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

MAGNETIC FIELD ADJUSTMENT OF 11M LONG UNDULATOR
Y. Shoji, S. Miyamoto, M. Niibe, LASTI, Himeji Institute of Technology, 678-1205, Japan
T. Tanaka, H. Kitamura, SPring-8, RIKEN, 679-5198, 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. The LU isseparable into eight units and the imperfection fields werereduced for each of eight units to prevent them fromexciting unnecessary betatron resonance in the ring.

1 INTRODUCTION
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. A
10.8 m long undulator (LU) [2] is set at one of the longstraight sections of NewSUBARU. The main parametersof LU are listed in Table 1. In the initial adjustment of theLU’s magnetic field, our effort was focused on theundulation phase to obtain a good undulator light, not on
the reduction of multi-pole imperfection fields. The gapsof each magnet pole were adjusted to give good field
distribution. However upon commissioning the LU, we
found that its considerably large imperfection field
reduced the beam life and the injection efficiency of thering. Following that, the second field adjustments took
place in 2001, using SPring-8’s field measurement system.
In 2001 we adjusted not only the beam orbit andphase but also reduced multi-pole field components. The
field was adjusted mainly by flipping or exchanging
magnets in LU [3]. A use of shim plates were limited toan adjustment of skew quadrupole field component. The
acceptable strengths of the integrated multi-pole
imperfection fields, listed in Table 2, were set at the samelevel as those of the ring magnets. Setting the limit to theintegration through the undulator was insufficient because
the betatron phase advances were 140O and 50O in
horizontal and vertical directions, respectively; twoTable 1: Main parameters of the LU.
TypeMagnetplanner,out of vacuum
permanent
Nd-Fe-B200opposite imperfection fields can never be cancelled out ifthey are apart. The LU is separable into eight units andthe integrated imperfection field through each unit should
be small.
The guideline of acceptable level for the photon
spectrum was that 7th harmonic light should be usable.
After the adjustment, the beam life and the injection
efficiency improved to approximately 80% of those withthe gap opened. Beam based measurements of linear
imperfection field proved the improvement of the field [4].
The 1st harmonic spectral line width agreed with thecalculation [4]. Here we report on our second fieldadjustment of LU.

2 FIELD MEASUREMENT SYSTEM
2.1 Field Measurement
We use Cartesian coordinate with the photon
propagation axis as a z direction, the horizontal axis as x
direction and the vertical axis as y direction in thefollowing discussions.
The integration of multipole field through 4 units weremeasured by 6-m long flipping coil. The tension of wires
were controlled and the height of wires were -1.0 mm at
the centre and +2.0 mm at the edges of the undulator(z=+2.7m), because they bended by their weights. The
magnetic field distribution was measured by temperature
controlled vertical and horizontal Hall probes, which aremounted on a 6 m long scanning table. Figure 1 shows
photograph of scanning Hall proves and flipping coil.

2.2 Data Processing
The flipping coil measurement gives an integration ofmagnetic field through 4 units (I) as a function of thehorizontal position (X) of the electron beam. A leastsquare fitting of measured I as a function of X gives
polynomial representing the integrated multipolecomponents. The measurements of vertical field (By) andTable 2: Guidelines on theacceptable integrated
imperfection field for thering magnets.
Field Type

Guide Line

54mm

Dipole4× 10-4 T m

10.8m

Quadrupole

7× 10-3 T/m m

Gap

119-30mm

Sextupole

0.3 T/m2 mK

0.3 - 2.5

Octupole

10 T/m3 m

Number of Periods
Period Length λu
Total Length L

Figure 1: Photograph of magnetic
field measurement system.

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

zn+1

I1n =

³ B(z) dz(1)zn

where zn = -L/2 + n λu/2 is the boundary between the nth and (n+1)th poles and B(z) is the magnetic field (Bx orBy) as a function of z. The calculation of I1n as a functionof X gives multipole components at each pole. This wasused to find magnets to be sorted (find the worst pole) andto check the uniformity along one undulator unit. We did
not use calculations of periods at both ends of theundulator because the combination of 4 units did notalways had end magnets.
From I1n at X = 0 we calculate an error storage ESn
defined as

reduce was the deviation of the field integral from the onaxis value.
The field adjustment took place at the gap of 25mm.

3.2 Adjustment of Frames
At the first step we re-set the mechanical magnet gap
equal and re-aligned the frame, to which the magnet array
was set. After the alignment of the basements of each unit
we adjusted the supporting frames measuring the field
distribution. The coordinate origin used to set gap, the tiltof the frame in z-direction were adjusted so that the peakfield distribution in z-direction be roughly uniform. Fig.2
shows the example of peak field distribution along z-axis
at before and at after the adjustment.
unit3B (Gauss)the horizontal field (Bx) give normal and skewed
components, respectively.
The Hall probes were used to measure the magnetic
field map in z-x plane. We calculate the first field integral
over the range of a specific magnet pole, which is definedas the deflection caused by the n-th magnet pole given bynESn = (1/<I>) Σ(° I1m °-<I>)
m=1

where <I> is the mean value of ° I1n °. The ESn has astorage correlation with the phase error [3]. We alsocalculate a field storage FSn defined asnFSn = (1/<I>) Σ(I1m - (-1)m <I> .

(3)

m=1

Here, the peak field at odd poles are assumed to bepositive. The FSn shows an accumulation of an error
deflection, an extra kick in addition to the normal
deflection corresponding to the K value of the undulator.
Therefore, FSn is a good approximation of the electron
orbit [3].

3 FIELD ADJUSTMENT

B (Gauss)

(2)

4600
4550
4500
4450
4400
-3000
4650
4600
4550
4500
4450

unit4

unit5

unit6
Initial

-2000

-1000

0z (mm)

1000

2000

3000

frame adjusted

Figure 2: Improvement of peak field distribution of unit
3-6 by the adjustment of the frames. Before (above) andafter (below) the adjustment.

