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PERFORMANCE OF THE TRISTAN-AR MAGNET
K. Egawa, H. Fukuma, Ta. Kubo, N. Kumagai, Y. Takeuchi, K. Endo
To cite this version:
K. Egawa, H. Fukuma, Ta. Kubo, N. Kumagai, Y. Takeuchi, et al.. PERFORMANCE OF THE TRISTAN-AR MAGNET. Journal de Physique Colloques, 1984, 45 (C1), pp.C1-241-C1-244.
�10.1051/jphyscol:1984148�. �jpa-00223704�
JOURNAL DE PHYSIQUE
Colloque C1, supplement a u n o 1, Tome 45, janvier 1984 page CI-241
PERFORMANCE OF THE TRISTAN-AR MAGNET
K. Egawa, H . Fukuma, Ta. Kubo, N . Kumagai, Y . Takeuchi and K. Endo lVationaZ Laboratory for High Energy Physics, Oho-machi, Tsukuba-gun, Ibaraki-ken, 305, Japan
Resums - Un systeme d ' a i m a n t s pour l ' a c c 6 1 6 r a t e u r accumulateur, TRISTAN-AR, ZF&rit du p o i n t de vue de l a f a b r i c a t i o n des performances e t des p r o p r i e - t s s o p t i q u e s d s d u i t e s des donnees de champs magnstiques.
A b s t r a c t - A magnet system o f t h e s t o r a g e a c c e l e r a t o r , TRISTAN-AR, i s d e s c r i b - ed w i t h r e s p e c t t o t h e f a b r i c a t i o n , performances and beam p r o p e r t i e s expected f r o m t h e f i e l d data.
The TRISTAN-AR (Accumulation Ring) magnet system /I/ c o n s i s t s o f 56 d i p o l e s , 86 quadrupoles, 40 s e x t u p o l e s and 54 s t e e r i n g d i p o l e s i n a d d i t i o n t o 56 b a c k l e g wind- i n g s . A l l magnets a l l o w t h e p u l s a t o r y e x c i t a t i o n t o a f f o r d t h e e l e c t r o n - p o s i t r o n c o l l i d i n g experiments a t t h e a c c e l e r a t e d energy. B o t h beams a r e i n j e c t e d a t 2.5 GeV and a c c e l e r a t e d up t o 6.5 GeV. I n t h e case when t h e AR r i n g serves as an i n j e c t o r t o t h e TRISTAN main r i n g , i t a c c e l e r a t e s up t o 8 GeV. Parameters o f magnets a r e g i v e n i n Table 1.
T - MAGNFT SYSTFM able L ~ a n r r t e n of ragnets
- . . . . -. . - . - . - . - . .
Dlwle Puadruple Iextuoole Iteeriop dlwle
D i o l e and uadru o l e Each 19 19 Ilr I X D STY l STY 1 I T H l I T " l
d i F o l e h a s q two \-shaped 1.29 m ,,-' ,., "-=,,o,,..o, " '* ' a
i r o n cores p l a c e d on a common g::;;:~~$] 60 - - - 130 111 71) I54
- 80 110 '12 91 - - - -
girder at an angle of 3.214 '0"''"""'" '"I" " "W 07"" """75 2'" 7 5 core o r o s r ~ r c t l o n l n 2 ) 160 1 $MI 101 r 106 800 A BOO 10 x 190 160 x 120 YO x 310 211 x L I D 130 r 1Y)
; h 1:; 6 7 1 L1W IMXl 130 PO0 ZP 66 10 1 B
120 680 11 16 16 66 ZO L6
degrees and has a s e t of common ,,,, ,, ,, ,, ,, ,, ,,,,, ,,,,,, ,,,, , , ,,,,
l t " r n U P ' l . 1
c o i l s . The v e r t i c a l and h o r i - 121:::t:::;=~~tio 1801 1110 1w
zontal apertures are 60 and 90 mm, r a x . field s t n n g t h L.15 T 20 T l n l l T/n 2 Y I T l m 2 tlOT1m' 0.0357 0 . 0 9 T (1.09 1 0.01 1
respectively The vertical aper- %::h::::I:I 8:::: 8%: I:li! :::It I:::, :::::: : 2:::' ::8.: : 2::&
ture allows the ul coupl ng + " : ""I qua"" "' : I""'"" w a d , """' : " 7 . ""'"W""" : V"" ""'"WI', I T 1 : I... rteertng dipole. I T H . hor. rteer(ng d4wle
o beam s i z e and t h e h o r i z o n t a l one
t h e z e r o c o u p l i n g + 10 u beam s i z e a t 6.5 GeV i n c l u d i n g t h e 9'mm s a g i t t a .
