A MAGNETOSTATIC CALCULATION OF FRINGING FIELD FOR THE ROGOWSKI POLE BOUNDARY WITH FLOATING SNAKE

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Submitted on 1 Jan 1984

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A MAGNETOSTATIC CALCULATION OF FRINGING FIELD FOR THE ROGOWSKI POLE

BOUNDARY WITH FLOATING SNAKE

Yan Chen, Fan Ming-Wu

To cite this version:

Yan Chen, Fan Ming-Wu. A MAGNETOSTATIC CALCULATION OF FRINGING FIELD FOR THE ROGOWSKI POLE BOUNDARY WITH FLOATING SNAKE. Journal de Physique Colloques, 1984, 45 (C1), pp.C1-889-C1-892. �10.1051/jphyscol:19841181�. �jpa-00223657�

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JOURNAL DE PHYSIQUE

Colloque C1, suppl6ment au n o 1, Tome 45, janvier ¹⁹⁸⁴ page ^Cl-889

A MAGNETOSTATIC CALCULATION OF FRINGING FIELD FOR THE ROGOWSKI POLE BOUNDARY WITH FLOAT1 NG SNAKE

Yan Chen and Fan Ming-wu

I n s t i t u t e of Atomic Energy, P.O. Box 275 (25), Peking, China

Resume - Une mgthode d1int6grale bornee est utilisge pour cal- culer la distribution de champ d'un p61e de Rogowski collier flottant pour un spectrographe magnetique QDDD de type M G 2 . L ' E F B est pratiquement reproduit par un calcul BIM. Comme cri- tPre suppl&mentaire, un calcul sur des p8les de Rogowski fix6s sans collier a Bt6 effectu6 e t le calcul d l E F B prssente u n par- fait accord avec l'expgrience. En 6valuant quantitativement l'effet des colliers, c e travail prgdit Gqalement les valeurs d'EFB pour deux positions diffgrentes des colliers.

A b s t r a c t

-

^ABoundary I n t e g r a l Method has been u s e d t o c a l c u l a - t e t h e f r i n g i n g f i e l d d i s t r i b u t i o n o f Rogowski p o l e boundary w i t h f l o a t i n g snake f o r a G 2 t y p e o f QDDD magnetic s p e c t r o g r a p h and t h e e x p e r i m e n t a l EFB is n e a r l y reproduced from BIM c a l c u l a - t i o n . A s a f u r t h e r c r i t e r i a , a c a l c u l a t i o n f o r clamped ~ o g o w s k i p o l e b u t w i t h o u t snake i s a l s o performed and t h e c a l c u l a t e d EFB shows p e r f e c t i d e n t i t y w i t h t h e experiment. F o r e v a l u a t i n g t h e e f f e c t o f s n a k e q u a n t i t a t i v e l y , t h i s work a l s o p r e d i c t s t h e EFB v a l u e s f o r two d i f f e r e n t p o s i t i o n s o f snake.

A s p e c i f i c Rogowski p o l e c o n f i g u r a t i o n w i t h f l o a t i n g s n a k e (1) i s used a t t h e D2 e x i t and D3 e n t r a n c e o f QMG2 t y p e charged p a r t i c l e magnetic s p e c t r o g r a p h (2) f o r post-manfacture a d j u s t m e n t of s h a p e s o f EFB a l o n g t h e boundary. I n t h e e x p e r i m e n t a l measurements of s u c h f r i n g i n g f i e l d ( 3 ) , a r e l a t i v e l a r g e d i s c r e p a n c y i s found between t h e EFB o f manufactured magnet and t h e o r i g i n a l d e s i g n . Comparing t h i s f a c t w i t h a s e r i e s measured d a t a o b t a i n e d from o t h e r t y p e s o f QDDD s p e c t r o g r a p h s ( 4 ) ( A EFGax-& 2.0 mm 1 s u c h l a r g e d e v i a t i o n i s anoma- l o u s , f o r example AEFB = 12.5 ma f o r D2 e x i t a s shown i n Fig.1.

In s e a r c h o f r e a s o n why SO l a r g e e r r o r e x i s t e d , a Boundary I n t e g r a l Method (5) was u s e d t o c a l c u l a t e t h e f r i n g i n g f i e l d d i s t r i - b u t i o n a l o n g t h e i n t e r m e d i a t e symmetric p l a n e i n s t e a d o f TRIM code.

A s t h e BIM code does n o t need boundary c o n d i t i o n , it is s u i t a b l e f o r a l a r g e g a p magnet c a l c u l a t i o n . The method i s based on _{- -} following

formuia, , ,-

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H = % - H ~ ; H = - 4 v ~ ? x s ( + ) d n j ; b = - v @

and

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A ~ = & ~ I n m M r ~ ( $ ) d ~ ,; 8 = p ( G s - v @ )

where H i s t h z f i e l d i n t e n g i t y which i s e x p r e s s e d a s t h e s o u r c e f i e l d H and f l e l d I&, o f induced m w n e t i ~ _ a t i o q . Q, ced p o t e n t i a l 8ue t o permeable m a t e r i a l and R = I ^{r ' -}rl i s ce from t h e s o u r c e p o i n t ? * t o t h e f i e l d p o i n t i'

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sum of is t h e

1 t h e d t h e indu- i s t a n - I f a magnet p o s s e s s e s r e l a t i v e l y s i m p l e geometry l i k e a common d i p o l e s t r u c t u r e w i t h l a r g e g a p and s a t u r a t i o n i n yoke is n o t inhomo- geneous v e r y much* BIM method has probably more a d v a n t a g e s o v e r o t h e r methods f o r a v o i d i n g t h e n e c e s s i t y o f imposing t h e f a r f i e l d b m n d a r y

c o n d i t i o n .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19841181

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C1-890 JOURNAL DE PHYSIQUE

O b v i o u s l y QWIG2 magnets s a t i s f y a l m o s t a l l c h a r a c t e r i s t i c s mentioned above. Because t h e d i p o l e magnet o f QlG2 s p e c t r o g r a p h h a s

