The 9th .Qymposium on Accelerator &ience and Technology, Tsukuba, Japan1993

Broad Band Impedance of the SPring-8 Storage Ring
T. Nakamura
RIKEN-JAERI SPring-8 Project Team
Hirosawa 2-1, Wako-shi, Saitama JAPAN

Abstract
The broad band impedance of the vacuum chamber of theSPring-8 storage ring was estimated with analytical andnumerical methods.
The vacuum chamber consists of the beam chamber andthe slot-isolated antechamber. The effects of the slot and theobstacles in the slot are estimated numerically.

I. INTRODUCfiON

The impedance obtained is shown in table 2. In thistable, the elements which have negative imaginary value
produce the inductive wake functions and their impedancee aer
assumed of the form Z = - i ro L.
The shape of the impedance of the RF cavities is assumed
to be Z =A {l+i)/..Jro based on theoretical estimations[?].
The L and A can be obtained from the peak value of wake
functions and the loss parameters.and both of them can becalculated with MAFIA Tim.
The theoretica value of the impedance of the slot[?]
between RF contact fingers used in the bellows and valves areof the order of -i Ixl0-4 [0] and we neglect it in Table 2.

The SPring-8 storage ring, which is 8-GeY
electron/positron storage ring for a high brilliance lightsource, should have flexibilities of the operation to meet thevariou~ requirements of the users oflight, including the highsingle bunch current.
To store such a high bunch current beam, the broad band
impedance of the storage ring should be kept lower as possible
to avoid the instabilities, to minimize the loss of the beamenergy and to avoid heating of the elements.
1c2 rThe c1esign value of the bunch current of the SPring-8_ _ _ _ n....:;.
_ j _ _ _ ~r::::storage ring is 5mA/bunch with less than 2 times higher valueof the energy spread than the natural.
To meet this requirement, the vacuum chamber iscarefully designed to reduce the discontinuities inthe beamchamber and adopt the antechamber scheme[!] for pumping
systems to reduce their effect on the beam.
The estimation of the impedance is performed with sometheoretical and approximated equations and with thesimulations by two and three dimensional codes of MAFIA
0 1 : k•T2 and T3[2], respectively.
Figure 2. The vacuum chamber cross section
In numerical simulation with MAFIA T2, theapprox[mation that the bear:~ chamber has round shape ofII. LOSS PARAMETERS OF t:LEMENTS
20mm radius while the real shape is ellipse of 20mm x35mm, and several models of the wake factions such as
The loss parameters of elements are estimated wilh thecavity like, inductive and resistive are assumed.
simulation with MAFIA T2/T3. The loss parameters areThe effect of the obstacles in the slots and antechambers related to the power lost at the elemnts and we can estimate
such as absorbers, pumping holes and NEG pumps are also the stregth of the heating of the elements by the beam.
estimated numerically with MAFIA T3 and S3.
The total loss parameters per tum are shown in the end ofTable3
II. IMPEDANCES OF ELEMENTS
The parasitic power loss in the elements is also calculatedwiththese loss parameters and listed in Table 4.
The impedance is estimated with some analyticalWith
this values, the voltage loss of the stored electrons
equations based on theories and experience for small gaps,
perturnare1.98 MY, 0.88 MY and 0.42 MY for bunch
shallow transitions, slots and cavities, and also estimated withlength3mm,5mmand IOmm, respectively.
numerical methods with MAFIA T2/T3 assuming several
Ther.m.s.
bunchlength is estimated to be 4mm - 5mm
model shapes of wake functions[3,4,5,6].
at
low
bunch
current
andwith the natural energy spread. But
The shape of the structures is modeled as Figure I. and thethepreliminary
resultof
the tracking simulation with thevalues of the parameters a, b, g, 81 and 82 of the elements areimpedance
showninFigure
2, the potential distortion caused
listed in Table I. They are the values at the worst case and theby
theinductancecomponentof the impedance may lengthens
vacuum group keep the real value below them.
the bunch to neary IOmm.

gI~e.

bu....;____._,:-324-ea

Table 3
Lo sspararneters o f a smg1e e ements
loss parameters [V /C]

Table 1
Dimension of the structures in the vacuum chamber
8281
gba3 mm

5 mm

10 mm

an RF cavity

8.07E+ll

6.43E+ll

4.82E+l1

90

a weldment

5.02E+09

2.78E+08

1.88E+07

9045a nange

6.61E+08

8.09E+07

7.58E+06

90.....()

an offset

2.81E+09

8.69E+08

1.21E+08

an ID section

8.46E+l0

1.07E+l0

1.26E+09

10

a transition at RF

8.57E+ll

1.56E+ 11

1.16E+l020

heightxlcngth is 2mmx5mm

an absorber at RF

2.56E+ll

l.22E+11

3.87E+l0transitions 1t RF

2050-1010

bellows

6.83E+l0".56E+l03.07E+09

absorbers at RF5035-

1010

A valve

1.50E+l0

6.04E+09

9.60E+08

bcllows"',T20251451010a slot opening

9.65E+08

1.08E+08

1.88E+06

Total (One Tum)

8.28E+l3

3.69E+l3

1.77E+l3

[mm]

[mm]

[mm]

[dcg]

[dcg]

Bunch Length[rms]RF cavities

50-2502209090

wcldments

20

220.590

nangcs r

20

220.5

offsets

20

20.5

-BPMs

20

ID sections

20

10

pumping slots-

10slot height is 10mm-12mm
20Slot to ante.and the depth is 3-4 x heightchambers
step at the top of the tapers.
outwardlmm
ahas* A bellows
t The bellows, the valves and the flanges have slots of width
0.5mm-lmm between their RF shielding fingers.
Table 2
Impedance of clements

total ?:JJ.. [n]nNumberEquations

MAFIA T2

Table 4.
Parasitic Loss Power of a single clements
at the stored current of 5mA/bunch x 20 bunch= 100 rnA
Parasitic Loss Power [W]Bunch Length[rms]

