PHYSICAL REVIEW SPECIAL TOPICS - ACCELERATORS AND BEAMS 13, 022003 (2010)

Eccentric-fluted beam pipes to damp quadrupole higher-order modes
M. Sawamura
Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, JapanT. Furuya, H. Sakai, T. Takahashi, and K. UmemoriHigh Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan

K. Shinoe
ISSP, University of Tokyo, Kashiwa, Chiba 277-8581, Japan(Received 3 November 2009; published 23 February 2010)
An eccentric-fluted beam pipe is proposed to damp quadrupole modes in a cavity. The eccentric flutes
act as a mode converter from quadrupole to dipole. Optimizing the parameters of the eccentric-fluted
beam pipe allows sufficient damping of both degenerate quadrupole modes. The external Q values of theeccentric-fluted beam pipe measured with a low power model cavity agree well with those calculated withthe 3D electromagnetic field simulation code MAFIA.
DOI: 10.1103/PhysRevSTAB.13.022003

PACS numbers: 29.20.Ej

I. INTRODUCTION
The superconducting rf accelerator is one of the fundamental technologies for present and future accelerator
facilities such as the International Linear Collider,
European X-ray Free-Electron Laser, Energy-Recovery
Linacs (ERLs), and the Spallation Neutron Source [1].
The intrinsic advantage of the superconducting rf accelerator is its extremely high Q values (low loss) for thecavity eigenmodes. Owing to the high Q values, the superconducting accelerator can generate high-power charged
particle beams with negligibly small heat losses dissipatingin the cavities. The high Q values of superconducting
cavities, however, cause a troublesome problem, resonant
excitation of higher-order modes (HOMs) in the cavity.
The amplitude of the fundamental mode, i.e., the accelerating mode, stored in the cavity is controlled to be constantby balancing the beam load and the input power fed
through the main coupler. HOMs excited in the cavity,
however, cannot be controlled in the same manner.
The resonant excitation of HOMs is a crucial issue
especially in high-current cw machines such as ERLs.
HOMs with high Q values induce beam breakup (BBU)
instabilities [2] and limit the beam current. This BBU
instability was observed experimentally at the JLab FEL
upgrade [2]. Increasing the beam current caused a growthof HOM voltage and beam losses. The BBU thresholdcurrent was found to be 2.7 mA in this measurement.
The multipass BBU instabilities in a recirculation linac
have been analyzed theoretically [3,4]. The threshold current of the BBU instability caused by dipole HOMs can beanalytically obtained for the simplest configuration consisting of a recirculation linac, a single cavity, a single
HOM, and a single loop. The threshold current is inversely
proportional to the HOM Q value.
1098-4402=10=13(2)=022003(9)In order to develop high-current superconducting accelerators of several 100 mA needed for such devices as the
future ERL light source, suppression of the HOM BBU is
one of the most important issues. In a design of a 5-GeV
ERL, a Cornell University group numerically studied
HOM BBU and found criteria of shunt impedance and Q
values for monopole, dipole, and quadrupole HOMs toachieve a 100 mA beam in the main linac [5]. They pointed
out that the quadrupole mode damping as well as the dipole
modes damping is important.
One possible way to damp HOMs is to enlarge the beam
pipes connected to both ends of the cavity. Table I shows
the relation between the cutoff frequencies and the beam
pipe diameter of the TESLA cavity [6], for example. The
three lowest cutoff frequencies correspond to the TE11
(dipole), TM01 (monopole), and TE21 (quadrupole)modes. Enlarging the beam pipe diameter enables these
HOMs to propagate along the beam pipe. The quadrupolemode requires the largest diameter among three modes asshown in Table I. Increasing the beam pipe diameter topropagate quadrupole modes causes the deeper penetrationof the fundamental mode into the beam pipes. This resultsin longer distance from the cavity to the HOM absorber anda lower packing factor.
Fluted beam pipes are another solution to damp HOMs
[7]. They also lower the cutoff frequencies of the HOMs,
but are insufficient to control quadrupole HOMs.
We propose an asymmetric fluted beam pipe, called here
an eccentric-fluted beam pipe (EFB), to solve these difficulties in achieving quadrupole damping. The EFB is
formed by displacing the direction of the flute away fromthe beam pipe center and/or by folding around the midpointof the flute to couple with quadrupole modes.
The present paper gives the results of calculation with
MAFIA and measurements of a low power model cavity