3-D c o n f i g u r a t i o n , a t r i c k h a s t o be u s e d t o c o n v e r t 3-D problem t o 2-D problem. Here we s h o u l d k e e p two r e q u i r e m e n t s i n mind. F i r s t , a f t e r c h a n g i n g 3-D t o 2-D t h e m a g n e t i c f l u x s h o u l d b e i n v a r i a n t . Second, t h e boundary c o n d i t i o n r e m a i n s s t a t i o n a r y i n t h e i n t e r e s - i n g r e g i o n and t h e e f f e c t o f yoke on p o l e boundary can be e l i m i n a t e d .

A s shown i n F i g . 2 , yoke 1 is r o t a t e d f o r a a n g l e i n a n t i c l o c k - w i s e d i r e c t i o n a n d yoke 2 t u r n s i n o p p o s i t e d i r e c t i o n f o r

- .

F i g . 3 shows t h e imaging s i m u l a t i o n and t h e first r e q u i r e m e n t is s a t i s f i e d . The boundary c o n d i t i o n n e a r t h e i n t e r e s t i n g s i d e AB h a s n o t been

changed, s o t h a t t h e s e c o n d r e q u i r e m e n t is a l s o s a t i s f i e d . The c a l c u - l a t i o n a l s o i n c l u d e s d i f f e r e n t p e r m e a b i l i t i e s and d i f f e r e n t p o s i t i o n s o f s n a k e f o r t h e p r a c t i c a l s i z e o f magnet. A s a f u r t h e r c r i t e r i a , a c a l c u l a t i o n on t h e clamped Rogowski p o l e boundary w i t h o u t s n a k e i s a l s o compared w i t h measured d i s t r i b u t i o n .

I n Bm c a l c u l a t i o n a boundary s h a p e c o r r e c t i o n f a c t e r S must be t a k e n i n t o a c c o u n t w h i l e t h e t h e o r e t i c a l r e s u l t and t h e measured

d a t a a r e compared,because t h i s method can d e a l w i t h

.

The r e s u l t s from BlT!4 c a l c u l a t i o n , o f c o u r s e , d e s c r i b e t h e d i s t r i b u - a 2-D problem o n l y t i o n s o f magnets w i t h s t r a i g h t b o u n d a r i e s .

The f i n a l r e s u l t s from BIN c a l c u l a t i o n s can be summarized a s f o l l o w i n g :

1. F o r t h e 02 e x i t boundary w i t h s n a k e t h e f r i n g i n g f i e l d d i s - t r i b u t i o n from BWI a p p r o a c h e s t h e measured n e a r l y . h EFB ( m e a s u r e d - t h e o r e t i c a l ) = -0.040 g a p , s e e F i g . 4 .

2 . T h e r e i s a s m a l l d i s p l a c e m e n t o f EFB f o r Rogowski boundary T h t h snake f o r d i f f e r e n t p e r m e a b i l i t i e s p = 750 and p = 1000 AEFB = 0.008 g a p .

3. The ETB w i l l d i s p l a c e inward magnet f o r a d i s t a n c e o f 0.075 g a p w h i l e t h e s n a k e i s moved o u t w a r d f o r a h a l f o f s n a k e t h i c k n e s s and v i c e v e r s a . It is f o u n d t h a t f o r a s t r a i g h t boundary t h e r a t l o o f EFB d i s p l a c e m e n t t o s n a k e d i s p l a c e m e n t

i s a b o u t 1:-9.5* where t h e minus symbol means o p p o s i t e d i - r e c t i o n f o r e a c h o t h e r .

4 . F o r t h e clamped D2 e n t r a n c e boundary t h e BIM d i s t r i b u t i o n r e p r o d u c e s t h e e x p e r i m e n t a l p e r f e c t l y , as shown i n F i g . 5

A EFB ( m e a s u r e d - t h e o r e t i c a l ) = -0.011 g a p .

It i s o b v i o u s t h a t t h e BIM c a l c u l a t i o n s i m u l a t e s t h e a c t u a l f r i n g i n g f i e l d d i s t r i b u t i o n s u c c e s s f u l l y . According t o t h e d e s i g n e d c o n s t r u c t i o n o f d i p o l e magnet, s u c h l a r g e i n w a r d - d i s p l a c e m e n t o f EFB i s i n t h e n a t u r e o f c a s e . It i s a l s o n e c e s s a r y t o p o i n t o u t t h a t t h e r e i s no n e e d t o u s e a v i r t u a l i r o n b a r c o n n e c t i n g s n a k e w i t h yoke f o r t h e p u r p o s e o f d e t e r m i n a t i o n o f m a g n e t i c p o t e n t i a l and a l s o no n e e d t o e n c l o s e t h e problem a r e a w i t h yoke f o r boundary c o n d i t i o n . A s i m p l e c o n c l u t i o n from above is t h a t t h e s n a k e i s o n l y a f l o a t i n g e l e m e n t and no f i e l d enhancement e f f e c t e x i s t s n e a r i t .

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s p e c t r o g r a p h magnets 4. M.Goldschmidt e t a1

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F i g . 1 A comparison o f D2 e x i t EFB between t h e t h e o r e t i c a l d e s i g n and t h e measured d a t a

F i g . 2 A s i m p l i f i e d s e c t i o n o f D2 magnet o f 3 4 G 2 m a g n e t i c s p e c t r o g r a p h

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F i g . 3 A s t r u c t u r e s i m u l a t i o n o f D2 magnet

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