ESTIMATION OF THE COUPLING IMPEDANCE FOR THE SPring-S STORAGE RING
T. Yoshiyuki, T. Kusaka, M. Hara, and s. H. Be
RIKEN-JAERI Synchrotron Radiation Facility Design Team
2-2S-S Honkomagome, Bunkyo-ku, Tokyo 113, Japan
Abstract
The coupling impedance of vacuum chamber components
is estimated for the SPring-S storage ring. Threedifferent approaches are discussed; analytical
calculation, numerical simulation, and measurement. The
results turn out that the contribution to the impedanceis mainly attributed to RF cavities, bellows, flanges,
and transitions to ID chambers.
Introduction
The SPring-S storage ring is under design to be a
low emittance synchrotron-radiation ring covering eventhe hard x-ray domain. High brilliance, which is
implied by the low emittance, is related to large
stored beam current in the ring. The beam current is,however, limited by the coherent instabilities ofbunched beam. The important ingredients to evaluate theinstabilities are a longitudinal coupling impedance
Z/n, and a transverse impedance Z~, the latter of which
is usually correlated to the former. The storage ringconsists of a large variety of structures which
contribute to the impedance: vacuum chambers, bellows,
gaps between flanges, step changes, box-like objects,
vacuum ports, slits of RF contacts, RF cavities, and soon. Charged particles passing through the above
components induce electromagnetic fields that act backon the beam, which results in energy losses andinstabilities. The impedance is usually employed todescribe the interaction of the beam with theenvironment. In order to estimate the effect on the
beam more precisely, a detailed impedance analysis iscarried out. In this report, we analyze thecontribution of several vacuum components to theimpedance, and suggest the way to minimize the energy
losses.
Motivation of impedance estimate
Before a quantitative estimation of the impedance,
we must get a reasonable idea on how much it can beallowed. The allowable impedance 1 Z/n 1 is , in aclassical stability criterion,! described by(1)

where a is the momentum compaction factor, E the total
particle energy, 8E/E the FWHM of relative energy
distribution, and Ip the peak current defined by
Ip = IAv 27tR
3Mcr 1(2)

IAv is the average current in M bunches, cr1 the rms
bunch length, and 27tR the circumference of the ring. n
is the ratio of storage ring circumference to thewavelength of perturbation traveling around the bunch.
For our storage ring; E = S GeV, a= 1.5 x 10-4, 8E/E =3 X 10-3 , lAY = 100 rnA, 27tR = 1,436 m, M = 1000, and q= 3.2 mm, therefore IZ/nl < 0.7 n. This quantity isrelatively small compared with the other rings, 2
indicating that the impedance problem is more serious
in our ring.

We can obtain the contribution of several simple
geometries to the longitudinal impedance analytically,
assuming a cylindrical symmetry.2 Naturally, it isfollowed that most of the vacuum components can not be
evaluated in this way owing to their complicatedgeometries.
The electromagnetic field, which is created by abunch circulating through a given section of the vacuum
chamber, can be computed numerically by means of TBCI3
and MAFIA. 4 Either TBCI or MAFIA computes wakepotentials as a function of delay with respect to thehead of bunch, together with the loss parameters, whena Gaussian-distributed rigid bunch is traveling instructures. The results of numerical computations canbe used for the longitudinal and transverse broad-band
impedances, z11 (co) and Z~(co), respectively, which are
given by

1+iQ(co, __!Q_)
Z_~_(co)=Rs-'- co,co co,

co 1+Q2(~-_!Q_)2
co co,, (3)where Rs is the shunt impedance, Q the quality factor,
and fr the resonant frequency (= cor/27t). The loss
parameters of different contributions are computed as avacuumand summed for all thefunction of cr1
elements. The de~ivation of impedance is based on thefact that the loss parameter is proportional to theintegral over the real part of impedance, according to(4)
Therefore, the parameters of a broad-band impedance(fr, Q, Rs) can be fitted to match a computed lossparameter curve.5
On the other hand, the loss parameter can bemeasured for each element of the vacuum chamber by acoaxial wire method as discussed later. In principle
every geometry can be measured in this method, but it
is impossible to measure the loss parameters for all
the kinds of elements of the storage ring. Practically,
the loss parameters of most of the elements are
acquired using both methods: numerical simulations andmeasurements.
Profile of vacuum chamber elements
The vacuum chamber is designed in a racetrackgeometry of S em wide and 4 em high with a slotisolated antechamber in which NEG strips are installed
for pumping. Figure l(a) shows the H-field lines forthe first TM mode at a frequency of 4.3 GHz. Figurel(b) also indicates deep penetration of electromagnetic--~~0~00·"~~(a)4.3GHz

ToAntechamber-fPumping Slot between
Beam Chamber and Antechamber

Method of impedance estimate
Since an exact analysis of the impedance of astorage ring is impossible, some different approaches
have been developed to estimate this quantity;- analytical calculations for several simple
geometries,- numerical simulations of electromagnetic fields insome elements of the vacuum chamber, and- impedance measurements for test components.

