I- C E A L - 1015

. A ,Prdcision ~nkrgg. Calibration - . . - v

D

:-.

MASSACHUSETTS I NSTJTUTE OF T E C H N O L ~ ~ Y and HARVARD UNIVERSITY

C A M B R I D G E 38, M A S S A C H U S E T T S

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

DISCLAIMER

Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

The mseamh work described in - bki8 qparc was perfoned W e r Contrae t A~(30-11-2076 bebeen the D.S, Atamic. $nergy GdmmissPon and the President a~@ Fellows of Harvard College.

M A S S A C H U S E T T S I N S T I T U T E O F T E C H N O L O G Y + H A R V A R D U N I V E R S I T Y

C A M B R I D G E E L E C T R O N A C C E L E R A T O R

HARVARD UNIVERSITY

42 OXFORD STREET

CAMBRIDGE, MASS. 02138 +

CEAL-1015 H e Winick 1 March 1965

A P r e c i s i o n Energy C a l i b r a t i o n

f o r t h e

Cambridge E l e c t r o n A c c e l e r a t o r

A b s t r a c t

The e x t e r n a l e l e c t r o n beam o f t h e C . E . A . was f o c u s s e d v e r t i -

c a l l y and b e n t upward .by a s i x f o o t d e f l e c t i n g magnet. - T h e de- '

f l e c t e d and u n d e f l e c t e d beams were a l l o w e d t o d r i f t 20 f e e t t h r o u g h

a vacuum p i p e p roduc ing a s e p a r a t i o n o f a b o u t 3 2 " . Accura te mea-

s u r e m e n t s o f t h i s s e p a r a t i o n were made by s u r v e y i n g t h e s p o t s pro-

duced by t h e beams on g l a s s s l i d e s . ' Combining t h i s measurement

of a n g u l a r d e f l e c t i o n w i t h a p r e c i s e mapping o f t h e f i e l d o f t h e

d e f l e c t i n g magnet y i e l d e d a c a l i b r a t i o n of t h e e n e r g y o f t h e syn-

c h r o t r o n a t nominal e n e r g i e s o f 1, 2 , 3, 4 , 5 , and 6 GeV. These

measurements s h o w . t h a t t h e peak s y n c h r o t r o n e n e r g y i s l i n e a r w i t h

peak s y n c h r o t r o n magnet c u r r e n t - Expressed i n t e r m s of t h e syn-

c h r o t r o n magnet D - C . c u r r e n t ( i n t e r m s o f m i l l i v o l t s on t h e s h u n t ) ,

t h e r e s u l t 62.73 mv p e r GeV was o b t a i n e d . T h i s r e s u l t i s a c c u r a t e

t o b e t t e r t h a n 20.2%. It was found t h a t c a r e f u l c o n t r o l of h y s t e r -

e s i s and eddy c u r r e n t e f f e c t s i n t h e d e f l e c t i n g magnet were e s s e n -

t i a l i n o b t a i n i n g r e p r o d u c i b l e magne t i c f i e l d p l o t s .

Soon a f t e r t h e e l e c t r o n beam was f i r s t e x t r a c t e d from t h e syn-

c h r o t r o n , and i n i t i a l measurements showed t h a t t h e e m i t t a n c e and

e n e r g y s p r e a d were b o t h s m a l l , , . ( l e s s t h a n 1 cm-mrad h o r i z o n t a l l y and

l e s s t h a n 0.3 cm-mrad v e r t i c a l l y ) , i t was s u g g e s t e d by G . A . Voss and

o t h e r s , t h a t a p r e c i s i o n e n e r g y measurement c o u l d be made on t h i s

beam by m a g n e t i c d e f l e c t i o n . Such measurements have now been made a t

nominal e n e r g i e s of '1, 2 , 3 , 4 , 5 and 6 GeV and a r e h e r e r e p o r t e d .

Measurement Technique

The a p p a r a t u s used i s shown i n f i g . I. The emergent .beam passed

t h r o u g h q u a d r u p o l e l e n s e s ~1 and Q2, and t h e n t h r o u g h t h e v e r t i c a l

d e f l e c t i n g 'magnet M , a f t e r which' i t d r i f t e d a b o u t 20 ' t o a l o c a t i o n

where i t produced da rkened s p o t s on 1" X 3't g l a s s mic roscope s l i d e s

p l a c e d i n t h e p r o p e r p o s i t i o n t o i n t e r c e p t t h e s t r a i g h t - t h r o u g h and

d e f l e c t e d beams. V e r t i c a l d e f l e c t i o n was chosen because t h e v e r t i c a l

s i z e o f s p a t s i s i n s e n s i t i v e t o f l u c t u a t i o n s i n power l e v e l s of t h e

c u r r e n t s t r i p and e j e c t i o n magnet which e j e c t t h e beam Proa t h e syn-

c h r o t r o n . Hence s p o t s a r e d e f i n e d v e r t i c a l l y b e t t e r t h a n t h e y a r e

h o r i z o n t a l l y . The beam t r a v e l l e d . i n vacuum e s s e n t i a l l y a l l t h e b a y

emerging f rom a t h i n Mindow jtr b e f o r e s t r i k i n g t h e s l i d e s . The s l i d e s

were h e l d on a 30'' d i a m e t e r wooden d i s k which was r e m o t e l y r o t a t a b l e . .

from t h e main c o n t r o l room.. T h i s d i s k had i t s p l a n e p e r p e n d i c u l a r t o

t h e u n d e f l e c t e d beam,and i t s h e i g h t was a d 2 u s t e d s o t h a t s l i d e s l o c a t e d

a t t h e bot tom wouid be a p p r o x i m a t e l y a't u n d e f l e c t e d b e a m a h e i g h t . The

l o c a t i o n of t h e wheel . a long t h e beam r u n was. s o chosen t h a t e l e c t r - o n s '

CEAL-1015

d e f l e c t e d by a b o u t 1/8 r a d i a n would s t r i k e t h e upper s l i d e s . Thus

a measurement o f t h e d e f l e c t i o n cou ld be made by a l l o w i n g t h e beam

t o s t r i k e t h e lower s l i d e , p r o d u c i n g a da rkened s p o t t h e r e w i t h t h e

magnet o f f and t h e n , w i t h o u t r o t a t i n g t h e whee l , t h e magnet was po-

r e r e d ( s e e magnet c y c l i n g * r o c e d u r e ) t o produce t h e nominal 118

r a d i a n d e f l e c t i o n and t h e upper s l i d e was exposed and a s p o t was

~ r o d u c e d t h e r e . The a p p e a r a n c e of t h e s e s p o t s i s shown d i a g r a m n a t -

i c a l l y i n f i g . 11, f o r t h e 5 GeV c a s e .

