DESIGN OF RF CAVITIES FOR THE SPring-S STORAGE RING
T.Kusaka, T.Yoshiyuki, T.Moro and M.Hara
RIKEN-JAERI Synchrotron Radiation Facility Design Team
2-2S-S Honkomagome, Bunkyo-ku, Tokyo 113 Japan
K. Inoue
Kobe Steel, Ltd.
1-5-5 Takatsukadai, Nishi-ku,' Kobe 673-02 Japan
Table 1Abstract
The SPring-S storage ring has been determined touse 50S.6MHz cavities, which are located in four 6.5-m
straight sections with low betatron functions. We
examined two types of RF systems and compared the RFcharacteristics of a single-cell cavity and a 3-cellcavity as preliminary studies. The threshold currents
due to coupled-bunch instabilities were evaluated basedon their measured impedances. Single-cell sphericallyshaped cavities were designed to reduce the impedancesin higher-order modes and to raise the thresholds above
the design current.

Beam energy
Beam current(multi-bunch)
Circumference
Revolution frequency
Radio frequency
Harmonic number
Synchrotron radiation loss
in bending magnets
Energy loss in Insertion devices
Parasitic energy loss per 100 rnAMaximum RF voltage
Number of 1-MW klystrons
Table 2Introduction
An SGeV synchrotron radiation facility named
Spring-S is now under design [l]. It consists of astorage ring, a booster synchrotron and lGeV electronand positron linacs. Both the RF systems of the storage
ring and the synchrotron operate at a frequency of50S.6MHz, which is identical to the RF frequency of theTRISTAN Main Ring. Since the goal beam current in thestorage ring is more than lOOmA in a multi-bunch
operation, it is necessary to design the RF system inconsideration of not only the efficiency of converting
RF power into beam power but also beam stability.
RF system design
The RF parameters of the SPring-S storage ring arelisted in Table l. The energy loss due to insertion
devices is estimated at 3.2MeV based on the typical
specifications of insertion devices. The peak RF
voltage is 16MV in order to get a sufficiently longquantum lifetime. Four 6.5-m straight sections with low
betatron functions are prepared for RF sections and a1-MW klystron and RF cavities are installed in eachsection.
Two types of RF systems are advantageous for RF
power efficiency, because the input power through an RFwindow and the dissipated power in a cavity arelimited. One system uses thirty-two single-cellcavities and the other uses fourteen 3-cell cavities.
Table 2 lists these system parameters. Here, it isassumed that the shunt impedance per unit length is
22.5MO/m and the threshold power of a window is 200kW
in both systems. Since each cavity has an input
coupler, the RF system using single-cell cavities has
the ability to accept a higher beam current than theother system. On the other hand, the RF system using 3cell cavities needs less RF power and includes simplertransmission lines from RF power sources to cavities.

RF parameters of the storage ring
S GeV
100 rnA
1429 m210 kHz
50S.6 MHZ
2424
S.3 MeV
3.2 MeV
0.5 MeV
16 MV
4Comparison between two types of RF systems
RF system using
single-cell cavities

RF system using
3-cell cavities

32
S cavities X 414
4 cavities X 3
2 cavities X 1

1.2 MW

0.9 MW

2.7 MW
0.2 A

2.3 MW
0.16 A

Number of cavities
Arrangementof cavities
Power dissipatedin cavities
Total RF powerat lOOmA
Maximum beam current

The model cavity was machined out of 6061 aluminumalloy. The overall machinery accuracy was within±O.lmm. Since the coupling slots in the 3-cell cavity
were not symmetric to the beam axis, a threedimensional code MAX3D [2] based on the finite element
method was used to investigate the influence of thecoupling structure. In the model cavity, two couplingslots whose azimuth was 45 degrees were machined toachieve more than 1% coupling with suppressing theextreme drop of the shunt impedance.
Four modes were precisely measured because theywere found to have high impedance values fromcalculations. Table 3 shows the results of measurement.
All impedances are expected for the copper-made cavity
and are corrected by using the ratio of the calculated
Q-value to the measured Q-value in the fundamental
mode. The shunt impedance of the 3-cell cavity was
nearly three times as high as that of the single-cellcavity, because a "flat" electric field was achieved in
the n mode. The maximum impedance of the 3-cell cavity
in the higher-order modes (HOMs) was about 1.5 times ashigh as that of the single-cell cavity in the TMllllike mode.