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Ó 2010 The American Physical Society

M. SAWAMURA et al.

Phys. Rev. ST Accel. Beams 13, 022003 (2010)

TABLE I. Relation between cutoff frequencies and beam pipe diameter for TESLA cavity.
Propagating mode

Dipole TE11

Monopole TM01

Quadrupole TE21

Cutoff frequency for 78 beam pipe (TESLA design)
Lowest HOM frequency of cavity corresponding to propagating mode
Minimum beam pipe diameter required for propagation of HOM
Decay constant for 1.3 GHz fundamental mode with above beam pipe
Beam pipe length needed for 99% decay of fundamental mode field

2.25 GHz
1.62 GHz
109 mm35:0 mm1
132 mm

2.94 GHz
2.34 GHz
98 mm
40:7 mm1
113 mm3.74 GHz
2.23 GHz
131 mm
24:7 mm1
186 mmII. ECCENTRIC-FLUTED BEAM PIPE
A. Principle
A fluted beam pipe, as shown in Fig. 1(a), can lower thecutoff frequencies of rf modes propagating along the beam
pipe. Propagation of quadrupole modes requires a large
fluted beam pipe. Furthermore, propagation of the HOMs
throughout the beam pipe requires that the flute extend
over the entire length of the beam pipe up to the HOM
absorber installed at the end of the beam pipe.
An example of the EFB is shown in Fig. 1(b). In thiscase, the flute is asymmetrically shifted from the center ofthe beam pipe and the field pattern around the flute can beassumed to include a dipole mode. This suggests that thequadrupole mode can couple with the EFB and propagate
as a dipole mode.
To confirm this principle of the EFB, the Fourier components of the rf field along the beam axis were calculatedwith MAFIA. The model used was a TESLA-type single-cellcavity with eccentric flutes of 60 mm length, 20 mm
height, 31 mm width, and 10 mm shift from the beam
pipe center. Figure 2 shows the calculated Fourier compo-

nents of dipole and quadrupole modes when the quadrupole mode is excited in the cavity. The cell was locatedfrom 0 to 113 mm and the eccentric-flute from 14 to74 mm. The dipole mode seen here was induced by the
eccentric-fluted beam pipe as the rf propagates through thispipe. The fact that the rf field was propagating at the end of
the EFB clearly suggests that the EFB acts as a mode
converter from quadrupole mode to dipole. It should benoticed that a normal fluted beam pipe cannot convert thefield pattern from the quadrupole mode to another mode.
These calculations also revealed that the EFB is effective for both of the degenerate quadrupole modes whichrotate 45 degrees around the beam axis, though the effect is
not the same for the degenerate quadrupole modes.
1.2
1.0
Fourier Component

with the EFB, which confirm the effectiveness of the EFB
in damping the quadrupole modes.

0.8

DipoleQuadrupole

0.6
0.4
0.2
0.0
-0.2
-600

width

-400

-200
0
Position (mm)

200

400

200

400

(d)

Fourier Component

ing a
bend

(c)

1.0

bendin
g

angle

(b)
ngle

(a)

shift

height1.2

FIG. 1. (Color) Beam pipe cross sections with normal flute (a)and eccentric flute (b)–(d): (b) shifting a flute from the beam pipe
center (type 1); (c) bending a flute around the beam pipe center(type 2); (d) combination of shifting and bending a flute (type 3).

