JAERI-Conf 95-021

PA30
Manufacture and Arrangement of Bending Magnets ofSPring-S Synchrotron
Kenji Fukami, Hiroto Yonehara, Hiromitsu Suzuki, Tsuyoshi Aoki, Norio Tani,Hiroshi Abe, Soichiro Hayashi, Y asuo Ueyama, Takayoshi Kaneta, Kenji Okanishi,Shigeki Ohzuchi, Hitoshi Tanaka, Hideaki Yokomizo, Tadashige Cyugun*
and Teruyasu Nagahuchi*
JAERI-RIKEN SPring-S Project Team, Kamigori, Hyogo, 67S-12, JAPAN*TOSHIBA co., 2-4 Suehiro-cyo, Tsurumi-ku, Yokohama, 230, JAPAN1. Introduction
The booster synchrotron of the SPring-S hasa circumference of 396.12 m with a FODO lattice of40 unit cells. The synchrotron ring contains 64
bending magnets. Basic ability have been test for apreceding magnet. Manufacture of bending magnets
have been finished on July in 1995. Field
measurements have been performed for all magnets.
Based on this results, we discussed sorting of 64
bending magnets in the synchrotron ring to suppress
horizontal closed orbit distortion (C.O.D.). Horizontal
C.O.D. was calculated by means of the code
"SYNCH". In case of the magnets are arrangedconsideration the phase of betatron oscillation, theC.O.D. decrease to about 117 in comparison with theC.O.D. without the above mentioned consideration.

Fig.1 The cross sectional distribution
horizontal position at the center of the pole.

~!

2. Field Measurement
Energy of a electron is increased from 1
GeV to S GeV in 0.4 sec by the synchrotron.
Following the ramping of the energy, the excitation
current of bending magnets were increased by eighttimes. To estimate the hysteresis of bending magnet,excitation was measured for three preceding magnets.
The excitation were measured by means of NMR
probe at the center of the pole. It was verified that themagnetic field was nearly in proportion to excitation
current within 0.2 % of linearity. Field distribution
were measured with a hall-probe for two excitation
current ( are equivalent to 1 GeV and S GeV ).
Horizontal field distribution and integrated field areshown in Fig.1 and 2, respectively. For three
preceding magnets, the variation of the former and thelatter were less than 2 X 104 and 1 X 10-3 for therange of + 30 mm, respectively.
The integrated field was measured for threeexcitation current ( are equivalent to 1 GeV, 4 GeV
and S GeV) by means of long-flip coil for all bending
magnets. The coil has 12 mm width, 3600 mm lengthand 3 turn. It is flipped by ISO deg during 5 ,_ 20

against<II

0.2

0:a~-0 • 1l;::l

1-0.2.5-+-1GeV

0.1 --- ----- --~V-v-+-8 GeV;.--'"""' ~------ e---- ---- -·-··- - · --40 -30 -20 -10

0101---~~

20~
3040

Position along x-axis
Fig.2 The integrated field distribution
horizontal position.

againstsec. The integrated field was measured along straightline. Consequently, the measurements were performed.at lS mm in the direction of the outside of electron
orbit at edge of the pole because sagitta of bending
magnet is 35.6 mm. Since the measurement wasperformed for a half year, a reference magnet wasmeasured in every measurement of a sample magnet tokeep long term stability. The deviation from the-109-

JAERI-Conf 95-021

average for all bending magnets were obtained as an
instrumental error. The instrumental error was lessthan ± 8 X 104 for three excitation current.
Histogram of the instrumental error for 1 GeV wasshown in Fig.3. The instrumental error were divided
into eight classes of"A" "' "H".

