Beam optics study of general ionex model 1545 linear particle accelerator, The

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By Lian He

ARTHUR LAIE^ LIBRARY

COLO$'-M)Q SCHOOL oi

MINES

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INFORMATION TO ALL USERS

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A t h e s i s s u b m i t t e d to the F a c u l t y and the B o a r d of T r u s t e e s of t h e C o l o r a d o S c h o o l of M i n e s in p a r t i a l f u l f i l l m e n t of the r e q u i r e m e n t s for the d e g r e e of M a s t e r of S c i ence ( P h y s i c s ) . Golden, Color a d o Date: U — i2 — t S i g n e d : Lian He A p p r o v e d : L Dr. F. E. Cecil Th e s i s A d v i s o r Golden, C olorado P r o f e s s o r and Head Physics D e p a r t m e n t ii

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A B S T R A C T

T h e t r a n s p o r t o p t i c s of a G e n e r a l I o n e x M o d e l 1545 L i n e a r P a r t i c l e A c c e l e r a t o r is s t u d i e d by u s i n g a s c a n n i n g t y p e b e a m p r o f i l e monitor. The e x p e r i m e n t a l d ata c o l l e c t e d at t h e t a r g e t c h a m b e r is a n a l y z e d to a t h e o r e t i c a l m o del t h r o u g h a F O R T R A N code, and the r e s ults a g r e e well as the r e s u l t s g i v e n by a t h e o r e t i c a l a c c e l e r a t o r d e s i g n p r o g r a m OPTICIAN.

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TABLE OF CONTENTS

Page

A B S T R A C T ... iii

LIST OF FIGURES ... v

LIST OF TABLES ... vii

A C K N O W L E D G E M E N T S ... vii.i C h a p t e r I. I N T R O D U C T I O N ... 1 C h a p t e r II. B A C K G R O U N D ... 4 2.1 The A c c e l e r a t o r ... 4 2.2 Optical Compo n e n t s ... 7 C h a p t e r III. E X P E R I M E N T ... 14 3.1 Beam Profile M o n i t o r ... 14

3.2 Beam O p tics Study ... 18

C h a p t e r IV. M O D E L FITTING 2 6 4.1 Fitting Data to an E q u a t i o n ... 2 6 4.2 Beam Profile S i m u l a t i o n ... 34 Ch a p t e r V. C O M P A R I S O N 3 8 R E F E R E N C E C ITED ... 4 2 S E L E C T E D B I B L I O G R A P H Y .... ... 4 3 A p p e n d i x A. N O R M A L D I S T R I B U T I O N 4 5 A p p e n d i x B. FORTRAN PROGRAM 4 8 iv

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LIST OF FIGURES

Page Figure 2-1 The General Ionex Model 1545 L i near

P article A c c e l e r a t o r ... 6 Figure 2-2 The Lens A c t i o n of a U n i p o t e n t i a l

Lens ... 9

Figure 3-1 The Detec t o r Cross Sect i o n V i e w ... 15 Figure 3-2 Circ u i t Diag r a m of the M u l t i p l e x i n g

E l e c t r o n i c ... 17 F igu r e 3-3 Best V o l t a g e S e t ting of Grid Einzel

Lens . . ... 19

Figure 3-4 A d j u s t i n g Range of Grid Einzel Lens

V o l t a g e ... 21

Figure 3-5 H o r i z o n t a l Beam Profile at 100 KV

A c c e l e r a t i n g V o l t a g e ... . 2 2 F i gure 3-6 H o r i z o n t a l Beam Profile at 50 KV

A c c e l e r a t i n g V o l t a g e ... 23 Figure 3-7 Beam Profile at 100 KV A c c e l e r a t i n g

V o l t a g e (Vg = 17.0 KV) ... 24 Figure 3-8 Beam Profile at 50 KV A c c e l e r a t i n g

V o l t a g e (Vg = 9.0 KV) ... 2 5 Figure 4-1 R e l a t i v e Beam Intensity as F u n c t i o n of n

and V g at 80 KV A c c e l e r a t i n g V o l t a g e ... 35 v

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F i gure 4-2 R e l a t i v e Beam I n tensity as F u n c t i o n of Sin#

and Vg at 80 KV A c c e l e r a t i n g V o l t a g e ... 3 6 Fi gure 4-3 Beam Profile at 80 KV A c c e l e r a t i n g

V o l t a g e (Vg = 15 KV) ... 3 7 F i g u r e 5-1 Beam Profile G e n e r a t e d by O P T I C I A N ... 40

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LIST OF TABLES Page T a b l e 2-1 A p p l i c a t i o n s of the A c c e l e r a t o r ... 5 T a b l e 2-2 Beam S p e c i f i c a t i o n s ... 7 T a b l e 2-3 T r a n s f e r M a t r i x ... 9 T a b l e 4-1 C o e f f i c i e n t s of P a r ameters in Esti m a t e Model ... 31 T able 4-2 C o e f f i c i e n t s of (j,x in E s t i m a t e Model .... 32 T a b l e 4-3 C o e f f i c i e n t s of P a r ameters in P r e d i c t o r Model 3 3 T a b l e 4-4 C o e f f i c i e n t s of n x in P r e d i c t o r Model .... 3 3 T a b l e 4-5 P e r f o r m a n c e s of P r e d i c t o r M o d e l s ... 34 Ta b l e 5-1 List Outp u t of O P T I C I A N at 100 KV A c c e l e r a t i n g V o l t a g e ... 39 vii

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A C K N O W L E D G E M E N T S

I w o u l d like to a p p r e c i a t e my entire T h e s i s Committee; Dr. F. E d w a r d Cecil for his long stan d i n g e n c o u r a g e m e n t and p a t i e n c e that m a d e this w o r k possible; Dr. J a m e s T. Brown for the k n o w l e d g e w h i c h I learned and for his sense of h u mor w h i c h m a d e my college life m o r e colorful; and Dr. W i l l i a m B. Law for his careful c o n s i d e r a t i o n of my a c a d e m i c background.

I w o u l d also like to t h a n k Mr. Rex R i d e o u t for his help in the e l e c t r o n i c circuit desi g n of the b e a m p r o f i l e m o n i t o r and to t h a n k Mr. H u a i z h u Liu for the helpful d i s c u s s i o n s on this thesis.