78 normal quadrupoles h a v i n g 80 mm b o r e d i a m e t e r a r e p l a c e d i n t h e r e g u l a r c e l l s , RF and d i s p e r s i o n suppressor c e l l s . 8 i n s e r t i o n quadrupoles w i t h 120 mm b o r e d i a m e t e r a r e p l a c e d i n t h e l o w R s e c t i o n s n e a r t h e i n t e r a c t i o n p o i n t s . B o t h quadrupoles have t h e symmetric p o l e p r o f i l e s because o f t h e i r good f i e l d symmetry. The h o r i z o n t a l and v e r t i c a l a p e r t u r e s a r e 69 and 4 1 mm r e s p e c t i v e l y f o r t h e normal quadrupole, w h i l e f o r t h e i n s e r t i o n quadrupole 104 and 8 1 rnm r e s p e c t i v e l y . The magnets o f t h e s t o r a g e a c c e l e r a t o r a r e e x c i t e d w i t h t h e dc c u r r e n t f o r a l o n g time. The c o i l di.mensions a r e so l a r g e t h a t t h e i r o n c o r e had t o be made separable i n t o 4 b l o c k s t o accommodate t h e c o i l s . B o t h upper two b l o c k s and l o w e r two b l o c k s were b o l t e d and a l s o welded a f t e r i n s e r t i n g t h e c o i l s . However, t h e upper and l o w e r c o r e s were l e f t s e p a r a b l e f o r t h e convenience o f t h e vacuum chamber i n s t a l l a t i o n .
The c o r e s o f b o t h d i p o l e and quadrupole were made o f t h e 0.5 mm t h i c k s i l i c o n s t e e l l a m i n a t i o n s , S23 (grade o f t h e Japanese I n d u s t r i a l Standards). The l a m i n a t i o n s h a v i n g t h e i n o r g a n i c i n s u l a t i o n l a y e r s were s t a c k e d between t h e SUS304 end p l a t e s and welded t o t h e i r o n b a r s on t h e s i d e s i n t h e s t a c k i n g f i x t u r e . As t h e magnetic p r o p e r t i e s of t h e s i l i c o n s t e e l had a d i r e c t i o n a l dependence (magnetic a n i s o t r o p y ) ,
two t y p e s o f sheets punched p a r a l l e l ( L ) and t r a n s v e r s e ( C ) t o t h e r o l l i n g d i r e c t i o n
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984148
C1-242 JOURNAL DE PHYSIQUE
w i t h two stamping d i e s were mixed s h e e t by s h e e t a u t o m a t i c a l l y b e f o r e s t a c k i n g . W h i l e f o r t h e d i p o l e , t h e s t e e l s h e e t was punched so t h a t t h e f l u x i n t h e p o l e r a n p a r a l l e l t o t h e r o l l i n g d i r e c t i o n which had t h e l a r g e s t p e r m e a b i l i t y .
The c o i l s were made o f t h e oxygen f r e e copper h o l l o w c o n d u c t o r and i n s u l a t e d w i t h t h e semi-cure f i b e r g l a s s t a p e pre-pregnated w i t h t h e r a d i a t i o n r e s i s t a n t epoxy r e s i n . F o r t h e ground wrapping, t h e same t a p e l i n e d w i t h mica was used. The i n s u l a t i o n system w i l l b e a r t h e r a d i a t i o n a b s o r p t i o n more t h a n 5 x l o 8 rad.
Sextupoles I n t h e AR, t h e momentum spread o f t h e e l e c t r o n beam i s 0.115 % a t 6.5 GeV. The c h r o m a t i c a b e r r a t i o n a r i s i n g f r o m t h e momentum dependence on t h e f o c u s i n g s t r e n g t h o f t h e quadrupole i s compensated w i t h t h e s e x t u p o l e s . The s e x t u p o l e s were made o f t h e 0.5 mm t h i c k S30 ( J I S ) s i l i c o n s t e e l . The i r o n c o r e was composed o f s i x l a m i n a t e d b l o c k s w i t h t h e l e n g t h s o f 170 and 270 mm f o r t h e s e x t u p o l e p l a c e d n e a r t h e h o r i z o n t a l l y and v e r t i c a l l y f o c u s i n g quadrupoles r e s p e c t i v e l y . The c o i l was made o f t h e 0.65 mm t h i c k anodized A1 r i b b o n w i t h 60 mm w i d t h . The Normex 410 sheets were e n f o l d e d between t h e l a y e r s t o ensure t h e i n s u l a t i o n . The o u t e r m o s t s u r f a c e o f t h e c o i l was covered w i t h t h e Cu s t r i p w i t h t h e c o o l i n g channel.
