DEVELOPMENT OF AN UNDULATOR MAGNET FOR THE DARESBURY SYNCHROTRON RADIATION SOURCE

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DEVELOPMENT OF AN UNDULATOR MAGNET FOR THE DARESBURY SYNCHROTRON

RADIATION SOURCE

R. Walker, M. Poole, D. Taylor

To cite this version:

R. Walker, M. Poole, D. Taylor. DEVELOPMENT OF AN UNDULATOR MAGNET FOR THE

DARESBURY SYNCHROTRON RADIATION SOURCE. Journal de Physique Colloques, 1984, 45

(C1), pp.C1-321-C1-324. �10.1051/jphyscol:1984165�. �jpa-00223721�

JOURNAL DE PHYSIQUE

Colloque C1, suppl6ment au no 1, Tome 45, janvier 1984 page C1-321

DEVELOPMENT OF AN UNDULATOR MAGNET FOR THE DARESBURY SYNCHROTRON RADIATION SOURCE

R.P. Walker, M.W. Poole and D.G. Taylor

Science & Engineering Research CounciZ, Daresbury Laboratory, Daresbury, Warrington WA4 4AD, U.K.

Resume

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A b s t r a c t . The d e s i g n of a 1 m long u n d u l a t o r composed of r a r e e a r t h c o b a l t blocks and t h e methods used t o c a l c u l a t e 3 4 i m e n s i o n a l f i e l d d i s t r i b u t i o n s and magnetic f o r c e s a r e described. A scheme f o r t e s t i n g t h e b l o c k s t o d e r i v e i n f o r m a t i o n on magnetisation e r r o r s h a s been developed. R e s u l t s a r e p r e s e n t e d and e v a l u a t e d i n terms of t h e e f f e c t on t h e e l e c t r o n beam t r a j e c t o r y .

1 . I n t r o d u c t i o n . An u n d u l a t o r i s a p e r i o d i c s t r u c t u r e producing a t r a n s v e r s e f i e l d d i s t r i b u t i o n v a r y i n g s i n u s o i d a l l y a l o n g i t s a x i s . The r e s u l t a n t u n d u l a t i n g t r a j e c t o r y of an e l e c t r o n beam p a s s i n g through t h e d e v i c e l e a d s t o emission of syn- c h r o t r o n r a d i a t i o n with modified p r o p e r t i e s t h a t a r e a t t r a c t i v e f o r experimental usage. Design of an u n d u l a t o r f o r t h e SRS s t o r a g e r i n g i s complete and a l l com- ponents a r e a v a i l a b l e f o r assembly which w i l l be completed b e f o r e t h e end of 1983;

i n s t a l l a t i o n i n t h e r i n g w i l l f o l l o w a t t h e f i r s t a v a i l a b l e o p p o r t u n i t y .

A previous MT-7 paper [ I ] reviewed g e n e r a l l i m i t a t i o n s on t h e d e s i g n of such magnets. Since t h e n g r e a t e r emphasis h a s been placed on t h e u s e of r a r e e a r t h c o b a l t (REC), u s u a l l y SmCog, permanent magnet m a t e r i a l r a t h e r t h a n on e l e c t r o - magnetic d e v i c e s and t h i s i s p a r t i c u l a r l y t r u e of f r e e e l e c t r o n l a s e r magnets. A companion paper i n t h e s e proceedings [21 d e a l s w i t h t h i s l a t t e r t o p i c .

2. Magnet Design.

2a. Optimization of parameters. Fig.1 shows t h e c o n v e n t i o n a l arrangement of REC blocks a s f i r s t used on t h e S t a n f o r d u n d u l a t o r [31. The peak f i e l d on a x i s f o r t h e c a s e of i n f i n i t e l y wide blocks [ I 1 i s given by:

S i n n/M -2*/Ao - W h o

B = 2 B - ( l - e

r n/M e

where B = remanent f i e l d of m a t e r i a l , M = number of blocks p e r p e r i o d , A = ma6net p e r i o d , h = h e i g h t of b l o c k s and g = magnet gap.

I n t h i s c a s e M = 4; a l a r g e r f i e l d can be produced w i t h more blocks p e r p e r i o d b u t t h e r e is a d i f f i c u l t y i n magnetizing t h e blocks a t an a n g l e t o t h e edges. Use of s q u a r e c r o s s - s e c t i o n , h = Ao/4, a l l o w s maximum f l e x i b i l i t y i n s e l e c t i n g block loca- t i o n s . A p e r i o d of 100 mm o p t i m i s e s t h e r a d i a t i o n i n t e n s i t y i n t h e range 10-1 00 A

a t t h e SRS o p e r a t i n g energy of 2 GeV and p r o v i d e s v i s i b l e l i g h t o u t p u t a t lower e n e r g i e s f o r d i a g n o s t i c s [41; t h e magnet g a p normally w i l l remain f i x e d a t i t s minimum v a l u e of 42 mm and 10 p e r i o d s can be f i t t e d i n t h e a v a i l a b l e length.