The shape o f t h e d e f l e c t e d spqt r e l l e c e s t h e e n e r g y s p r e z d i n

1 t h e beam, due l a r g e l y t o t h e f a c t t h a t t h e beam i s s p i l l e d o v e r a

I p e r i o d o f s e v e r a l hundred mic roseconds n e a r t h e peak of t h e magne t i c

f i e l d . The e n e r g y o f t h e beam v a r i e s q u a d r a t i c a l l y w i t h t ime meas-

u red r e l a t i v e t o t h e t i m e of peak e n e r g y , and i s down by 0.9% a t

0.5 m i l l i s e c o n d s . The i n t r i n s i c e n e r g y s p r e a d due t o quantum f l u c -

t u a t i o n s i s c a l c u l a t e d by K . Robinson t o v a r y l i n e a r l y w i t h e n e r g y

~ above 3 GeV and t o e q u a l a b o u t 20.1% a t 6 GeV. The h i g h e s t e n e r g y

I '

i i n t h e beam i s q u i t e w e l l d e f i n e d a s t h e l o w e s t p o i n t i n t h e def1ec . - .

t e d s p o t , and i t s l o c a t i o n , r e l a t i v e t o t h e u n d e f l e c t e d beam pos-

i t i o n , . is used t o c a l c u l a t e t h e e n e r g y c o r r e s p o n d i n g t o peak mag-

n e t i c ' f i e l d .

I The e x p o s u r e t ime was judged by o b s e r v i n g ' t h e s p o t s d a r k e n i n g

on c l o s e d c i r c u i t t e l e v i s i o n . T y p i c a l exposure t i m e was a b o u t 30

seconds . The l o c a t i o n of t h e s e s p o t s was l a t e r measured t o an a c c u r -

a c y of 40.01tt u s i n g two Wild L e v e l s and a v e r t i c a l hangin.g p r e c i s i o n

?Oscale . The s e p a r a t i o n o f t h e s e s p o t s , d , combined w i t h t h e

d i s t a n c e between t h e d e f l e c t i n g magnet and t h e s l i d e s , L , p e r m i t

a c a l c u l a t i o n .of t h e bend ing a n g l e . A c t u a l l y , s i n c e t h e rema-

nence f i e l d i n t h e magnet was n o t n e g l i g i b l e , two s p o t s were

t a k e n w i t h t h e magnet o f f , one w i t h e a c h p o l a r i t y o f remanence

f i e l d . The c e n t e r of t h e s e two s p o t s was used a s t h e u n d e f l e c t e d

beam p o s i t i o n . The s e p a r a t i o n o f t h e d e f l e c t e d and u n d e f l e c t e d

beams ( a b o u t 32") c o u l d t h e r e f o r e be measured t o b e t t e r t h a n

+0.02" which r e s u l t s i n l e s s t h a n 20.06$ e r r o r i n t h e c a l c u l a t i o n - I

of bend ing a n g l e . The d i s t a n c e L was measured t o +- 16 which

r e s u l t s i n l e s s t h a n ~ 0 . 0 3 % e r r o r i n t h e c a l c u l a t i o n o f bending

a n g l e .

During t h e . s l j . d e e x p o s u r e s , e s p e c i a l l y d u r i n g t h e c r i t i c a l

e x p o s u r e s w i t h t h e d e f l e c t i n g magnet powered, c a r e f u l r e c o r d was

k e p t o f t h e f o l l o w i n g :

1. S y n c h r o t r o n magnet c u r r e n t .

2. RF f r e q u e n c y -

3. . D e f l e c t i n g magnet c u r r e n t . .

4. Timing o f emergent beam r e l a t i v e t o t h e magnet c y c l e

( s p i l l t ime') .

The manner of measur ing e a c h of t h e s e , and t h e e f f e c t s of

v a . r i a t i o n s on t h e s y n c h r o t r o n e n e r g y w i l l now be d i s c u s s e d

s e p a r a t e l y .

1. S y n c h r o t r o n Magnet C u r r e n t : The magnet c u r r e n t h a s a . . wave form g i v e n ' b y :

The peak c u r r q n t i s :

- 'peak - IDC + 1!tak

U n t i l r e c e n t l y IDC was measured on a 2 O . 1 $ s h u n t

which developed 0.1 mv p e r amp. T h i s s h u n t would have

l i m i t e d t h e p r e c i s i o n o f t h e p r e s e n t measurements , p r i -

m a r i l y because i t s o u t p u t v o l t a g e was low - o n l y 6.3 mv

a t 1 GeV l e v e l . I n a n t i c i p a t i o n o f t h e p r e s e n t ' m e a -

su remen t s a more p r e c i s e ( 2 0.04$) , h i g h e r s i g n a l ( 1 mv

p e r amp.) Leeds and N o r t h r u p , s h u n t was p r o v i d e d by t h e

E l e c t r i c a l ~ n g i n e e r i n ~ ' Department and i n s t a l l e d i n

s e r i e s w i t h t h e s y n c h r o t r o n magnet D.C. Both t h i s new

s h u n t and t h e o l d s h u n t were r e a d d u r i n g t h e s e measure-

ments u s i n g two Leeds and Nor throp p o t e n t i o m e t e r s .

