The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

PRECISE DESIGNING OF RF COUPLER FOR ACCELERATORSTRUCTURE
A. Lounine, T. Higo, KEK, 1-1, Oho, Tsukuba, Ibaraki, 305-0801, Japan
Abstract
Coupler design for travelling wave accelerator structure
was performed using 3D EM code, HFSS. How toimprove the accuracy was firstly investigated. The actual
design was confirmed by comparing with theexperimental measurement. The calculation accuracy inreflection coefficient was found to be better than 0.05.

INTRODUCTION
According to Global Linear Collider Project Report,
the accelerator structures for the X-band main linacs are
based on the constant-gradient, travelling-wave, diskloaded type design [1]. The structure is operated at 5π/6mode with its active length of 60 cm where the groupvelocity varies from 4% to 1% of light velocity. KEK
takes a major part at manufacturing prototypes of Xband structures for GLC project based on the capability of
the high-precision machining of cells. The principle of thestructure fabrication at KEK is to eliminate the tuning
process after assembly and bonding procedures.
PmTmt1

H60VG3K1 [3], were designed, fabricated and lowpower measured at KEK. The description of the wholeprocess is the theme of this paper.

PROPER USAGE OF THE ANSOFT HFSS
All of the physical structure parameters a, b and t aresmoothly varying functions of the cell number. Therefore
short section of the structure close to the coupler can betreated as periodic structure with constant parameters andthe well-known “Kroll’s” method could be applied [4].
For the field evaluation the ANSOFT HFSS code ver.8.5
was used [5].
All calculations were performed with structure
dimensions at manufacturing temperature at 200C.
Because operation temperature of the structure is 450C weshifted the calculation frequency (according to thethermal factor of Cu) from 11.424 GHz to 11.429 GHz.
Since the structure parameters were determinatedbeforehand with a high-precision frequency domain code[3], the cell-to-cell phase advance value was firstly
investigated in order to establish the accuracy treatmentof the regular section necessary for precise coupler
simulation. Because the frequency separation between thecenter and the higher end of the passband near the output
region is as narrow as several MHz, we believe that thetolerable frequency error in calculation is less than 1 MHz,
which corresponds to 10 per cell.

a1Am

BmaFig.1 Input coupler of H60VG3 accelerating structure.
Up to date the coupler is one of the critical parts of thehigh gradient accelerating structure. Since it matches thesufficiently large reflection from the diaphragmatic
circular waveguide, high intensity electric and magnetic
fields appear at the surface of the coupler. This may cause
the RF breakdowns resulting in future surface erosion. Onthe way to minimize these fields several coupler designs
were proposed [2]. Considering the low surface fields, theshort length of low accelerating field and probably thegood coupling to the trapped dipole modes, we preferredso called “waveguide” coupler design. Here, as shown in
Fig.1, the matching element is the fat diaphragm in awide wall of rectangular waveguide.
The present candidate for the final structure design,
H60VG3, 0.6 m long with a phase advance of 5π/6 percell. To keep the constant gradient the group velocity(vg/c) is changed from 3% to 1% along the structure. Bothinput and output couplers of this type structure,

Fig.2 Pseudo 2-D model of accelerating structure.
The HFSS uses a finite-element method for solving
electro-magnetic fields. It requires defining mesh points
and the result of calculation depends on the quality of theused mesh.
In order to obtain the optimum mesh, first a narrowangle segment (pseudo 2-D model) of a structure wascalculated (Fig.2). Fig.3 illustrates the dependence of thecell-to-cell phase advance along the structure on themaximum mesh cell size and that on the number ofdivisions of a circle applied to the rounded diaphragmsurface. In order to obtain the closest phase advance value
to the design, we concluded that the maximum mesh cellsize should be less than 1 mm and the optimum numberof segments for defining rounded diaphragm is 24.