except for an interval of two magnets.
3-1 Arrangement of two pairs of magnets
Since horizontal tune is designed to be
11.73, the phase advance of betatron oscillation to be,....., 105 deg every one cell. A number, k, of cells is
equivalent to about 180 deg phase advance are k =2,5,12,15,19,22,29,36,39 cells. Distance of twomagnets should be short because the C.O.D. remain
for an interval of two magnets. It is wished that thephase advance is closer to 180 deg. In this reason, twomagnets were arranged with separation distance 5cells (call first pair).
In order to cancel remained C.O.D., a pairof magnet with opposite sign were put ( call secondpair). There are two bending magnets every one cellin a normal cell because of FODO lattice. Let theposition of the magnet of upstream in n th cell and thatof downstream in n th cell are (n,u) and (n,d),respectively. The first pair were put (n,d) and (n+5,d)and the second pair were put (n+l,u) and (n+6,u).
Since the phase advance is approximately 26 deg from(n,d) to (n+1,u), the remained C.O.D. decreases toless than 1/2.
To confirm the above mentioned discussion,
the C.O.D. was calculated by SYNCH with following
three cases.
(1) One magnet with A BIB = -0,05· % was put at(4,d).
(2) First pair of magnets with A BIB= -0.05% wereput at (4,d) and (9,d).
(3) Add second pair of magnets with A BIB =+0.05 %were put at (5,u) and (lO,u) to case (2).
In case of (1), maximum of the C.O.D, was 0.33 mm
and root mean square (r.m.s.) of the C.O.D. was 0.18
mm. In case of (2), r.m.s. of the C.O.D. decrease to
0.09 mm. However, maximum of the C.O.D. was 0.45mm for the interval of two magnets. Thus, the C.O.D.
was remained for the interval. In case of (3),maximum and r.m.s. of the C.O.D. were obtained tobe 0.16 mm and 0.04 mm, respectively. It wasconfirmed that the C.O.D. was decreased to about 1/3
for the interval of the first pair due to insert the secondpair.
3-2 Arrangement of all magnets
Electron beam size is maximum at 1 GeV
and become minimum at 8 GeV 2>. To suppress theC.O.D. at 1 GeV, 64 magnets were arranged based on
the result for 1 GeV. For example, two magnets whichwere taken from class of "B" in Fig.3 ( first pair )were put at the position of (3,d) and (8,d). The second
pair were selected from class of "G" and were put at
the position of(4,u) and (9,u).
Horizontal C.O.D. was calculated at theaA

BCDEFGH·Class of the instrumental error

Fig.3 Histogram of the instrumental error of integrated
fields. The symbols of"A" "' "H" indicate the classof instrumental error. Where, A: -0.08 ,..._, -0.06 (%),
B: -0.06 "' -0.04 (%), C: -0.04 "' -0.02 (%), D:0.02 ,...... 0 (%), E: 0 "' 0.02 (%), F: 0.02 "' 0.04(%), G: 0.04 ,...... 0.06 (%) and H: 0.06 ,...... 0.08 (%).
3. Arrangement of the magnets

All bending magnets are excited seriallymake use of one power supply. Thus, horizontal
C.O.D. is generated by the field error of bending
magnets. The instrumental error is equal to the fielderror of bending magnets. Let the direction of electron
beam as the s coordinate axis, horizontal C.O.D. x(s)is shown as 1 ) ,x(s)= - - - - c o s { 7l' 11 + .U(s)- .U(s 1)}
2sin 7l' 11X(A BIB) 6(3-1)
where, s 1 is position of the field error, {3 (s) isbeta function (m), ,u (s) is phase advance (rad), 11
is horizontal tune, A BIB is the field error and 6 is
bending angle (rad). From eq. (3-1), a sign of x(s)changes as phase advance to be 180 deg. We assume
that the field error is generated at the center of themagnet. If two magnets with same instrumental error
were arranged at distance is equivalent to 180 deg,
kicked electron by first magnet is returned to design
orbit by second magnet. The C.O.D. is canceled-110-JAERI-Conf 95-021

upstream of every quadrupole magnets (location ofmonitors ) by "SYNClf'. The C.O.D. against themonitor number was shown in Fig.4 by the solid line.
Maximum and r.m.s. of the C.O.D. were 0.35 mm and0.10 mm, respectively. For comparison, the C.O.D.
was also shown in Fig.4 by the dotted line when the ·magnets were put according to the order of productionof magnets. fu this case, maximum and r.m.s. of theC.O.D. were 1.71 mm and 0.69 mm, respectively.
These results show that the C.O.D. was decreased to.about 1/7 by discussion of section 3-1.

t~.

IQ

8'3c00N·c~-I-2~~~~~~~~~~~~~

01020

30

4050

60

7080

Monitor Number

Fig.4 Horizontal C.O.D. against the monitor number.
Monitor number 1 indicates the position of the inlet of
ftrst quadrupole magnet from the injection point ofeleetron beam. Eighty monitors are equivalent to acircumference of the synchrotron. The solid line
indicate the C.O.D. for the magnets are arranged
consideration the phase of betatron oscillation. The
dotted line indicate the C.O.D. without the above
mentioned consideration.
4. Conclusion
Integrated field were measured forall bending magnets of synchrotron. The
variation of integrated fteld was less than ± 8 X
10-4. We decided the arrangement of bending
magnets based on the result to suppress horizontal
C.O.D.
References
1) OHO '88 (1988) plll-2.
2) JAERI-memo 04-289 (1992).

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