rf heating in the slac rotatable collimator design liling xiao advanced computations department

L. Xiao, LARP-CM12, April 9, 2009

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

Omega3P calculates the trapped modes below 2GHz and provides HOM parameters for beam heating and coupled-bunch stability studies

F(Hz)

Beam Frequency Spectrum


4

Rectangular Vacuum Tank Design Circular Vacuum Tank Design

The collimator jaw will move in and out with a 2mm to 42mm gap.

Easier for fabrication

Beampipe R = 42mm, Fc(TE11) = 2.1GHz, Fc(TM01) = 2.7GHz

Rotatable Collimator


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Simulation Model

Rectangular Design Circular Design

y

x

z

¼ Omega3PModel


6

Finite Element Mesh Tetrahedras with 2nd order curved surface

Denser mesh along beam path plus 3rd order basis functions for better accuracy


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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.


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Loss factor for a Gaussian bunch with sigma=7.6cm

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

5.0E+07 2.5E+08 4.5E+08 6.5E+08 8.5E+08

F (Hz)

Klo

ss (V

/c)

open gap=42mm

closed gap=2mm

Loss factor for a Gaussian bunch with sigma=7.6cm

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E+08

5.0E+07 2.5E+08 4.5E+08 6.5E+08 8.5E+08

F (Hz)

Klo

ss (

V/c

)

open gap=42mm

close gap=2mm

Loss Parameters vs. Jaw’s 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 gap=42mm.

Longitudinal Trapped Modes


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Quality Factor

100

1100

2100

3100

4100

5100

6100

7100

8100

9100

5.0E+07 5.5E+08 1.1E+09 1.6E+09

F (Hz)

Q0

round tank for open gap=42mm

rectangular tank for open gap=42mm

RF Parameters for fully retracted jaws, gap=42mm

Vacuum tank is made of stainless steel, σ=0.116e7s/m. Two jaws are made of copper, σ=5.8e7s/m

Shunt Impedance for a Gaussian bunch with sigma=7.6cm

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

5.0E+07 5.5E+08 1.1E+09 1.6E+09 2.1E+09

F (Hz)

R (o

hm)

round tank for open gap=42mm

rectangular tank for open gap=42mm


R

Q0


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Cir. Tank: f1=93MHz, Q=1662The trapped mode spreads around the jaws. Q is higher.

E-field

B-field

Rec. Tank: f1=82MHz, Q=279The trapped mode locates between the jaw and chamber wall. Q is lower.

E-field

B-field


Lowest Trapped Mode Field Pattern


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Transient Heating Effects

Transient beam energy losses is total energy left by the passage of the bunch train through the collimator.

WrecPJerecE

WcirPJecirE

nsTnCqN

TNEPkNqE

b

bi

7.0.)(,55.)(

7.)(,45.)(

25,4.18,2808

)*/(,2

The transient heating power normally causes no problem for structures with good thermal conduction.



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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 (Td>>Tb):

WrecP

WcirP

ATqI

QeQ

RIP

b

ic

ii

15.)(

515.)(

582.0/

,*)(222 2/2

The trapped mode frequencies should be shifted away from 40MHz beam harmonic thus reducing the resonant heating power.



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Kick Factor

1.E+07

1.E+08

1.E+09

1.E+10

1.E+11

1.E+12

1.E+13

1.E+14

1.E+15

5.00E+07 4.50E+08 8.50E+08 1.25E+09 1.65E+09 2.05E+09

F (GHz)

Kick

Fac

tor (

V/C/

M)

Round tank for closed gap=2mm

Rectangular tank for closed gap=2mm

RF Parameters for fully inserted jaws, gap=2mmQuality Factor

100

1100

2100

3100

4100

5100

6100

7100

8100

9100

5.00E+07 4.50E+08 8.50E+08 1.25E+09 1.65E+09 2.05E+09

F (GHz)

Qual

ity F

acto

r

Round tank for closed gap=2mm

Rectangular tank for closed gap=2mm

When the two jaws are fully inserted with gap=2mm, the kick factors are highest due to the strongest Ey between the two jaws.

Transverse Trapped Modes

Kick

Q0


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Lowest Trapped Mode Field Patterns


Rec. Tank: f1=79MHz, Q=382The trapped mode is between the two jaws and the jaw and chamber wall. Q is lower.

Cir. Tank: f1=85MHz, Q=1344The trapped mode is between the two jaws. Q is higher.

E-field

B-field

E-field

B-field


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Loss ParametersLoss Factor for rectangular tank with gap=2mm, Gaussian

bunch=7.6cm

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

5.00E+07 4.50E+08 8.50E+08 1.25E+09 1.65E+09 2.05E+09

F (GHz)

Loss

Fac

tor (

V/C)

at o

ffset

y

offset y=0.05mmoffset y=0.075mmoffset y=0.1mm

Loss Factor for round tank with gap=2mm, Gaussian bunch=7.6cm

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

5.00E+07 4.50E+08 8.50E+08 1.25E+09 1.65E+09 2.05E+09

F (GHz)

Loss

Fac

tor (

V/C)

at o

ffset

yoffset y=0.05mmoffset y=0.075mmoffset y=0.1mm

Rectangular Tank Circular Tank

Loss factors of transverse modes depend on the beam offset.



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Max. Power dissipation on wall

Beam offset at y-direction

0.075mm

(Max.)

0.050mm

Rectangular Vacuum Tank

Transverse Modes (<2GHz) gap=2mm

6W 3W

Longitudinal Modes (<2GHz) gap=42mm

15W

Circular Vacuum Tank

Transverse Modes (<2GHz) gap=2mm

15W 7W

Longitudinal Modes (<2GHz) gap=42mm

515W

To be safe, beam heating due to the longitudinal trapped modes in the circular vacuum design needs to be reduced.

Trapped Mode Heating


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Chosen Lossy Material

“First Studies for a Low Temperature Higher-Order-Mode Absorber For the Cornell ERL Prototype”, M. Liepe, et al.

At room temperature and 100K

“Measurements of ε and μ of Lossy Materials for the Low Temperature HOM LOAD”, V. Shemelin, et al.

Re. ε Im.ε

Re. μ Im. μ

F=0~2GHz, ε~10-j0.2, μ~2-j10 at 297k


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TT2-111R Ferrite Tile t=2mm

Attaching ferrite tiles on vacuum wall above the top and bottom of the jaws can strongly damp the longitudinal trapped modes.

Jaw fully retracted gap=42mm

Damping Longitudinal Trapped Modes w/ Ferrites

t

ε=10-j0.2, μ=2-j10

Longitudinal trapped mode in round tank design

1

10

100

1000

10000

0.0E+00 2.0E+08 4.0E+08 6.0E+08 8.0E+08 1.0E+09 1.2E+09 1.4E+09

F (Hz)

Q-v

alu

e

w ithout ferrites

w ith ferrites at 297k


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Lowest Trapped Mode Field Patterns

After adding ferrite tiles, the trapped mode is absorbed in the lossy material.

E-field

B-field

Without Ferrite Tiles With Ferrite Tiles

Cir. Tank without ferrite tiles: f1=93MHz, Q=1662

E-field

B-fieldCir. Tank with ferrite tiles: f1=86MHz, Q=10



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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 ferrite’s 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.

rf heating in the slac rotatable collimator design liling xiao advanced computations department

Documents

transverse modes

collimator power dissipation

q0 beam energy loss

beam path

ghzrotatable collimator

loss parameters

loss factors

retracted jaws