-302-(b) 15.3 GHz

Fig. 1

Calculation of the H-fields lines for thevacuum chamber; (a) the first TM mode, 4.3
GHz, (b) higher-order mode, 15.3 GHz.

K loss longitudinal

Cavity0 0.7.,.---..-------- ---,c.

E

Cavityc.

~ 0.6

K Joss transverse(3 5.0with nose cones

~ 4.5

4.0
:;; 3.5
1i)
~ 3.0

g_ 25
2.0 +-~-.--~-.--~-.--..--1
40
30
20
10
0

Bunch length

Fig. 3Fig. 2

Calculation results
Analytical c~lcul~tion
We have estimated the impedances of the various
kinds of elements analytically: free space, spacecharge, resistive wall, bellows, flanges, pick-up
electrodes, step changes, and slits and holes. Table lshows the impedances of typical elements. This
preliminary study suggests that the bellows must be
securely screened and RF contacts are effective toscreen them. It also shows that transitions to ID
chambers and flanges must be improved to achieve thedesign goal.

Table 1 Preliminary study of the impedance foranalytical calculations
NumberFree space
Space charge
Resistive wall
Bellows(without RF contact)(with RF contact)
Flanges (1 mm gap)
Step changes
Pick-up electrodes
Vacuum pump holes

IZ/nl
(f

10 GHz)4 X 1o-6(f0.1
0.01 (f100 MHz)

0.2

912

9.0
3.9 x 1o-6
0.39

96

0.26

432

0.05
0.005

336
336

-300

(Q)

3.8 GHz)

8 ·+_td

1 =I mm.....-.... d = !50 mm

K loss longitudinal

0c. 50J~~'-'""""
400

1ii

E 20

'"
0

0

e(3 600
:;;

1ii

E 200

"'c.

'"

U)
U)

_J

d = 20.33 mm

K Joss transverse~:;; 3010-c.

Step changes

~ 40

"'c.

Cavities x 32
Flanges x 912
Step changes x 96

Step change

Flangefields into the pumping slot at frequencies above 15
GHz. A distortion of the H-field lines is remarkable
compared with the beam chamber without antechamber. In
case of a short bunch below 5 mm in length, as themodes above 15 GHz have a large contribution to theloss parameter according to Eq. (4), it may be that theslot has significant effects.
The RF contact screens the bellows to reduce theenergy losses, and keep the electric contact between
the chambers, as shown in Fig. 2. The numerous long andnarrow slits absorb the shrinkage of bellows at baking,and make between the RF contact and bellows evacuated.
We adopt the Conflat flanges for our ring. The
outer diameter gets over 350 mm in case of theconnection between vacuum chambers. The gap between
conventional Conflat flanges comes even to a few mm
with a gasket inserted, but a special flange isdesigned so as to reduce the gap below 0.5 mm for aless impedance.
There is a radius discontinuity between the normal
and insertion-device (ID) chamber. In fact, a taperedtransition is used in place of a step change between
different chambers.· Nevertheless, the calculation was
carried out assuming the step changes in the aspect ofsafety.

Impedance source

Loss parameters for cavities both with andwithout nose cones; (a) longitudinal case,(b) transverse case.

Calculation geometry

RF contact by which the bellows are screenedon the vacuum chamber.

(mm)

U)
U)

0

Fig. 420

30

Bunch length

(mm)

10

40

0

_J

0
0

20
10
Bunch length

30
(mm)

40

Total loss parameters of the whole ring for
typical components; (a) longitudinal case,(b) transverse case.

Numerical sjmulation

A 2D code, TBCI, is used to calculate the loss
parameters, assuming again cylindrical symmetry. The
simulation was carried out for longitudinal (monopole
fields) and transverse impedance (dipole fields)
independently, and applied to RF cavities, bellows,flanges, and transitions to ID chambers.
As far as RF cavities are concerned, thecalculation has been done for the single-cell cavities
both with nose cones, which have been already studied,
and without nose cones, which are under design6 as a
low impedance cavity for our ring. The loss parameters
for both cases are plotted in Fig. 3 as a function ofbunch length. We expected the loss parameters of thecavity without nose cones to be lower than those of thecavity with nose cones for every bunch length, but theloss parameters become reversed for short bunch
lengths. The HOM impedances which have a harmful effecton the beam are suppressed in the cavity without nose
cones as in Ref. 6, but the other HOM impedances seemto get larger than we expected, especially over cut-off
frequency. In either case, it turns out that thecontribution from the RF cavities to the loss parameterare inevitable.
Figure 4 shows the total loss parameters of thewhole ring, considering only the elements which havelarge contributions to the impedance. The bellows
themselves have large loss parameters, because thenumber is large (N = 336) and the shape looks like apill-box type of cavity. On the other hand, once they
are screened adequately by the RF contacts, the loss
parameters are decreased tremendously even not to beplotted in Fig. 4. It turns out that in longitudinalcase step changes have a large effect on the .impedance,and step changes and flanges do in transverse one.
However, as far as step changes are concerned, the loss
parameters are, in fact, reduced further as thetransitions to ID chambers get tapered. In case offlanges, the real loss parameters can be also reduced-303-

Cavity under test

Cavity~(t)

K loss longitudinal

0.7

00.