0.8

DipoleQuadrupole

0.6
0.4
0.2
0.0
-0.2
-600

-400

-200
0
Position (mm)FIG. 2. (Color) Fourier components of electric field of the crosssection along the axis. The polarities of quadrupole against theeccentric flute are shown in the figures.

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ECCENTRIC-FLUTED BEAM PIPES TO DAMP . . .

Phys. Rev. ST Accel. Beams 13, 022003 (2010)

150000type-1
type-2type-3External Q

100000

50000

0

0

5

10
15
20
25
type-1:shift (mm)type-2&-3:flute angle (deg)

30

35

40

FIG. 3. (Color) Comparison of external Q values of three typesof EFPs as a function of shift distance (type 1) and bending angle(types 2 and 3).

center (type 1), the second bends the flute at the beam pipe
center (type 2), and the third is a combination of the above
shapes both shifting and bending the flute (type 3).
Figure 3 shows the calculated external Q values for the
TESLA-type single-cell cavity with the three types of the
EFB. The EFB is located 14 mm from the end of the cell.
The EFB is 60 mm long, 20 mm high, and 70 mm wide.
The flute for type 3 is shifted by half of the height from thebeam pipe center and bent at the beam pipe center. The
bending angle of type 3 is defined as plus towards theshifted flute. Since the minimum external Q values forthe three types are almost the same, we selected the type
2 EFB because of its ease of fabrication.
To determine the optimum shape of the EFB, the external Q values were calculated for various EFB bending
angles, lengths, widths, and positions removed from thecell end.
III. MEASUREMENT OF Qext OF ECCENTRIC
FLUTES

B. Method to calculate external Q value
The properties of the EFB were estimated by calculatingexternal Q values of the EFB. A method to calculate theexternal Q value with nondissipative codes was proposed
elsewhere [8,9]. The external Q value for a line consistingof a TE wave can be calculated by


2 

Qext ¼
R þ R ;(1)  E  H
RRR 2
jEj dV;RE ¼ RR 2
jEj dS(2)

RRR
jHj2 dV
RH ¼ RR;
jHj2 dS(3)

where  and  are, respectively, the wavelengths in a freespace and in a waveguide. The volume and surface integrations are performed, respectively, over the cavity volume and over a beam pipe cross section which has anelectric field antinode in Eq. (2) and a magnetic field
antinode in Eq. (3). These can be calculated with MAFIA.

A. Model cavity measurement
A low power EFB model made of aluminum was fabricated to estimate the external Q value of the EFB.
Figure 4 shows the setup for the measurement. The EFB
model consisted of seven pieces of angularly divided beam
pipe as shown in Fig. 5. The flute angle could be chosen to
be from zero to 45 degrees in five-degree increments bychanging the order of the pieces. The flute parameters
could be chosen as follows: length from 60 to 100 mm in
10 mm increments, width from 50 to 85 mm in 5 mmincrements, and position from 14 to 49 mm in 5 mm increments. The EFB was attached to one side of a TESLA
three-cell cavity. A drive antenna was installed at the sideof one end cell and a pickup antenna was installed at theside of the other end cell at the same angle. Two types ofantenna such as a loop and a pin were used to measure thedegenerate modes separately. A rolled-up ferrite sheet was
set inside the beam pipe as a HOM absorber. Loaded Q
values of TE211 modes were measured with a network
analyzer with various ferrite positions, defined as thelength of the interval indicated in Fig. 4.

C. Eccentric-flute shapeThree EFB types with different asymmetrical configurations of flutes were considered, as shown in Figs. 1(b)–1(d). The first simply shifts the flute from the beam pipe

B. Method of estimating external Q value
Figure 6 shows measured examples of loaded Q valuesof the three-cell cavity with and without the EFB. The flute

pickup antenna
drive antenna

ferriteposition

ferriteeccentric-flute

FIG. 4. (Color) Setup for the Q value measurement of the EFB.

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M. SAWAMURA et al.