Finally, I w o u l d l ike to t h a n k Dr. J. U. T r e f n y w h o b r o u g h t me the o p p o r t u n i t y to c o m e to C S M a n d to t h a n k the P h y s i c s department, the G r a d u a t e School, and the U. S. D e p a r t m e n t of E n ergy for t h e i r financial support.

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C h a p t e r I I N T R O D U C T I O N

S i nce B e c q u e r e l 1s d i s c o v e r y of r a d i o a c t i v i t y in 1896, the e x p e r i m e n t a l and theo r e t i c a l studies in n u c l e a r physics h a v e p l a y e d a p r o m i n e n t role in the d e v e l o p m e n t of t w e n t i e t h c e n t u r y p h y s i c s . F r o m t h e s e s t u d i e s , w e h a v e t o d a y a r e a s o n a b l y good u n d e r s t a n d i n g of p r o p e r t i e s of nuclei and of the stru c t u r e that is r e s p o n s i b l e for those properties.

L a b o r a t o r y e x p e r i m e n t s in n u c l e a r p h y s i c s h a v e b e e n a p p l i e d to the u n d e r s t a n d i n g of an i n c r e d i b l e v a r i e t y of problems, from the i nteractions of quarks, to the p rocesses t h a t o c c u r r e d d u r i n g the e a r l y e v o l u t i o n of the u n i v e r s e j u s t a f t e r the Big Bang. Today, a g o o d u n d e r s t a n d i n g of e x p e r i m e n t a l t e c h n i q u e s and the p r o p e r use of e x p e r i m e n t a l i n s t r u m e n t s are e v e n m o r e i m p o r t a n t for an e x p e r i m e n t a l p h y s i c i s t .

P art i c l e a c c e l e r a t o r s are the m ost useful tools for the r e s e a r c h in n u c l e a r physics. The b e a m s p r o d u c e d from those m a c h i n e s can be u s e d to d i s i n t e g r a t e nuclei, p r o d u c e new u n s t a b l e isotopes, and investigate the p r o p e r t i e s of n u c lear

f o r c e s .

T h e p u r p o s e of an a c c e l e r a t o r of c h a r g e d p a r t i c l e s is to b o m b a r d a t a r g e t w i t h a b e a m of a s p e c i f i c kind of

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p a r t i c l e s of c h o s e n energy. T h e r e a r e m a n y v a r i e t i e s of m e t h o d s for a c c o m p l i s h i n g t h i s task, all u s i n g v a r i o u s a r r a n g e m e n t s of e lectric and m a g n e t i c fields.

As an e l e c t r o n i c device, the a c c e l e r a t o r r e q u i r e s a source of c h a r g e d particles, an e lectric field to a c c e l e r a t e the particles, focu s i n g e l e m e n t s to c o u n t e r a c t the n a t ural t e n d e n c y of the b e a m to diverge, d e f l e c t o r s to aim the b e a m in the d e s i r e d dire c t i o n , a t a r g e t c h a m b e r to h o u s e all the c o m p o n e n t s in h i g h v a c u u m to p r e v e n t the b e a m f rom s c a t t e r i n g in c o l lisions w i t h m o l e c u l e s in the air.

T h e d e s i g n of a c c e l e r a t o r s v a r i e s g r e a t l y w i t h t h e p u r p o s e for w h i c h t h e y w i l l be used. S o m e of t h e m are o p e r a t e d at h i g h e n e r g y r a n g e up to T e V (106 MeV) , the T e v a t r o n at F e r m i l a b has r e c e n t l y b e e n m o d i f i e d to o p e r a t e as a p r o t o n c o l l i d e r w ith each beam h a v i n g an e n e r g y 1 TeV; some of t h e m are p h y s i c a l l y large, the t w o - m i l e long 32 GeV l i n e a r e l e c t r o n a c c e l e r a t o r at Stanford, 2.2 km rings 26 GeV p r o t o n s y n c h r o t r o n a c c e l e r a t o r at CERN (the Cent e r Euro p e a n f o r N u c l e a r R e s e a r c h ) . A l t h o u g h t h e d e t a i l s of t h e s e a c c e l e r a t o r s may be rather t e c h n i c a l l y difficult, they have a b a s i c r e q u i r e m e n t to p r o d u c e h i g h i n t e n s i t y a n d w e l l c o n t r o l l e d b e a m s w h i c h can r e d u c e the s t a t i s t i c a l e r r o r of e x p e r i m e n t a l data and d i f f i c u l t i e s of a c c e l e r a t o r operation. U n d e r s t a n d i n g of the b e a m optics (or b e a m transport) system

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of an a ccelerator, w h i c h c o n s i s t s of a n u m b e r of e l e c t r i c and m a g n e t i c devi c e s that focus the b e a m and b end or deflect it a l o n g the d e s i r e d path, b e c o m e s m o r e i m p o r t a n t for the a c c e l e r a t o r o p e r a t i o n and maintenance.

This t h e s i s will c o n c e n t r a t e on the b e a m o p tics study of the General Ionex Model 1545 linear p a r t i c l e accelerator. A t h e o r e t i c a l b e a m o p t i c s model of the a c c e l e r a t o r w i l l be g i v e n at full o p e r a t i o n conditions.

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C h a p t e r II B A C K G R O U N D

The b e a m t r a n s p o r t in the a c c e l e r a t o r is a p r o c e s s in w h i c h c h a r g e d p a r t i c l e s i n t e r a c t w i t h the e l e c t r o m a g n e t i c f i e l d s p r o d u c e d b y the c o m p o n e n t s of the a c c e l e r a t o r . To st u d y the process, we s h o u l d h a v e a good u n d e r s t a n d i n g of the a c c e l e r a t o r s tructure and functions of its components.