S t e e r i n g d i p o l e and b a c k l e g w i n d i n g 44 v e r t i c a l s t e e r i n g d i p o l e s a r e used f o r t h e v e r t i c a l o r b i t c o n t r o - l and 10 h o r i z o n t a l s t e e r i n g d i p o l e s and 56 b a c k l e g w i n d i n g s wound around t h e yokes o f t h e main d i p o l e s f o r t h e h o r i z o n t a l o r b i t c o n t r o l . Each s t e e r i n g d i p o l e o r b a c k l e g w i n d i n g i s e n e r g i z e d i n d i v i d u a l l y .
I 1 - PERFORMANCES OF MAGNETS
The f i e l d p r o p e r t i e s o f a l l magnets were measured. The f i e l d measuring systems were designed t o a l l o w t h e f a s t and a c c u r a t e measurements w i t h few persons. The m a i n d i p o l e s were measured s t a t i c a l l y w i t h t h e 3 m l o n g f l i p c o i l d r i v e n w i t h t h e p u l s e motors a t b o t h ends. The induced v o l t a g e was i n t e g r a t e d d u r i n g t h e r o t a t i o n o f t h e c o i l w i t h t h e a c c u r a t e i n t e g r a t o r and t h e n measured w i t h a d i g i t a l v o l t m e t e r , FLUKE 8502 A. The d i g i t a l d a t a were s t o r e d i n t h e minicomputer, PDP11/34, v i a GPIB i n t e r f a c e i n t h e CAMAC c r a t e /2/. The e f f e c t o f t h e i n c l i n e d two c o r e s was c o r r e c t e d w i t h t h e d a t a o f t h e p o i n t measurements.
The d i f f e r e n t measurements were made t o t h e quadrupoles, because t h e r o t a t i o n o f t h e l o n g t w i n c o i l s was d i f f i c u l t i n t h e small gap. P l a c i n g t h e l o n g t w i n c o i l s p a r a l l e l t o t h e c o r e a x i s , t h e f i e l d g r a d i e n t s were measured a t 10 f i e l d l e v e l s d u r i n g a p u l s a t o r y e x c i t a t i o n . A t each p r e d e t e r m i n e d f i e l d l e v e l t h e t r i g g e r p u l s e was g e n e r a t e d by comparing i t w i t h t h e f i e l d g r a d i e n t o f t h e r e f e r e n c e quadrupole which was connected s e r i a l l y t o t h e concerned quadrupole. The t r i g g e r p u l s e was used t o measure t h e i n s t a n t a n e o u s o u t p u t o f t h e i n t e g r a t o r w h i c h i n t e g r a t e d t h e i n d u c e d v o l t a g e o f t h e l o n g t w i n c o i l s . The remanent f i e l d g r a d i e n t was measured by r o t a t i n g t h e same t w i n c o i l s around t h e c o r e a x i s and added t o t h e d y n a m i c a l l y measured data.
The s e x t u p o l e s and t h e s t e e r i n g d i p o l e s were measured w i t h t h e c o m m e r c i a l l y a v a i l -
a b l e r o t a t i n g c o i l . The s e x t u p o l e component was o b t a i n e d b y d i f f e r e n t i a t i n g t w i c e t h e raw data.
The f i e l d measuring c o i l s were moved a u t o m a t i c a l l y p r o v i d i n g t h e a c c u r a t e number o f t h e d r i v i n g p u l s e s t o t h e p u l s e motors t h r o u g h t h e s t e p p i n g motor c o n t r o l l e r s f r o m t h e computers. A s e r i e s o f measurements was done o n l i n e f o r t h e d i p o l e and t h e quadrupole. T a b l e 2 g i v e s t h e summary o f t h e f i e l d measurements.