S h u n t s o f t h i s t y p e ( i . e . 1 mv p e r amp. 2 0.04% pre -

c i s i o n ) were used f o r a l l measurements o f s y n c h r o t r o n

magnet c u r r e n t and d e f l e c t i n g magnet c u r r e n t .

peak i s measured by o b s e r v i n g t h e s e p a r a t i o n of 'AC

p u l s e s from an u n b i a s e d t o r o i d a l peak ing s t r i p , which

s u r r o u n d s a magnet c u r r e n t c a b l e and p r o d u c e s a p u l s e

when t h e c u r r e n t p a s s e s ' t h rough ze ro . The c u r r e n t i s

made t o p a s s t h r o u g h z e r o t w i c e on e a c h magnet c y c l e by

peak making 'AC > 1.

'DC

The s y n c h r o t r o n i s u s u a l l y oper .a ted ' w i t h a 1 m i l -

l i s e c o n d s p a c i n g bet,ween t h e s e z e r o c u r r e n t p u l s e s . I f

T i s t h e s e p a r a t i o n o f t h e z e r o c u r r e n t p u l s e s t h e n

~ ( t ) = 0 a t t = .T/2. S u b s t i t u t i n g t h i s i n Eq(1) y i e l d s

1:Eak = s e c

ID c 2'

For T = 1 m i l l i s e c o n d s e c p'J= 1.017 and 2

'peak = 2.017 IDC

Most of t h e d e f l e c t i o n measurements were made w i t h

a s t a b l e peak ing s t r i p s p a c i n g ( v a r i a t i o n of l e s s t h a n

+ 34 p s e c ) . However, a t t h e 1.0 GeV e x c i t a t i o n t h e - spackng v a r i e d by 2 0.1 m i l l i s e c o n d s . An a t t e m p t was

m a d e ' t o make a measurement a t 0 .5 GeV b u t t h e magnet

i n s t a b i l i t y t h e r e was v e r y g r e a t , r e s u l t i n g i n much

l a r g e r beam s p o t s . S i n c e it was d i f f i c u l t t o e s t i m a t e

t h e a c t u a l peak magnet c u r r e n t t h i s measurement was

d i s c a r d e d .

The e f f e c t o f a v a r i a t i o n i n p e a k i n g s t r i p s p a c i n g

on t h e peak magnet c u r r e n t (and hence peak machine

e n e r g y ) may be o b t a i n e d by d i f f e r e n t i a t i n g Eq(2) w i t h

r e s p e c t t o T t o y i e l d :

-6-

peak I,,

2 A 1 AT peak 7 9 T

A peak

The l a s t p a r t of t h i s e q u a t i o n i s o b t a i n e d by approx ima t ing

E ¶ ( 3 ) I p e a k - - 21DC, and assuming t h a t any v a r i a t i o n s i n

peak ing ' s t r i p s p a c i n g a r e due t o v a r i a t i o n s i n e i t h e r A.C.

o r D .C . b u t n o t bo th .

A T For = 377 (60 C.P.S.) , T-1 m i l l i s e c , and = . I Eq(4)

y i e l d s ~ ( P c ) = 0.18$, t h e c o r r e c t i o n a p p l i e d t o t h e 1 GeV PC

measurements . A t a l l o t h e r e n e r g i e s t h e p e a k i n g s t r i p s p a c i n g

was a c c u r a t e and s t a b l e . t o b e t t e r t h a n 230 p s e c which c o r r e s -

ponds t o a n e r r o r i n peak e n e r g y o f l e s s t h a n 20.06$.

2. RF Frequency: The r f f r e q u e n c y was measured t o a p r e c i s i o n of

+ 2kc on a f r e q u e n c y c o u n t e r . S i n c e t h e r f f r e q u e n c y a t ' t h e - peak of t h e magnet c y c l e i s r e l e v a n t t o t h e peak e n e r g y , c a r e

was t a k e n t o e x c l u d e from t h e measurement t h e two m i l l i s e c o n d

i n t e r v a l at i n j e c t i o n when t h e f r e q u e n c y i s h i g h e r . T h i s i s

most s imply done by s e l e c t i n g a s h o r t s ampl ing p e r i o d ( 1 m i l l i -

s econd) f i r t h e f r e q u e n c y c o u n t e r and i g n o r i n g t h e o c c a s i o n a l

h i g h e r f r e q u e n c y d i s p l a y e d when t h e sampl ing p e r i o d happens t o

o c c u r n e a r i n j e c t i o n t i m e when t h e f r e q u e n c y i s h i g h e r .

Al though t h e rf f r e q u e n c y was c o n s t a n t d u r i n g a s i n g l e e n e r g y

measurement , i t v a r i e d from a low 475.659 Mc t o a h i g h o f

457.701 d u c i n g t h e s e r i e s o f measurements.

A change i n r f f r e q u e n c y , b f , i s r e l a t e d t o a n e n e r g y

change O ( p c ) by t h e r e l a t i o n ' s h i p :

whe re i s t h e a v e r a g e momentum c o m p a c t i o n f a c t o r and

h a s a v a l u e o f 0 .031. Thus t h e 42 kc r a n g e o f f r e q u e n c i e s

e n c o u n t e r e d d u r i n g t h e measu remen t s c o r r e s p o n d s t o a 0 . 2 9 %

e n e r g y change* A l l r e s u l t s p r e s e n t e d h e r e a r e n o r m a l i z e d

t o a n r f f r e q u e n c y o f 475.7.00 Mc. I n a n y a t t e m p t t o u s e

t h e s e r e s u l t s a c o r r e c t i o n must be made f o r a n y d i f f e r -

e n c e i n r f f r e q u e n c y f rom 475 -700 Mc. u s i n g ~ ~ ( 5 ) .

3 . D e f l e c t i n g Maenet C u r r e n t : '. The d e f l e c t i n g magnet c u r r e n t

was measured u s i n g a Leeds and N o r t h r o p (20 .045 p r e c i s i o n )

a i r c o o l e d s h u n t i n a s e . r i e s w i t h t h e magne t* The s h u n t

v o l t a g e was measu red on a Dymec 5 d i g i t v o l t m e t e r (Model

2401A) and a Leeds a n d N o r t h r o p p o t e n t i o m e t e r . The magne t

c u r r e n t was s t a b l e t o b e t t e r t h a n 2 0 . 0 2 $ d u r i n g a n i n -

d i v i d u a l measurement .

