Proceedings of the 11th Annual Meeting of Particle Accelerator Society of Japan
August 9-11, 2014, Aomori, Japan

PASJ2014-SUP042

FABRICATION OF QUADRANT-TYPE X-BAND SINGLE-CELL
STRUCTURE USED FOR HIGH GRADIENT TESTS
Tetsuo Abe∗ , Yasuo Ajima, Yoshio Arakida, Toshiyasu Higo, Hitoshi Inoue, Noboru Kudo,
Shuji Matsumoto, Toshikazu Takatomi,
KEK, Tsukuba, Ibaraki 305-0801, Japan
Yasuo Higashi, OIST, Onna-son, Kunigami-gun, Okinawa 904-0495, Japan
Abstract
A most commonly used method to fabricate acceleratingtubes is machining, followed by stacking of disks, and thenbonding such as diﬀusion bonding and brazing. In accelerating structures fabricated with this kind of method, surface
currents associated with magnetic ﬁelds ﬂow across disk-todisk junctions. On the other hand, we focus on a quadranttype structure, where no surface currents ﬂow across any
junctions although naive such structures have some disadvantages. In this paper, based on our new ideas to overcome
all of the disadvantages, we present a fabrication process ofa quadrant-type X-band accelerating structure in the form ofa single-cell test cavity [1], together with results on machining of quadrants and test of electron beam welding (EBW).

(a) Example of the disk-type structures.

INTRODUCTION
High-gradient accelerating structures with gradients of≈ 100 MV/m or higher are linchpins of high-energy accelerators to search for new physics in particle physics, andare also useful to make compact accelerators such as medical linacs. Most of such structures, made of oxygen freecopper (OFC), have been fabricated so far by machining,
followed by stacking of disks, and then bonding such as diffusion bonding and brazing (hereinafter referred to as disktype). An example of the disk-type structures is shown in
Fig. 1a. However, accelerating structures, fabricated withthis kind of method, could have a potential problem that
surface currents associated with magnetic ﬁelds (typically≈ 108 A/cm2 during high-gradient operation) ﬂow acrossdisk-to-disk junctions, where perfect bonding of neighboring disks at the inner surface is not guaranteed. For example, in the report [2], there are gaps with some microscopic
objects between the diﬀusion-bonded disks seen in the SEM
images. Although we do not know the details of RF breakdown mechanism dominantly contributing to breakdown
rates (BDRs) of accelerating structures, such defects should
be deeply concerned because signiﬁcant impact of surface
magnetic ﬁeld on BDRs has been discovered [3, 4].
In this paper, based on the new ideas, we present a fabrication process of a quadrant-type X-band accelerating
structure in the form of a single-cell test cavity, together
with results on the machining of quadrants and EBW test.
In single-cell structures, there are only three cells: a central cell to be tested (test cell), a matching cell, and an end∗ tetsuo.abe@kek.jp(b) Example of the quadrant-type structures.

Figure 1: Two orthogonal methods to fabricate acceleratingtubes.

cell, so that such structures are easier to make and test thanmulti-cell structures.
In this study, we focus on a fabrication method ofquadrant-type structures as shown in Fig. 1b, where quadrants are machined with ultra-high precision milling, followed by bonding of quadrants. For quadrant-type structures, no surface currents associated with magnetic ﬁelds
ﬂow across any junctions, so that no above-mentioned concern on disk-type structures arises.
In 2008, we fabricated a quadrant-type accelerating
structure with 18 cells (Fig. 1b), and performed a highgradient test. The result was that the accelerating gradient(Eacc ) was limited to 60 MV/m or lower, and we observed
no conditioning eﬀects [5].
We go back to basics on the comparison between disktype and quadrant-type structures. Disk-type structures
have advantages of• Very smooth surface (typically Ry ≈ 30 nm), and• Shallow damage of machining (< 1 μm),
while the disadvantages are• Dozen of disks to be stacked and bonded, and• Surface currents associated with magnetic ﬁelds ﬂowing across disk-to-disk junctions.