3 mm

5 mm

10 mm

an RF cavity

1.93E+03

1.54E+03

1.15E+03

a weldmcnt

1.20E+01

6.66E-Ol

4.51E-02

a nange

1.58E+OO

1.94E-01

1.81E-02

RF cavities

32

l.5xl0s 1+i
nvn

1.3x10 5 l±i
nvn

an offset

6.73E+00

2.08E+00

2.90E-Ol

wcldmcnts

2000-0.005 i-0.006 i

an ID section

2.03E+02

2.56E+Ol

3.01E+00

700-0.005 i-0.005 ia transition at RF

2.05E+03

3.74E+02

2.78E+01-0.013 i-0.019 i

an absorber at RF

6.13E+02

2.92E+02

9.28E+Ol

bellows

1.63E+02

6.14E+01

7.34E+00-0.014 ivalves

3.59E+01

1.45E+Ol

2.30E+00-a slot opening

2.31E+00

2.59E-Ol

4.50E-03

llangcs
offsets

2700

BPMs t300

ID sections

40pumping slots

6000

-360
n·-·-·-0.018 i-1-72·

transitions at RF

4n-0.005 i

absorbers at RF

12-0.007 i-0.003 i

bellows

400--0.032 ivalves(transverse slit)

100-0.004 i
20+ n-0.002 i

Slot to antechambers
resistive wall

200-86 in1.9 (1-i)-0.001 i *--0.005 i..

·-III. EFFECT OF OBSTACLES IN SLOTS AND
ANTECHAMBERS
In the slots and the antechambers, there exist many
structures such as absorbers and pumping systems such asNEG, pumping hole.

------.,;n0.026
synchrotron
radiation* Th1s value IS obtained with MAFIA T3.
t A BPM is modeled as transverse slit of gap 0.5mm wideFigure 3. The structure used to estimate the effect in theobstacles in slot.

-325-

,........
0::lC\1>
0~'-"t:.2....
(.)

t:::lt.l..

0104-<

00::lC\1>><Slot Heght-lOmm····· 12mm--- 14mm

-1-2

10-3

10100~~The total impedance of the SPring-8 storage ring isestimated to be -0.1 n for n = (J) I Wrev. - (c I cr)IWrev. - 2 X
I o4 and with this value, we estimated that the bunch currentof - 5mA I bunch can be stored with twice of the naturalenergy spread 1x1o-3 for the microwave instability.
The numerical simulation shows that the obstacles in theantechamber do not affect the stored beam and that the slo_t
opening slao small effect on the stored beam.

1010"'-4-5''....

' ,,..,

'""t

-6

10
1.0""',,

-7

c:ll

""'

t:
0~~,.

·c(.)

-8

........ +············ ---········+t:

10::l::<jt.l..

~00

12~~3Depth/Height
Figure 4. Wake Function vs. Depth I Height of the slot

Bunch Length (r.m.s.)
··ll·

4-<

00::lfor different height(from ref. [3])1073mm·+·· Smm-o- 10mm~>~+-- •• '+---- •••• -••••••••••••••• •.••••~

20

Bunch Length (r.m.s.)

40

Slot Depth [mm]·+· Smm-o- 10mm·a- 15mm

Figure 6. Wake Function vs .. Siot Depth

ACKNOWLEDGMENT
The author thanks the vacuum group of the SPring-8
storage ring for helpful discussions on the chamber structures.

4-<0306g 10C\1>

REFERENCES[1] W. Watanabe, eta!., "Vacuum Chamber and Crotch
Absorber for the SPring-8 Storage Ring VacuumChamber," submitted to The 1993/EEE Particle~0200400600
Slot Length [mm]800

Accelerator Coriference.

Figure 5. Wake Function vs .. Slot Length
The effects of these obstacles in the slot and antechamber
is estimated numerically with MAFIA T3[3]. The structures
used in this simulation with MAFIA T3 are shown in Figure
3. The size of a test obstacle is a hole of 10mm long xiOmm
deep x slot height 10mm-14mm opened to the end wall of theslot as show in Figure 3.
The effect of the opening of the slot to the beam chamber
is estimated with MAFIA T3. The results for different lengthand depth of the slot are shown in Figure 5 and Figure 6. In
them, the slot heght is 12mm.
The strength of the wake functions weekly depends on thelength and the depth of the slot

[2] R. Klatt and T. Weiland, "Wake Field Calculations with·Three-Dimensional BCI," Proc. of Linear Accelerator
Conference, SLAC, (1986) 282.1][3] T. Nakamura., "Estimation of Broad Band Impedance of theSPring-8 Storage Ring," submitted to The 1993 IEEE

Particle Accelerator Conference.
[4] S. Heifets, "Broad Band Impedance of The B-Factory,"
SLACIAP-93(1992).
[5] K. L. F. Bane, "Bunch Lengthening in The SLC Damping
Rings," SLAC-PUB-5177(1990)[6] M. Takao, T. Higo and K. L. F. Bane, "Estimation of theLongitudinal Impedance of the ATF Damping Ring,"

Conference Record of the 19911EEE Particle Accelerator
Conference, Vol. 2, pp.506-508.
[7] S. Heifets, "Broad Band Impedance of Accelerating
Structures:Perturbation Theory," SLAC-PUB-5792(1992).

IV. CONCLUSION-326-