2.1 The A c c e l e r a t o r

T h e G e n e r a l I o n e x M o d e l 1 5 4 5 L i n e a r P a r t i c l e a c c e l e r a t o r s [GE82] are t y p i c a l of the e x p e r i m e n t t o o l s in low e n e r g y n u c l e a r p h y s i c s since it can p r o d u c e 0 -18 0 KeV c o n t i n u o u s l y v a r i a b l e energy high intensity beams. T a b l e 2-1 shows the a p p l i c a t i o n s of the accelerator. T h e a c c e l e r a t o r has a s i m p l e s t r u c t u r e w h i c h c o n s i s t s of an ion source, e x t r a c t i o n gap, E i n z e l lens, c r o s s e d - f i e l d a n a l y z e r (or e l e c t r o m a g n e t i c m a s s a n a l y s i s magnet), a c c e l e r a t i o n tube, g rid Einzel lens, source pump manifold, and a s s o c i a t e d power s upplies as shown in Figure 2-1.

The b a s i c o p e r a t i o n of the a c c e l e r a t o r star t s at the ion source. N e u t r a l (Hydrogen or H e l i u m for example) gas atoms enter the top of the ion source and are ionized in the

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T a b l e 2-1. A p p l i c a t i o n s of the A c c e l e r a t o r [GA89] A p p l i c a t i o n s Features Cross S e c t i o n M e a s u r e m e n t s Plasma D i a g n o s t i c Ion I m p l a n t a t i o n Low E n e r g y B a c k s c a t t e r A n a l y s i s D e t e c t o r C a l i b r a t i o n M a t e r i a l s M o d i f i c a t i o n H i g h C u r rent up to 0.3 mA H i g h Beam S t a b i l i t y H e a v y Ion C a p a b i l i t y

W i d e E n ergy Range 18 0 KeV P recise Beam Optics

P ositive Ions

v i c i n i t y of a h o t f i l a m e n t w h i c h p r o v i d e s an e l e c t r o n discharge. A strong axial m a g n e t i c field p r o d u c e d by a coil a r o u n d t h e ion s o u r c e c o n s t r i c t s t h e ions to a n a r r o w p l a s m a b e a m a l o n g the axis of the e x i t a p e r t u r e and a l s o c o n c e n t r a t e s the electrons leaving the filament to increase the i o n i z i n g effic i e n c y . T h e p o s i t i v e l y c h a r g e d ions are t h e n e x t r a c t e d by the e x t r a c t i o n gap w h i c h is a n e g a t i v e h i g h v o l t a g e p r o b e e l e c t r o d e . A d i v e r g e n t i n i t i a l b e a m h a v i n g an ener g y up to 3 0 KeV is formed. Then, the b e a m is focussed by the first Einzel lens and bent by the a n a l y z i n g m a g n e t to t h e t o p of a c c e l e r a t i o n tube. T h e i m p u r i t i e s , d i f f e r e n t isot o p i c species, are s e p a r a t e d by the a n a l y z i n g m a g n e t due to the m a s s difference. A d d i t i o n a l a c c e l e r a t i o n up to m a x i m u m b e a m e n e r g y or d e c e l e r a t i o n d o w n to m i n i m u m

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Extraction Gap (30 kV) B n zel Lens 1 Ion Source Magnet Source Rack 'T a b le (floats at a c c e le ra tio n p o te n tia l) In s u la tin g

Lucite Rods Glassman™ _{150 kV}

Power Supply S tepper M o t o r ' Ar r a y Gate Grounded Safety Fence In te rm e d ia te

Control Rack Beam Tube

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b e a m e n e r g y is p r o v i d e d by the a c c e l e r a t i o n tube. Finally, the g r i d E i n z e l lens f o c u s e s the b e a m to an a p p r o p r i a t e s ize (about 0.4 cm diameter) at the t a r g e t p o s i t i o n for e x p e r i m e n t s .

A f t e r t h e b e a m w a s f o r m e d at t h e ion s o u r c e , its p r o p e r t i e s are d e p e n d e n t on t h e f u n c t i o n of t h e o p t i c a l c o m p o n e n t s of the accelerator, E i nzel lenses and a n a l y z i n g m a g n e t , t h a t f o r c e t h e b e a m to a d e s i r e d p a t h w i t h a d e s i g n e d shape. The b e t t e r the opera t i n g c o n d i t i o n s of these components, the b e t t e r the b e a m symmetry achieved. T a b l e 2-2 shows the d e s i g n e d b e a m specifications.

T able 2-2. Beam S p e c i f i c a t i o n s [GA89]

Energy(KV) Current (fiA) D i v e r g e n c e (1/2 angle,mrad)

150 300 15

20 150 20

1 1 100

2.2 Optical C o m ponents

Charged p a r t i c l e optics is similar to light optics. For g e o m e t r i c light optics it has been c u s t o m a r y since the time of N e w t o n to use an a l g e b r a i c formulation for all e q uations

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involved. H owever, t h i s m e t h o d has b e e n r e p l a c e d in m a n y c a s e s b y t h e u s e of t r a n s f e r m a t r i c e s w h i c h o f f e r s an u n e x c e l l e d s i m p l i c i t y a n d c l a r i t y for a c o m p l e x o p t i c a l system.

In t h e m a t r i x r e p r e s e n t a t i o n , w e c a n d e s c r i b e t h e r e l a t i o n s h i p b e t w e e n image space (2) and object space (1) of a b u n d l e rays p a s s i n g t h r ough an optical s y stem as

r- m u m i 2

^ 2 1 ^ 2 2

r r i

(2 - 1 )

w h e r e r is the d i s t a n c e from the axis of the syst e m (z-axis) and d is the angle b e t w e e n the rays and the axis.

The m a t r i x M = [mj, j ] is c a l l e d t r a n s f e r m a t r i x of the system. T a b l e 2-3 shows the t r a n s f e r m a t r i c e s of some simple optical system.

The g r e a t adva n t a g e of this m e thod is that we can write a t r a n s f e r m a t r i x of a c o m plex system as the m u l t i p l i c a t i o n of the t r a n s f e r m a t r i c e s of each comp o n e n t

CM t o t a l ] = CM n3 tM n-i] ' ’ ' ’CM 2 1 1 (2 ~ 2 )

If e a c h t r a n s f e r m a t r i x of the c o m p o n e n t is specified, the o ptical p r o p e r t i e s of a system are determined.

We w ill u s e the t r a n s f e r m e t h o d to s t u d y each o p t ical c o m p o n e n t of the accelerator.