3.3 Multipole Field Adjustment
First, the skew quadruple components were reduced byputting shim plates on the magnet pole face. Next we
reduced other multipole field components by flippingmagnets. Fig.3 schematically shows how the magnets
were flipped. A change of multipole field components by
the correction is listed in Table 3.

3.1 Order of Correction of Magnets
LU was too long to measure all eight units at a time.
Measurements and adjustments period was divided into
three parts. At the first period, central 4 units (unit 3, 4, 5and 6) were adjusted. At the second period, the upstream
4 units (unit 1, 2, 3 and 4) were set up. Field distributionof 4 units was measured and the magnets of unit 1 andunit 2 were adjusted. At the third step, the downstream
units (unit 5, 6, 7 and 8) were set up and the magnets ofunit 7 and unit 8 were adjusted..
Our sorting procedure of a period had three steps. Atthe first step we cleared the results of the first adjustment,
which meant the equal gap for all magnets. The second
step was the multipole field reduction. The third step was
the spectral improvement. The order of these steps was
not definite. It happened many times that we had to go
back to the former step.
We were concerned about the dipole (or the on-axis
field integral) because steering coils, usually attached at
the undulator, can easily correct them. What we should(a) flipping in x-axis(b) flipping in y-axis

Figure 3: How to flip magnets in x-direction and ydirection. The white arrows in the magnet blocks show
the direction of the magnetization. The thick arrow
indicate the move of magnets. Both of the flipping ofvertically magnetized blocks and azimuthally (zdirection) magnetized blocks work.
Basically the flipping magnets and putting shim plates
reduced the multipole components of the integration over4 units and the exchange of magnets improved theuniformity along z-axis. We exchanged a magnet in thesection where the error field storage increased and that
where it decreased. Fig.4 shows the X dependence of theThe 14th Symposium on Accelerator Science and Technology, Tsukuba, Japan, November 2003

B (Gauss)

800

Bx

400

Bx

ESn (%)

00-4-8ESn (%)-84-16200pole
800050100150-4-8END OF UNIT 3-6-8-16

Fig.6 Magnetic performances as a function of the pole
number at before (above) and after (below) theadjustment. The thin lines are ESn and the thick lines areFSn.

03.5 Results of total 8 units

By

- 400
- 800

By

- 1200
BEFORE

AFTER- 1600-6-4-202X (cm)46 -6-4-202X (cm)46

Figure 4: Improvement of integrated multipole field
distribution through unit 3-6.
50unit4

unit3

unit5

unit6

BEFORE

Norm Q (Gauss)

8STARTFSn (kG cm)

Table 3: The effectiveness of putting shim plates andflipping magnets. The multipole field components
represented by D, Q, S and O are dipole, quadrupole,sextupole and octupole field component. The correctionchanges the multipole component labeled by “C” and do
not labeled by “N”.
Multipole fieldnormalskewCorrection
D Q S O D Q S O
C N C N N C N CShim plate
A pair of shim plates N N N N N C N CC C C C N N N N
Flipping in x-axis
N C N C C N C N
Flipping in y-axis

4FSn (kG cm)

integration through 4 units at before and at after theadjustment. Fig. 5 shows an improvement of thedistribution of normal quadrupole field component.

AFTER0

X0.1

X0.1
- 50

pole 050

100

150

2000

50

100

150

200

Figure 5: Improvement of normal quadrupole field
distribution of unit 3-6 before (left) and after (right) theadjustment. The circles are contributions of each poles.
The lines are the integration (error field storage) divided
by 10. The maximum error per unit before the adjustment
was -341 Gauss of unit3. After the adjustment it wasreduced to -132 Gauss of unit4.

3.4 Adjustment of Undulator Field
Exchanging magnets under the limitation, that theexchange did not damage uniformity of multipoledistribution, reduced the ESn and FSn.
A control of space between units was efficient tominimize ESn (phase error). The spaces were adjusted tobe less than 0.2 mm, with which the contributions ofspace was negligibly small. Fig.6 shows an example ofthe adjustment.

The total field of 8 units was estimeted from twomeasurements, that of unit 1-4 and that of unit 5-8. The
integrated multipole fields were small enough as are listed
in Table 4. The total standard deviation of phase error was
4.4 degrees, which was capable of usage of higher
harmonic undulator light.
Fig. 4 Total multipole field components through 8 units.
Field
Multipole
InitialCorrected
Bydipole (Gauss cm)-70
180(normal) quadrupole (Gauss)-290-10
sextupole (Gauss/cm)
80-10octupole (Gauss/cm2)
40-3-352
decapole(Gauss/cm3)
Bxdipole (Gauss cm)
60-240(skew)
quadrupole (Gauss)
900
70
sextupole (Gauss/cm)
130-30octupole (Gauss/cm2)
-90
-1124
4decapole(Gauss/cm3)

4 ACKNOWLEDGEMENT
The authors thank Prof. A. Ando and Prof. T.
Mochizuki of LASTI and Mr. Zakou of MHI for theirsupport to this work.

5 REFERENCES[1] A. Ando et al., J. Synchrotron Rad. 5, 342-344 (1998).
[2] S. Hashimoto, et al., NIM A467-468 (2001) 141-144.
[3] T. Tanaka, et al., NIM A465 (2001) 600-605.
[4] Y. Shoji, et al., "Beam Based Search for LinearImperfection Fields in 11 m Long Undulator at
NewSUBARU", this proceedngs.
[5] M. Niibe et al, "Characterization of Light Radiatedfrom 11 m Long Undulator", SRI’03, to be published
as AIP Conference Proceedings.