Phys. Rev. ST Accel. Beams 13, 022003 (2010)

Eccentric flute

Eccentric flute

Complexz =0
FIG. 5. (Color) Angularly divided eccentric-fluted beam pipe.

25000

20000
Loaded Q

z=z

Real

z=0

1
1
g
¼
þ
;
QL
Q0 Qext

10000

100

200
300
400
500
600
position of ferrite sheet from cell end (mm)700

FIG. 6. (Color) The loaded Q values as a function of the ferrite
position with and without the EFB.

angle was 25 degrees. The figure shows that the loaded Q
value without the EFB remains constant until the ferrite
sheet comes close to the cell, at which position the quadrupole mode penetrates into the beam pipe. The loaded Q
value with the EFB varied with shift in the ferrite position,even far from the cell. This indicates that in the quadrupolemodes, energy propagates through the beam pipe.
If the HOM absorber has ideal properties of perfectabsorption and no reflection, the loaded Q values should
be constant regardless of the position of the HOM absorber.
Since the HOM absorber reflects to some extent in practice,g¼

z = z − dz

FIG. 7. (Color) Equivalent circuits of beam pipe with the HOM
absorber.

15000

0

Ŷr

however, the loaded Q value varies according to the position of the HOM absorber.
We can estimate the external Q value from the measured
loaded Q values by the following procedures. When theload in the transmission line connected with a cavity has anormalized conductance of g, unloaded, loaded and external Q values are related by the following equation:

w/o. EFB
w. EFB5000

z = z − dzYˆ ( z)where QL , Q0 , and Qext are loaded, unloaded, and external
Q values, respectively. In this expression, it is assumed thatexternal Q values except for the transmission line areadded to the value of Q0 . The normalized conductance g
is a function of the position of the HOM absorber.
We assume that the load located at the position z has^
normalized admittance YðzÞas shown in Fig. 7 (left).
^
Although YðzÞ is complex, we assume that it becomesreal viewed at the distance dz from the load. This isequivalent to locating the load of real normalized admittance Y^ r at the position of z  dz as shown in Fig. 7 (right).
The normalized admittance of this load viewed from z ¼ 0
can be expressed asY^ þ tanhðz  dzÞ
^
Yð0Þ
¼ r
;
1 þ Y^ r tanhðz  dzÞ11gðz; Y^ r ; ; ; dzÞþ
:¼
QL ðzÞ
Q0
Qext

(7)

(5)

where  is a propagation constant expressed as  ¼  þj,  is an attenuation constant, and  is a phase constant.
The normalized conductance g is the real part of Eq. (5).
The normalized conductance can be expressed as

2Y^ r cosh2ðz  dzÞ þ ð1 þ Y^ 2r Þ sinh2ðz  dzÞ:
ð1 þ Y^ 2r Þ cosh2ðz  dzÞ þ 2Y^ r sinh2ðz  dzÞ þ ð1  Y^ 2r Þ cos2ðz  dzÞ

The loaded Q value can be expressed as a function of z
with the constant parameters of Y^ r , , , dz, Q0 , and Qext :

(4)

(6)

The method of estimating the external Q value is summarized as follows: (1) Measure the loaded Q values whilechanging the position of the HOM absorber. (2) Fit theloaded Q values to Eqs. (6) and (7).

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ECCENTRIC-FLUTED BEAM PIPES TO DAMP . . .
TABLE II.

Angle (deg)Width (mm)Length (mm)Position (mm)Phys. Rev. ST Accel. Beams 13, 022003 (2010)

Parameters of the EFB used for the Q value measurement and calculation.
Figure 8

Figure 9

Figure 10

Figure 11

0–45 step 5
70
60
14

20
50–85 step 5
60
14

20
85
60–100 step 10
14

20
70
60
14–49 step 5

IV. COMPARISON OF CALCULATIONS AND
MEASUREMENTS
The eccentric-flute parameters which were varied for
calculation and measurement are shown in Table II.