Although an a n a l y t i c a l method e x i s t s f o r i n v e s t i g a t i n g t h e e f f e c t of f i n i t e block width t51 it was convenient t o use a n e x i s t i n g g e n e r a l computer program, PMU3D

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984165

C1-322 JOURNAL DE PHYSIQUE

I- _{A,; 100rnm} J

Fig.2 Fig.1 Basic SRS u n d u l a t o r geometry

Block width.w (mm)

V a r i a t i o n of f i e l d s t r e n g t h and homogeneity with block width.

[61, t h e b a s i s of which i s t h e c a l c u l a t i o n of t h e f i e l d from a s i n g l e block d e r i v e d with a 3-dimensional c u r r e n t s h e e t model:

I n d i c e s i, j and k t a k e v a l u e s 1 , 2 o r 3 r e s p e c t i v e l y f o r t h e x, y and z c o o r d i n a t e s of block c o r n e r s . The t r a n s v e r s e f i e l d d i s t r i b u t i o n i s approximately quad;atic [ 7 1 :

Fig.2 shows t h e dependence of ax, a y and Bo on block width. A s t h e e l e c t r o n motion i s n o t s t r o n g l y e f f e c t e d by t h e inhomogeneity 181 a somewhat a r b i t r a r y width c h o i c e of 90 mm was made, providing a f i e l d amplitude c l o s e t o t h e 2D l i m i t i n d i c a t e d i n t h e f i g u r e .

2b. h d design. To e n s u r e t h a t t h e e l e c t r o n beam emerges from t h e u n d u l a t o r with no n e t d e f l e c t i o n o r displacement r e q u i r e s a f i e l d d i s t r i b u t i o n symmetric a b o u t t h e magnet c e n t r e and end p o l e s c o n t r i b u t i n g h a l f t h e f i e l d i n t e g r a l ( 4 d z produced by t h e c e n t r a l p o l e s . The p r o p e r t i e s of REC mean t h a t u s e , o f end blocks of h a l f l e n g t h ( s e e Fig.1) meet t h i s requirement e x a c t l y . Figure 3 shows t h e computed f i e l d d i s - t r i b u t i o n , B1, with t h i s arrangement with t h e l e f t hand p h y s i c a l end of t h e magnet a t z = 0. B2 i s t h e f i e l d of an i d e n t i c a l magnet whose r i g h t hand end i s l o c a t e d a t z = 0. By s u p e r p o s i t i o n (91 t h e s u m i s t h e s i n u s o i d a l d i s t r i b u t i o n , B, which e x i s t s i n t h e c e n t r e of t h e magnet. I n t e g r a t i n g over t h e end f i e l d r e g i o n ( + ho) t h e n g i v e s t h e following r e s u l t :

Ib

+

-

By symmetry however B2(z) = B1(-z) and s o both i n t e g r a l s must be z e r o a s r e q u i r e d . This scheme a v o i d s t h e complication of a r o t a t a b l e f u l l block used i n p r e v i o u s designs [31 and a l s o has t h e advantage of being independent of gap s e t t i n g . I n p r a c t i c e however d i f f e r e n c e s between t h e magnetization s t r e n g t h s of h a l f and f u l l blocks w i l l r e q u i r e some a d d i t i o n a l compensation by means o f s m a l l t r i m c o i l s .

2c. Magnetic f o r c e c a l c u l a t i o n s . The f o r c e a c t i n g between two REC blocks can i n p r i n c i p l e be c a l c u l a t e d by a n a l y t i c a l means w i t h a c u r r e n t s h e e t model. For t h e simple c a s e i l l u s t r a t e d i n Fig.4 a 2-dimensional model g i v e s t h e r e s u l t :

Force B 2

-

[

I ^-

((2a+b) 2 + a 2 ) 1 / 2

-.

Block separation, b (mm) Fig.3 F i e l d d i s t r i b u t i o n n e a r t h e end Fig.4 Magnetic f o r c e between two

of t h e undulator. blocks.