Table 2 S u m r y of the f i e l d lnearurementr f&)/&iol at;, I =:":Z,
guadrupole Sextupole and &2yll :
ndgnet Olpole steering dipole r ( m l
$%;,I : ::z'"2,,
P ~ o b e long f l - p c o l l long twin co7ls rotatlng c a l l ERet:tio" statlC
Raw data ~ ~ ~ ~ ~ r $ ~ ~ , , q t h R-nent
f i e l d included Accuracy
;:;;:&r POP11134
integrated f i e l d gradient lnearured w i t h the rupplenental m e s u v m n t
s t a t i c f,eld strength a t each polnt included
' I " I
F i g . 1 R a d i a l d i s t r i b u t i o k s o f ' t h e e ' f f e c t i v e d i p o l e l e n g t h a f t e r t h e end shim c o r r e c t i o n .
D i p o l e The r a d i a l d i s t r i b u t i o n s o f t h e e f f e c t i v e d i p o l e l e n g t h a r e shown i n Fig.
1. The s l i g h t c o r r e c t i o n o f t h e f i e l d was made a t t a c h i n g t h e s i m p l e shims shown i n t h e same f i g u r e a t b o t h magnet ends. The e f f e c t i v e l e n g t h i n c r e a s e d by 0.01 % 0.02 % a t t h e b o t h a p e r t u r e ends and t h e a l m o s t f l a t d i s t r i b u t i o n was obtained.
The s t a t i s t i c a l d i s t r i b u t i o n o f t h e e f f e c t i v e l e n g t h s a t 6.5 GeV i s g i v e n i n F i g . 2(a). The s t a n d a r d d e v i a t i o n i s 0.038 % r e f l e c t i n g m a i n l y t h e c o r e l e n g t h d i s t r i b u - t i o n r a t h e r t h a n t h e gap h e i g h t e r r o r s and t h e p e r m e a b i l i t y f l u c t u a t i o n s . The e f f e c - t i v e l e n g t h d i s t r i b u t i o n o f t h e remanent f i e l d ( F i g . 2 ( d ) ) r e f l e c t s t h e v a r i a t i o n o f t h e c o e r c i v e f o r c e .
Q u a d r u p o l e The r a d i a l d i s t r i b u t i o n o f t h e e f f e c t i v e l e n g t h o f t h e f i e l d g r a d i e n t had t o be c o r r e c t e d due t o t h e l a r g e v a r i a t i o n i n t h e a p e r t u r e as shown i n F i g . 3.
The b e s t c o r r e c t i o n was f o u n d a f t e r t r y i n g v a r i o u s t y p e s o f t h e l a m i n a t e d shims a t a l l p o l e ends. Several r e s u l t s a r e shown i n F i g . 3 w i t h t h e shim s t r u c t u r e . Apply-
101 Effecl!ve length (65-V) l b ) Core length (C) Gap error ~ r m l p ~ d r u p ~ k -
( d l Effective Ienglh of ( e l Cwrcive force l f 1 Permeability remonsnt fiald (amitx . i . 5 ~ ) at Hi5000A/m
u ( l g ) = 3.2 % <HC>,,~= 0.8 OC 2;rl=y2",y
n u = 4 . 2 X m
A t s ( % ) He15 (0s) p (emu)
F i g . 2 S t a t i s t i c a l d i s t r i b u t i o n s o f t h e F i g . 3 R a d i a l d i s t r i b u t i o n s o f t h e e f f e c t i v e d i p o l e l e n g t h , f a b r i c a t i o n e r r o r s e f f e c t i v e quadrupole l e n g t h a f t e r t h e and m a g n e t i c p r o p e r t i e s o f t h e s i l i c o n v a r i o u s end shim c o r r e c t i o n s f o r t h e s t e e l H23 (S23 g r a d e ) f o r t h e d i p o l e s . normal quadrupoles.
i n g t h e shims t h u s determined, i t was p o s s i b l e t o l e v e l t h e r a d i a l d i s t r i b u t i o n w i t h i n ? 0.01 % i n t h e a p e r t u r e .