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August 9-11, 2014, Aomori, Japan

PASJ2014-SUP042

Figure 2: Quadrant-type X-band single-cell structure basedon the new ideas. The splotched-red planes indicate reference planes in machining. There are grooves on the surfaces
near the mechanical contact between the quadrants to suppress heat diﬀusion at EBW points.

Quadrant-type structures have advantages of• No such currents ﬂowing across any junctions, and• Simple assembly process,while the disadvantages are• Not very smooth surface (typically Ry ≈ 1 μm),
• Deep damage of machining (≈ 10 μm),
• Possible virtual leak from quadrant-to-quadrant junctions (see bellow), and• Field enhancements at the corners of quadrants (seebellow).
We have therefore proposed new ideas on quadrant-type
structures to overcome all of the above-mentioned disadvantages, to be explained in the following section.

Figure 3: Parametrization of a concave structure.

Figure 4: Example of enhanced ﬁelds at a concave.

NEW IDEAS
The ideas proposed in [6] are summarized in this section.
The quadrant structure we tested in 2008 (Fig. 1b) was assembled without bonding; the quadrants were just clamped
and put in a vacuum chamber for the high gradient test. In
such a case, virtual leak from the ﬂat-surface contact between the quadrants might arise due to high ﬁelds on thecontact. Therefore, as a realistic solution, we make a ﬁnite
gap of 100 μm between quadrants. (G = 100 μm in Fig. 3).
As for the ﬁeld enhancements at the corners of quadrants,
we start at a concave structure parametrized as in Fig. 3,
where Δ corresponds to mis-alignment plus machining error of quadrants . In such structure, ﬁelds are enhanced asin Fig. 4 for example. Local ﬁelds can be calculated withhigh accuracy by numerical computations in a stochastic approach [7]. Field enhancement factors, calculated with suchmethod, are shown in Fig. 5 [8], where ﬁeld enhancement
factor is deﬁned as a ratio of the maximum ﬁeld strengtharound the concave structure and the reference ﬁeld strength
in the case of no concave structure. It should be emphasizedthat there is a minimum value among the ﬁeld enhancement
factors, that is 1.23 in the case of G = 0 and Δ = 0, whichis independent of R. Therefore, we should allow 20 to 30 %enhancement of ﬁelds. From Fig. 5, it is found that R should

Figure 5: Field enhancement factors for the geometry in
Fig. 3.

- 1067 -Proceedings of the 11th Annual Meeting of Particle Accelerator Society of Japan
August 9-11, 2014, Aomori, JapanG = 0, Δ = 0

2.5

Field Enhancement Factor

Shunt Impedance [MΩ]

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2.4

2.3

2.2
0

200

400

600

G = 100 [μm], Δ = 0
1.4

1.35

1.3

1.25

1.2
0

800

R [μm]

200

400

600

800

R [μm]

Figure 6: Shunt impedance as a function of R in the caseof G = 0 and Δ = 0 for the X-band single-cell structure described in [6].

Figure 7: Field enhancement factor as a function of R in thecase of G = 100 μm and Δ = 0 for the geometry in Fig. 3.
The arrow indicates our selection on R.

Figure 8: Schematic diagram of the X-band single-cell structure designed based on the new ideas to overcome the disadvantages of quadrant structures. Mechanical contact areas are shown in hatching.
be as large as possible; the enhancement is about 30 % even
if Δ = 100 μm in the case of R = 400 μm. However, large
R decreases the shunt impedance of the accelerating modeas shown in Fig. 6. Based on the R dependence of the shunt
impedance and ﬁeld enhancement factor (Fig. 7), we havedetermined the optimum value of R to be 400 μm for G =100 μm [9]. If we adopt a larger gap (G > 100 μm), we needa larger R, leading to a lower shunt impedance.
As for the surface roughness by milling, we will apply
electro-polishing to quadrants after ﬁnal machining in orderto have smoother surface with a target of Ra ≈ 10 nm.
Figure 8 explains the above. new ideas schematically.
Figure 9 shows an electromagnetic ﬁeld of the accelerating mode with an operation frequency of f acc =11.424 GHz. This TM mode corresponds to π-mode, oneof the three modes in the three-cavity system. The othertwo modes, corresponding to 0-mode and π/2-mode, havefrequencies about 90 MHz and 140 MHz lower than f acc ,respectively. Here we have to pay attention on TE modes,
which could have mode frequencies close to f acc becauseof the 100 μm gap between the quadrants. Actually, there isa signiﬁcant TE mode, as shown in Fig. 10, with a mode
frequency close to f acc . Therefore, in our new design,
the shape of the mechanical contact is slightly modiﬁed,
as shown in Fig. 11. Figure 12 shows how the TE mode
frequency changes as the parameter Δ (deﬁned in Fig. 11)changes. Finally, we have adopted Δ = 3 mm. As a result,
there are no signiﬁcant eﬀects of TE modes in a frequency
range of f acc ± 200 MHz.

