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

BEAM BASED SEARCH FOR LINEAR IMPERFECTION FIELDS IN 11 M
LONG UNDULATOR AT NEWSUBARU
Y. Shoji, S. Miyamoto, M. Niibe, S. Hashimoto, and A. Ando,
NewSUBARU/SPring-8, LASTI, Himeji Institute of Technology, 678-1205, Japan

Abstract
The NewSUBARU storage ring has an 11 m long,permanent magnet planner undulator. We adjusted its
magnetic field distribution to minimize the imperfection
fields mainly by an in-situ sorting method developed by T.
Tanaka et al. of SPring-8. The imperfection fields wereminimized for each of eight units to prevent them fromexciting unnecessary betatron resonance in the ring. We
measured the gap dependence of linear imperfection
fields, dipole and quadrupole field components, using thestored electron beam in the ring. The results confirmedthat the field adjustment reduced the imperfection fields.
Strengths of the dipole imperfection fields in theundulator were at the same level as the earth field. The
normal and skewed quadrupole imperfection fields wereabout three times of the guideline, but were smaller than
the imperfections produced by the ring magnets.

1 INTRODUCTION

focusing quadrupoles, etc. These are shown in Table 2.
The LU is separable into eight units and the integrated
imperfection field through each unit should be small.
Setting the limit to the integration through all eight units
was insufficient because the betatron phase advances
through the LU were 140O and 50O in horizontal andverticaldirections,respectively;
twoopposite
imperfection fields can never be cancelled out if they areapart. The details of this field adjustment is explained inanother report of this proceedings [4].
After the adjustment, the beam life and the injection
efficiency improved to approximately 80% of those withthe gap opened. A part of the reduction of the beam life
by 11% was explained by the modulation of the verticalbeta function produced by the intrinsic focusing of the LU[5]. The improved spectral line was reported by M. Niibe
et al. [6] at SRI’03.
The gap dependence of linear imperfections in the LU
was measured by observing the electron beam behavior in
the storage ring, at points before and at after the second
adjustment. Here we report the reduction of dipole andquadrupole imperfection fields with respect to the secondadjustment.
We performed some measurements on the strength of
non-linear imperfections of LU before the adjustment [7].
However non of them were definite or quantitative proofof the existence and we do not report about them.

The synchrotron radiation facility NewSUBARU [1] isan EUV and Soft X-Ray light source at the SPring-8 site.
The Laboratory of Advanced Science and Technology forIndustry (LASTI) at the Himeji Institute of Technology isin charge of its operation collaborating with SPring-8.
The ring has two operation modes: In the 1.5 GeV mode,the beam is accelerated to 1.5 GeV and stored. In the 1.0
GeV top-up mode, the beam current is kept at2 MEASUREMENTS
250±0.15mA by an occasional injection with theThe LU’s normal dipole imperfection field (∆By) wasundulator gap closed.
calculated
from the currents of the steering magnets,
A permanent magnet, planner type, out of vacuum
wherec.o.d.
was corrected to zero. The skewed dipole
10.8 m long undulator (LU) [2] is set at one of the longimperfectionfield(∆Bx) was calculated from the changestraight sections of NewSUBARU. The main parametersofhorizontal
c.o.d.
The imperfections are expressed byof LU are listed in Table 1. In the initial adjustment of theLU’s magnetic field, our effort was focused on the kicks (dX' in the horizontal and dY' in the verticalundulation phase to obtain a good undulator light, not on direction) and displacements at the center of the LU (dXthe reduction of multi-pole imperfection fields. Upon in the horizontal and dY in the vertical direction). The
commissioning the LU, we found that its
Table 1: Main parameters of the LU.
considerably large imperfection field
Table 2: Guidelines on theplanner,Type
reduced the beam life and the injection
acceptable integrated
outofvacuum
efficiency of the ring down to about 60%
imperfection field for the ringpermanent
Magnetof those with gap opened. Following that,magnets.
Nd-Fe-B
the second field adjustments took place inField
TypeGuide Line
200
Number of Periods
2001, using SPring-8’s field measurement
Dipole4× 10-4 T m
54mm
Period Length
system [3]. The acceptable strengths of theQuadrupole
7× 10-3 T/m m
10.8m
Total Length
integrated multi-pole imperfection fields
were set at the same level as those of theSextupole
0.3 T/m2 m
119-30mm
Gap
ring magnets, bending dipoles, and3K

0.3 - 2.5Octupole

10 T/m m

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

0.1

0.2

0.5

0.05

0.1

0.4

0.5
(before)dY'dY(after)