The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003a)

b)

160

160

Number of segments
158

158

Nseg = 18

154

Nseg = 24
Nseg = 30

156

Phase advance, [degree]Phase advance, [degree]

Nseg = 12156152150148146154152150148Max. mesh size
1463.0 mm
1.5 mm
1.0 mm
0.7 mm

14414414214214014020304050206030405060

Z, [mm]Z, [mm]Fig.3 Pseudo 2-D model; cell-to-cell phase advance along
the structure vs. a) maximum mesh element size and b)
the number of segments of rounded diaphragm.

were varied slightly around the optimum values to see thechange of VSWR as shown in the Fig. 5(b) for output
coupler case. The VSWR changes nearly symmetricallyas the matching parameters vary. Thus, the required
tolerances are also symmetrical around optimum values.
The most severe tolerance is for Bm (outer radius of thecell) parameter. To keep the VSWR from output coupler
less than 1.1 we need to have the tolerance of Bm
dimension to be 2 µm. Other matching parameters are notso sensitive and the manufacturing tolerance is 10 µm.
For input coupler we found the same tolerance
requirements.
a)
1.5b)

1.5

Bm

152
150
148
146
144

5 degree3 degree2 degree

2030

40

50

60

VSWR
-10

11.439-50510Deviation, [mkm]152

Calculation on experimental setup

150
148
146

142

140

11.434

Fig.5 Coupler optimization results, a) VSWR vs. freqs.
and b) the tolerance calculations for output coupler atfreq. 11.429 GHz; Bm, Am, Pm are matching coupler
parameters.

154

144

142

11.429140
20Z, [mm]30405060Z, [mm]Fig.4 3-D model, cell-to-cell phase advance along thestructure vs. a) maximum mesh element size and b) thestep of rotation.
Taking the above mentioned cares on meshing torepresent the geometry of the structure, we are now readyto simulate the coupler itself.

CALCULATION RESULTS
Actual coupler calculations
The coupler matching elements are shown in Fig.1. The
dimensions which affect the matching are aperture Am andthickness Tm of diaphragm, the outer diameter Bm and amatching period Pm. Since two of them (aperture Am andthickness Pm) freely vary the amplitude and phase ofreflection coefficient we can fix the remaining parameters.
We chose that Bm was equal to the outer diameter of first
regular cell for the input coupler case and to that of thelast regular cell for the output coupler case. The thickness
Tm of the diaphragm was chosen to be large enough toreduce the electric fields on the diaphragm surface.
Therefore, we only need to execute the two parameter
optimization to match the coupler. The optimization was
done using Hooke-Jeeves method [6]. The results for both
input and output coupler are shown in Fig.5.
The required tolerances for the coupler fabrication werestudied. For this end the relevant matching parameters

Before making the actual H60VG3K1 structure, weperformed the low power measurements on the similarcoupler setup to prove the above calculation method. Twocold models, one for input and the other for output
couplers, were studied. Each setup consists of the coupler
itself and several regular cells terminated by a special
matching cell at the end followed by a circular waveguidewith a movable conical RF load. The matching cellcompensates the reflection of TM01 mode between thecircular waveguide and the regular part of the structure.
Thus, we can study the reflection from the cold model ofthe coupler with a matching load at the end of circular
waveguide. The results of calculations are shown in Fig.6.
Red solid lines show the reflection only from the coupler
itself whereas red dotted lines that only from matchingcell. The blue lines show the reflection from the actual
cold measurement setup which combines reflections bothfrom coupler and matching cell. We understand that thesesetups are good enough for our comparison purpose, but
it should be noted that this output coupler setup was not
optimized yet simply due to time limitation.
a)

b)

1.5

1.5
Input coupler
Match. Cell
Total SWR

1.4

Output Coupler
Match. Cell
Total SWR

1.41.3

1.3SWR

Phase advance, [degree]

Phase advance, [degree]154

11.424Frequency, [GHz]

Rotation step
156

1.0

1.0
11.4191585 mm
2.5 mm
1.5 mm1.1

1.1160Max. mesh size

156

1.21.2b)

158

PmSWRa)
160

Am

1.3

1.3

SWR

Next step was to repeat the similar study with 90
degree segment (3D-model) of a structure. The results ofthese calculations are shown in Fig.4. We found thatmaximum mesh size for this case should be less than 1.5mm and the optimum number of rotation step to specify90 degree segment is 45 (2 degree step) to maintain theerror in the phase advance per cell less than 10 per cell.

