Proceedings of the 1st Annual Meeting of Particle Accelerator Society of Japanand the 29th Linear Accelerator Meeting in Japan (August 4 - 6, 2004, Funabashi Japan)

PROPOSAL FOR TeV-SUPERCONDUCTING LINEAR COLLIDER
K.Saito*, M.Yoshioka, KEK Accelerator Lab, Tsukuba-shi, Ibaraki-ken, 305-0801, Japan
Abstract

2. FIELD LIMITATION OF SRF CAVITY

L-band superconducting (SC) RF technology is an
excellent choice for a sub-TeV e+/e- linear collider (LC),which is currently being considered by the world highenergy physics community. This technology has several
advantages compared to X-band warm technology such as
beam stability, high luminosity, and cost effective
operation performance. However, the gradient is currently
limited to 35MV/m, which is lower than that of the Xband (52MV/m with beam loading). In this paper, wewill describe how to upgrade the gradient up to 50MV/m
in the cold. In addition, applying a superstructure canimprove the fill factor of RF structures. Thus, a way to 1
TeV SCLC will be developed in a 33km tunnel.

At least a gradient of 45MV/m is needed in order toreach 1 TeV in a 33km long tunnel. At first, we will
discuss the present high-gradient limitation with a Nb SCcavity. Figure 1 shows the last decade history of the highgradient with L-band single cell Nb cavities. In the early
1990s, it was steadily improved by the industrial highpurity Nb production, 1400°C titanium post purification,and so on. In 1995, a high-pressure ultra-pure water
rinsing (HPR) became standard in cavity preparation,
which resulted in a step-like improvement since the fieldemission problem was eliminated, but since then thegradient appears to be saturated around 40MV/m.
Recently, the DESY group realized 40MV/m for aTESLA 9-cell cavity using their own electropolishing(EP) facility1.
40MV/m corresponds to a surface peak magnetic fieldof Hp =1750Oe for a TESLA cavity shape. This magnetic
field limitation is typical for different cavity shapes (e.g.
Nb cavity with β = 0.45 for proton LINAC [1]) ordifferent cavity fabrications (Nb bulk seamless cavities,Nb/Cu clad seamless cavities [2]). These experimental
facts suggest that the Nb SC cavity already meets thefundamental SRF critical magnetic field around 1750Oe.
The other interesting experimental results are the direct
measurements of the SRF critical field (HCrf) at Cornell

1. INTRODUCTION
Since the 1980s, linear collider (LC) R&D has been
aggressively conducted worldwide. The energy reach of
LC is noted in “the parameter for Linear Collider”1,
which says “ the strong likelihood that there will be newphysics in the 500-1000GeV range means that theupgradability of the LC to about 1 TeV is the highest
priority step beyond the baseline”. ITRP 1 (InternationalTechnical Recommendation Panel) will choose betweenthe cold (L-band superconducting: TESLA) and the warm
(X-band: GLC/NLC or C-band) technology by the end of
this year. TESLA collaboration has already accomplishedthe ranking 1 R&D issues1 (R1), which is required fromthe TRC (Technical Review Committee), for TESLA-500.
On the other hand, the maximum energy of the original
TESLA scheme is limited to 800GeV, which is lower
than that of X-band warm scheme. The authors areconvinced that TESLA-500 is feasible, but we feel thatthe energy upgradability should be more seriously
considered. Thus, we seek the possibility of creating not
800GeV, but 1 TeV in a 33km long tunnel. One scenario
to achieve >1TeV is to adopt a 46.8km long tunnel,
which is being considered by the US study group for theUS site. However, this long of a tunnel inflates the costin early TESLA-500 construction. We propose to start
TESLA-500 with a gradient of 35MV/m using theexisting 9-cell cavity design in the 33km long tunnel.
Then this tunnel should be filled with 2x8-cellsuperstructures that have a 45MV/m operational gradientin order to achieve 1 TeV (hereafter SCLC).
The aim of this paper is to demonstrate using
experimental and theoretical viewpoints that a gradient ofnearly 50MV/m is possible with a niobium (Nb) SCcavity. We will also show how to achieve 50MV/m andfinally to propose a 1 TeV SCLC as the upgrade scenario
in a 33km tunnel by applying 2x8-cell superstructure.

50

Eacc,max [MV/m]

40

3020

Saclay(HT,CP)CEBAF(HT,CP)CEBAF(CP,HPR)
Cornell(HT,CP,HPP)
KEK(EP,HPR)
DESY/CERN/Saclay/KEK(EP,HPR)
DESY/JLAB/KEK(Nb seamless cavity, EP,HPR)
DESY/JLAB (Nb/Cu clad cavity, CP,HPR)
INFN-LNL/KEK(Nb spun cavity, EP,HPR)

100
'90

'92

'94

'96
Date (Year)

'98

'00

'02

Figure 1: History of high gradient with an L-band single
cell cavity.