- 1068 -Proceedings of the 11th Annual Meeting of Particle Accelerator Society of Japan
August 9-11, 2014, Aomori, Japan|S11|

PASJ2014-SUP042

1
0.8
0.6
0.4
0.2
0
11.2

Δ = 0 mm
Δ = 1 mm
Δ = 2 mm
Δ = 3 mm
11.3

11.424 GHz

Figure 9: Electromagnetic ﬁeld of the accelerating mode to
be used in high gradient tests. (a) Electric-ﬁeld vectors. (b)Magnetic-ﬁeld vectors.

11.4

11.5

11.6

11.7

11.8

11.9

12

Frequency [GHz]

Figure 10: Electromagnetic ﬁeld of the TE mode with amode frequency close to f acc . The unloaded quality factorof this mode is 167.

Figure 12: Simulation results on the reﬂection coeﬃcient(|S11 |) for Δ (deﬁned in Fig. 11) values of 0, 1, 2, and3 mm with an input RF wave of TE11 in the circular duct
(φ22.86 mm), where the circles indicate calculation points
in the frequency domain computation, and 100%IACS electric conductivity (5.8 × 107 S/m) is assumed for the quadrants. The excited mode is shown in Fig. 10, where the input
RF wave comes from the right.

Figure 11: Mechanical contact areas to be added, shown inyellow. The parameter Δ is deﬁned in this ﬁgure.

FABRICATION PROCESSThe fabrication process consists of the following steps:
1. Ultra-high precision milling to form quadrants from a
OFC (class1) bar
2. Electro-polishing (EP)
3. EBW of the quadrants
4. Brazing of beam ports and ﬂanges
Figure 13 shows one of the quadrants of single-cell structure, to be used in high-gradient tests, which were machinedin 2013, where achieved surface roughness and proﬁle accuracy are Ry  1 μm and ≈ 5 μm, respectively. Figure 14
shows examples of the proﬁle measurements. In the ﬁnal
machining, we used a ﬁve-axes milling machine with a ballend mill (φ1.5 mm) made of cemented carbide. In the future, we will use a ball end mill made of single-crystal diamond. As for EP, a study to select appropriate conditions

Figure 13: One of the quadrants of single-cell structure, machined in 2013, to be used for high-gradient tests.

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August 9-11, 2014, Aomori, Japan

PASJ2014-SUP042

formation elsewhere, we can estimate a corresponding frequency change to be +12 MHz in f acc . Although this frequency change of 12 MHz is still within the tuning range,
the shrinkage of 15.8 μm is taken into consideration in designing the quadrants machined in 2013 (Fig. 13).

Figure 14: Examples of the proﬁle measurements of thesingle-cell quadrants as shown in Fig. 13. The blue (black)solid lines indicate measured (nominal) proﬁles. The redcircles indicate points outside the proﬁle tolerance of 5 μm
(between the red and magenta solid lines). Both of the measured and nominal proﬁles are shown with respect to the reference planes in machining (splotched-red planes in Fig. 2).
(a) Cross section along the beam axis. (b) Cross section of
the test cell, perpendicular to the beam axis, where the left
and right sides are openings for the HOM waveguides.
is on-going. We assemble the four quadrants into a cavity
with EBW for the purposes of both bonding and vacuum
sealing. The details of the EBW is described in the next
section. The brazing of beam ports and ﬂanges could be replaced by EBW ﬁnally in the future so that no high temperature processes are used, making it possible to fabricate thestructure made of only hard copper(-alloy) which is strong
against metal fatigue due to high surface currents [10].