0.4

dY'dY

00.3

-0.05

-0.1

0.2

0.2

-0.1

-0.2

0.1

0.1

-0.3

00-0.4-0.1

00.3

component, the difference between them (DIFF), areplotted in Fig.3. In addition to this measurement, theimperfection was also estimated by making vertical local
bumps in the LU and observing the change in thehorizontal c.o.d. The results of the two measurements
were consistent with each other [8].
0.012

SkewQ (mrad/mm at 1.0GeV)

results are summarized and shown in Fig.1
Normal quadrupole field imperfection was estimatedfrom the gap dependence of betatron tune, and the resultsof the measurements are shown in Fig.2. After theadjustment, the vertical tune shift agreed with thecalculation within the margin of uncertainty of the ringlattice model. The field imperfection could be estimatedfrom the horizontal tune shift, which was negligibly small
in the calculation. However, the disagreement between
the data at 1.0 GeV and at 1.5 GeV, because of themeasurement error, was comparable to the shift by theimperfection field

0.01(before) (after)
SUM
SUM
DIFF
DIFF

0.008
0.006
0.004
0.002
0-0.00220(before)(after)

dX'dX

dX'

-0.2
204060dX-0.220406080 100gap (mm)-0.2
120 140dY (mm)-0.580 100 120 140gap (mm)dX (mm)dX' (mrad)

-0.25

-0.1

dY' (mrad)-0.15

Figure 1: Horizontal (left) and vertical (right) dipole kickerrors vs. LU gap at 1 GeV. They are defined to be zero atan LU gap of 120 mm. The non-zero points at the 120
mm gap represent changes of errors by adding a magnetic
shield to the undulator field. The open symbols, circles
and squares, represent the error before the adjustment,
while the shaded symbols represent the error after theadjustment. The lines are the fitted functions using Eq. (1).
1.0 GeV

sub-integer part of t he tune

0.3

νx-6 (after)

0.27

νy-2 (before)

0.25

νy-2 (after)

0.23

0.18

νy-2 (after)
νx-6 (before)

0.14
20

4060

80

100gap (mm)1201400.21204080 100 120 140

gap (mm)Figure 3: A pair of skew Q magnets are set at both ends ofLU. The symmetric component, SUM = sum of two(circle), and the asymmetric part, DIFF = difference oftwo (square) are plotted. They are defined to be zero atthe LU gap of 120 mm. The non-zero points at the 120
mm gap represent changes of imperfections by themagnetic shield to the undulator field. The open symbols,
circles and squares, represent the imperfection before theLU adjustment, while the shaded symbols represent theimperfection after the LU adjustment. The lines are thefitted functions. The gap dependence was not measured
before the LU adjustment.

3 ANALYSIS

AO+AGAP(G-120)/100+AK1(K-K120)+AK2(K2-K1202). (1)

0.26

0.22

60

The gap dependences of imperfections wereparameterized by fitting with the following function,

1.5 GeV0.29νx-6 (after)

4060

80100gap (mm)120140Figure 2: The gap dependence of the betatron tune at 1.0GeV(left) and at 1.5 GeV (right). The open symbols,
circles and squares, represent the imperfection before theadjustment, while the shaded symbols represent theimperfection after the adjustment. The lines are the fittedfunctions. The tunes at the 120 mm gap were set at
different points at before and after the adjustment. Thereis no data for 1.5 GeV before the adjustment.
The skewed quadrupole imperfection was estimatedfrom the gap dependence of the correction magnet’scurrents. These magnets were a pair of correction magnets
set at the both ends of the LU. Those were adjusted toeliminate the coupling resonance: νx-νy=4. Here, νx andνy are vertical and horizontal tunes. The symmetriccomponent, the sum of them (SUM), and the asymmetricHere, AGAP, AK1 and AK2 were fitting parameters, while K
is a K parameter of the LU. The gap G is measured inmillimeters, and K120 is a K value at G=120. One moreparameter, AO, not obtained by the fit, is the imperfection
when the gap is opened (G=120). The results of the fit aresummarized in Table 4.
We had observed large dipole imperfections (dY anddY') and skew quadrupole imperfections with the gap
opened (AO terms); however, they almost disappeared
after the adjustment. The considerable imperfections,which were proportional to the gap (dY' and the tune shift
were observed), also disappeared. The large quadrupole
imperfection before the adjustment was thought to be themain reason why the beam life had been worse.
The moments of integrated imperfection fields along
the azimuthal direction (s) were calculated from theresults of the above measurements. The results at 35mmgap, after the adjustment, are listed in Table 5 with theresults of field measurements using a flipping coil.
The dipole imperfection fields after the adjustment
were small enough, even smaller than the contribution of
the earth field. The normal quadrupole imperfection

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

calculated from the beam based measurement and thatfrom the flipping coil measurement agreed within themeasurement error, however the error was the same level
as the guideline. They were roughly three times of theguideline at the gap where the adjustment did not takeplace. The asymmetric skew quadrupole imperfection waslarger than the expected from the flipping coilmeasurement, roughly three times of the guideline.
However, those normal and skewed quadrupole
imperfections were smaller than the harmonic
imperfections produced by the ring magnets, 0.2 T ofnormal quadrupole and 0.04 T of skewed quadrupole.