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Table 2-3. T r a n s f e r M a t r i x

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W h e n a ray (consider p o s i t i v e ions only) p r o c e e d s in th e d i r e c t i o n of i n c r e a s i n g p o t e n t i a l , it e x p e r i e n c e s a r a d i a l e l e c t r o s t a t i c f orce c a u s e d by the g r a d i e n t of the p o t e n t i a l w h i c h d e c e l e r a t e s it and p u s h e s it r a d i a l l y away f r o m t h e a x i s t h a t is a d i v e r g e n t action. The o p p o s i t e p r o c e e d i n g is a c o n v e r g e n t action. In general, w h e n a ray p r o c e e d s in the d i r e c t i o n of i n c reasing potential, a concave e q u i p o t e n t i a l h a s a c o n v e r g e n t e f f e c t a n d a c o n v e x e q u i p o t e n t i a l has a d i v e r g e n t effect. S i n c e the ions w h i c h h a v e a h i g h e r e n e r g y in a conv e x e q u i p o t e n t i a l r e g i o n are e x p o s e d for a s h o r t e r t i m e to the d e f o c u s s i n g f ield t h a n t h e y are k e p t in the c o n c a v e e q u i p o t e n t i a l r e g i o n w h e r e is a f o c u s s i n g field. The net e f fect is that the p o s i t i v e focusing effect always dominate. It is also true if the ions p r o c e e d into an E i nzel lens in the d i r e c t i o n of d e c r e a s i n g potential. The Einzel lens is a l ways a c o n v e r g i n g element. The Einzel lens also has an important feature that the beam enters and leaves the lens w i t h the same energy.

U n d e r the a s s u m p t i o n that ions m o v e alone to the axis, the p araxial ray e quation of m o t i o n for an axia l l y symm e t r i c e l e c t r o s t a t i c field can be w r i t t e n as [BA66]

d 2 r

+ + --- r = 0 (2-3)

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w h e r e V 0 is the axial potential. T h e t r a n s f e r m a t r i x of an E inzel lens is found by s o l ving Equat i o n (2-3) as

w h e r e V x is the p o t e n t i a l of the o u t s i d e electrodes, V 2 is the p o t e n t i a l of t h e c e n t r a l e l e c t r o d e and d is the h a l f l e ngth of the cylinders.

The grid Einzel lens is a symmetrical Einzel lens with the c e n t r a l e l e c t r o d e r e p l a c e d by a m e s h g r i d w h i c h will give a b e t t e r optical qual i t i e s than the Einzel lens.

T h e a n a l y z i n g m a g n e t is a l s o an i m p o r t a n t o p t i c a l e l e m e n t for d e f l e c t i o n and f o c u s s i n g of c h a r g e d p a r t i c l e s in t h e a c c e l e r a t o r . The m a g n e t can focus the ion b e a m in e i t h e r or b o t h r a d i a l a n d v e r t i c a l p l a n e s d e p e n d i n g on t h e f i e l d c o n f i g u r a t i o n . T h e s e p a r a t i o n of the b e a m is d e t e r m i n e d by its m o m e n t u m spread.

In t h e a n a l y z i n g m a g n e t , t h e i ons e x p e r i e n c e the Lorentz force w h i c h causes a p a r t i c u l a r m ass to be selected by the magnet. If the m a g n e t i c field B is p e r p e n d i c u l a r to the m o v i n g d i r e c t i o n of the ions, the s e l e c t e d m a s s can be

2(V

x

V 2)^

M (2-4)

3 V 1- 3 V 2 ( J v 7 - J v j (3Jv7-Jv7) 8 J V 1V 2 - 3 V 1- 3 V 2

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w r i t t e n as

m = (qBR)2 / 2 E 0 (2-5)

w h e r e R is the radius of c u r v a t u r e of the m a g n e t and E 0 is the initial e n e r g y of ions b e f o r e e n t r a n c e the magnet. For ions h a v i n g d i f f e r e n t masses, the paths are d i f f e r e n t w h i c h w i l l a f f e c t t h e o p t i c a l p r o p e r t i e s of the beam. U s i n g a rela t i v e m o m e n t u m spread A P / P as a compo n e n t in the initial and final colu m n v e c t o r in a d d i t i o n to r and 6 , a t r a n s f e r m a t r i x for normal entrance into the sector m a g n e t is [LI69]

M =

Cos (6a) R<S-1 Sin (<Sa) R S ~ 2 [ 1-Cos ( S o l) ]-| •R” 1 <5Sin (6a) Cos(<5a) 6-1 Sin (<5a)

0 0 1

(2 - 6 )

w h e r e a is the b e n d i n g angle of the sector m a g n e t and 6 is g i v e n by

r dB

S = (l - n )h = (1 + ---- )% (2-7)

B dr

in w h i c h n is called the field index. For a u n i f o r m B field, n is zero.

The a c c e l e r a t i o n t ube is a m u l t i - e l e c t r o d e s t r u c t u r e th a t i m p arts e n e r g y to the ions in s u c c e s s i v e l y stages. As th e ions t r a v e l a l o n g the tube, t h e i n c r e a s e d p o t e n t i a l

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e n e r g y of ions c o n v e r t to t h e k i n e t i c e n e r g y t o w a r d a d e s i r e d b e a m energy. M a n y studies h a v e i n d i c a t e d t h a t the o ptics of an a c c e l e r a t i o n tube are e s s e n t i a l l y linear. It is c o n v e n i e n t to r e p r e s e n t a t ube as a l i n e a r s y s t e m in terms of the t r a n s f e r matrix.

All of the above d i s c u s s i o n n e g l e c t s the s p a c e - c h a r g e e f f e c t w h i c h is p r o d u c e d b y the ion b e a m itself. So, the o p t ical p r o p e r t i e s of t h e s e c o m p o n e n t s of the a c c e l e r a t o r are in the p a r a x i a l region. A t 1 mA of b e a m current, the s p a c e - c h a r g e e f f e c t is two orders s m a l l e r t h a n our result. S ince the b e a m current of the a c c e l e r a t o r is less than 1 mA, t h e a p p r o x i m a t i o n of n e g l e c t i n g s p a c e - c h a r g e e f f e c t is a p p r o p r i a t e . T h e h i g h e r o r d e r o p t i c a l p r o p e r t i e s c a n be o b t a i n e d e i t h e r b y s o l v i n g P o s s i o n ' s e q u a t i o n w i t h the s p a c e - c h a r g e d e n s i t y p at a s e t of p r o p e r b o u n d a r y c o n d i t i o n s e x a ctly or by solving E q u a t i o n (2-3) a d d i n g term

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C h a p t e r III E X P E R I M E N T

A s c a n n i n g type b e a m p r o file m o n i t o r has been d e s i g n e d and i n s t a l l e d on the a c c e l e r a t o r . U s i n g the b e a m p r o f i l e m o n i t o r , t h e f i n a l b e a m p a t t e r n s w e r e s t u d i e d . A l l e x p e r i m e n t data w e r e c o l l e c t e d at the targ e t c h a m b e r t h r o u g h the b e a m p r o f i l e m o n i t o r w h e n the E x t r a c t i o n Gap v o l t a g e was set to 20 KV and the first Einzel Lens v o l t a g e was set to 15 KV.