4. S p i l l Time: The s i g n a l f rom a s c i n t i l l a t i o n c o u n t e r

n e a r t h e e m e r g e n t beam r u n was d i s p l a y e d on a n o s c i l -

l o s c o p e a l o n g w i t h t h e p u l s e which i n d i c a t e s t h e peak

o f t h e m a g n e t i c f i e l d ( B ~ ~ ~ ) - The a c c e l e r a t o r o p e r a t o r

a d j u s t e d t h e beam bump a m p l i t u d e a n d t i m i n g t o keep t h e

s c i n t i l l a t i o n c o u n t e r s i g n a l c e n t e r e d on t h e Bmax p u l s e .

The s p i l l t i m e was s t a b l e d u r i n g e a c h measurement , and

a lways i n c l u d e d t h e t ime o f peak magne t i c f i e l d .

Magnet ic Measurements.

It was d e s i r e d t o c o n s t r u c t a p o i n t - b y - p o i n t f i e l d map of

t h e d e f l e c t i n g magnet t o an a c c u r a c y o f 20 .1% o r b e t t e r . A f i r s t

a t t e m p t was made w i t h H a l l p robes which were c a l i b r a t e d a g a i n s t

a n u c l e a r magne t i c r e s o n a n c e d e v i c e i n a s t a n d a r d magnet. A l -

t hough i n d i v i d u a l r e a d i n g s cou ld be made t o t h e r e q u i r e d p r e -

c i s i o n , t h e c a l i b r a t i o n o f t e n a b r u p t l y changed by a s much a s

0.65. More s u c c e s s was had u s i n g a n u c l e a r magne t i c r e s o n a n c e

(NMR) probe and a r o t a t i n g c o i l . The NMR ( V a r i a n t y p e F-8) was

used t o measure t h e un i fo rm f i e l d s f a r i n s i d e t h e magnet and up

t o 2" from t h e magnet ends . The l a r g e g r a d i e n t s p r e s e n t c l o s e

t o t h e magnet e n d s , and i n t h e f r i n g e f i e l d s , p r e c l u d e d i t s u s e

a t t h e s e l o c a t i o n s , s o a r o t a t i n g c o i l (Rawson t y p e 820 0 .1%

d i f f e r e n t i a l g a u s s m e t e r ) was used h e r e . The r o t a t i n g c o i l was

c a l i b r a t e d b e f o r e and a f t e r each s e t of f r i n g e f i e l d measure-

ments a t a p o i n t 6" i n s i d e t h e magnet. The two c a l i b r a t i o n s

a g r e e d t o ~ 0 . 1 $ o r b e t t e r . S i n c e t h e f r i n g e f i e l d c o n t r i b u t e s

o n l y a b o u t 116 of t h e t o t a l magne t i c l e n g t h t h i s p r e c i s i o n i s

q u i t e a d e q u a t e . The NMR of c o u r s e i s e x t r e m e l y p r e c i s e , g i v i n g

f r e q u e n c i e s which were r e a d on t h e f r e q u e n c y c o u n t e r t o b e t t e r

t h a n 20.005% and which r e p e a t e d t o b e t t e r t h a n i0.02$.

T h i s i n s t r u m e n t a t i o n proved a d e q u a t e f o r o b t a i n i n g t h e h i g h

p r e c i s i o n measurements r e q u i r e d - However, t h e r e s u l t s were n o t

9

r e p r o d u c i b l e f rom d a y t o day . It was found t h a t t h e r e l a t i o n s h i p

be tween magnet e x c i t a t i o n c u r r e n t and m a g n e t i c f i e l d was a f u n c t i o n

o f t h e . p r e v i o u s h i s t o r y o f t h e magnet. The f a c t o r s t h a t were mos t

i m p o r t a n t were :

a . The l e v e l t o which t h e magnet had been p r e v i o u s l y e x c i t e d .

b. The t i m e r a t e o f change o f magnet c u r r e n t i n a r r i v i n g ' a t

t h e new c u r r e n t .

The f i r s t f a c t o r was r e a d i l y c o n t r o l l e d by e s t a b l i s h i n g a

p a t t e r n f o r c y c l i n g t h e magnet t h r o u g h f u l l e x c i t a t i o n i n . one p o l - .

a r i t y t o f u l l e x c i t a t i o n i n t h e o p p o s i t e p o l a r i t y p r i o r t o s e t t i n g

t h e c u r r e n t t o t h e d e s i r e d v a l u e . I n e f f e c t t h i s p u t t h e magnet

on a p a r t i c u l a r h y s t e r e s i s c u r v e . .

The second f a c t o r was more i n t r a c t a b l e and was overcome o n l y

a f t e r c h a n g i n g t h e r e g u l a t i o n c i r c u i t r y of t h e magnet power s u p p l y .

I n i t i a l l y t h e r e g u l a t o r c i r c u i t i n t h e power s u p p l y c o n t a i n e d a

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

A f r a c t i o n of t h i s v o l t a g e was s e l e c t e d by a m o t o r - d r i v e n p o t e n t i o -

I meter which was powered r e m o t e l y , and t h i s v o l t a g e was f e d t o t h e I

c u r r e n t r e g u l a t o r c i r c u i t o f t h e power s u p p l y . With t h i s a p p a r -

a t u s t h e manner of a r r i v i n g a t a g i v e n magnet c u r r e n t ( o r a g i v e n

f r a c t i o n of t h e r e f e r e n c e v o l t a g e ) was n o t e a s i l y c o n t r o l l a b l e o r

r e p r o d u c i b l e . The o p e r a t o r would watch a me te r measu r ing magnet

c u r r e n t and jog t h e t o g g l e s w i t c h which powered t h e m o t o r i z e d p o t e n -

t i o m e t e r u n t i l a r r i v i n g a t t h e d e s i r e d c u r r e n t .