4 CONCLUSION
The measurement of the beam behaviour confirmed thatthe second field adjustment was effective. As far as we
see the linear imperfection fields, the residual
imperfections are at the acceptable level.

5 ACKNOWLEDGMENTS

the field without their support and help. We also thankmembers of the SPring-8 accelerator division for theirsupport to NewSUBARU.

6 REFERENCES[1] A. Ando et al., J. Synchrotron Rad. 5, 342-344 (1998).
[2] S. Hashimoto, et al., Nucl. Instr. Meth. A467-468 (2001)
141-144.

[3] T. Tanaka, T. Seike and H. Kitamura, Nucl. Instr. Meth.
A465 (2001) 600-605.
[4] Y. Shoji, et al., "Magnetic Field Correction of 11m Long
Undulator at NewSUBARU", this proceedngs.
[5] Y. Shoji, "Improvement of beam life time by an optimizationof vertical orbit and a correction of a modulation of verticalbeta function at NewSUBARU", this proceedings.
[6] M. Niibe, et al., "Characterization of Light Radiated from 11m Long Undulator", SRI’03, to be published as AIP
Conference Proceedings.
[7] A. Ando, internal report (in Japanese).
[8] Y. Shoji, "Methods of Searching Skewed Quadrupole
Imperfection Field along the Straight Section", thisproceedings.

The authors thank Dr. T. Tanaka and Prof. H.
Kitamura of the SPring-8 (RIKEN). We could not adjust

Table 4: Parameters of gap dependence of the linear imperfection fields. The values for before and after the adjustment
are separated by arrows (befor−>after). The fittings were good, as shown by the figures. Where we have no data thecolumn in the table is blank. We used three free parameters for the fit if they were necessary, although this was notalways the case. When that happened, the column on unused parameter remained blank. The vertical tune shift after theadjustment was consistent with the calculated shift. The calculated horizontal tune shift was negligibly small, and thevalues listed below represent either field imperfections or measurement errors.
Field Imperfection
Dipole Kick(mrad)
Dipole Displacement(mm)
Tune Shift at 1GeV
Tune Shift at 1.5GeV
Skew Quadrupole(mm/mrad)

AO

AGAP

AK1

dX'

0.02−>0.05

0.04 −> 0.029-0.11−> 0.026

dY'dXdY

0.31−>0.01
0.01−>0.00
0.47−>0.15

0.23 −> 0.014
0.27 −> 0.13
0.10−>-0.11
8.6−>1.6-22.0−> -0.6

0.14−>-0.024-0.12 −>-0.01-0.28 −> -0.16

νXνYνXνYSUMDIFF10−> 1-3−> 0−> 1.8−>-1.6−> 1−>12−> -1−> 25

AK20.20 −> 0.08
-0.02 −> -1.12
34.3 −> 19.8−>0.67−>10.4−> -6−>7

Table 5: Residual imperfection fields at after the second adjustment. The measurements with the flipping coil took
place with 30mm gap (G = 30) before the re-installation of LU. The imperfections calculated from the beam behavior
were those with G = 35. Here ∆By'=d∆By/dx and ∆Bx'=d∆Bx/dx. The ³∆By'ds by the beam based measurement is avalue for ³∆By'βXds /<βX> at 1.0GeV. According to the measurement at 1.5GeV, ³∆By'βXds /<βX> = 0.003 at G = 35
and ³∆By'βXds /<βX> = 0.000 at G = 30.
Field Imperfection

Guide Line
Flip-Flop Coil Meas.
Beam based Meas.

Dipole Imperfection ( 10-4Tm)³s ∆By ds³∆By ds³s ∆By ds ³∆By ds<»s⏐><»s⏐>44-2.4-1.8-0.3
1.4-1.4
0.3

Quadrupole Imperfection ( T )³s2∆Bx'ds³∆Bx'ds³s ∆Bx'ds
<s2>
<»s⏐>
0.007
0.007
-0.0007-0.001(<0.017)-0.003-0.021-0.002³∆By'ds