3.1 Beam Profile M o n i t o r

The b e a m p r o f i l e m o n i t o r c o n s i s t s of a d e t e c t o r and an a n a l o g e l e c t r o n i c circuit. The d e t e c t o r was m a d e by A. G a v i r i a [ G A 8 9 ] . T h e e l e v e n c o p p e r r i n g s a c t i n g as c h a r g e collectors, each has the w i d t h of 1/8 inches s e p a r a t e d from one a n o t h e r by 1/32 inches, are m o u n t e d on a c e r a m i c rod w h i c h is p o s i t i o n e d a c ross a d i a m e t e r p e r p e n d i c u l a r to the d i r e c t i o n of b e a m propagation. The cross section v i e w of the d e t e c t o r is shown in Figure 3-1. Each c o p p e r ring intercepts an amou n t of charge that is p r o p o r t i o n a l to the inte n s i t y of the b e a m at that point. W i res from each individual ring w ere b r o u g h t out of the target c h a m b e r and fed into the switc h i n g

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.. CHAMBER FLANGE

SUPPORTING

ROD CERAMIC ROD

a n

ROTATING GRID

COPPER RINGS

ROTATING SHAFT _{CERAMIC ROD}

SLIDES IN AND OUT ROTATING ARM

WIRES TO THE OUTSIDE

BEAM

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e l e c t r o n i c circuit [GA84].

The c h a r g e c o l l e c t e d by each c o p p e r ring is s t o r e d in a 1 iiF c a p a c i t o r (the e l e v e n c a p a c i t o r s w e r e s e l e c t e d for b e t t e r t h a n 1% m a t c h ) , v i a a v a r i s t o r - d i o d e - n e o n - v a r i s t o r p r o t e c t i o n network. The v o l t a g e on each c a p a c i t o r is sampled by an a n a l o g m u l t i p l e x e r IC d r i v e n at a c o n v e n i e n t rate (11 kHz) b y a f r e e - r u n n i n g c o u n t e r . T h e o u t p u t of t h e m u l t i p l e x e r is sent d i r e c t l y to the s t o r a g e o s c i l l o s c o p e w i t h the time base t r i g g e r e d by the c o u n t e r and sweep speed set so t h a t one c o m p l e t e scan of the e l e v e n inputs is one sweep. The s c h e m a t i c of s w i t c h i n g c i r c u i t d i a g r a m is s hown in F i gure 3-2.

The b e a m p r o f i l e w h i c h can be s e e n on the s c o p e was d i v i d e d to e l e v e n channels. Each channel g ives the v o l t a g e across each 1 jiY c a p a c i t o r and is p r o p o r t i o n a l to the amount c h a r g e c o l l e c t e d b y e a c h ring. T h e o u t p u t of a c e r t a i n channel repre s e n t s the relative beam intensity at that p oint of b e a m c r o s s section. By r o t a t i n g the d e t e c t o r c r o s s i n g the a c c e l e r a t e d beam, r e c o r d i n g d ata at each posit i o n , a c o m p l e t e d b e a m p r o f i l e is achieved.

At zero v o l t a g e input of the b e a m prof i l e monitor, the d i f f e r e n c e of output b e t w e e n channels caused by the leaking c u r r e n t of the diodes is less than 20 m V and is m u c h s m a ller t h a n t h e o u t p u t at n o r m a l o p e r a t i o n c o n d i t i o n , w h i c h is

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to scope +15V scope trigger 10M IK ■ **Vv 10K peon * . varistor protection integrator input

for each input clock llKHz counter 7 11 out 8 input analog 1 multiplexer 2 CE out 1 8 input analog 2 multiplexer CE

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b e t w e e n 1 to 15 V. The b e a m p r o f i l e m o n i t o r is test e d stable and r e l i a b l e in the b e a m current range of the accelerator.

3.2 Beam Profile Study

Two e x p e r i m e n t s w e r e d e s i g n e d to s t udy the final b e a m profiles. In the first experiment, the d e t e c t o r was fixed at the c e n t e r of t h e t a r g e t c h a m b e r for w h i c h y is zero and m e a s u r e d the r elative b e a m intensity as the function of the v o l t a g e of the Grid Einzel Lens ( G E L ) , w h i c h gives a c e r tain fo cal s t r e n g t h of t h e beam, at d i f f e r e n t a c c e l e r a t i n g voltage. A b e s t v o l t a g e s e t t i n g of G E L was found for each a c c e l e r a t i n g v o l t a g e w h i c h g a v e t h e h i g h e s t s y m m e t r i c ou tput from b e a m prof i l e monitor. In the second experiment, we m e a s u r e d the beam profile at the best v o l t a g e setting of G E L w h i c h we found in the p r e v i o u s e x p e r i m e n t at d i f f e r e n t a c c e l e r a t i n g voltage. Both e x p e r i m e n t s w e r e p e r f o r m e d w h e n Ex t r a c t i o n Gap v o l t a g e was set to 20 KV, the v o l t a g e of the f irst E i n z e l Lens was set to 15 KV and the a c c e l e r a t i n g v o l t a g e w a s s e l e c t e d at 0 KV, 25 KV, 50 KV, 75 KV and 100 KV.