For a = 25 mm, width = 90 mm and Br = 1.0 T Fig.4 shows t h e r a p i d f o r c e i n c r e a s e a t s h o r t d i s t a n c e s , r i s i n g t o 532 N f o r blocks i n c o n t a c t . A t l a r g e r s e p a r a t i o n s i t f a l l s a s (a+b)-4 s i n c e blocks can be r e p r e s e n t e d by elementary d i p o l e s s i t u a t e d a t t h e block c e n t r e s . A s i m p l e r numerical c a l c u l a t i o n h a s been undertaken f o r t h e u n d u l a t o r , summing f o r c e s between s u r f a c e element p a i r s and moments a b o u t block c e n t r e s . The t o t a l a t t r a c t i v e f o r c e between a r r a y s i s about 2650 N and t h e end blocks experience t h e l a r g e s t couple, a b o u t 1 Nm.

3. Permanent magnet blocks. The m a t e r i a l chosen was Hitachi Hicorex-22A samarium c o b a l t (SmCog). Because of t h e l a r g e dimensions each block comprises 4 s m a l l e r p i e c e s glued by t h e manufacturer b e f o r e magnetization. Block magnetic p r o p e r t i e s have been s t u d i e d by t a k i n g p o i n t f i e l d measurements of t h e component By a t posi- t i o n s i n d i c a t e d i n Fig.5, e n a b l i n g t h e magnetization s t r e n g t h and an o f f s e t between magnetic and p h y s i c a l c e n t r e s f o r each c o o r d i n a t e d i r e c t i o n t o be c a l c u l a t e d :

where Cl-Cg a r e c o e f f i c i e n t s c a l c u l a t e d u s i n g eqn.(2). A f t e r l o c a t i n g a block i n a simple h o l d e r a s e t of d a t a could be taken a u t o m a t i c a l l y i n about 10 minutes with t h e Daresbury magnet t e s t f a c i l i t y [I01 employing a H a l l p l a t e .

The r e s u l t s of measurements c a r r i e d o u t on 84 blocks a r e summarised below:

Fig.6 i s a histogram of t h e main magnetisation component which shows a t o t a l s p r e a d of 2.58, a f a c t o r of two b e t t e r t h a n t h e m a n u f a c t u r e r ' s quoted spread. The same technique was a p p l i e d t o t h e h a l f blocks. The major d i f f e r e n c e i n t h i s c a s e was t h e h i g h e r remanent f i e l d s t r e n g t h , 0.936

*

4. T r a j e c t o r y c a l c u l a t i o n s . The most i m p o r t a n t e f f e c t s a r i s e from M and M e r r o r s which cause f i n i t e t r a n s v e r s e f i e l d i n t e g r a l s a l o n g t h e magnet, c a l c u l a t e d as

-

C1-324 JOURNAL DE PHYSIQUE

Magnetlratlon My (TI

Fig.5 Scheme f o r magnetic measurements. Fig.6 V a r i a t i o n i n main magnetization s t r e n g t h .

A. 1 / 2

a x = i 2 $ a g [ ~ i 2 ] =0.08mrn a ^X' = h ae = 0.13 mrad

AS a check f i e l d v a l u e s o b t a i n e d from PMU3D have been used t o c a l c u l a t e t h e e l e c t r o n t r a j e c t o r y a s f o l l o w s ( v a l i d f o r x' << 1 ) :

~ o t i o n i n t h e y p l a n e was a l s o checked a l t h o u g h f o c u s i n g f o r c e s i n t h i s p l a n e [ I l l w i l l modify t h e t r a j e c t o r y . A s e r i e s of r u n s with random magnetization e r r o r s agreed with t h e simple model t o w i t h i n t h e s t a t i s t i c a l e r r o r . The e f f e c t of magnetic c e n t r e o f f s e t s of 0.1 mm was a l s o found t o be n e g l i g i b l e .

5. Magnet c o n s t r u c t i o n . The n e c e s s a r y novel assembly techniques developed f o r a s i m i l a r magnet [21 w i l l a g a i n be u t i l i s e d . Each block w i l l f i r s t l y be glued i n t o an i n d i v i d u a l h o l d e r and t h e n b o l t e d o n t o t h e b a s e p l a t e u s i n g a s p e c i a l j i g t o overcome t h e l a r g e magnetic f o r c e s . Random block l o c a t i o n w i l l be p o s s i b l e because of t h e small computed t r a j e c t o r y e r r o r s , b u t t h e measured block dimensions imply an o v e r a l l l e n g t h

-

Acknowledgements. D e t a i l e d e n g i n e e r i n g d e s i g n h a s been undertaken by R.J. Bennett, N. B l i s s and R. Punter. We a r e a l s o g r a t e f u l f o r t h e encouragement g i v e n by D.J. Thompson, SRS D i v i s i o n Head.

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[I11 WALKER R.P., t o be published i n Nucl. Instrum. Meth.