Figures 8–11 show the external Q values of calculationand measurement as a function of flute angle, flute width,flute length, and flute position, respectively.

1/3 π mode E-boundary (meas.)
2/3 π mode E-boundary (meas.)
π mode E-boundary (meas.)
1/3 π mode E-boundary (calc.)
2/3 π mode E-boundary (calc.)
π mode E-boundary (calc.)

1010

108

109

1/3 π mode E-boundary (meas.)
2/3 π mode E-boundary (meas.)
π mode E-boundary (meas.)
1/3 π mode E-boundary (calc.)
2/3 pi mode E-boundary (calc.)
π mode E-boundary (calc.)

107
External Q

External Q

108
107
106

106

105

105
104

0

10

20
30
Flute Angle (deg)

40

104
40

50

1/3 π mode M-boundary (meas.)
2/3 π mode M-boundary (meas.)
π mode M-boundary (meas.)
1/3 π mode M-boundary (calc.)
2/3 π mode M-boundary (calc.)
π mode M-boundary (calc.)

109

108

107

106

80

90

80

90

1/3 π mode M-boundary (meas.)
2/3 π mode M-boundary (meas.)
π mode M-boundary (meas.)
1/3 π mode M-boundary (calc.)
2/3 π mode M-boundary (calc.)
π mode M-boundary (calc.)

106

105

105

104

60
70
Flute Width (mm)107
External Q

External Q

108

50

0

10

20

30

40

104
40

50

Flute Angle (deg)FIG. 8. (Color) Calculated and measured external Q values ofthree-cell cavity with the EFB as a function of bending angle.

50

60
70
Flute Width (mm)FIG. 9. (Color) Calculated and measured external Q values ofthree-cell cavity with the EFB as a function of flute width.

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M. SAWAMURA et al.

108

Phys. Rev. ST Accel. Beams 13, 022003 (2010)

1/3 π mode E-boundary (meas.)
2/3 π mode E-boundary (meas.)
π mode E-boundary (meas.)
1/3 π mode E-boundary (calc.)
2/3 π mode E-boundary (calc.)
π mode E-boundary (calc.)

109

108

External Q

External Q

107

10

1/3 π mode E-boundary (meas.)
2/3 π mode E-boundary (meas.)
π mode E-boundary (meas.)
1/3 π mode E-boundary (calc.)
2/3 π mode E-boundary (calc.)
π mode E-boundary (calc.)

6

107

106

105

105
104
50

60

70
80
90
Flute Length (mm)

100

104
10

110

15

20

25

30

35

40

45

50

45

50

Flute Position from cell end (mm)108

1/3 π mode M-boundary (meas.)
2/3 π mode M-boundary (meas.)
π mode M-boundary (meas.)
1/3 π mode M-boundary (calc.)
2/3 π mode M-boundary (calc.)
π mode M-boundary (calc.)

1010
109

107

108
External Q

External Q

1/3 π mode M-boundary (meas.)
2/3 π mode M-boundary (meas.)
π mode M-boundary (meas.)
1/3 π mode M-boundary (calc.)
2/3 π mode M-boundary (calc.)
π mode M-boundary (calc.)

106

105

107
106
105

104
50

60

70
80
90
Flute Length (mm)

100

104
10

110

15

20

25

30

35

40

Flute Position from cell end (mm)FIG. 10. (Color) Calculated and measured external Q values ofthree-cell cavity with the EFB as a function of flute length.