At t h e b e s t v o l t a g e s e t t i n g of GEL, we f o u n d t h e h i g h e s t s h a r p p e a k from t h e b e a m p r o f i l e m o n i t o r w h i c h i n d i c a t e s t h e b e s t a c h i e v e d o p t i c a l p r o p e r t i e s of t h e

ARTHUR LAKES LIBRARY C O L O A & D O SCsiCOL ot MINES

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B e s t V o lt a g e 20 120 80 100

20

60 0 40

Ac ce lera ting Voltage (KV)

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accelerator. F i g u r e 3-3 shows the r e l a t i o n s h i p b e t w e e n the a c c e l e r a t i n g v o l t a g e (Va ) and the b e s t v o l t a g e s e t t i n g of G E L (Vg) . The g o o d l i n e a r r e g r e s s i o n l e a d s to the l i n e a r o p e r a t i o n c o n d i t i o n of the accelerator.

The b eam spreads out as the v o l t a g e of G E L goes off its b e s t p o s i t i o n . T h e v o l t a g e a d j u s t i n g r a n g e of G E L g r o w s a l m o s t l i n e a r l y as the a c c e l e r a t i n g v o l t a g e i n c r e a s e s as s hown in F i gure 3-4. The h o r i z o n t a l b e a m p r o f i l e s are also s t u d i e d at five d i f f e r e n t a c c e l e r a t i n g v o l t a g e s . Some of th e m are shown in Figure 3-5 and Figure 3-6 in w h i c h we can see c l e arly the p e a k m o v i n g as a function of G E L voltage. In next chapter, we w ill find a t h e o r e t i c a l m o d e l w h i c h will r e p r e s e n t this kind r e l a t i o n s h i p when y is set to zero.

In the s e c o n d exper i m e n t , we m e a s u r e d five c o m p l e t e b e a m p r ofiles, some of t h e m are s h o w n in F i g u r e 3-7 and figure 3-8. From these plots, we found that the shape of the b e a m p r o f i l e is stable for the studied range of a c c e l e r a t i n g v o l t a g e and the p e a k of the b e a m p r o f i l e is a l i t t l e bit b e l o w the c e n t e r of the t a r g e t c h a m b e r w h i c h m a y d e p e n d on the p o s i t i o n setting of the detector.

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20

120

20 40 80

0 60 100

Acc eler ating Voltage (KV)

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45 O E G R E E S R O T A T I O N A B OUT Z-AXIS. k k s % (a) * - 45 O E G R E E S R O T A T I O N A B O U T Z-AXIS. (b) F i g u r e 3-5. H o r i z o n t a l B e a m P r o f i l e at 100 A c c e l e r a t i n g V o l t a g e KV

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IN T E N S I T Y

,

IN T E N S I T Y * 45 D E G R E E S R O T A T I O N A B OUT Z-AXIS. (a) -45 D E C R E E S R O T A T I O N A B O U T Z-AXIS. (b) F i g u r e 3-6. H o r i z o n t a l B e a m P r o f i l e a t 50 K V A c c e l e r a t i n g V o l tage

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S

I

N

C

A

N

G

L

E

)

1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11 A .26 26 .17 17 08 01 10 19 .19 28 .28 37 .37 .46 55 .55 * CONTOUR INTERVAL 64 LL 1. 0 0 .64 2.00 3.00 4.00 5.00 6.00 7.00

8

00 9.00 1 0 . 0 0 11

00 CHANNEL NUMBER

F i gure 3-7. Beam Profile at 100 KV A c c e l e r a t i n g V o l t a g e (Vg = 1 7 . 0 KV)

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S

I

N

C

A

N

G

L

E

)

> -1.00 2.00 3. 7.00 8.00 9.00 10 * CONTOUR INTERVAL = 2 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8 . 0 0 ' 9.00 10.00 1

CHANNEL NUMBER

1.0 0 j n 0.26 - 0.17 ^ 0.08 ^ -0 . 0 1 3 -0 . 1 0 ^ - 0 . 1 9 - - 0 . 2 8 - - 0 . 3 7 : - 0 . 4 6 ^ - 0 . 5 5 ^ - 0 . 64 1. 0 0

Figure 3-8. Beam Profile at 50 KV A c c e l e r a t i n g V o l t a g e (Vg = 9 . 0 KV)

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C h a p t e r IV M O D E L FITTING 4.1 F i t t i n g Data to an E q u a t i o n F r o m the s t u d y of p r e v i o u s c hapter, we f o u n d t h a t t h e r e l a t i v e i n t e n s i t y of t h e final b e a m p r o f i l e is a m u l t i - v a r i a b l e function w h i c h can be w r i t t e n as D = D ( E , V a , v g , x, y) (4-1)

w h e r e E is the final e n e r g y of the p a r t i c l e s , V a is the a c c e l e r a t i n g voltage, Vg is the v o l t a g e of Grid Einzel lens, and, x and y are the c o o r d i n a t e s at the t a rget chamber.

S i n c e the two l e n s e s in the a c c e l e r a t o r are E i n z e l lenses w h i c h incre a s e and d e c r e a s e the e n e r g y of p a r t i c l e s in the same amount, we can w r i t e the final ener g y for a b eam

E = Z e ( V ex + V a )

w h e r e Ze is the total charge of the b e a m p a r t i c l e and V ex is the v o l t a g e of E x t r a c t i o n Gap. In the case of our study, Z is one for phot o n b eam and V ex is 20 KV. E q u a t i o n (4-1) now is s i m p l i f i e d to

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F i t t i n g the e x p e r i m e n t a l data to E q u a t i o n (4-2) is a c o m p l e x problem. A correct w o r k i n g p r o c e d u r e should be made for s o l v i n g the p r o b l e m like this. T h e p r o c e d u r e t h a t we will f o llow is l i sted b e l o w w h i c h indi c a t e s the w o r k to be d one and the deci s i o n s to be made at each stage.

The p r o c e d u r e of fitting: Step 1. O b j e c t i v e

1. Esti m a t e effects 2. Predict responses

S tep 2. C o n s t r u c t Full Equat i o n 1. P revious study results

2. Search for cand i d a t e equation Step 3. S e l e c t i o n of Subsets of Vari a b l e s

1. S a m p l i n g each individual v a r i a b l e in full e quation 2. Study the v a r i a n c e of each v a r i a b l e

3. C o m b i n a t i o n of r e a sonable v a r i a b l e s 4. R e d u c e of functional v a r i a b l e s

5. A p p r o p r i a t e v a l u e s of c o e f f i c i e n t s in l i n e a r or n o n l i n e a r functional form of each r e m a i n i n g v a r i a b l e 6. Find i n g useful estim a t e equation

Step 4. Final P r e d i c t o r E quation

1. A d j u s t i n g all s elected p a r ameters 2. M i n i m i z i n g the total square residual

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Now, w e follow the p r o c e d u r e to find our t h e o r e t i c a l m odel of the final b e a m p r o f i l e of the accelerator.