EBW TESTWe have performed a EBW test using mockups as shownin Fig. 15. Table 1 shows our selection of the EBW conditions, with which we performed the EBW test. The EBW
process consists of the followings steps:
1. Tack EBW on the front and back surfaces,
2. Final EBW on the front and back surfaces,
3. Final EBW on the top and bottom surfaces, and
4. Final EBW on the side surfaces.
Before, after, and during the above EBW process, we measured 3D positions of some points on the surfaces of eachquadrant, and calculated lengths of line segments, in thelongitudinal (beam) and transverse directions, as shownin Fig. 16. Figure 17 shows changes of the line-segment
lengths before, after, and during the EBW process. It has
been found that the changes are small, < 5 μm, in the longitudinal direction (within the machining tolerance on the
inner surfaces of the quadrants), while the changes in thetransverse directions are pretty large; the average shrinkage
is about 35 μm before the brazing, and 15.8 μm after thebrazing. The shrinkage change from ≈ 35 μm to 15.8 μm inthe transverse directions is a result of stress release by thebrazing (BAu 35/65, 1010 degC). If we assume that such
shrinkage in the transverse directions is attributed to shrinkage only at the mechanical contact areas, and there is no de-Figure 15: Mockup quadrants for the EBW test, made of
OFC, with the inner surfaces simpliﬁed. In this photography, 3D positions on the surfaces are being measured after
tack EBW on the front and back surfaces.
Table 1: Selected conditions for the EBW.
Cathode voltage
Beam current
Spot size (near the groove)
Spot size (oﬀ the groove)
Table speed in the tack EBWTable speed in the ﬁnal EBW

150
10≈ 2 in diameter≈ 1 in diameter
5.8
4.5

kV
mA
mm
mm
mm/s
mm/s

Figure 16: Deﬁnition of line segments. 3D positions of theendpoints on the surfaces of the mockup quadrants (shownin the inserted ﬁgure as green circles for Quad. No.1) were
measured. “Quad.” means a quadrant. LS_1 to 5 are deﬁned also for Quad. No.2 to No.4 with rotational symmetry. LS_A to H are deﬁned 3 mm away from the font or backsurface.

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August 9-11, 2014, Aomori, Japan

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20

ΔL// [μm]ΔL// [μm]Figure 18 shows the mockup quadrants after the EBW.
No vacuum leak higher than 3 × 10−10 Pa m3 /s has been
conﬁrmed by a leak test.
Figure 19 shows measured line-segment lengths in thetransverse directions, which means that the mis-alignment
plus machining error of the mockup quadrants is within ±10 μm, and the shrinkage by the EBW is uniform, i.e. no
deformation on the outer surfaces.

15
10
5

20
15
10
5

0

0

-5

-5

-10

Quad. No.2
1

2

3

4

5

6

-10

7

Quad. No.3
1

2

20
15
10
5

Quad. No.1
4

5

6

7

5
0

3

6

10

-5

2

5

15

-5
1

4

20

0

-10

3

Meas. Number
ΔL// [μm]ΔL// [μm]Meas. Number-10

7

Quad. No.4
1

2

Meas. Number

3

4

5

6

7

Meas. Number

20

ΔL⊥ [μm]

ΔL⊥ [μm](a) Longitudinal direction. The black, red, green, blue, and yellow
plots are measurements for LS_1, 2, 3, 4, and 5, respectively. The
plot at the measurement number of 7 for LS_3 on Quad. No.1 isa mis-measurement including a micro scratch on the surface.

Front

10
0
-10
-20

20
0
-10
-20

-30

-30

-40

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-50

1

2

3

4

5

6

7

Meas. Number

Figure 18: Mockup quadrants after the EBW.

Back

10

-50

SUMMARY AND CONCLUSIONS
1

2

3

4

5

6

7

Meas. Number(b) Transverse directions. The black, red, green, blue, yellow,
magenta, light blue, and gray plots are measurements for LS_A,
B, C, D, E, F, G, and H, respectively.

