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

HIDDEN COD OF NEWSUBARU
Y. Shoji, LASTI, Himeji Institute of Technology, 678-1205, JapanAbstract
We point out one problem of the orbit control of thering, a shift of horizontal COD, which is not observablewith the present beam position monitor system.

1 INTRODUCTION
The synchrotron radiation facility NewSUBARU [1] isa VUV and Soft X-Ray light source at the SPring-8 site.
Laboratory of Advanced Science and Technology forIndustry (LASTI), at the Himeji Institute of Technology isin charge of its operation, collaborating with SPring-8.
Fig. 1 shows the beta functions and dispersion function ofthe ring. The ring has two operation modes for users. In
the 1.5 GeV mode, the beam is accelerated to 1.5 GeV
and stored, while in 1.0 GeV top-up mode, the beam
current is kept at 250+0.15 mA by an occasional injection
with the gaps of undulators closed.
There exists a shift of horizontal Closed Orbit
Distortion (COD), which is not observable with thepresent beam position monitor system. NewSUBARU
storage ring has 18 horizontal electric beam position
monitors (BPM) and 18 horizontal steering magnets (sth).
The steering family is capable of setting beam position tothe centre at these BPM locations. However we are blindto the beam position between BPMs.

βX

the energy displacement then the horizontal COD appears,
which is proportional to the dispersion function. The 18
steering magnets steer the beam and get it back to theoriginal position at the BPMs although the beam position
between the BPMs and fRF do not come back to the initialstate.
In this report we explain how we proved the existence
and evaluated this hidden COD.

2 ORBIT CALCULATION2.1 Orbit Displacement
We calculated the expected horizontal orbit
displacement, the hidden COD, using the present linear
optic model at NewSUBARU.
When the beam energy is displaced by δ =(E-Eo)/Eo,
the electron beam is deflected at the bending dipole andCOD (∆X) appeared according to the dispersion function
η. Proper deflections at 18 steering magnets steer the orbitto ∆X=0 at 18 BPMs, however the orbit displacement ∆X
is not always zero at the other locations (s) than at BPMs.
This hidden COD is written by the equation,√βX
18∆X = η δ + –––––– Σ√βXNθN cos[πνX+ΨX-ΨXN].
2sinπνX N=1(1)Here νX, βX and ΨX are horizontal betatron tune, betafunction and the betatron phase. The θN, βXN and ΨXN aredeflection, beta function and the betatron phase at N-thsteering magnet. The 18 θN s are set so that ∆X =0 at 18BPMs.
The θNs and ∆X are calculated for δ=+1% using thelattice model of NewSUBARU. The results are shown inFig.2 and Fig.3.

βY(m)s(m)ηFigure 1: Horizontal and vertical beta functions (above)and the dispersion function (below) along 1/4 ofNewSUBARU.
The problem was that the control of the RF frequency
does work as the 19th horizontal steerers. This one extra
degree of freedom could change the orbit between theBPMs. The change of the RF frequency (fRF) produces∆X(mm)s(m)Figure 2: The calculated pattern of horizontal hidden
COD in 1/4 of the ring. The circles denotes the locationsof BPMs, where ∆X =0. The energy shift is δ=+1%. Thecircumference of the ring becomes smaller by 44.6mm.
This was calculated using the linear lattice model ofNewSUBARU.

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

3 MEASUREMENTS

0θN (mrad)-1

3.1 Beam Displacement at B Magnets-2-3-4-5-6
1

2

345

678

9 10 11 12 13 14 15 16 17 18

N (steering #)Figure 3: Steering kick (θN) for the hidden COD when theenergy displacement is δ=+1%. This was calculated using
the linear lattice model.

The best way to observe the shift is to measure thebeam position in a bending magnet. There exists one
beam profile monitor observing the synchrotron lightfrom a bending magnet (we refer it by SR monitor). We
intentionally made a shift like that of Fig.2. The fRF waschanged while steering magnets were adjusted so that theobserved COD at BPMs was not changed. We observed ahorizontal shift of beam profile in the SR monitor screen.

3.2 Beam Displacement at Q Magnets
The shift of the RF frequency (∆fRF) was absolutelydifferent from that expected from the energy displacement(δ) and the momentum compaction factor (α). The shiftby the hidden COD is calculated by∆fRF –∆L1
∆X–––– = –––– = ––– ³ ––––- ds .
fRF0L0L0ρ

(2)

Using the parameters of NewSUBARU, calculation gives∆fRF/fRF0 = 0.0372δ , while α=0.0014. For the same δ thehidden COD produces much larger ∆fRF with opposite
sign.

