heating power normally causes no
problem for structures with good thermal
conduction.
12
Longitudinal Trapped Modes
Resonant Heating Effects
Resonant power losses are due to the excitation
of these trapped modes. Assuming all bunches are
in phase with them and mode decay is lower from
bunch to bunch (TdgtgtTb)
The trapped mode frequencies should be shifted
away from 40MHz beam harmonic thus reducing the
resonant heating power.
13
Transverse Trapped Modes
RF Parameters for fully inserted jaws, gap2mm
Kick
Q0
When the two jaws are fully inserted with
gap2mm, the kick factors are highest due to the
strongest Ey between the two jaws.
14
Transverse Trapped Modes
Lowest Trapped Mode Field Patterns
E-field
E-field
B-field
B-field
Rec. Tank f179MHz, Q382 The trapped mode is
between the two jaws and the jaw and chamber
wall. Q is lower.
Cir. Tank f185MHz, Q1344 The trapped mode is
between the two jaws. Q is higher.
15
Transverse Trapped Modes
Loss Parameters
Circular Tank
Rectangular Tank
Loss factors of transverse modes depend on the
beam offset.
16
Trapped Mode Heating
Max. Power dissipation on wall Beam offset at y-direction 0.075mm (Max.) 0.050mm
Rectangular Vacuum Tank Transverse Modes (lt2GHz) gap2mm 6W 3W
Rectangular Vacuum Tank Longitudinal Modes (lt2GHz) gap42mm 15W 15W
Circular Vacuum Tank Transverse Modes (lt2GHz) gap2mm 15W 7W
Circular Vacuum Tank Longitudinal Modes (lt2GHz) gap42mm 515W 515W
To be safe, beam heating due to the longitudinal
trapped modes in the circular vacuum design needs
to be reduced.
17
Ferrite-Loaded Collimator
Chosen Lossy Material
At room temperature and 100K
Re. e
Im.e
Re. µ
Im. µ
F02GHz, e10-j0.2, µ2-j10 at 297k
First Studies for a Low Temperature
Higher-Order-Mode Absorber For the Cornell ERL
Prototype, M. Liepe, et al.
Measurements of e and µ of Lossy Materials for
the Low Temperature HOM LOAD, V. Shemelin, et al.
18
Ferrite-Loaded Collimator
Damping Longitudinal Trapped Modes w/ Ferrites
TT2-111R Ferrite Tile t2mm
t
e10-j0.2, µ2-j10
Jaw fully retracted gap42mm
Attaching ferrite tiles on vacuum wall above the
top and bottom of the jaws can strongly damp the
longitudinal trapped modes.
19
Ferrite-Loaded Collimator
Lowest Trapped Mode Field Patterns
Without Ferrite Tiles
With Ferrite Tiles
E-field
B-field
Cir. Tank without ferrite tiles f193MHz, Q1662
Cir. Tank with ferrite tiles f186MHz, Q10
After adding ferrite tiles, the trapped mode is
absorbed in the lossy material.
20
Summary

• All trapped modes below 2GHz in the SLAC 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-value. In the
  worst case, the total power heating can reach
  500W if they all interact with the beam in
  resonance.
• The heating due to the transverse trapped modes
  are negligible but the transverse kick on the
  beam needs to 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 ferrites thermal/mechanical
  effects.
• Using the amplitude ratio of longitudinal and
  transverse modes to determine the position of the
  beam is underway.

Special thanks to Fritz Caspers for his helpful
discussions and advice.