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

THE GROWTH POTENTIAL OF THE ARES CAVITY SYSTEMTOWARD SUPER KEKB
T. Kageyama, T. Abe, H. Sakai, and Y. Takeuchi
KEK, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, 305-0801, JAPAN
Energy Storage Cavity

Abstract

Accelerating Cavity
Coupling
CavityNormal conducting RF accelerating cavities named ARES
(Accelerator Resonantly coupled with Energy Storage) havebeen operated to store high-current beams stably in the KEKB
double-ring electron-positron collider with the design
luminosity of 1×1034 cm-2s-1. The ARES cavity is based on athree-cavity system stabilized with the π/2-mode operation
scheme, where a HOM-damped accelerating cavity is coupledwith a large cylindrical energy storage cavity via a coupling
cavity between. Together with the current operational
performance of the ARES cavity, we discuss its growthpotential toward the Super KEKB project of boosting theluminosity frontiers beyond 1035 cm-2s-1.

INTRODUCTION
The operation of conventional normal conducting accelerating
cavities with heavy beam loading would give rise to a serious
problem with longitudinal CBI (Coupled Bunch Instability)
due to the fundamental mode, other than the HOM-driven CBI.
In electron storage rings, the resonant frequency of theaccelerating mode is usually detuned downward with respect
to the RF frequency fRF to compensate for the reactive componentof the beam loading. The optimum detuning ∆fa is given by
Isinφ s R
P tanφ s∆f a = −×× f RF = − b
,
(1)
2Vc
4 πU
Q0
where I is the beam current, φs the synchronous phase, Vc thecavity voltage, R the shunt impedance, Q0 the unloaded Q
value, Pb the beam power, U the stored energy. Loaded with thedesign beam current of 2.6 A for the KEKB LER (Low EnergyRing), the amount of detuning ∆fa required for the accelerating
cavity would become about 2~3 times the beam revolution
frequency frev = 99.4 kHz, leading to the strong excitation of
longitudinal CBI with a growth time on the order of 100 µs,
much faster than the radiation damping time of 23 ms.
The ARES cavity developed as a countermeasure against
this problem is based on a three-cavity system [1], where an
accelerating cavity is coupled with a high-Q energy storage
cavity via a coupling cavity between. Figure 1 shows the frontand side views of the ARES cavity for KEKB. Its design isbased on a high-power conceptual demonstrator ARES96 [2]with a cylindrical energy storage cavity operated in the TE013
mode. The accelerating mode is the π/2 resonant mode of thethree-cavity system. According to an equivalent circuit model[1], the stored energy ratio for the π/2 mode is given by(2)
U s /U a = k a2 / k s2 ,where Ua is the stored energy in the accelerating cavity, Us in
the storage cavity, ka the coupling factor between the accelerating
and coupling cavities, and ks between the storage and coupling

Two-Bullet Shape SiC Absorbers
per Rectangular HOM Waveguides

Grooved Beam Pipe
Half-Cell
Coupling Cavity

Eight SiC Tiles
per Groove

1000 mmFigure 1: Front and side views of the ARES cavity system.

cavities. The energy ratio for the π/2 mode can be kept almost
constant against detuning by ∆fa for the accelerating cavity
loaded with the beam. Therefore, the detuning for the π/2 mode
will be reduced as∆f π 2 =∆f a.
1 + U s /U a

(3)

Actually, the design ratio Us/Ua = 9 for the KEKB ARES cavity
gives∆fπ/2 = -20 kHz, small enough compared with the revolution
frequency, so that the growth rate of the severest –1 mode of the
CBI can be reduced to a level of τ = ~10 ms where some RF
feedback system [3] could damp it.
In KEKB, 20 ARES cavities have been successfully operated
to store the positron beam up to 1.8 A in the LER, while 10
ARES cavities in combination with 8 super conducting cavities
to store the electron beam up to 1.1 A in the HER (High EnergyRing). According to the operational performance so far, we
will probably be able to manage with the current version of the
ARES cavity for the Super KEKB HER with 4.1 A, 1.6 times
the design beam current of 2.6 A for the KEKB LER. On theother hand, we need to upgrade the ARES cavity toward theSuper KEKB LER with 9.4 A.

