RF Design of Crab Cavity
Parasitic modes in the coaxial coupler
Modifications of the coaxial coupler
Stop band of the notch filter
Rotation of the notch filter
HOM measurement
HOM power estimation

Yoshiyuki Morita
Mar. 19, 2007
Accelerator Review Committee

Parasitic modes in the coaxial coupler-Straight coaxial coupler designCoaxial coupler
Cut-off: 600 MHz

1/4λ mode•
3/4λ mode••
5/4λ mode

Mode Freq.(MHz)

R/Q

Q

1/4λ

595

5.7

106

3/4λ

602

0.17

9000

5/4λ616

1.24

3000

Coaxial coupler has parasitic modes
like a quarter wave resonator.
These parasitic modes are very
dangerous because of its high Qvalues.
The most dangerous mode is thehorizontally polarized TE-λ/4mode.

Modifications of the coaxial coupler

The most dangerous mode
TE-1/4λ-H modef = 595 MHz
R/Q = 5.3 Ω
Q = 106¼ wave length

Tip cutting

600 MHz

Tapered structure

568 MHz530 MHz620 MHz

Three modifications were applied to damp this mode.
1. Tapered coupler design for lower cut-off.
2. TE stop band splitting of notch filter.
3. Tip cutting design to raise freq. of TE-1/4λ-H mode

454 MHzComparison of TE-1/4λ-H mode damping

Straight structure + notch filter

Tapered structure + stop band splitting notch filter+ Tip cutting
Typef

R/Q(MWS)

Q(HFSS)

Straight

595 MHz

5.7 Ω

106

Tapered602 MHz

5.2 Ω5800

Tapered + tip cutting

607 MHz2.1 Ω2700

Stop band splitting design of the notch filter
Notch filter: reject TEM-coupled crab mode
Notch filter has stop band for TE mode.
An axially-symmetric design has a stop bandaround 630 MHz. This stop band is close to theTE-1/4λ-H mode.
A stop band splitting notch filter has partitions in
mid-plane to separate stop bands.

Partitions

Frequency (MHz)Stop band(H-V splitting)
TEM

509 MHzTE(H)650 MHzTE(V)570 MHz
Frequency (MHz)Transmission property-Stop band splitting notch filter-

509 MHz
Crab mode rejection

TEM

TE-H polarization

570 MHz

650 MHz

TE-V polarization

New idea: Rotated notch filter
What will happen when the notch filter rotates ?
Mixing of TE modes occurs.

TE-H pol.

TE-V pol.

Rotation angle: 60o

H to V
V to HQ and R/Q of λ/4-H, λ/4-V and TE101 modes
QR/Q

10000
8000
6000l/4-H
TE101

4000l/4-V

Mode0 deg.

45 deg.

90 deg.

l/4-H

5.24

5.32

5.36l/4-V

4.98

5.30

5.17

TE101

10.3

10.1

10.8

R/Q: no change
We applied 60o rotation angle

2000
00

1020304050607080

90Rotation angle (deg.)

Q value of the λ/4-H mode significantly
decreases as rotating the notch filter.

Tip cutting design
Q of λ/4-H = 2700
R/Q of λ/4-H = 2.1

Growth time
60Machine parameters

Growth time (ms)5040l/4-H30

TE101l/4-V

20HERLEREnergy (GeV)

83.5

Current (A)

1.3

1.6

Beta-x (m)20040

Beta-y (m)

13.5

38.5

10001020304050607080

90

Rotation angle (deg.)

Present crab cavity
λ/4-H : HER, Horizontal
λ/4-V, TE101: LER, VerticalHOM/LOM measurement

Monitor port (H/V)

Input coupler

NetworkAnalyzer

HER crab cavity

Measurement Result (HER at RT)
TE011

HER crab cavity
1st horizontal test*: 0o
2nd horizontal test: 60o

λ/4-V*Coaxial coupler:
not at designed position
Notch0Notch60-80

TE101dB-60

LOM-40

Crab mode-20

coaxTE-H

λ/4-H

H-port-100-120-140400

450500550
Freq. (MHz)600

650700Measurement Result (HER at RT)

dBTM120

λ/4-V-60

LOM-40

Crab mode

-20

TE101

λ/4-H

V-portNotch0Notch60-80-100-120-140400450500550
Freq. (MHz)600

650700Summary of measurement-HER crab cavity at RTmode

R/Q

f and Q at 0o *f and Q at 60o

LOM

80.1

409 / 164409 / 142

λ/4-H

5.24

604 / 1257

603 / 893

λ/4-V

4.98

597 / 394

594 / 1329

TE101

10.33

642 / 327

643 / 721

*coaxial coupler: not at designed position

Acceptable for KEKB

Model cavity
Recently a model coupler was made to check the mode damping scheme.

Coaxial coupler

Network analyzer

Notch filter
Stub support
Crab cavity

Summary of measurement-Comparison with calculation and model measurementRotation angle: 0omodef and Q (calc.)

f and Q (HER)*

f and Q (model)

LOM

406 / 48409 / 164407 / 131

λ/4-H

602 / 5774

604 / 1257

602 / 1775

λ/4-V

597 / 1681

579 / 394

601 / 486TE101

641 / 181

642 / 327

646 / 305

*coaxial coupler: not at designed position

Rotation angle: 60omodef and Q (calc.)

LOM

f and Q (HER)

f and Q (model)

409 / 142

407 / 133

λ/4-H

603 / 1687

603 / 893

602 / 886

λ/4-V

596 / 958

594 / 1329

600 / 653TE101

642 / 850

643 / 721

647 / 889

Further investigation with model cavity

HOM PowerDamper loss

Power Flow Estimation
Beam passing through the cavity•Monitor E and B fields during
beam passing
Calculate the Poynting vector
Integrate the Poynting vector
on the monitoring surface••

Power flow
Beam-in4 10 20EM fields after beam passing

LBP

2 10 20

Integr.Pds (J/s)

CoaxialBeam-out

LBP

SBP0Coaxial-2 10 20-4 10 20

SBP0Monitor positions

5101520Time (ns)

25

30

35

Expected HOM LoadDamper Load (kW)

30

LBP

25

1400 bunches

20

14.5 kW1518 kW

10Coax

6.4 kW

50
0

0.5

1

1.5

2Current (A)HOM dampers for crab cavity
High power tested up to 10 kW
Capability up to 18 kW (Mitsunobu et al)Summary• Parasitic mode damping of the coaxial coupler– Rotation of the notch filter improves mode damping– Optimum rotation angle found– No need for tip cutting design ?
• HOM/LOM measurement– LOM: Q=142, larger than calculated Q value– λ/4 mode at 60o: consistent with calculation– λ/4 mode at 0o: significant discrepancy with calculation– Further investigation with a model cavity• HOM power estimation– LBP: 6.4 kW, coax: 1.4 kW (1A, 1400 bunches)