University [3]. They measured it by a short pulse method
on Nb, Nb3Sn, and Pb cavities. This method can provide
HCrf without the heating problem at temperatures above
the λ-point (2.18K). In contrast, below the λ-point, CW
measurement (KEK) can provide HCrf if the cavity does
not have defects since the niobium cavity has a small
surface resistance and He-II has a very high thermal
conductivity.
*ksaito@post.kek.jp, 1 http://www.ligo.caltech.edu/~donna/ITRP_Home.htm,
81Proceedings of the 1st Annual Meeting of Particle Accelerator Society of Japanand the 29th Linear Accelerator Meeting in Japan (August 4 - 6, 2004, Funabashi Japan)

The classical superheating model does not fit the data[3]. The newly proposed formula [4] can fit the data quite
nicely, which is obtained by a line vortex flux nucleation
model.
rfH c (T) = 2 ⋅ξ(T)H (T)
⋅ H (T) = 2 ⋅ cλ(T) cκ(T)a new cavity shape with a small Hp/Eacc ratio around
35Oe/(MV/m) must be designed. Here, Hp is a surface
peak magnetic field and Eacc is an electric field gradienton the beam axis. For such a low field ratio, the volume
occupied by magnetic field in the cell must be increased
and the magnetic density must be reduced. In order tosatisfy these requirements, the bore radius becomes
smaller. A smaller bore radius creates three problems in:1) poor HOM extraction, 2) weak cell-to-cell coupling,and 3) EP procedure. We must consider these trade offs in
the new cavity shape design.
Fortunately, J. Sekutowicz et al. published a reference
design at 1500MHz [5]. Their purpose was not for highgradient application, but a high Q for the CEBAF
upgrades CW operation. Figure 3 is from their paper.
They propose a LL (low loss) shape for CW operation.
OC is the CEBAF original cavity shape and HG (highgradient) is for the TESLA shape. Table 1 summarizes
the RF characteristics for each shape. These RFcharacteristics are frequency independent from each other.
The LL shape has a lower Hp/Eacc ratio: 37.4 O/[MV/m],of which the gradient is expected Eacc = 47MV/m.
Sekutowicz et al. already examined the HOM issue on a7-cell superstructure and did not detect any problem withthis shape.

(1)Here, HC is the thermodynamical critical field, ξcoherence length, λ magnetic field penetration depth, andκ the Ginzburg-Landau kappa parameter. The factor 2
appears due to the effective magnetic field in the ACapplication. The temperature dependence of κ is obtainedfrom Abrikosov theory and produces the explicit
temperature dependence of HC rf as:
H rfc (T) =2⋅ TH c (0) ⋅ 1 −κ(0)  Tc 4(2)here, TC is the critical temperture of the superconductor.
Figure 2 shows the fit for the Cornell data using formula(2) and the KEK results with L-band Nb cavities by CW
measuements. This fit does not have free-parameters andall parameters like HC(0), κ(0), and TC are fromexperimental results for Nb cavities. The absolute value isconsistent with the experimental results. This modelshows that the HCrf is 1750±50 Oe for the Nb cavity. The
improvement in HCrf (0) is only expected to be 5% forultrapure Nb material (RRR=2000) [4]. The requirment,
however, is 25% for 50MV/m, which is impossible torealize by just further improving the Nb material. For theother cavities (Nb3Sn, Pb), the amplitudes are fitted as
free-parameters. TC is from experimental results. The
fitting results are very nice. One will notice that there is€

3.2 Cell-to-cell coupling
The LL shape has a smaller cell-to-cell coupling κ CC
between each cell compared to that of TESLA: 1.72. Cellto-cell coupling relates to the field error in each cell. Theerror is given by κ CC as:
N 2 ⋅ ΔfΔEacc ∝κ cc

3500
Hcr Nb-cornell
Hcr Nb-KEK
Hcr-Nb3Sn
Hcr-Pb

3000

2000

HC

RF

[Oe]

2500

where, N is the number of cells in the cavity, and Δf error
in the frequency among cells. If the same field error as theTESLA shape is required, the resultant number of cells is
8 as determined by:
N = 9⋅

1500

3.3 Ep/Eacc ratio
The LL shape has a slightly larger Ep/Eacc ratio: 2.17
compared to the TESLA shape: 1.89. Here, Ep is theelectric surface peak field, which relates to the fieldemission (FE) problem. HPR technology nearlysuppresses the FE problem. KEK has experienced 1750Oe
without field emission in a cavity with Ep/Eacc = 5.1,
which is fabricated SC for a proton linac [1]. EP
technology could reduce the high Ep/Eacc problem in theLL shape.

1000
500
000.2

0.4

0.6

0.8

1.49= 7.99 ≈ 8
1.72

1T/TcFigure 2: Data fitting by the proposed formula (2) on Nb,
Nb3Sn, and Pb cavities.
no hope for a high gradient in a higher TC material like
Nb3Sn.

