The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

Transverse Kick by RF Cavities Observed in the SPring-S Storage Ring
K. Soutome*, R Ego, T. Ohshima, J. Schimizut, M. Takao, H. Tanaka, H. Ohkuma
SPring-8, Hyogo 679-5198, JapanAbstract
In the SPring-S storage ring a stored electron beam isdumped by lowering the RF voltage and hence the RF
bucket height. During this sequence an orbit distortion ofthe order of a few tens JJID was observed. The harmonicsof this distortion correspond to the horizontal and verticalbetatron tunes. The kick source seemed to be at the RF
section where the RF voltage was changed. We then carried out machine studies on this phenomenon, analyzed themeasured orbit changes to deduce a transverse kick angle
and finally found that a field distortion of the accelerating
TMOlO mode ofRF cavities can generate such a transverse
kick. The distortion is a result of the symmetry breakingof the RF cavities caused mainly by a coupler port and afrequency tuner attached to them. The magnitude and direction of the experimentally deduced kicks were found tobe in good agreement with the calculations by MAFIA.

1 INTRODUCTION
In an SGeV electron storage ring at SPring-S the lattice has
four-fold symmetry and correspondingly there are four RF
accelerating sections (RF-A, B, C and D stations) in thering. Each station has eight cavities and can give the maximu~ RF voltage of about 4.0-4.5MV. In usual beam operatwn the voltage of each station is set to be 4.0MV andthe total value is 16.0MV. On the other hand, the one-turnl~ss of the beam energy is about S.9Me V. We are then possible to store the beam with three RF stations at 12MV withenough beam lifetime, since the momentum compaction
factor is small ("'0.000146).
We sometimes change the RF voltage to dump the storedb~am and in machine tuning. By comparing the closed orbit before and after this change, we found that a transverse
kick is generated at the RF section. To understand this phenomenon, we performed machine studies and found thatthe magnitude of the transverse kick is proportional to theamount of change in the RF voltage and the direction of thekick is the same for all RF stations.
One might think that there can be a possibility that thedirection of the electron beam passing through cavities isdifferent from the axis of RF acceleration and has a crossing angle. However, by simple estimations, we see that themagnitude of a transverse kick by such a cause is muchsmaller than observed experimentally.
Another possible explanation will be the distortion ofthe accelerating TMOlO mode. We then calculated the; Corresponding author; Email: soutome@springS.or.jp
Permanent address: The Japan Research Inst. Ltd., Osaka 550-0013

electro-magnetic fields in the RF cavity by using MAFIA
and found that the order of magnitude and the direction of
the experimentally observed kick can be explained by thisfield distortion effect.
In the following we present the results of field calculations and compare the kick angle with experimentally deduced one. We also discuss how the transverse kick contribution is extracted from measured closed orbit data. After
subtracting the kick contribution we see that the residual
orbit change in the horizontal direction agrees well withsimulation results obtained by considering the energy loss
at magnets and the energy gain at RF cavities.

2 FIELD CALCULATIONS
In each RF section of the storage ring eight bell-shaped
single-cell cavities are installed[!, 2]. Each cavity has
an RF input coupler, a frequency tuner for the accelerating TMOlO mode (TMOlO-tuner), a tuner for higher-ordermo~~ (HOM-tuner) and a plunger with a fixed length. The
position of the TMOlO-tuner is automatically adjusted in~earn operation within a range of a few mm and the positwn of the HOM-tuner is usually fixed. The coupler port
and the TMOlO-tuner are settled along one direction andthe HOM-tuner and the plunger are settled along anotherdirection perpendicular to the former. RF cavities with ah?rizontally ~irected RF input coupler and with a verticallydirected RF mput coupler are arranged alternately in thetunnel of the storage ring.
In order to simulate the field distortion in the cavity we used MAFIA and calculated a longitudinal shunt
impedance RL and a transverse shunt impedance RT ofTMOlO mode. Since the cavity structure is complicatedas explained above, it is difficult to perform a full model
calculation with a huge number of mesh points. We thenadopted a simple cavity model having the coupler port witha diameter of llOmm and the TMOlO-tuner. The HOMtuner and the plunger were neglected, since the HOM-tuner
position is fixed and its value is almost the same as theplunger position on the opposite side. This cavity model
has a symmetrical structure and can be divided into four
equiv~lent p~eces. w~ then performed calculations by using
one piece wtth four times larger number of mesh points[3].
In this model the field distortion of the TMOlO modeoccurs in the direction of the axes of the coupler port andthe TMOlO tuner. The transverse kick is also generated
along this direction.
The transverse kick (JT can be calculated from RL andVv/2RT/(kRL), E isVT/ E, where VT
RT as BTvoltage and k is theacceleration
theis
the beam energy, VL-313-==