Wi th t h e a s s i s t a n c e of t h e E l e c t r i c a l E n g i n e e r i n g Depar tment

t h e problem was s o l v e d by u s i n g v o l t a g e r e f e r e n c e s a t t h e l o c a t i o n

from which t h e power s u p p l y was b e i n g c o n t r o l l e d . Two E l e c t r o n i c

Development C o r p o r a t i o n p r e c i s i o n D . C . v o l t a g e r e f e r e n c e s o u r c e s were

connec ted t o a s e l e c t o r s w i t c h t h r o u g h which t h e - o u t p u t of e i t h e r one

c o u l d be a p p l i e d t o t h e power s u p p l y c u r r e n t r e g u l a t i o n c i r c u i t . The

f o l l o w i n g p r o c e d u r e was t h e n used t o a r r i v e a t a g i v e n magnet c u r -

r e n t :

S t a r t w i t h t h e two v o l t a g e r e f e r e n c e s o u r c e s " A v q and "B" s e t t o

0 v o l t s .

1. . With t h e power s u p p l y o f f and t h e s e l e c t o r s w i t c h p u t t o

v o l t a g e r e f e r e n c e " B u , r e f e r e n c e "All was s e t t o a p a r t i c -

u l a r v o l t a g e ( 5 . 0 0 0 v ) , c o r r e s p o n d i n g t o t h e maximum c u r r e n t

t h a t cou ld be drawn from t h e power s u p p l y used (208 amps).

2. The power s u p p l y was t h e n t u r n e d on , f o l l o w i n g which t h e

s e l e c t o r s w i t c h was c h . a n g e d ' t o r e f e r e n c e "A" . The power

s u p p l y would t h e n approach a c u r r e n i of 208 amps. TUs

c u r r e n t would be s t a b l e a f t e r a b o u t two minu tes .

3 . The s e l e c t o r s w i t c h was t h e n p u t t o r e f e r e n c e "BN which was

s t i l l a t 0 v o l t s . The power s u p p l y would t h e n approach a

veny s m a l l c u r r e n t ( a b o u t 0.4 amps) a f t e r which t h e power

s u p p l y was t u r n e d o f f and i t s p o l a r i t y r e v e r s e d .

4. A f t e r t u r n i n g on t h e power s u p p l y t h e s e l e c t o r s w i t c h was

p u t t o "A1' , which was s t i l l a t 5 . 0 0 0 ~ . The power s u p p l y

' would now approach a c u r r e n t of 208 amps. i n t h e r e v e r s e

p o l a r i t y .

5 . The s e l e c t o r s w i t ~ h was t h e n p u t t o ttBtt which was s t i l l a t

0 v o l t s caus ing t h e power supply t o approach 0.4 amps a f t e r

which i t was t u rned o f f . \

The c y c l e ( s t e p s 1 t o 5 ) was r epea t ed 3 o r 4 t i m e s , ending w i th

t h e complet ion of s t e p two on t h e l a s t c y c l e , i . e . t h e magnet i s l e f t

w i t h 208 amps f lowing i n t h e normal p o l a r i t y . Then a p a r t i c u l a r c u r r e n t ,

cor responding t o a 118 r a d i a n d e f l e c t i o n a t one of t h e nominal e n e r g i e s ,

would be s e t i n two more s t e p s .

6. S e t "B" t o a v o l t a g e cor responding t a t h e c u r r e n t d e s i r e d f o r

t h e measurement,

7. " Change the s e l e c t o r sw i t ch t o "Bw. The magnet would now

approach t h e d e s i r e d c u r r e n t ,

I n t h i s way t h e magnet cou ld be cyc led i n a s t a n d a r d manner a long : : .

a p a r t i c u l a r h y s t e r e s i s l oop , and any d e s i r e d c u r r e n t could be a r r i v e d .. . I ,

a t i n a manner which reproduced t h e r a t i o of magnet ic f i e l d t o magnet f . . . . * . , .

c u r r e n t t o b e t t e r t han f0.02$, Th i s magnet c y c l i n g and c u r r e n t s e t -

t i n g procedure was used d u r i n g t h e magnetic measurements and d u r i n g t h e

a c t u a l d e f l e c t i o n measurements,

According t o t h e p r e s c r i p t i o n o u t l i n e d above, t h e magnet was broueh t

t o a d e s i r e d c u r r e n t f o r a measurement a f t e r i t had been s e t t o 208 amps .

i n t h e normal p o l a r i t y . Th is was a r b i t r a r y , and ano the r p r e s c r i p t i o n

could have been chosen which, i f fo l lowed c l o s e l y , would y i e l d e q u a l l y

r e p r o d u c i b l e r e s u l t s , b u t w i t h d i f f e r e n t va lue s of t h e r a t i o of magnetic

f i e l d t o magnet c u r r e n t . During t h e course of t h e measurements t h e

fo l l owing d i f f e r e n t p r e s c r i p t i o n was once used:

The h i g h e s t B x c i t a t i o n ( t h e 6 GeV l e v e l ) was s e t a f t e r t h e normal

c y c l i n g p rocedure . The lower e x c i t a t i o n s were s e t d i r e c t l y i n se-

quence w i t h o u t go9cg t h r o u g h t h e c y c l l f i g p rocedure . The m e n s v e m e n t s

of magne t i c f i e l d made w i t h t h i s p r o c e d u r e r e s u l t e d i n a q u i t e d i f f e r -

e n t r a t i o of magnet ic f i e l d t o magnet c u r r e n t f rom t h e r a t i o o b t a i n e d

w i t h t h e s t a n d a r d p r o c e d u r e ( s e e t a b l e I f o r t h e s t a n d a r d p r o c e d u r e

r a t i o s ) . The new r a t i o s were h i g h e r by t h e f o l l o w i n g p e r c e n t a g e s :

Magnet C u r r e n t I n c r e a s e i n F i e l d t o C u r r e n t R a t i o

109.0 amps .02$

88.4 amps 03%

65.3 amps . lo$

42.5 amps

21.4 amps . .

11.6 amps 8374 * . . i .

.: '.

The need f o r a s t a n d a r d p r o c e d u r e i n s e t t i n g magnet cur ren ' t s . when '

making prec . i s i .on magne t i c measurements i s obv ious .