2.3 Tune shifts
The hidden COD shifts the betatron tune through twoprocesses; a change of focusing force of Q magnets by theenergy displacement (∆νNAT ), and the orbit displacement
at the sextupole field (∆νSEXT ). The horizontal and vertical∆νNAT are calculated from the natural chromaticity. The∆νSEXT are separately calculated for the sextupolemagnets (∆νSEXT-M ) and for the sextupole component at
the edge of B magnets (∆νSEXT-B ). The results ofcalculations, using the present parameters ofNewSUBARU, are listed in Table 1.
Table 1: Betatron tune shift by the hidden COD.
The values with * are the shift corresponding to ∆fRF of 30 kHz.
calculation
H -11.67
V-5.55
H-0.45∆νSEXT-B /δ
V2.26
H -12.12∆νNAT+-3.29∆νSEXT-B )/δ V
H-4.54∆νSEXT-M /δV 13.45
18.7∆fRF /δ (MHz)measurement∆νNAT /δ∆νNAT+∆νSEXT-B *∆νSEXT-MHVHV∆fRF* (MHz)

0.014
0.005
0.00
0.025
-0.03

The other way was to use quadrupole magnets as abeam position monitor. We changed the strength of one Qfamilies (Q3) between the bend and the inverse bend by0.0043 mrad/mm (reduced the horizontal focusing). Thereare three Q3s in 1/4 of the ring, at s=12.4m, 15.8m and28.0m in Fig.1. The orbit displacement at Q3 makes adeflection. The strength and locations of the deflection
was obtained by analysing the change of COD, assumingthat the error locations were at the steering magnets (sth).
The results of the analysis are shown in Fig.4. Thelocations of Q3 families are close to the sths numbered 2,5, 8, 11, 14 and 17. All of deflections at these 6 locations
were negative, which means that ∆X<0 at all locations ofQ3. The averaged kick at Q3 was 0.0019mrad. Then theaveraged ∆X at Q3 was estimated as -0.44mm. This meanthat δ= 0.13%.
1error kick( µ radian)

2.2 Shift of RF frequency

0-1-2-3-4-512345678

9 10 11 12 13 14 15 16 17 18error location (N=steering #)Figure 4: Result of the error analysis for Q3 change of0.0043mrad/mm. The locations of Q3 families are close
to the locations of #2, #5, #8, #11, #14 and #17 in thefigure.

3.3 Horizontal Steering Pattern
The horizontal steering deflections at that time,
including the deflections to cancel the dipole field error,
is shown in Fig. 5 together with the expected for∆E/E=0.13%. The hidden COD explains why most ofhorizontal steering magnets had negative deflections.
If this estimation was correct, the RF frequency would
be 24kHz higher than that of the ideal orbit. The lightsource point in the bend would be displaced by -0.9mm at
the maximum

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

March 2001

3.5 Tune ShiftdP/ P=0.13%

The tune shift by the hidden C.O.D. at the sextupole
magnets were measured by comparing the betatron tunes
with sextupole magnets turned on and off. The results arelisted in Table 1 as ∆νSEXT-M, which were consistent withthe energy displacement of δ≈0.15%.

0.6steering kick (mrad)

0.4
0.2
0- 0.2- 0.4- 0.6

3.6 Shift of RF frequency

- 0.8
-1
12345678

9 10 11 12 13 14 15 16 17 18steering #Figure 5: Horizontal steering pattern in March 2001 andthe calculated steering pattern for the hidden COD
corresponding to δ=0.13%.

3.4 Time Drift
We observed a shift of fRF in a long time range. An
analysis of the steering pattern would make it clear if theshift of fRF came from the hidden COD or the groundmotion. The steerings were grouped into three, six at thedispersive sections (#2, #5, #8, #11, #14 and #17; group“IB”), four at the non-dispersive long straight sections (#3,#4, #12 and #13; group “LSS”), and eight at the nondispersive short straight sections (#1, #6, #7, #9, #10, #15,#16 and #18; group ”SSS”). The shifts of the averages ofsteering deflections of each group for more than a month
are shown in Fig.6 (a) with the shift of fRF. The plot of
deflections with respect to the shift of fRF made it clearthat the most part of the shift of fRF was explained by thehidden COD.
(a)-0.1

fRF
group SSS

6-0.15-0.2-0.25

54-0.3

Apr 19Apr 25

Apr 11group IBdateMay 17
May 22fRF -499950 (kHz)7

Averaged deflection of each steering group (mrad)group LSS
83(b)

-0.05

9group LSSgroup SSS

group IB-0.35

56

7

fRF-499950 (kHz)

Figure 6: Time drift fRF and the horizontal steering pattern.
The left (a) shows a typical drift in 40 days. The right (b)is the re-plot of the same data to see the correlation of theshifts of fRF and the steering. The straight lines are not thefit but the prediction from the calculation of hidden COD.

We raised the fRF by 30kHz keeping ∆X=0 condition atBPM location. The displacement at Q3 became very small,but was still existed. The betatron tune shift by thischange is listed in Table 1. This shift was consistent with
δ≈ 0.15%.

4 CONCLUSION
The existence of the hidden COD at NewSUBARU wasconfirmed. That produces an shift of fRF more than 30kHz, and the energy displacement of more than +0.15%.
The horizontal displacement in the bending magnet
amounts to about -1mm.
The other problem was that the hidden COD made thefRF not stable. We developed a steering control programwith which the COD is adjusted to zero keeping fRF in
499955500+300 Hz.

5 REFERENCES[1]A. Ando, et al., J. Synchrotron Rad. 5, 342-344 (1998).