~
Reference chamber

~(t)

~

0.6

Q;

0.5

1D
E

~

ctl

0.4

(/)

0.3

lii
0.
en
0

_J

0.2
0
rise time
time resolution

Fig. 5< 20 ps< 1 psFig. 7

Set-up for the measurement of the loss
parameter.

at the rate of reduction of the gap, but they are stilllarger than those of the cavities in transverse case.
The impedance needs to be decreased more.
In the next step, we calculate the loss parametersof the asymmetric geometries using the 3D code MAFIA.
But as a 3D simulations have limitations such as thenumber of meshes, minimum bunch length, andcomputational time, there is some room for improvement.
Measurement of loss parameter
The coaxial wire method which has been described by
Sands and Rees7 is a widely-spread tool for benchmeasurements of beam coupling impedance. By the
introduction of a thin wire into the chamber components
under test, a surface current distribution on the innersurface of the beam pipe can be obtained, whichcorresponds approximately to the current distribution
produced by a passing bunch. When this image-current
distribution has been perturbed by a discontinuity, areaction on the wire takes place similar to that of a
perturbed wake field on the bunch.
A measurement set-up is shown in Fig. 5. A nearly
Gaussian pulse is generated with 50 ps of the minimum
pulse width by a pulse generator. It travels througheither the reference chamber with a thin wire at theaxis of beam, or a component under test of the samemechanical length. Both signals, reference signal io(t)and object signal im(t), are recorded sequentially,and stored in a sampling oscilloscope which has time
resolution below 1 ps. The data acquired into theoscilloscope are sent to a controller and then thelongitudinal loss parameter k0 (~) is calculated by(5)

RF Cavity
Reference chamber

50 ps

j)

.I

30.7900 ns

Fig. 6'31.0400 ns

30

(mm)

40

Loss parameters of the RF cavity formeasurements and numerical simulations.

where Zo is the characteristic impedance of the coaxial
line formed by the reference chamber with wire and ~the length of the Gaussian pulse. Figure 6 shows therecorded output pulses from both the reference chamber
and an RF cavity with nose cones. The measured loss
parameters are plotted in Fig. 7 together with thecalculated results by TBCI. They were obtained for four
pulse widths; about 50, 100, 150, and 200 ps. The
measurement data look somewhat overestimated, but bothmeasurement and calculation show the same distribution
property. The causes of overestimation are consideredsuch that the generated pulse didn't have a perfect
Gaussian distribution and the coaxial line in thetapered chamber didn't match well with the 50 Q cableand connectors.
Measurement method has its drawbacks: the first is
the measurement precision and the second is that theobjects are limited in number. In the next step, we
improve the measurement precision and then measure theloss parameters of a vacuum chamber with antechamber, aConflat flange, and RF contact.
Conclusion
The impedances of vacuum chamber components turns
out to be serious problem in our storage ring. A
special attention has to be paid on the design of eachcomponent in order to achieve the designed performance.
The most critical elements have been found to betransitions to ID chambers, flanges, and RF cavities.
However, the transitions to ID chambers are, in fact,
tapered smoothly and the impedance gets small. On theother hand, the impedance of bellows can be reduced
sufficiently by screening them with RF contacts.
We have estimated the impedance in three ways:
analytical calculation, numerical simulation, andmeasurement. The analytical calculation is only
preliminary and limited to simple geometries. The
numerical simulation and measurement also have many
limitations. We need to estimate almost all the vacuum
components of the storage ring by using three ways.
From now on, we have to advance the calculation
efficiency and have a plan to employ a 3D code, MAFIA.
We also have to improve the measurement precision andestimate the other vacuum components: a crotch, gate
valve, and so on.

!400 mV

References------:---+
r

20

Bunch length10I31.2900 ns

Recorded output pulses Io(t) for thereference pipe and Im(t) for the RF cavity.

E. Keil and W. Schnell, CERN-ISR-TH-RF/69-48, 1969.
A. G. Ruggiero, BNL Informal Report, Aug. 1979.
T. Weiland, Nucl. Inst. Meth. 212, 1983.
R. Klatt, et al., Proceeding of the 1986 Linear
Accelerator Conference, SLAC, 1986.
5. B. Zotter, CERN LEP-TH/87-34, 1987.
6. T. Kusaka, et al., presented at this symposium.
7. M. Sands and J. Rees, SLAC-report PEP-95, 1974.

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