We h ave a total of 1408 sets of e x p e r imental data w h ich we c o l l e c t e d in the two e x p e r i m e n t s d i s c u s s e d in p r e v i o u s chapter. Each set of data c o n t a i n s five m e a s u r e m e n t s w h i c h are V a , Vg, x, y and D. In the g e n e r a l o p e r a t i o n of the accelerator, for a c e r t a i n a c c e l e r a t i n g voltage, we s h o u l d h a v e a c e r t a i n V g t h a t g i v e s t h e b e s t b e a m p r o f i l e r e g a r d l e s s of a d j u s t i n g Vg from down side or up side. The a d j u s t a b l e range of V g s h o u l d be s y m m e t r i c a r o u n d the its b e s t p o s i t i o n that l eads a n o r m a l d i s t r i b u t i o n of Vg at c e r t a i n a c c e l e r a t i n g v o l t a g e V a . L o o k i n g o v e r the t h r e e d i m e n s i o n a l p lots in C h a p t e r III, we also found t h a t t h ere is a m o r e or less n o r m a l t y p e d i s t r i b u t i o n in the b e a m p r o f i l e in b o t h x a n d y d i r e c t i o n s . S i n c e d i f f e r e n t Vg should also affect x and y parts, the Equa t i o n ( 4 - 2 ) b ecomes

D = D [ V g ( V a ) , x ( V a , V g ), y ( V a , V g )] ( 4 - 3 )

If w e a s s u m e v a r i a b l e V g = V g ( V a ) is i n d e p e n d e n t of v a r i a b l e x and y, use the symbol N to repr e s e n t the normal distribution, we have our full equation of the model

D = D 0 N(Vg) N(x,y) (4-4)

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factor in the c o m p u t e r p r o g r a m (see A p p e n d i x B ) .

An n d i m e n s i o n a l normal d i s t r i b u t i o n can be d e t e r m i n e d c o m p l e t e l y by its w e i g h t p o i n t (/Zj ,/u2 , . . . ,/xn ) and X m a t r i x (see A p p e n d i x A). If we put the normal c o n s t a n t s of N(Vg) and N(x,y) into a function C ( V a/Vg), now the forms of N(Vg) and N(x,y) are

N ( V g ) = C ( V a/V g ) exp <(-v cr - M ( V a ) a ( Vg ) (4-5) N(x,y) = exp <-2 (1 ~p x y 2 ) x - n ( x ) ( ) a(x) x - fji(x) y - jLt(y) - 2 p_xy CT(X) _{o ( Y )} + (' y - m(y) ° ( y ) (4-6)

w h e r e ji is the v a r i a b l e mean, a 2 is the v a r i a b l e v a r i a n c e and px y ( IPx y I ~ 1) c o r r e l a t i o n c o e f f i c i e n t b e t w e e n v a r i a b l e x and v a r i a b l e y. All p s and as are functions of V a and Vg.

B e fore study i n g N(Vg) and N(x,y), we set up c o n v e n i e n t x-y coordinates. In the x-axis, the ceramic rod w i t h eleven c o p p e r rings on, since each ring has the w i d t h of 1/8 inches s e p a r a t e d from one a n o t h e r 1/32 inches, we let 5/32 inches be the u nit of x. So x can be r eplaced by the channel number shown on the scope. If let the length of rotat i n g arm on the

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d e t e c t o r w h i c h is 3/4 inches be the unit of y, we can write y as sin# w h e r e # is the angle from the c e n t e r p o s i t i o n of the detector. For all the calculations, we r e p l a c e x and y by channel n u m b e r n and S i n # .

F o l l o w i n g the p r o c e d u r e Step 3, we s t u d i e d the total 1408 set samples of D(x) , D(y) , and D(Vg), in w h i c h o t her v a r i a b l e s w ere kept as constants. We find our e s t i m a t e model

N(Vg ) = N , (0) expj

-vq - M, (Vq ) -

I

( V g ) + N (0) exp «-r Vg - M 2 (Vg) ^2 (Vg) (4-7) N ( n ,0) = exp \ -2 ( 1 — /? x y 2 ) n - Mx 2

n - /ix Sin# - jiy

- 2 p_xy _{+ (■} Sin# - fiy 2-| a_x

cr.

a, (4-8) wh e r e is g i v e n by CTx = CTx ( ° ) e x P 1 ---1 (" Vg — fl(O^) ---1 2 2 L o ( o x ) (4-9) and D 0 = 1.000

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p X y = 0.500 My = “ 0.2078

The r e m a i n i n g p a r a m e t e r s in the model are r e g r e s s e d to the p o l y n o m i a l s of V a and V g . The c o e f f i c i e n t s of t h e s e p o l y n o m i a l s are listed in T able 4-1 and Table 4-2.

Based on the o b s e r v a t i o n of Figure 3-5 and Figure 3-6, N (Vg) c o n t r i b u t i o n to t h e b e a m p r o f i l e is not s y m m e t r i c a b o u t its b e s t s e t t i n g w h i c h has a s l o w - r i s i n g f r ont and f a s t - f a l l i n g tail, we w r i t e N ( V g ) as c o m b i n a t i o n of two normal distributions.