1.4Input coupler
Output coupler

1.4

1.2

1.2

1.1

1.1

1.0
11.41911.424

11.429

FRQ, [GHz]11.43411.4391.0
11.41911.424

11.42911.43411.439

FRQ, [GHz]Fig.6 Coupler cold model calculations. VSWR vs. Freqs.
a) for input and b) output coupler cold models.

The 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

Rcoupler = S11 + S21 = S22 + S12(5)Couplermodel

Matching cell
Sliding RF load
S22, S12S11, S21

PC station
HP 8510C

GPIB busa)b)

1.5

1.4

1.5

Calculation
Measurement

Measurement
Calculation

1.4

1.3

1.3

VSWR

Two low-power models mentioned in the previous
chapter were measured using the scheme as shown in
Fig.7. The RF signals generated in sequence by HP
8510C network analyzer are fed to the corresponding
rectangular waveguide input of the coupler, and S11,S12 or S22, S21 set of S-parameters are measured
independently. For nominal operation the coupler should
be fed symmetrically. Therefore we need to add signals
from both RF ports of network analyzer in order to obtain
the reflection from the coupler (Rcoupler) in nominal
operation. Taking into account the symmetry ofmeasuring setup, we can derive:

The comparisons of measured data with the calculated
ones are shown in Fig.9. Here the frequency correction
was performed taking into account the thermal expansionof copper material and the dielectric constant of the gases,
air with water vapor, filling the setup. An experimental
formula was applied for the dielectric constant [7].

VSWRCOMPARISON WITH THEMEASUREMENTS

1.2

1.2

1.1

1.1

1.0
11.41911.424

11.42911.43411.4391.0
11.40911.414

FRQ, [GHz]11.41911.424

11.42911.434

FRQ, [GHz]Fig. 9 The low power measurement results for a) input
coupler model and b) output coupler model.
In the case of input coupler the measured VSWR atworking frequency is below 1.05 and the behavior of thecalculated curve coincides well with the measured one.
That of the output coupler is rather worse, about 1.2, due
to non-optimal dimensions of the matching cell in thesetup. The measured VSWR also agrees well to thecalculated one. From these comparisons, we concluded
that the calculation agrees with the experiment within theerror of the reflection coefficient of 0.05.

CONCLUSIONS
Fig.7 The experimental setup for low-power coupler
model measurements.
The matching RF load is connected to the circular
output of the coupler. Because it is difficult to make theideal, non-reflected RF load, the measured reflection
includes the reflection from the load. A set of complex
reflection coefficients at different load positions wasobtained, as shown in the Fig. 8. The reflection points
form a circle on a complex plane when shifting the loadin a circular waveguide. The center of this circle
represents the actual reflection from the coupler with aperfect matched load.
Im(x)
90
120

150

60

30

Coupler & nonideal load
Coupler & perfect load

180

00.00

0.02

0.04

0.06

210

0.08

Re(x)

330

240

300
270Fig. 8 Reflections from the experimental setup withdifferent RF load positions.

Coupler design for traveling wave accelerator structure
was performed using 3D electromagnetic code, HFSS.
The accuracy of the calculations was investigateddepending on various input geometry parameters andinternal code settings. The low-power models of thecouplers were fabricated using high precision machining
technology. The actual design was confirmed bycomparing with the experimental measurement. The
calculation accuracy in reflection coefficient was found tobe better than 0.05.

REFERENCES[1] Global Linear Collider Project Report, pp.194-195,
KEK, 2003[2] C.D. Nantista et al, “Novel Accelerator StructureCouplers”, PAC2003, May 12-16, 2003, Portland, US[3] Zenghai Li, “X-band Low vg Structure Design”,
ISG8, June 24-27, SLAC, US[4] N.M.Kroll et al, “Applications of Time Domain
Simulations to Coupler Design for PeriodicalStructure”, LINAC2000, Aug. 21-25, 2000,Monterey, California.
[5] Ansoft High Frequency Structure Simulator, Ver. 8.5,
Copyright 1994 - 2003 Ansoft Corporation.
[6] R.HOOKE, T.A.JEEVS, “Direct search solution ofnumerical and statistical problems”, Journ. Ass.
Comput. Mech., 8, 1961.
[7] G. Montgomery,Technique of Microwave
Measurements, MIT Rad. Lab. Series, vol. 11, 1947