The NMR and r o t a t i n g c o i l p r o b e s were used t o make a s e t of 104

p o i n t measurements of magne t i c f i e l d a l o n g t h e a x i s of t h e magnet a t

e a c h o f t h e seven e x c i t a t i o n s . The NMR ,measurements were t a k e n a t 2"

' i n t e r v a l s s i n c e t h e f f e l d . v a r i e s s lowly i n s i d e t h e magnet. The r o t a t i n g

c o i l measurements were t a k e n a t v a r y i n g i n t e r v a l s down t o '0..1'" depend ing

on t h e s t e e p n e s s of t h e g r a d i e n t .

Dur ing t h e magne t i c measurements t h e magnet c u r r e n t w a s . m o n i t o r e d

c . o n t i n u o u s l y on a 5 d i g i t v o l t m e t e r and a c c ~ a s s i o n a l l y on a Leeds and

Nor'throp p o t e n t i o m e t e r . The power s u p p l y (number 6 0 1 , . a P a c i f i c

E l e c t r i c Co. t ype ) func t ioned very we l l . Although i t s c u r r e n t r e g u l a t i o n

r a t i n g i s on ly 20.1% it was never observed t o vary by more than 20.02%

d u r i n g t h e t ime r e q u i r e d t o make a s e t of meas.ur.enien.ts ( * hour t o sev- . .. .

e r a 1 hours ) .

The po in t -by-po in t measurements were f ed i n t o a computer,.which

computed / ~ ( x ) d x a long t h e cen . t e r l i ne of t h e magnet.

The o v e r a l l accuracy of t h e s e f i n a l r e s u l t s i s b e t t e r t han 20.065.

The magnetic measurements were made and t h e computer c a l c u l a t i o n ca r - .. .

r i e d o u t , f o r each of t h e se.vien nomi-nal e x c i t a t i o n s ' corresponding t o

118 r a d i a n d e f l e c t i o n . : a t t h e . seven e n e r g i e s t o be measured. The

r e s u l t s a r e p r e s e n t e d i n , t ab l e - I and . f i .g . 111. For completeness a l e s s .

p r e c i s e (20.3%) measurement. made wi th a H a l l probe ( a t .consid.era.bly

h ighe r e x c i t a t i o n i s inc luded .

Four sets of measurements of t h e f i e l d v a r i a t i o n t r a n s v e r s e t o '\ . ' \ _ . ' .

. . . . : . . .. . ' , . . ,.

t h e magnet a x i s ( o r e l e c t r o n d i r e c t i o n ) were a l s o . made a t each exc i - , , .

. .

t a t i o n , a t 36" i n s i d e the magnet, 20" i n s i d e , 6#l i n s i d e , 14" ou t s ide .

These d a t a were l a t e r used . t o , c o r r e c t H(.x.)dx a long t h e a x i s f o r t h e S s s l i g h t l y d i f f e r e n t f f e l d s a l o n g t h e a c t u a l e l e c t r o n . t r a j e c t o r y .

These magnetic mea.surements. were a l l made wi th t h e vacuum box

i n s i d e t h e magnet. The vacuum box has .5" t h i c k carbon s t e e l t o p and

bottom p l a t e s arid. s t a i n l e s s .steel s i d e plates a n d . e f f e c t i v . e l y reduces

t h e 3" a p e r t u r e o f . t h e magne,t t o 2". he magnet ic measurements were

made a t a tmospher ic pressur.e w i , t h t h e end p l a t e s ,off t o a l l ow a c c e s s

f o r probes.. S ince tlie a c t u a l d e f l e c t f on measurements: on. t h e .. e l e c t r o n

beam were made w i t h t h e box under vacuum, a check was made , to d e t e r -

mine t h e e f f e c t of t h e vacuum on t h e magnetic f i e l d . It was found

t h a t u n d e r vacuum t h e f i e l d a l o n g t h e magnet c e n t e r l i n e i n c r e a s e d

by .0.05$. A c o r r e c t i o n f o r t h i s s m a l l e f f e c t was made t o t h e f i n a l

e n e r g y measurement d a t a , b u t i t h a s n o t b e e n i n c l u d e d i n t a b l e 1.

R e l a t i o n s h i p o f Magne t i c F i e l d t o C u r r e n t i n t h e S y n c h r o t r o n Magnets . . . . .

A s t u d y was made t o d e t e r m i n e t h e e f f e c t o f p r e v i o u s magnet

h i s t o r y on t h e r e l a t i o n s h i p o f m a g n e t i c f i e l d t o c u r r e n t i n t h e s y n -

c h r o t r o n magne t s . The dynamic remanence f i e l d ( i . e e , t h e m a g n e t i c

f i e l d a t t h e i n s t a n t a t which t h e magnet e x c i t a t i o n c u r r e n t i s z e r o )

was measu red a t s e v e r a l e x c i t a t i o n s w i t h s e v e r a l d i f f e r e n t p r e v i o u s

' e x c i t a t i o n s o f t h e magnet . F o r i n s t a n c e , t h e dynamic remanence f i e l d

a t 1 GeV l e v e l was measured a f t e r r u n n i n g a t ' 6 GeV l e v e l a n d a l s o

a t 2 GeV l e v e l . Unb ia sed t o r o i d a l p e a k i n g s t r i p s where u s e d t o s e n s e

~ t h e t i m e o f z e r o c u r r e n t and u n b i a s e d w i r e p e a k i n g s t r i p s i n t h e mag-

I n e t i c f i e l d d e t e c t e d t h e - t i m e o f z e r o m a g n e t i c f i e l d . From t h i s d a t a

1 t h e dynamic remanence c o u l d b e c a l c u l a t e d . I t was f o u n d t h a t t h e

I I dynamic remanence f i e l d was a c o n s t a n t a t a g i v e n e x c i t a t i o n , i n -

d e p e n d e n t o f p r e v i o u s e x c i t a t i o n . The a c c u r a c y was a b o u t + 1 g a u s s

which i s a b o u t .1$ o f t h e peak f i e l d a t 1 GeV l e v e l .

R e l a t i o n b e t w e e n momentum, m a g n e t i c f i e l d and d e f l e c t i o n a n g l e .