The e f f e c t i v e l e n g t h s o f t h e f i e l d g r a d i e n t s o f t h e normal quadrupoles d i s t r i b u t e s t a t i s t i c a l l y as shown i n F i g . 4 ( a ) . T h e i r s t a n d a r d d e v i a t i o n i s 0.089 % r e f l e c t i n g a l s o t h e c o r e l e n g t h d i s t r i b u t i o n . T h i s v a l u e corresponds t o t h e t h i c k n e s s o f a s h e e t o f t h e l a m i n a t i o n . The mechanical d e v i a t i o n s o f t h e b o r e d i a m e t e r s a r e w i t h i n t h e t o l e r a b l e l i m i t and t h e symmetry o f 4 p o l e s i s s a t i s f a c t o r y . The mechanical d i f f e r e n c e s o f t h e minimum gap h e i g h t s a t t h e h o r i z o n t a l and v e r t i c a l p l a n e s a r e 0.003 k 0.015 mm and 0.002 i 0.015 mm, r e s p e c t i v e l y . The f i e l d g r a d i e n t e r r o r a r i s i n g f r o m t h e p o l e asymmetry i s i g n o r a b l e . The e f f e c t i v e l e n g t h s o f t h e remanent
( a ) Effective I q t h of l b l Core length ( C l Bore dia. arror field grcdient ( 6 . 5 GeV)
, ( L ) = 0.094 % <Ad> =-O.Ol2mm
w ( l o ) = 0 . 0 8 9 X ~ ( 6 1 : 0.016 X
I d ) Effective Ienglh of ( e l Coercive force I f l Permeability remonent field gradient ( B1 . 5 ~ ) ~ ~at 5 0 0 0 A l m ~
d t o ) = 4 . 3 % (~~),,,=0.84 00 < p ~ t c > = 277emu
, = 5.6 W ( P L . C ~ = 0 . 2 8 % n
A l o 1%) Hc (0s) p (emu1
F i g . 4 S t a t i s t i c a l d i s t r i b u t i o n s o f t h e e f f e c t i v e q u a d r u p o l e l e n g t h , f a b r i c a t i o n e r r o r s and m a g n e t i c p r o p e r t i e s o f t h e s i l i c o n s t e e l RM23 (S23 grade) f o r t h e normal quadrupoles.
l o ) Effednve ImgIh l b ) Core length ( c l Bwt dm error of field gradmnt ( 6 5 - V ) ,(L1 =0035X <Ad)= -002mm
r = 0 0 2 7 X w ( d ~ = O O l O ~
F i g . 5 S t a t i s t i c a l d i s t r i b u t i o n s o f t h e e f f e c t i v e q u a d r u p o l e l e n g t h and f a b r i c a - t i o n e r r o r s f o r t h e i n s e r t i o n
quadrupoles.
C1-24Q JOURNAL DE PHYSIQUE
f i e l d g r a d i e n t s a r e g i v e n i n F i g . 4 ( d ) . T h e i r v a r i a t i o n a l s o r e f l e c t s t h e d i s - t r i b u t i o n o f t h e c o e r c i v e f o r c e .
F o r t h e i n s e r t i o n quadrupoles, t h e s i m i l a r s t a t i s t i c a l d i s t r i b u t i o n s a r e g i v e n i n F i g . 5. The s t e e l p r o p e r t i e s a r e same as F i g . 4. The asymmetries o f t h e p o l e s measured a t t h e minimum gaps a r e 0.015 + 0.013 mm h o r i z o n t a l l y and 0.003 +- 0.010 mm v e r t i c a l l y . The e f f e c t i v e l e n g t h o f one quadrupole was s m a l l e r by 0.2 1 and was c o r r e c t e d by i n c r e a s i n g t h e t h i c k n e s s o f t h e p o l e end shims. F i g . 5 ( a ) was o b t a i n e d a f t e r t h i s c o r r e c t i o n .
Sextupole The e f f e c t i v e l e n g t h s o f t h e s e x t u p o l e f i e l d o f Table 3 were o b t a i n e d
Table 3 Effective l e n g t h of t h e r e x t u p o l e
Table 4 Effective lengths o f s t e e r i n g dipoles e f f e c t i v e sextupole l e n g t h Inn)
core l e n g t h STV 1 STV 2 STH i STH 2
(""0 30A 80A 100A
SXF 170 191 190 1 9 1 gap h e i g h t (m) 130 154 70 154
SXD 270 274 278 278 e f f . l e n g t h ( m ) 356 214 275 291
f r o m t h e f i e l d mapping o f each t y p e o f t h e s e x t u p o l e s . The two dimensional d i s t r i b u - t i o n s o f a l l s e x t u p o l e s were measured a t t h e l o n g i t u d i n a l c e n t e r s o f t h e magnets.