FUNDAMENTAL MODE ISSUES
The beam current of 9.4 A will be supported by 28 ARES
cavities for Super KEKB, whereas 2.6 A to be supported by 20
ARES cavities for KEKB. With the heavier beam loading, theaccelerating cavity itself needs to be further detuned by ∆fa =-200 kHz to -710 kHz. Consequently, the amount of detuning
for the π/2 mode will become large comparable with therevolution frequency if the current energy ratio Us/Ua = 9
unchanged. Therefore, the first upgrade item should be toincrease the energy ratio further. The ARES cavity system canbe mechanically separated into two cavity parts: the storage
cavity and the accelerating cavity part with the coupling cavity
brazed. We are planning to remodel the accelerating cavity part
together with the HOM loads, whereas the storage cavity will
be reused. Table 1 presents RF parameters for three cases with
Us/Ua = 9, 15 and 18. As the energy ratio being increased, theunloaded Q value Q0 increases whereas the input coupling

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

Table 1: RF parameters of ARES cavity for Super KEKB LER.
Us/UaI
# of Cavities
fRF
h
Vc
Q0
(R/Q)π/2
input β
Pc
∆fπ/2

9

15
9.4 (2.6)
28 (20)508.887
5120
0.5
1.27
9.4
4.1
210
-45

1.11
15
5.4 (2.7)
150-72 (-20)

18
A
MHz

1.32
7.9
3.8
240
-38

MV
×105
Ω
kW
kHz

Numbers in ( ) for KEKB LER

Re( Z// )/Cavity [Ω]

4

10

3

10

104
Growth Rate [ s-1 ]Us/Ua = 9
Us/Ua =15
Us/Ua =18510

µ = −1103
102µ = −2101µ = −3

2

10

0

-3

-2

-1
0
1
( f – fRF ) / frev

2

3

Re ( Z// )/Cavity [Ω]Figure 2: Coupling Impedance ofthe π/2 mode loaded with 9.4 A,
for Us/Ua = 9, 15, 18.

(R+- R )/Cavity [Ω]factor β decreases. According to a computer-aided simulation
study, we need to increase the height of the rectangular aperture(width = 120 mm) between the accelerating coupling cavities
from 160 mm to 175 mm for Us/Ua = 15, to 182 mm for Us/Ua= 18. Increasing the aperture height up to 185 mm is probably
acceptable without significant changes to the fabrication.
Figure 2 shows the real part of the coupling impedance of theπ/2 mode, calculated for each case. As the energy ratio being
increased, the detuning ∆fπ/2 reduces less than one half of therevolution frequency, and furthermore the resonance becomesa little sharp. That is because the loaded Q value, QL = Q0/(1+β),
increases as Us/Ua being increased. Figure 3 shows the growth
rates calculated for the -1, -2, and -3 modes of the CBI driven
by the π/2 mode, plotted as a function of the energy ratio Us/Ua.
By increasing the energy ratio from 9 to 15, the growth rate of
the -1 mode can be reduced by one order of magnitude to a
manageable level with τ = 1.5 ms. Balancing the relaxation in
the growth rate and the increase in the cavity power Pc (seeTable 1), the energy ratio Us/Ua around 15 is favorable.
Another issue is about the parasitic 0 and π modes broughtby the coupled-cavity scheme. Both parasitic modes can bedamped with an antenna-type coupler attached to the center ofthe coupling cavity, whereas the π/2 mode does not couple tothe coupler because of its field distribution with the electricshort boundary condition at the vertical mid plane of thecoupling cavity. Furthermore, the 0 and π modes are locatedalmost symmetrically with respect to the π/2 mode tuned into
the vicinity of the RF frequency. Therefore, the impedancecontributions from the damped 0 and π modes can becounterbalanced between the exciting and damping terms for
the CBI. However, the field distributions of the 0 and π modes
are subject to the first order term of tuning errors. For example,
when the accelerating cavity is detuned by ∆fa, the first orderterm of perturbation is proportional to ∆fa/(fπ - f0) . Therefore,
the delicate counterbalancing may be deteriorated with heavier
beam loading. Figure 4 shows the coupling impedance of the
0 and π modes calculated for three cases: Us/Ua = 9 with 2.6 A,
Us/Ua = 9 with 9.4 A, Us/Ua = 15 with 9.4 A. The impedance
imbalance with respect to the RF frequency is also shown,
where the positive to excite and the negative to damp, and thefastest growth time is indicated. The calculation was carriedout as follows: the perturbation due to ∆fa was taken into
account up to the first order; and the external Q value of thecoupling cavity to the antenna coupler was assumed to be 50(the same as for KEKB), which gives QL =100 for theunperturbed 0 and π modes with Ua = Uc. As the accelerating
cavity being detuned downward, the field distribution changes
as Ua > Uc for the 0 mode, whereas Ua < Uc for the π mode,
where the energy imbalance is proportional to ∆fa/(fπ - f0). For
KEKB, the impedance imbalance is at an allowable level
below 500 Ω/cavity, so that the CBI is expected to be suppressed
well and actually has not been observed so far. For SuperKEKB, the growth time will become 3.3 ms when Us/Ua = 9.
As Us/Ua being increased to 15, it will be eased a little to 4 ms
-1
because ∆fa/(fπ - f0) roughly reduces as ∝ka , i.e. ∝(Us/Ua)-1/2.
Anyway, some bunch-by-bunch longitudinal feedback will beneeded to suppress the CBI due to the 0 and π modes.

