DESIGN OF INPUT AND OUTPUT COUPLERS FOR LINEAR ACCELERATORSTRUCTURES
S.Yamaguchi, Y.Igarashi,* A.Enomoto and I.Sato
National Laboratory for High Energy Physics (KEK)
1-1 Oho, Tsukuba, Ibaraki, 305 Japan* Mitsubishi Heavy Industries, Ltd. Nagoya Aerospace Systems
10, Oye-cho, Minato-ku, Nagoya, 455 Japan
Abstract
The input and output couplers for 2m-long S-band linearaccelerator structures for the KEKB linac upgrade have been
designed and tested. The dimensions of the coupler cavities
were estimated by a simulation of the Kyhl method using theMAFIA code, and determined by low-power tests using theKyhl method. It has been shown that the coupler dimensions
can be predicted with precision to be less than 0.5 mm. The
asymmetry of the electromagnetic field (amplitude and phase)in the couplers has been corrected by a crescent-shaped cut on
the opposite side of the iris. The total performance of theaccelerator structures with these couplers is also described.
Introduction
A reinforcement of the PF linac at KEK is now under
way for the KEKB project.[1] The beam energy of the linac isbeing upgraded from 2.5 GeV to 8.0 GeV. For this energy
upgrade, about seventy new accelerator structures (54 cells,2m-long, S-band, quasi-constant gradient, 2π/3-mode,electroplated and no dimpling) are to be fabricated. The input
and output couplers for the new accelerator structures havebeen redesigned, because the existing couplers have insufficientperformance concerning the reflection, phase shift, asymmetryof electromagnetic fields and RF breakdown limit. Fig. 1
shows a cross-sectional view of the coupler. The adjustableparameters are W (iris width) and 2b (inner diameter). So far,the coupler dimensions have been determined by trial and error.
A method for estimating the coupler dimensions by anumerical simulation using the MAFIA T3 module has been
proposed [2]. In this paper, we present a new method toestimate the coupler dimensions by simulating the Kyhl
method [4] using the MAFIA E module.
A correction for the asymmetry of the electromagnetic
fields in the coupler cavities was performed by making acrescent-shaped cut on the opposite side of the iris.
Simulation of the Kyhl method
The simulation of the Kyhl method was carried out asfollows:
1. Generate a mesh structure constructed with the coupler
cavity, half cell and waveguide (Fig. 2). Although thecurvature, (R) of beam hole edge (see Fig. 1) had been 3 mm
for the existing couplers, it was changed to be 7 mm in orderto improve the vacuum-breakdown limit.

34.0mm72.1
mm

1stcellWRtX

Fig. 2. MAFIA geometry for the Kyhl method simulation.
2bC

crescent-shapedcutFig. 1. Cross-sectional view of the coupler cavity (R=7mmand t=2mm).

2. Obtain the resonant frequency (fres) and external Q (Qext ) for
this structure by simulating the Slater’s tuning curve
method[4].
3. Determine fres and Qext for various W and 2b. Fig. 3 showsfres(W,2b) and Qext (W,2b).
4. Obtain W and 2b at the cross point of two lines (Fig. 4):
one isfres=fave ≡(f2π/3 +fπ/2 )/2.

(1)

The other is
Q ext =Qtarget.

This set of W and 2b is the design value of coupler cavities.
Here, fπ/2 (resonant frequency for the π/2 mode) were obtainedby a dispersion curve measured using 6 cell accelerator
structures (standard cavities ). Qext was determined as follows:
Let Qext be inversely proportional to v g,

f r es=f ave

f ave [MHz]

2900
2880
2860
2840
2820
2800
29(2)

Qext ∝ 1/v g .

(3)

81
81.5
30
W [mm]

82 2b [mm]31

The relation between 2a and v g is given by the following
equation, which is obtained by the dispersion curves for several
standard cavities:
v g/c=0.959887x10-5(2a)3-0.514516x10-3(2a)2+0.0105696(2a)-0.0735666.

(a)

(4)

From equations (3) and (4), and data for a coupler with good
matching and tuning characteristics (2a=26.3 mm, andQext =96.195), Qext is given as a function of a as follows:

Q ext=Q target

1/Qext =4.31109x10-6(2a)3-2.31082x10-4(2a)2+4.74707x10-3(2a)-0.033040.