The 13th Symposium on Accelerator Science and Technology, Suita, Osaka, Japan, October 2001

0.1

wave number of the 1M010 mode. The results are shownin Fig. 1 for the case of VL = 500kV.

! Horizontal[4MV.
:3MV0.05e!

VL = SOOkV

6--TiMV.
'lMV0~·0.05-O.l0288

2162880.02
L __ _L __ _L __ _L __ _L __ _L __ _L __ _L_~

102030TMOlO-Tuner Position [mm]400.01

Iq

Figure 1: Voltage in the transverse direction due to fielddistortion of the 1M010 mode (calculation by MAFIA).
In Fig. 1 VT is plotted as a function of the 1MO 10-tuner
position. The acceleration voltage of 500kV per cavity corresponds to 4MV per one RF station. The kick voltage andthe kick angle in the transverse directions of each RF station are summarized in Tablel.
Table 1: Calculation results of the voltage and the kick inthe transverse directions (H: horizontal, V: vertical) when
the acceleration voltage VL is 4MV at each RF station.
station VH[kV] Vv[kV] BH[pnad] Bv[J.trad]
A
16.5
16.4
2.1
2.1
B
15.0
15.0
1.9
1.9
c
14.9
16.1
1.9
2.0
D
16.2
15.8
2.0
2.0

0

-0.01

-0.02
0144
BPMNumberFigure 2: Orbit change when the voltage of the RF-A station is increased from OMV to 4MV.
The effect of this local energy balance can be seen bycomputer simulations. Since we developed a 6-by-6 simulatioh code[4], we can calculate the local beam energy andthe closed orbit when the RF voltage is varied.
We show in Fig. 3 the local beam energy for the twocases: an ideal ring with RF-A station on(A:4MV, total:16MV) and off(A:OMV, total:12MV). The energy difference between the two cases generates the horizontal orbit shift in dispersive sections. This shift is shown in Fig. 4by the solid line.

COMPARISON WITH EXPERIMENTS

As explained in the introduction, we carried out machinestudies and changed the voltage of one RF station in therange between OMV and 4MV. By comparing the closed
orbit before and after this change we can estimate the magnitude and direction of the kick generated at the RF section.
In Fig. 2 we show the difference of measured closed orbits along the whole ring when the voltage ofRF-A station
is increased from OMV to 4MV. The upper graph shows
the horizontal orbit change and the lower shows the verticalone. We see that both horizontal and vertical orbit changebecome large as the voltage becomes high. We can obtain
similar results as in Fig. 2 when a voltage of the other RF
station is changed.

3.1

216

BPMNumber03144

02

Energy Balance along the Ring

6x6 Tracking Simulation

>

RF-A

6" 8001 t:"·· ..._£ll 8000"=""e 7999=" 7998..

7997
0359

718

1077

1436

Path Length [m]Figure 3: Local beam energy in an ideal ring with RF-A
station on and off obtained by tracking simulations.

3.2

The horizontal orbit shift shown in Fig. 2 contains contributions from a change of the local energy balance along thering. It is determined by the energy loss at magnets and theenergy gain at RF cavities. In order to obtain a transverse
kick by RF sections these contributions must be subtracted
from measured orbit shifts.