A t a n y p o i n t s on t h e t r a j e c t o r y o f a p a r t i c l e i n a m a g n e t i c

f i e l d , t h e f i e l d , H ( s ) i n g a u s s , t h e r a d i u s o f c u r v a t u r e , p ( s ) i n , ,

ctn, and t h e momentum o f t h e p a r t i c l e , pc i n GeV a r e r e l a t e d by:

where c i s t h e v e l o c i t y of l i g h t i n cm/sec*

For a n a r b i t r a r y p a t h d e f i n e d i n a r e c t a n g u l a r c o o r d i n a t e

sys t em by a f u n c t i o n ~ ( x ) , t 'he r a d i u s of. c u r v a t u r e a t a p o i n t

s ( c o o r d i n a t e s x , y ) on t h e cu rve i s g i v e n by:

Using t h i s and e q u a t i o n (6) one o b t a i n s :

where t h e i n t e g r a l s a r e o v e r t h e e n t i r e r e g i o n o f magnet ic f i e l d .

The l e f t hand s i d e o f t h i s e q u a t i o n i s d i r e c t l y i n t e g r a b l e y i e l d -

i n g ;

s i n Qf - s i n ei = c x 1 0 PC

where : 0 = t a n - ' ( d ~ ) dx

T h i s v e r y u s e f u l r e l a t i o n i s e x a c t and q u i t e g e n e r a l . It was

f i r s t p o i n t e d o u t t o me by T - L a C o l l i n s . It may be a ' pp l i ed

t o t h e p r e s e n t c a s e by s e t t i n g up a r e c t a n g u l a r c o o r d i n a t e sys t em

w i t h t h e x - a x i s i n t h e median p l a n e o f t h e magnet and perpen-

d i c u l a r t o t h e end f a c e s ( i . e . t h e p r i n c i p l e a x i s of t h e magnet ) .

Then f o r a symmetr ic t r a j e c t o r y th rough ' t h e magnet ,

(ei = - e f ) eq (7) r e d u c e s t o :

1 6

where 8 i s t h e t o t a l d e f l e c t i o n a n g l e . F u r t h e r m o r e , f o r t h i s symmetr ic

c a s e , t h e i n t e r s e c t i o n p o i n t of t h e i n i t i a l and f i n a l beam d i r e c t i o n s

i s * a t a p o i n t e q u i d i s t a n t ' f r o m t h e end f a c e s of t h e magnet , and t h e

t a n g e n t of t h e t o t a l d e f l e c t i o n a n g l e 8 i s e q u a l t o t h e ' d e f l e c t i o n , d ,

o v e r t h e l e n g t h L , measured from t h i s % n t e r s e c t i o n p o i n t t o t h e l o c a t i o n

a t which t h e d e f l e c t i o n i s measured. (See f i g . I ) .

Eq (8) and t h e above d e s c r i b e d method of o b t a i n i n g t a n 8 a r e

s t r i c t l y t r u e o n l y f o r t h e symmetr ic t r a j e c t o r y t h r o u g h t h e magnet. A

t r a j e c t o r y t h r o u g h a r e c t a n g u l a r magnet w i l l b e symmetr ic i f t h e

f o l l o w i n g a r e s a t i s f i e d :

a . The ups t r eam and downstream h a l v e s o f t h e magnet must be

s y m m ~ t r i c r e l a t i v e t o t h e midplane of t h e magnet.

b. The p r i n c i p l e a x i s 09 t h e magnet must make a n a n g l e w i t h t h e

incoming r a y of one h a l f t h e f i n a l d e f l e c t i o n a n g l e .

These two c . o n d i t i o n s were s a t i s f i e d t o a s u f f i c i e n t p r e c i s i o n i n

t h e p r e s e n t c a s e , a s w i l l now be shown..

a . The magne t i c measurements made on t h e d e f l e c t i n g magnet

i n d i c a t e t h a t one h a l f of t h e magnet, t h e ups t ream h a l f ,

r c o n t r i b u t e d 0.258 more t o j Adx t h a n d i d t h e o t h e r h a l f .

T h i s s m a l l asymmetry i n t h e magnet r e s u l t s i n a 0.01% l a r g e r

d e f l e c t i o n 20 f e e t downstream of t h e magnet t h a n would

o b t a i n from a p e r f e c t l y symmetr ic magnet , hence t h i s

asymmetry o f t h e magnet may be Pgnored..

b. Dur ing t h e d e f l . e c t i o n measurements t h e magnet was o r i e n t e d

w i t h i n 5 m i l l i r a d i a n s of t h e c o r r e c t a n g l e . A change o f . 5

m i l l i r a d i a n s i n t h e magnet a n g l e r e s u l t s i n a change o f l e s s

t h a n 0.02% i n t h e f i n a l d e f l e c t i o n 20 f e e t downstream o f t h e

magnet , hence t h e magnet was , a l i g n e d s u f f i c i e n t l y a c c u r a t e l y .

Thus, Eq ( 8 ) may be used d i r e c t l y t o d e t e r m i n e pc. The v a l u e s o f

/ ' . ' J ~ ( x ) d x l i s t e d i n t a b l e I were c o r r e c t e d t o o b t a i n r H ( s ) d x a l o n g a

symmetr ic t r a j e c t o r y . T h i s c o r r e c t i . o n was 0.05% o r l a s s . The d z f l -

e c t i o n magnet c u r r e n t s a c t u a l l y used d u r i n g t h e d e f l e c t i o n measurements

were a b o u t 3% h i g h e r t h a n t h e c u r r e n t s e t t i n g s f o r whi,ch t h e m a g n e t i c

measurements were made. A computer program was w r i t t e n which took t h e

b a s i c d a t a of t h e d e f l e c t i o n measurements ( d e f l e c t i o n d , d i s t a n c e

between magnet and g l a s s s l i d e s L , d e f l e c t i o n magnet c u r r e n t , synch-

?o t ro .n D.C. c u r r e n t , and r f f r e q u e n c y ) and t h e d a t a of t h e magne t i c

measurements ( d e f l e c t i o n magnet c u r r e n t and [ ~ d x ) , ~ e r : f o r m e d t h e

r e q u i r e d n o r m a l i z a t i o n s f o r d i f f e r e n t d e f l e c t i o n magnet c u r r e n t s and

f o r a s t a n d a r d r f ' f r e q u e n c y ( s e l e c t e d f o r conven ience a t 475.700 Mc),

and used Eq (8) t o compute pc and t h e r a t i o o f s y n c h r o t r o n D O C . c u r -

r e n t ( e x p r e s s e d i n mv on t h e s h u n t : 1 mv = 1 amp) t o pc. T h i s r a t i o is

t h e s i m p l e s t way t o e x p r e s s t h e r e s u l t s of. t h e measurements , and t h e

r a t i o s a r e l i s t e d i n t a b l e I1 and f i g I V . A 1 msec peak ing s t r , i p

, p u l s e s p a c i n g i s assumed.