(5)100817581.5

502930W [mm]3182

2b [mm]From this equation, the target value of Qext can be obtained.
The coupler dimensions were determined by cold tests
based on the Kyhl method. A very few iterations of machining
were required before an optimal configuration could beobtained. A comparison between the measured and predictedvalues of the coupler dimensions is shown in Fig. 5 for three
types of couplers with different 2a.
33(b)

85
W (predicted)

32

W (measured)
2b (measured)

30

31.5

29f

31

res=fW [mm]308227812625202b=81.37 mm
W=30.16 mm

29.5

2122232425
2a [mm]26278028Fig. 5. Comparison between the predicted and measured
values ofW and 2b.

2928.580.88328ave

Qext =Qtarget

30.5842b (predicted)

31Fig. 3. (a) fres(W,2b) and (b) Qext (W,2b).

W [mm]

Q ext

1258181.2 81.4 81.6 81.8
2b [mm]8282.2

It is shown that the coupler dimensions (W and 2b) canbe predicted with an accuracy of less than 0.5 mm.
Correction of the Field Asymmetry in Couplers

Fig. 4. Lines of fres=fave and Qext =Qtarget. The values at thecross point gives the designed values of W and 2b.

The asymmetry of the electromagnetic field (amplitude Eand phase) in a couplers was corrected by a crescent-shaped cut

(depth of the cut is C) on the opposite side of the iris (see Fig.
1) using following procedures:
1. Measure the electric-field distribution for two couplers withdifferent values of C. The field distribution has been measured
by the bead pull method based on the non-resonant
perturbation theory [7].
2. Obtain a relation between C and the factor k, defined asfollows: (Fig. 6)

RF characteristics of the accelerator structure
The phase distribution for the accelerator structure withnew couplers was measured using a nodal-shift technique (Fig.
8). A standard deviation of 0.9° was achieved (note that ouraccelerator structure was fabricated without dimpling). The
SWR was 1.07.
6420-2x=±4 mm
x=±8 mmx=±12 mm

E/E [%]∆-4-60102030
Number of the cell

4050Fig. 8. Phase distribution for the accelerating structure after
electron-beam welding of the couplers.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15C [mm]Fig. 6. ∆E/E as a function of C.
3. Obtain the optimum value of C by interpolation orextrapolation.
Fig. 7 shows the field distributions (amplitude and phase)
for a coupler with an optimum value of C.
phase ( w cut )phase ( w/o cut )0.008

400.007300.006

200.005

100.00400.003-100.002-200.001
0crescent-shaped cut

wave guide-2010-100X [mm]20The design of the coupler dimensions was achieved by asimulation based on the Kyhl method. The dimensions
obtained by this method are in good agreement with that
determined by cold tests. It has been proven that theasymmetry of the electromagnetic fields in the coupler can becorrected by a crescent-shaped cut.
Acknowledgments
The authors wish to thank S.Takeda, H.Matsumoto
T.Higo and S.Miura for their valuable comments on thiswork.

amplitude [arbitrary unit]

amplitude ( w cut )amplitude ( w/o cut )Summary-30-40

Fig. 7. Effect of the correction of an electromagnetic-fieldasymmetry by a crescent-shaped cut.
With this correction, the asymmetry of amplitude (∆E/E)
and phase was reduced from 8% to 1% and 1.3° to 1.1°,
respectively at X=8mm.

References
phase [degree]

1211109876543210(6)Phase [degree]k=∆E/EX=0 [%],
∆E=EX=X0-EX=0,
X0=4,8,12 [mm].

[1] A.Enomoto, “Upgrade to the 8 GeV Electron Linac for KEKB,”
these proceedings.
[2] C.-K. Ng and K.Ko,”Numerical Simulations of Input and Output
Couplers for Linear Accelerator Structures,” SLAC-PUB-6086.
[3] E.Westbrook, “ Microwave Impedance Matching of Feed
Waveguides to the Disk-Loaded Accelerator Structure Operatingin the 2π/3 Mode,” SLAC-TN-63-103, 1963.
[4] J.C.Slater, Microwave Electronics (D.Van Nostrand, NewYork,1950).
[5] H.Deruyter, et al. “Symmetrical Double Input CouplerDevelopment,” Proceedings of 1992 Linac Conf., Ottawa(1992) 407.
[6] N.P.Sobenin, et al. “DESY Linear Collider Accelerating
Section Coupler,” Proceedings of 1994 Linac Conf., Tsukuba(1994) 74.
[7] C.W.Steele, MTT-14,,No2, Feb. 1966, p.70.