3. NEW CAVITY SHAPE
3.1 Cavity shape
The above analysis indicates that SRF technology
meets the theoretical limitation and cannot be further
improved. To achieve a 25% upgrade in the high gradient,€Figure 3: Typical cavity shapes
82

Proceedings of the 1st Annual Meeting of Particle Accelerator Society of Japanand the 29th Linear Accelerator Meeting in Japan (August 4 - 6, 2004, Funabashi Japan)

Table 1: RF parameters for the three shapes
ParameterΦequator[mm]OC187.0

HG
180.5

LL
174.0

Φiris[mm]κCC
Ep/Eacc
Hp/Eacc [Oe/(MV/m)]
3.2 Cell-tocell coupling
R/Q[Ω]

70.0
3.29
2.56
45.6
96.5

61.4
1.72
1.89
42.6
111.9

53.0
1.49
2.17
37.4
128.8

5. PROPOSED 1 TeV SCLC IN
A 33KM TUNNEL
We propose to construct SCLC-500 in a 33km tunnel
and to operate the cavities at 35MV/m. The 35MV/m
operation will be realized in 2006 at DESY, which iswhat remains of R1 for the TESLA-800. The DESY
group has already started to produce 40MV/m 9-cellstructure and there will be less risk in engineering anupgraded structure. This high-gradient operation of35MV/m will reduce the project cost for the SCLC-500.
The 50MV/m cavity R&D can be carried out in parallelwith SCLC-500 construction and operation. Thus, there
is enough time for these developments. After successfuldevelopments, the 7x(2x8-cell) super-structure modules
will be newly re-installed in the same tunnel. This
scheme can reach 1020GeV at 45MV/m. Table 2
compares the current proposed SCLCs.

LL shape has the smaller cell-to-cell coupling: κ CC ==1.49.
TESLA one: 1.72. κ273.8
to field error
CC is related
265.5
280.3inΓ[Ω]

3.4 Electropolishing
The smaller iris may cause a problem with EP. We needto place a cathode with a large enough diameter in thecavity beam hole in order to achieve optimum current
density during EP. When scaled to 1.3GHz, the bore
diameter of the LL shape is 61 mm. Usually, a diameter
greater than 60mm is sufficient for 1.3GHz cavity.
Therefore, there should not be a problem with EP.

Table 2: Current proposed SCLCs
EnergyReach[GeV]

4. 2_8-CELL SUPERSTRUCTURE
As mentioned above, an 8-cell structure is recommended
for the LL shape. However, the lower cell number lowers
the fill factor. Here the fill factor is defined as the ratio of
the total effective accelerating length over the LINAC
length. Using the superstructure, which was invented by J.
Sekutowicz in DESY [6], solves this problem. Figure 4
illustrates the 2x9-cell superstructure for TESLA-800. In
this case, two 9-cell cavities are welded through one beampipe, which is half a wavelength long. If two 9-cellcavities are directly connected into an 18-cell structure,
the field error seriously increases by a factor 4. This
problem is relaxed by connecting the two cavities so thatthey are offset by a half of a wavelength. This structure
has two advantages: 1) an increased fill factor due to theshortness by one beam pipe length and 2) the number of
input couplers is cut in half, which can reduce the cost.
We propose to use seven 2x8-cell superstructures in theTESLA-type 17m long cryomodule.

Gradient(MV/m)

LNAC
Effective
Length（km)Fillfactor(%)

LINAC
Length(Km)TunnelLength(Km)TESLA500

23.4

21.8

74.7

29.43

33

TESLA80035.0
2x9-cell
ss.

23.25

79.0

29.43

33

US
SCLC500

28.0

17.58

74.7

23.53

46.8

US
SCLC1000

35.0

28.30

74.7

37.88

46.8

SCLC500

35.0

14.07

74.7

18.84

33

SCLC1000

45.0
2x8-cell
ss.

22.80

77.47

29.43

33

References[1] K.Saito, Proc. of the SRF2001, p.588-590.
[2] W.Singer, et al. Proc. of the SRF2001, p.170-176.
[3] T. Hays and H. Padamsee, Proc. of the SRF1997,
p.789 – 794.
[4] K.Saito, http://srf2003.desy.de, MoO02.
[5] J Sekutowicz et al., Proc.of the PAC2003, p.1395.
[6] J.Sekutowicz et al., Phys. Rev. Special Topics
AB,1999.

Figure 4: 2x9-cell superstructure for TESLA-800.
The total length of the seven structure-sets is 0.25m
shorter than that of the TESLA-500 12x9-cell cavities
scheme. In addition, a total of 112 cells can be installedin the module, which is 4 more cells than the TESLA500 scheme (108 cells) and results in a 20MeV higher
energy gain when the structure is operated at 45MV/m.

83