Figure 17: Changes of the lengths of the line segments, deﬁned in Fig. 16, before, after, and during the EBW process.
ΔL // (ΔL ⊥ ) indicates a measured length minus the designin the longitudinal (transverse) direction. The measurement
number indicates each step in the EBW process, 1: Before
starting the EBW, 2: Just after the tack EBW on the front
and back surfaces, 3: Just after the EBW on the front andback surfaces, 4: Just after the EBW on the top and bottom
surfaces, 5: Just after the EBW on the side surfaces, 6: Just
after additional machining for brazing of the ports, and 7:
Just after brazing of the ports.

Based on the new ideas to overcome all of the disadvantages of quadrant-type structures, we have designed andmachined a quadrant-type single-cell structure to be used
for high-gradient tests. We have also shaped a fabrication
process, including EBW. The test of EBW for the purposesof both bonding and vacuum sealing of the quadrants was
successfully performed, and we have found that the average shrinkage in the transverse directions is 15.8 μm, corresponding to +12 MHz in f acc , for the selected EBW conditions, and such shrinkage is uniform; the quadrants haveno deformation on the outer surfaces.

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August 9-11, 2014, Aomori, Japan

PASJ2014-SUP042

z [mm]

Front (x 200)

REFERENCES

80[1] V. A. Dolgashev, S. G. Tantawi, C. D. Nantista, Y. Higashi
and T. Higo, “Travelling wave and standing wave single cellhigh gradient tests,” SLAC-PUB-10667, 2004.

60[2] M. Aicherer, CERN EDMS, “TD18 post-mortem SEM observation:Update,” presentation at CERN, 10 Nov. 2010.

40[3] V. A. Dolgashev, S. Tantawi, Y. Higashi, B. Spataro,“Geometric Dependence of Radio-Frequency Breakdown in Normal Conducting Accelerating Structures,”Appl. Phys. Lett. 97, 171501, 2010.

20[4] F. Wang, C. Adolphsen and C. Nantista, “Performance Limiting Eﬀects in X-Band Accelerators,” Phys. Rev. ST Accel. Beams 14, 010401, 2011 [Addendum-ibid. 15, 120402(2012)].

0
0

20

40

60

[5] T. Higo, “KEK activities on CLIC X-band Accelerating Structures,” presented at the mini-workshop
on CLIC X-band structure R&D at THU, 2010(http://indico.cern.ch/event/89913/).

80

x [mm](a) Front side.

[6] T. Abe, Y. Higashi, Y. Arakida, T. Higo, S. Matsumoto,T. Shidara and T. Takatomi, “Quadrant-Type X-Band SingleCell Structure for High Gradient Tests,” in Proceedings of
the 9th Annual Meeting of Particle Accelerator Society ofJapan, August 2012 (Paper ID: THPS095).

z [mm]

Back (x 200)
80

[7] T. Abe, “Study of Surface Field Enhancements due to Fine
Structures,” in Proceedings of the 8th Annual Meeting ofParticle Accelerator Society of Japan, August 2011 (Paper
ID: TUPS086).

60

40[8] The results are obtained for a boundary with two parallel
plates. Using a circular boundary, the results are almost thesame [6].

20[9] The optimum value of R might depend on the geometry of
the accelerating structure.

0[10] V. Dolgashev, S. Tantawi, A. Yeremian, Y. Higashi and
B. Spataro, “Status of High Power Tests of Normal Conducting Single-Cell Standing Wave Structures,” Conf. Proc. C
100523, THPEA060 (2010).

0

20

40

60

80

x [mm](b) Back side.

Figure 19: Measured line segments in the transverse directions. The yellow areas indicate the design, and thegray dashed lines indicate ± 10 μm tolerance magniﬁed 200
times in this ﬁgure. The black bars are EBW beads. The
gray bars, red bars, and blue lines indicate measurements
before the EBW process, just after the EBW process, andafter the brazing, respectively. All of the measurements areshown with the diﬀerences from the design magniﬁed 200
times in this ﬁgure. Cartesian coordinates (x, y, z) are deﬁned in Fig. 16.

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