Preliminary experiments
It is necessary to compare the RF characteristics
of two types of cavities. A single-cell cavity with reentrant nose cones and a 3-cell cavity with inductive
coupling slots have been fabricated. The 3-cell cavity
is shown in Fig. 1, while the single-cell cavity isassembled with the center cell of the three cells andtwo end plates. The shunt impedance is optimized bytaking the gap size between nose cones as a parameter.

-Fig. 1. Cross section of the 3-cell cavity with reentrant nose cones and coupling slots.

83-Table 3 Comparison of impedances which are expectedvalues for the copper-made cavity and are correctedby using the ratio of Ocalc./ Oexp. for thefundamental mode.
mode type
TMOlO
TMOll
TMllO
TMlll

Impedance
Single-cell
9.3
1.8
1624

(MQie-40

""
0;

.

TM110
TM112

30

TM111uor MCl/m)
3-cell27
3.42435;:•" 20!!"".
:::0010-&-"=fThreshold current due to coupled-bunch instability!-

The HOMs of accelerating cavities cause a coupledbunch oscillation in a multi-bunch operation. Thisoscillation is executed at harmonics of the revolution
frequency [3). Because the spacing between harmonics,
210kHz, is not wide enough compared with the bandwidthof a HOM impedance, it will be difficult tosignificantly suppress coupled-bunch instabilities bychanging the accelerating frequency and the betatrontune in the operation. Therefore, it is necessary toevaluate the threshold beam current of theinstabilities, which is approximately calculated byequalizing their growth-rate with the radiation damping
rate. The calculated threshold current using the ringparameters and the impedances listed in Table 3 aregiven in Table 4. Here, only radiation damping due tobending magnets is considered, although contribution by
insertion devices is expected. In addition, HOM damping
by damping couplers and Landau damping are anticipated.
The calculations are carried out on condition that theHOM frequencies of all the cavities are separated sothat there is no superposition of the impedance. It
will be realizable by adjusting the sizes of blankflanges of the cavities. Since the transverse impedanceof the TMlll-like mode is so high, the thresholdcurrents due to transverse coupled bunch instabilities
in both RF cavities are lower than lOOrnA.
Table 4 Threshold beam current due to coupled-bunch
instabilities
Threshold current (rnA)
Single-cell
3-cell360
190
Longitudinal
85
58
Transverse
type20Fig. 2. Variations of transverse impedances as afunction of the gap length.
L2.....-..:We decided on the following design policies of thecavities for the SPring-S storage ring after the above
studies and the RF system using thirty-two single-cellcavities was chosen.
(1) The intrinsic HOM impedances of the cavities arereduced as much as possible.
(2) The shunt impedance in the accelerating mode ismore than 6.8Mn/cell in order to suppress the excessive
thermal load in the cavity.
(3) The cavity structure is made simple in order toease fabrication, cooling and maintenance.
Since transverse impedances are high in thecavities with re-entrant nose cones, their variation
was calculated as a function of the gap length. The
results are shown in Fig. 2. It is obvious that themaximum transverse impedance is reduced with thedepression of nose cones. Therefore, we made the cavity
shape model without nose cones.
The geometry of the cavity in this study is shownin Fig. 3. It consists of two circles connected by astraight line and a flat body. The beam pipe radius waskept at a constant '100rnrn. The cavity radius R wasadjusted to obtain a 508.6MHz fundamental resonant mode
frequency.
Thecavity
length wasset to2*Ll=A/2=294.7rnrn. The RF characteristics of several

RLlI
IIII
II

00IIII--t-----------------------4-,IFig. 3. Cavity shape model with design parameters.
cavities with various combinations of design
parameters, Rl,R2 and L2, were calculated with thenumerical codes SUPERFISH and URMEL. Then, thedependence of the impedances in the four modes on thedesign parameters were investigated. The results areshown in Fig. 4 (a) through (d). The impedances inTMOlO-like and TM111-like modes are dependent strongly
on a parameter R2+L2. And the impedances in theremaining two modes are relevant to the value of Rl. Itis necessary to compromise in determining the values ofthese parameters in order to get the desired shunt
impedance in th~ accelerating mode and reduce the HOM
impedances. The variations of other longitudinal
impedances were also calculated as a function of cavity

i.cCavity design30

Gap length (em)

..

e3..
;

.c

B

::E~.