The E boundary plotted in the graphs represents theelectric boundary conditions of the modes on the plane
along the axis symmetrically cutting the EFB, and the M
boundary represents the magnetic boundary conditions of
the same.
The measurements agreed well with the calculations.
V. DISCUSSIONAs shown in Figs. 8–11, the external Q values of the and 2=3- modes were smaller than those of the 1=3-
mode. Since the TESLA-type cavity was designed to en-

FIG. 11. (Color) Calculated and measured external Q values ofthree-cell cavity with the EFB as a function of flute position fromthe cell end.

hance some HOMs in one end cell and others in the otherend cell through asymmetric end cell shaping [6], the fieldstrength of all cells was not equal. In our setup, the TE211
1=3- mode excited a weaker cell field at the side of the
EFB near the cells than at the far side, as shown in Fig. 12.
The weak cell field at the near side of the EFB caused weakcoupling between the field and the EFB. This resulted in an
external Q value of the TE211 1=3- mode larger thanthose of the  and 2=3- modes. When the field distribution is not uniform due to the asymmetric shape of the end

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ECCENTRIC-FLUTED BEAM PIPES TO DAMP . . .

1.2

Phys. Rev. ST Accel. Beams 13, 022003 (2010)
10 7

1/3 π mode (meas.)
1/3 π mode (calc.)(R/Q)Q/f ( Ω/cm GHz)

1.0

Normalized E 2

0.6
0.4
0.2

10 4
10 3
10 2

0.0

-100

0

100

200

300

400

10 1

500

Position (mm)

1.2

10 5

4

0.8

-0.2
-200

TE211 E-boundary
TE211 M-boundary

10 6

π/3

2π/3

π

mode

2/3 π mode (meas.)
2/3 π mode (calc.)

FIG. 13. (Color) The calculated values of ðR=QÞQ=f for TE211
modes of TESLA-type three-cell cavity with the EFB.

1.0

Normalized E 2

0.8
0.6
0.4
0.2
0.0
-0.2
-200

-100

0

100

200

300

400

500

300

400

500

Position (mm)1.2

π mode (meas.)
π mode (calc.)

1.0

Normalized E 2

0.8
0.6
0.4
0.2
0.0
-0.2
-200

-100

0

100

200

Position (mm)FIG. 12. (Color) Calculated and measured field distributions ofTE211 1=3 pi (top), 2=3 pi (middle), and pi (bottom). The
eccentric flute is located from 14 to 114 mm. The cells arelocated from 0 to 344 mm.

cell, and the quadrupole field at the end cell on the EFB
side is small, installing EFBs into both ends of the beam
pipes enables damping of all the quadrupole modes.
The quadrupole mode criterion for the 100 mA ERL
designed by the Cornell University group [5] wasðR=QÞQ=f < 4  106 =cm4 GHz, where R, Q, and f
are shunt impedance, Q value and frequency, respectively.
The calculated values of ðR=QÞQ=f for the TE211 modesof a TESLA-type three-cell cavity with the EFB meet thiscriterion as shown in Fig. 13. The flute is 60 mm long,
20 mm high, 70 mm wide, 20 degrees angular, and locatedat 14 mm from the end of the cell. Since the seven-cell ornine-cell cavity is used for a real machine, the values of
ðR=QÞQ=f were calculated for the TESLA-type nine-cellcavity with the EFB of the same parameters as shown in
Fig. 14. Though the values of ðR=QÞQ=f were worse forthe nine-cell cavity than those for the three-cell cavity, allmodes except for the TE211 1=9- mode meet the criterion. Similar to the three-cell cavity, the TE211 1=9-
mode of the TESLA-type nine-cell cavity weakly couples
with the EFB due to asymmetry end cell shaping. Installing
the EFBs into both ends of beam pipes and/or improving
the field flatness of HOMs will reduce values of ðR=QÞQ=f
for the HOMs including the 1=9- mode and realize acavity design to meet the criterion for a 100 mA ERL.
The flute length dependence shown in Fig. 10 indicatesthat a long EFB is not always effective in damping thequadrupole, since a long EFB can increase the external Q
value. Since the EFB works as the mode converter from thequadrupole to the dipole, it can be also considered to be amode converter from the dipole mode to quadrupole. Thismeans that a long EFB may reconvert the dipole mode to
the quadrupole mode. Calculated external Q values withthe longer EFB are shown in Fig. 15. The external Q values