Energy (GeV)

CEAL-1015

T a b l e I1 - R e s u l t s

1 2 3 4 5 6

D.C. M i l l i v o l t s p e r 62.74 62.63 62.78 62.78 62.77 62.61 GeV a t 473.700Mc and 1 msec p e a k i n g s t r i p p u l s e s p a c i n g

P r e c i s i o n

The e r r o r s i n d i c a t e d a r e c o n s e r v a t i v e e s t i m a t e s o f t h e combined

e f f e c t s of t h e s e v e r a l c o n t r i b u t i n g e r r o r s . The e r r o r i s l a r g e r a t

1 GeV due t o t h e magnet i n s t a b i l i t y t h e r e , and a t 6 GeB due t o t h e

~ ,,

s m a l l and v a r y i n g a c c e l e r a t e d beam i n t e n s i t y which n e c e s s i t a t e d a

~. l o n g e r e x p o s u r e t i m e ,

~ D i s c u s s i o n

~ The f i n a l r e s u 1 , t s a r e q u i t e c o n s i s t e n t w i t h a c o n s t a n t r a t i o of

I

I D.C. m i l l i v o l t s p e r GeV f o r t h e e n e r g y r a n g e 1 t o 6 GeV. The we igh ted

a v e r a g e o f t h e i n d i v i d u a l measurements g i v e s 62.73 mv p e r GeV a t

475.700 Mc and 1 msec peak ing s t r i p p u l s e s p a c i n g , a r e s u l t which i s

a c c u r a t e t o 20.2% o r b e t t e r .

I n u s i n g t h i s r e s u l t it i s i m p o r t a n t t h a t a c o r r e c . t i o n be made

~ f o r a n y d i f f e r e n c e i n r f f r e q u e n c y from 475.700Plc, 'using .Eq ( 5 ) . The

~ f r e q u e n c y used must c o r r e s p o n d t o t h e peak of thesmagne t c y c l e ,

1 a v o i d i n g t h e 2 m i l l i s e c o n d p e r i o d n e a r i n j e c t i o n when t h e r f f r e q u e n c y

i s h i g h e r . Also t h e r e s u l t a p p l i e s o n l y t o t h e e n e r g y of t h e c i r c u -

l a t i n g b e a m , . o r any beam p u t on a t a r g e t , o r e x t r a c t e d 'from t h e

s y n c h r o t r o n , by t h e beam bump method ( i . e . a beam t h a t i s i n phase

synchronism w i t h t h e ~ f j . I f rf t u r n o f f i s u s e d , a c o r r e c t i o n must

be made f o r t h e e n e r g y l o s s of t h e e l e c t r o n s a s t h e y s p i r a l inward t o

t h e t a r g e t p o s i t i o n . This c o r r e c t i o n i s g i v e n by

where i s a g a i n .03,1, r i s t h e a v e r a g e d i s t a n c e f rom t h e c e n t e r o f t h e

s y n c h r o t r o n t o t h e o r b i t (1420 i n ) , and Ar i s the. d i s t a n c e between t h e

! t a r g e t t o be engaged and t h e l o c a l e q u i l i b r i u m o r b i t ( t y p i c a l l y

ACKNOWLEDGEMENTS

~ The h e l p of James P a t e r s o n i n s e t t i n g up t h e emergent e l e c t r o n

I beam, ~ . ~ v e r i l l i n t h e remanence f i e l d measurements on t h e s y n c h r o t r o n

magnets , ~ i c h a r d Levy i n making t h e magne t i c measurements on t h e d e f l e c -

t i n g . * ~ m a g n e t , F o r r e s t Tomes and John C e r i n o i n a l i g n i n g t h e beam r u n ,

l and 3. C a r r i n c a l i b r a t i n g s h u n t s i s g r a t e f u l l y acknowledged. The

I c o n t i n u e d i n t e r e s t (and i n i t i a l p a r t i c i p a t i o n ) o f Thomas C o l l i n s i n

t h i s p r o d e c t r e s u l t e d i n many v a l u a b l e s u g g e s t i o n s r e g a r d i n g t h e t e c h - I I n i q u e and a n a l y s i s of t h e measurements .

CEAL-1015

TABLE I

Magnet ic Measurements

Nominal D e f l e c t i n g ( X ( x ) d x a l o n g H(x)dx P r e c i s i o n Energy Magnet

C u r r e n t C e n t e r l i n e C u r r e n t

6 GeV

5 GeV

4 CeV

3 GeV

2 GeV

1 GeV

0.5 GeV

200.2 amps

131 0390

109*294

88.454

65.316

42.574

21.395

11.660

6.580 k g - i n amp.

7.4408

, Notes: The measurement a t 200.2 amps, was made w i t h a H a l l

probe. A l l o t h e r s w e r e made w i t h N.M.R. and r o t a t i n g

c o i l . These measurements a r e a t a t m o s p h e r i c . p r e s s u r e .

Under vacuum t h e d i s t o r t i o n a t t h e vacuum box c a u s e s

t h e f i e l d a l o n g t h e magnet c e n t e r l i n e t o i n c r e a s e by

0 .05%.

ATING ELECTRON BEAM

EMERGENT ELECTRON BEAM

MONI TOR

PLAN VIEW

4 SLIDE (I>EFLECED SPO

- - - - - - . . - - - - -

30" OtAM. WOOD DSC DEFLECTION C/\ 32"

SPOT DEFLECTED BY POSl TI VE UNDEFLEC TED BEAM

REMANENCE Fl POS.lT/ON I - - -

SPOT DEFLECTED BY NEGATIVE OWER SLIDE

FIG lr

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