F i g . 6 shows t h e r e s u l t s w i t h t h e f a b r i c a t i o n e r r o r s . The v a r i a t i o n o f t h e c o r e l e n g t h s i s v e r y s m a l l and t h e d i s t r i b u t i o n o f t h e e f f e c t i v e s e x t u p o l e l e n g t h s may be e s t i m a t e d f r o m F i g . 6 ( a ) .
S t e e r i n g d i p o l e The i r o n c o r e was n o t l a m i n a t e d b u t t h e ramped e x c i t a t i o n from 0 t o 10 A d u r i n g 10 sec d i d n o t show t h e f i e l d d e t e r i o r a t i o n due t o t h e eddy c u r r e n t . The e f f e c t i v e l e n g t h s o f each t y p e a r e g i v e n i n Table 4.
I 1 1 - SPECULATIONS ON BEAM PROPERTIES
101 B " l x = y = s = o l I bl Bore dim error
01 IOOA - 0 0 3 6 m m
0 = 0 7 3 % 1 1 r = 0 . 0 2 % I
n E s t i m a t i n g f r o m t h e e f f e c t i v e l e n g t h
v a r i a t i o n , t h e c l o s e d o r b i t d i s t o r t i o n i s a b o u t 1 mm a t 6.5 GeV. O t h e r sources o f t h e d i s t o r t i o n a r e t h e a l i g n m e n t
e r r o r s o f t h e quadrupoles, s t r a y f i e l d AB'I%I r)d (mm) and t h e t i l t s o f t h e d i p o l e s . T a k i n g (Cl Average cote length dtrtribvtron
t h e s e sources i n t o c o n s i d e r a t i o n , a few SXF SXD
mm o f t h e o r b i t d i s t o r t i o n w i l l - b e ex- e = 0 0 3 % r = 0 0 3 %
pected.
For t h e s t o r a g e a c c e l e r a t o r , i t u s u a l l y -015 L & z
-&
t a k e s f o r a l o n g t i m e t o accumulate t h e AL lmm) A L lmml i n t e n s e beam. Sometimes t h e m i s - t u n i n g
o f t h e a c c e l e r a t o r happens t o l o s e t h e F i g . 6 S t a t i s t i c a l d i s t r i b u t i o n s o f t h e s t o r e d beam. I t i s d e s i r a b l e t o keep s e x t u p o l e s t r e n g t h and f a b r i c a t i o n e r r o r s . t h e beam l o s s a t a minimum. To a t t a i n
t h e h i g h l y r e l i a b l e machine, t h e beam s h o u l d remain a t t h e same c o n d i t i o n i f i t d i s p l a c e d w i t h i n t h e a p e r t u r e . The e f f e c t i v e l e n g t h d i s t r i b u t i o n s o f F i g . 1 and F i g . 3 a f t e r t h e c o r r e c t i o n s w i t h t h e p o l e end shims w i l l a s s u r e t h i s c o n d i t i o n .
The w i d t h o f t h e h a l f i n t e g r a l stopband e s t i m a t e d f r o m t h e e f f e c t i v e g r a d i e n t l e n g t h o f F i g . 4 ( a ) i s 0.02. It i s f a i r l y s m a l l . The t u n e s h i f t s a r e e s t i m a t e d t o b e l e s s t h a n 0.0002 f o r b o t h t h e h o r i z o n t a l and v e r t i c a l motions f r o m t h e o c t u p o l a r f i e l d d e t e r i o r a t i o n e s t i m a t e d f r o m F i g . 3 a f t e r t h e shim c o r r e c t i o n . The h o r i z o n t a l and v e r t i c a l t u n e spreads due t o t h e c h r o m a t i c a b e r r a t i o n a r e + 0.02 and + 0.03 a t 6.5 GeV, r e s p e c t i v e l y . B o t h spreads can be compensated w i t h t h e s e x t u p o l e s w h i c h a r e e x c i t e d i n 4 f a m i l i e s .
References
1 ) K. Endo, H. Fukuma, A. Kabe, Ta. Kubo, To. Kubo, N. Kumagai and Y. Takeuchi, KEK I n t e r n a l 82-10 (1982).
2 ) N. Kumagai, Y. Takeuchi and K. Endo, IEEE Trans. MAG-17 (1981) 1606.