10

9

12

15
Us/Ua

18

Figure 3: Growth Rates of
the CBIs (µ = -1, -2, -3) due
to the π/2 mode, plotted as afunction of Us/Ua.

6000
4000
2000

Us/Ua = 9with 2.6 A

02000-100

-50

1000

0
50
τ = 3.3 ms
τ = 4.0 ms for Super KEKB

100

Us/Ua = 9with 9.4 A
Us/Ua =15
with 9.4 A

0
-1000

τ = 46 ms for KEKB

-2000
-100

-50

0
( f - fRF ) / frev

50

100

Figure 4: Coupling Impedance (top) of the 0 and π modes, andthe imbalance (bottom) with respect to the RF frequency.

HIGHER ORDER MODE ISSUESThe HOM-damped structure for the ARES cavity system wascarefully designed to be smoothly embedded into the wholescheme without any structural or electromagnetic
incompatibility. The toughest problem was an inevitableboundary condition: two large rectangular coupling aperturesat both sides of the accelerating cavity. One aperture is open to
the coupling cavity, and the other to a half-cell coupling cavity
for the π/2-mode termination to restore mirror symmetry forthe accelerating field with respect to the vertical mid plane.
The HOM-damped structure based on ARES96 consists offour rectangular HOM waveguides (WGs) attached to theupper and lower sides of the accelerating cavity and two
Grooved Beam Pipes [4] (GBPs) to both end plates, as shownin Fig. 1. The monopole and vertically polarized dipole HOMs
are guided out through the HOM WGs. The extracted HOM
power is guided via an E-bend in the horizontal direction andfinally dissipated in two bullet-shape SiC ceramic absorbers
directly water-cooled. The power capability was verified up to

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

SUMMARY
We have investigated the growth potential or the critical limitsof the ARES cavity toward Super KEKB with the LER beam