-m9::: 70G

ae0N

N

6
10

11

12

130

R2+L2 (em)

3

1616.

eB.c 14140;:;;:

5 13~.
GE 1s150-2Rl (em)(b)(a)
Eam08e.cGa13-.... 1212N

N111110103Rl (em)810111213R2+L2 (em)(C)(d)
Fig. 4. Dependence of the impedances on the designparameters; (a) in the TMOlO mode, (b) in the TMOllmode, (C) in the TM110 mode, (d) in the TMll1 mode.

-84-length for cylindrical cavities. The impedances in theTM020-like and TM021-like modes are reduced with thecavity length.
Four design parameters, Rl, R2, Ll and L2, wereadjusted to reduce all HOM impedances. In this process,priority was given to the impedances in lower resonant
frequencies, because HOM frequencies in the thirty-two
different cavities are easily separated in higher
frequencies. The designed RF cavity is shown in Fig. 5.
It is a spherically-shaped cavity similar to thesuperconducting cavities now widely used. The computed
impedances are shown in Fig. 6, compared with the onesof the re-entrant model cavity. The shunt impedance inthe accelerating mode is 7.4Mn, which is about 20%
lower than the one of the re-entrant cavity. However,
the maximum transverse impedance decreases byapproximately one-half. Therefore, coupled-bunch
instabilities are suppressed and the threshold current
is raised above lOOrnA.

[W/cm2]

Fig. 7. Power distribution at a total power of40kW/cell.

__! 100 J.Lm

(b)

Fig. 8. (a) Temperature distribution of the cavity;(b) deformation of the cavity; the dashed lines show
the original mesh and the solid lines show thedisplaced mesh.
cooled by eight parallel thin channels along the cavity
wall. The temperature distribution is shown in Fig. 8(a), when the velocity of the cooling water is 1.5m/s
and the initial temperature of the cavity is 2o•c. The
increase of the surface temperature is about 16°C
uniformly. Therefore, the loss in shunt impedance isestimated to be less than 4%. Figure 8 (b) shows
deformation due to thermal stress. The resonant
frequency change is calculated to be about 80kHz and it
can be easily compensated with a frequency tuner.

020

Fig. 5. Cross section of the designed sphericallyshaped cavity.

.

~ 10,---------------------~ !E 30,------------------- ---,!

II Spberically-lhaped cavityA Re-entrant cavity.
.

...
!

~ 20.

:;;;;,.

"~c.
.s.. .· . ... ..
·... ....

10~"~~ o+-------~------~~~~..JConclusion

1000

Frequency

(a)

2000

(MHz)

~

2000

1000

Frequency

{MHz)

(b)

Fig. 6. Comparison of computed impedances between twotypes of cavities; (a) in longitudinal impedances,(b) in transverse impedances.

The RF system using thirty-two single-cellcavities is adopted for the SPring-8 storage ring. Thecavities were designed to be spherically-shaped inorder to reduce the HOM impedances. We are going tofabricate a model cavity and confirm the RFcharacteristics. Furthermore, high power tests using a1-MW klystron are planned to determine the detailed
specification of the practical cavities.
References

Thermal analysis of the cavity
It is important to calculate the temperature
distribution and dimensional changes in the cavity
structure and to estimate the loss in shunt impedance
resulting from the decrease of electrical conductivity.
In the RF system of the SPring-8 storage ring, 40kW of
RF power will be dissipated in the wall of the singlecell cavity. The power is distributed as shown in Fig.
7.

A general purpose computer code, ABAQUS [4], basedon the finite element method was used to calculate thethermal characteristics of the cavity. The cavity is-[1] M. Hara et al., "Storage Ring Design for the 8 GeV
Synchrotron Radiation Facility in Japan," 14thInternational Conference on High Energy Accelerator,
August, 1989, Tsukuba, Japan.
[2] M.Hara et al., "Three Dimensional Analysis of RF
Electromagnetic Field by the Finite Element Method,"
Proc .11th Int. Conf. on Cyclotrons and theirApplications, pp.337-340, 1987.
[3] H.Kobayakawa et al., "Critical Test of CoupledBunch Instability Theory," Jpn. J. Appl. Phys., 25,
pp.864-874, 1986.
[4] Hibbitt, Karlsson & Sorensen, Inc., "ABAQUS User'sManual," 1988.

85-