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Phys. Rev. ST Accel. Beams 13, 022003 (2010)

10 13
TE211 E-boundary
TE211 M-boundary

10 11

10

π mode dipole
π mode quad

10-2

10 10
10 5
10 4
10 3
10 2

10-3
10-4
10-5
10-6
10-7

10 1
10 0

0

10-1

Fourier Component

4(R/Q)Q/f ( Ω/cm GHz)

10

12

10-8
-600

π/9 2π/9 3π/9 4π/9 5π/9 6π/9 7π/9 8π/9 π

mode

-400

-200

0
200
position (mm)

400

600

800

FIG. 14. (Color) The calculated values of ðR=QÞQ=f for TE211
modes of TESLA-type nine-cell cavity with the EFB.

FIG. 16. (Color) Calculated Fourier components of electric fieldof the cross section along the axis for the long EFB.

varied periodically according to the EFB length. Figure 16
shows the calculated Fourier components along the beamaxis with the EFB of 230 mm length, 30 degrees angle, and
70 mm width, and located from 14 to 244 mm. These
indicate that the quadrupole mode decreases at the entranceof the beam pipe because there is a lower frequency thanthe cutoff frequency, and that the quadrupole mode increases as the position gets farther from where there isquadrupole attenuation. The quadrupole at such a removed
position is considered to be reconverted from the dipolemode.

VI. CONCLUSION

1/3 π mode E-boundary
2/3 π mode E-boundary
π mode E-boundary
1/3 π mode M-boundary
2/3 π mode M-boundary
π mode M-boundary

1010
109

External Q

108
107
106
105
104

0

50

100
150
Flute Length (mm)

200

250

FIG. 15. (Color) Calculated external Q values of the long EFB
as a function of flute length.

Much investigation has been made into a superconducting cavity which does not have multipass BBU instabilities
due to HOMs. A HOM free cavity for the electron coolingproject with ERL with an optimized cavity shape and beam
pipes with ferrite absorbers has been proposed [10].
Although that cavity can damp the dipole and the monopole modes sufficiently, the quadrupole modes are notdamped. The EFB we developed is effective in damping
the quadrupole modes.
Since quadrupole modes are converted into dipole
modes by EFB and penetrate from the cavity into thebeam pipe, the optimum structure of the EFB is virtually
uninfluenced by the cavity shape design. The EFB is inprinciple independent of the number of cells of the cavity,
so that the design of the EFB can easily be adapted to thetypical nine-cell cavity. A suitable EFB can be installed at
any type of cavity optimized for dipole damping as far as
quadrupole modes penetrate into a beam pipe. After installation of the EFB, the quadruple modes will be dampedby the absorber at the beam pipe together with the dipole
modes.
The EFB makes it possible to damp the quadrupolemodes which cannot be effectively damped by enlarging
the beam pipes and optimizing cell shapes, and thus toincrease the threshold current which is limited by quadrupole BBU instabilities. This realizes a high-current ERL
machine of over 100 mA, something not possible heretofore due to quadrupole modes trapped in a cavity.
The ERL project in Japan is proceeding with the cooperation of JAEA, KEK, ISSP, and other SR institutes torealize 5 GeV class ERLs [11–14]. The superconducting
main linac with a nine-cell cavity has been designed tosuppress the monopole and dipole HOM BBU instabilities

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ECCENTRIC-FLUTED BEAM PIPES TO DAMP . . .

Phys. Rev. ST Accel. Beams 13, 022003 (2010)

by optimizing the cell shapes with enlarged beam pipes[15–17]. A BBU simulation showed that this cavity canstrongly damp the dipole modes and thus achieve over
600 mA beam current without HOM randomization [18].
Installing the EFB in this cavity is expected to satisfy therequirement of our ERL machine for strong damping ofmonopole, dipole, and quadrupole modes. A niobium test
cavity with the EFB based on our design has been fabricated, and the measurement of cavity performance is underway.

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