5

0.7
Total HOM PowerWG HOM Power
GBP HOM Power
Prediction from Cavity Loss Factor
Prediction from GBP Loss Factor

AC + 2 x GBP
2 x GBPAC + 2 x CBP

0.6

k (fundamental) = 0.12 V/pC

0.5
Loss Factor [V/pC]

4

Power / Cavity [kW]3.3 kW per bullet (26.4 kW per cavity) with use of a 1.3-GHz
CW klystron, but this limit was only due to the maximum
power stably supplied from the klystron. The horizontally
polarized dipole HOMs are guided out through the twofold
GBPs with upper and lower grooves. In each groove, eight SiC
tiles are arranged in a line to absorb the extracted HOM power.
Each SiC tile is brazed to a water-cooled copper plate with acopper compliant layer between. The GBP HOM load was also
tested, with use of the same klystron, up to 0.5 kW per groove(2.0 kW per cavity) without any significant vacuum pressure
rise observed.
Figure 5 shows the WG and GBP HOM load powers per
cavity plotted as a function of the KEKB LER beam current(1224 bunches with 4-bucket spacing), together with the sumof these, i.e. the total HOM power dissipation per cavity. These
data are based on the calorimetric measurements for the WG
and GBP loads at the downstream side with respect to the beam
direction, and obtained by simply doubling the measured dataowing to the mirror symmetry (see the side view in Fig. 1).
Furthermore, the total HOM power and the GBP HOM power
are compared with theoretical predictions shown by the solidand dashed curves, respectively. These two predictions are
based on the loss factors computed with 3D-MAFIA for thefollowing two cases: the whole damped structure (AC +2×GBP) and the two GBPs only (2×GBP), where the bunch
length σz = 7 mm was assumed according to other measurements.
Figure 6 shows the computed loss factors plotted as a functionof the bunch length, together with simulation results computedwith 2D-ABCI assuming a simplified axially symmetricaccelerating cell with circular beam pipes (AC + 2×CBP)
instead of the GBPs. Taking into account errors in thecalorimetric measurements, estimated as 10% for WG loadand 13% for GBP load, the total HOM power data agrees wellwith the theoretical prediction. On the other hand, the excess ofthe measured GBP power over the prediction might be due tothe mirror asymmetry of the accelerating cavity (see the front
view in Fig. 1). The half-cell coupling cavity can restore mirror
symmetry for the fundamental mode only.
According to the HOM power measurements and the loss
factor computations, the WG and GBP HOM powers per
cavity have been estimated as ~80 kW and ~20 kW, respectively,
for the beam current of 9.4 A (4896 bunches with σz = 3 mm).
Therefore, we will need to upgrade both of the WG and GBP
loads, for example: to increase the number of absorbers per
WG load, depending on the results of the high power testing to
be resumed soon; to replace the current GBP with a winged
chamber loaded with directly water-cooled SiC absorbers asshown in Fig. 7. Actually, this kind of chamber has alreadybeen developed under collaboration between the KEKB vacuum
and ARES cavity groups, and several chambers have been
installed to absorb the HOM power at the mask chamber
sections in KEKB [5].

3

2

0.4
0.3
0.2

1

0.1
0
0

200

400 600 800 1000 1200 1400
LER Beam Current (mA)

Figure 5: HOM load powers
per cavity measured in the
KEKB LER, compared withtheoretical predictions.

0
2

4

6
8
Bunch Length (mm)10Figure 6: Loss factors computedfor the whole damped structure
and the GBPs only, together withthose for a simplified axiallysymmetric strucutre with circularbeam pipes (CBPs).

SiC

Slot

Beam Chamber

Figure 7: Winged chamber [5] loaded with directly
water-cooled bullet-shape SiC abosrbers.

current of 9.4 A. By increasing the stored energy ratio Us/Uafrom 9 to 15, the severest -1 mode of the longitudinal CBI due
to the π/2 mode can be eased by one order of magnitude anddown to a level with τ =1.5 ms where some RF feedback system
could manage to damp it. The growth time of the CBI due to theimpedance imbalance between the parasitic 0 and π modes has
been estimated as τ = 4 ms, faster than that for KEKB by one
order of magnitude. However, this growth time may becomparable with those expected for other HOM-driven CBImodes. Anyway, some bunch-by-bunch longitudinal feedback
system will be needed. As for the HOM issues, we need to
upgrade the power capabilities of the WG and GBP loads up to~80 kW and ~20 kW per cavity, respectively. Therefore, weshould first resume high-power testing for the HOM-loads,
hopefully with a new klystron supplying more than 10 kW.

ACKNOWLEDGMENT
The authors are grateful to K. Akai and S. Yoshimoto forvaluable suggestions and discussions.

REFERENCES[1] Y. Yamazaki and T. Kageyama, Part. Accel. 44 p107, 1994.
[2] T. Kageyama et al., "Development of High-Power ARES
Cavities", Proc. PAC97, Vancouver, 1997[3] S. Yoshimoto et al.,"The -1 mode damping system for KEKB",
in this conference.
[4] T. Kageyama, "Grooved Beam Pipe for Damping Dipole
Modes in RF Cavities", Proc. the 8th Symposium on
Accelerator Science and Technology, p116, 1991.
[5] Y. Suetsugu et al., "Development of Winged HOM
Damper for Movable Mask in KEKB", Proc. PAC2003,
Portland, 2003.