8002

Transverse Kick at RF Cavities

Since a simple transverse kick cannot generat¥ such a horizontal orbit shift as in Fig. 4, we can deduce a strength anda direction of the horizontal kick by assuming an amountof the kick at the RF section and fitting the measured orbit
shift.
After subtracting the transverse kick contribution from-314-

The 13th Symposium on Accelerator Science and Technology, Suita, Osakn, Japan, October 2001

0.1

i Horizontal
~0.05

I..

IR:J?:o.

~:.;.

~...=

2 f···+·····,········

I. Sf ..... , ........ :. /'.. :<01 f·+ / ; .. ,.: ... ,....

~.;:j~ 0. Sf· ···+···:..... ; ........ , ..... ··:···-0.05

iVL [MV]

-0.1

0359

1077

718

1436

Path Length [ m]Figure 4: Horizontal orbit shift due to the local energy difference where the RF-A station is on. Calculation results
are shown by the solid line. For comparison, experimental data at beam position monitors is also plotted by solidcircles.

:0=;.
';;'t

...=

<~

2 , ..... ,.... , ...

~

2~

~-1.5

<=

If··+/'

1 ,...,.. /_.. ... ,.

~~ O.Sf·····+·······,.,,, .... , ....

~ o.s,........,......... ,./··+ ......, .... .

0 o~~~~2~~3~~4~~

measured data there remains a contribution due to the local energy difference in the horizontal direction. Figure 5shows the horizontal and vertical orbit changes after subtracting a transverse kick contribution.

72144

216

VL [MV]VL [MV]

Figure 6: Transverse kick angle at each RF section deduced
from measured orbit change.
pected from the calculations by MAFIA. We also see thatthe kick angle at VL = 4MV is about 2,urad and close to
the values listed in Table 1 especially in the horizontal direction. These facts suggest that the transverse kicks at RF
cavities are generated by the field distortion of the TM010
mode.
It should be noted that the magnitude of the kick angle
in the vertical direction Bv is smaller than expected but theratio of Bv to VL is not so far from the expected value of2,urad/4MV. These values are listed in Table 2. At present
the reason for this discrepancy is unknown but will be due
to errors of fitting or an effect of HOM-tuners and plungers
which we neglected in constructing our cavity model. If
more precise calculations of the electro-magnetic field distortion become possible, this point will be clarified.

288

BPMNumber-0.01
Transverse Kick Subtracted-0.02 '-'-'-~~~~~~~.c.L.~~~..w..~~~..L.LJ
072
144
216288
BPMNumber

Figure 5: Orbit change after subtracting a transverse kickcontribution from measured data shown in Fig. 2. A sharp
spike seen in the lower graph at around the RF-D sectionis due to noise. Though hard to distinguish, there are four
curves in the lower graph corresponding to the 1, 2, 3 and
4MV difference as in the upper graph.
The data for the 4MV difference in the horizontal direction is also plotted in Fig. 4 by solid circles. We see a good
agreement between the calculation and the experimentallydeduced data. This means that we could successfully separate a transverse kick contribution and the effect of thelocal energy difference. The obtained kick angle at each
RF station is shown in Fig. 6.
The direction of the observed kick is the same as ex-Table 2: The experimentally deduced kick angle in thetransverse directions as a ratio to the acceleration voltage.
station
BH/VL
Bv /VLA
1.8 ,urad/4MV 1.8 ,urad/4MV
B
2.3 ,urad/4MV 1.2 ,urad/4MVC
2.0 ,urad/4MV 1.6 ,urad/4MVD
1.9 ,urad/4MV 1.4 ,urad/4MV4REFERENCES[1] H.Ego, et.al., Nucl. lnstr. andMeth. A400 (1997) 195.
[2] M.Hara, et.al., Proc. 1997 Particle Accelerator Conf., Vancouver, 1997, p.2971.
[3] H.Ego, unpublished note, 2001.
[4] J.Schimizu, et.al., in these proceedings.

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