T a b l e 4-1. C o e f f i c i e n t s of P a r ameters in Estim a t e Model

C ONSTANT V a (x 1 0 “ 2 ) V a 2 (x10~4 ) V a 3 (x 1 0 “ 6 ) N, (0) 3 .27800 19.1647 -37.310 21.23 N 2 (0) 5.66341 40.7526 -48.962 17 . 85 M, (Vg ) 1. 84860 11.1890 -78 . 890 3 . 51 ( V g ) 2 . 29971 12.4936 1. 094 - 0 . 66 ( V g ) 0.52050 - 0.7460 10.417 - 4 . 8 7 ( V g ) 0.18800 0.7380 3 . 160 - 1.34 o X b 2 . 29776 - 1.5799 2 . 375 - 0.91 M(CTX ) 1.73580 10.7510 - 3.813 - 2.22 a ( o x ) 0.64759 1.2800 6. 954 - 0.23 ° y 0.25551 - 0.1972 0. 502 - 0.35

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Table 4-2. C o e f f i c i e n t s of p x in E s t i m a t e Model

C O N S T A N T V a (10"2 ) > pH O 1 rH V a 2 (10“ 4 ) > pH o 1 CO V aV g (10-3 )

6.51700 5. 7621 -4.8442 -4 . 9774 12 . 476 1.9901

A d j u s t i n g all the p a r a m e t e r s and m i n i m i z i n g the total s q u a r e r e s i d u a l in t h e e s t i m a t e m o d e l b y t h e c o m p u t e r program, the final p r e d i c t o r model is achieved. The final p r e d i c t o r has the s a m e f orm of the e s t i m a t e m o d e l w i t h d i f f e r e n t p a r a m e t e r s w h e r e

D 0 = 1.585

p X y — 0.062

jLty = -0.1989

and rest of them are listed in Table 4-3 and T a b l e 4-4.

T o t e s t if o u r p r e d i c t o r m o d e l is r e a s o n a b l e a p p r o x i m a t i o n or g o o d fit, we i ntroduce a quantity, w h i c h r e p r e s e n t s the r e l i a b i l i t y of the model, R

jX [Dj_ (FIT) -Di (MEASURE) ]2

R T S R Li

R = 1 --- = 1 --- (4-10)

SF X D i(F I T )

i

w h e r e R T S R is the s q u a r e root of the total s q u a r e residual and SF is the sum of function of the p r e d i c t o r model. Since R T S R r e f l e c t s to the e s t i m a t e d s t a n d a r d d e v i a t i o n of the

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T a b l e 4-3. C o e f f i c i e n t s of Parameters in P r e d i c t o r Model CONST A N T V a (xlO- 2 ) V a 2 (x 1 0 “ 4 ) V a 3 (xl0~6 ) N, (0) 3.31266 18.8748 -41.084 24 . 86 N 2 (0) 5.69437 40.3708 -53.568 22 . 97 M. (Vg ) 1.89867 11.0703 -12.164 7 . 82 ^2 (^g) 2.34978 12.9835 - 0.565 0 . 04 (v g) 0.57057 - 0.8734 5 . 921 - 0.55 ^ 2 (Vg) 0.23799 1.1534 4 . 090 - 2.74 a x (0) 2.34714 - 1.9105 2 . 007 0 .20 M ( a x ) 1.78587 11.1331 - 3.491 -10.90 o ( o x ) 0.69766 1.7097 10.264 3 . 15 ° Y 0.28093 - 0.3999 0 . 667 - 0.35 T a b l e 4-4. C o e f f i c i e n t s of n x in P r e d i c t o r Model CO N S T A N T v a (io~2 ) V g (10“ M v a 2 (10~ 4 ) > "t_p 1—1 o 1 CO V aV g (10-3 ) 6 . 51838 6 . 0413 -4 .8170 - 5.59 12.730 2 . 173

model, the b i g g e r R is, the b e t t e r fitting is achieved.

T he c o m p u t e r p r o g r a m also can g ive several local m o dels at c e r t a i n o p e r a t i o n cond i t i o n s . T h e p e r f o r m a n c e s of the p r e d i c t o r m o d e l s in d i f f e r e n t range of a c c e l e r a t i n g v o l t a g e

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are l i s t e d in T a b l e 4-5 w h e r e the d a t a w i t h * m a r k are p r o d u c e d by the local models.

T able 4-5. P e r f o r m a n c e s of P r e d i c t o r M o d e l s V a ( K V ) V g ( K V ) SF R T S R R (% ) SF* RTSR* R* (%) 0 2 . 5 303.55 23 . 03 92 . 4 374.56 17 . 52 95.3 25 6.0 335.21 23 . 10 93 . 1 395.77 17 .36 95.6 50 9 . 0 487.69 24 .81 94 . 9 3 9 5.34 17 . 54 95 . 6 75 13 . 5 341.83 21.47 93 . 7 398.36 18 .49 95 . 4 100 17 . 0 396.01 17 . 49 95. 6 375.31 17 . 01 95.5

4.2 Beam Profile Simu l a t i o n

U s i n g the p r e d i c t o r model, we can s i m u l a t e the b e a m p r o f i l e at a n y o p e r a t i o n condition. F i g u r e 4-1 to F i g u r e 4-3 s h o w s t h e r e l a t i v e i n t e n s i t y of t h e b e a m at 80 KV a c c e l e r a t i n g voltage.

F r o m the model, we can p r e d i c t the shape of b e a m spot and best v o l t a g e setting of the Grid Einzel Lens at required o p e r a t i o n c o n d i t i o n w h i c h is h e l p f u l i n f o r m a t i o n for d e s i g n i n g the t a rget and u s ing the accelerator.

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Vg

C

K

V

)

1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 2 0 . 0 0 i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i m i i i i i i 2 0 , 18.00 16. 14. 1 2

.

10. 00 8. 4. 2.i * CONTOUR INTERVAL 1. 0 _LL 1 . 2.00 3.00 4.00 5.00 6.00 7.2

CHANNEL NUMBER

18.00 16. 14, 1 2, 1 0, 8.00 9.00 10.00 1 1 F i g u r e 4-1. R e l a t i v e Beam I n t e n s i t y as F u n c t i o n of n and Vg at 80 KV A c c e l e r a t i n g V o l tage

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A

N

G

E

L

(

D

E

G

)

0 . 0 0 2 . 0 0 4 . 0 0 6 . 0 0 8 . 0 0 1 0 . 0 0 1 2 . 0 0 1 4 . 0 0 1 6 . 0 0 1 8 . 0 0 2 0 . 0 0 2 7 . 0 0 27. * C O N T O U R INTERVAL 18. 1 8 . 0 0 00 00 - 9 . 0 0 - 1 8 . 0 0 - 1 8 . - 2 7 . 0 0 - 2 7 . - 3 6 . 0 0 - 3 6 . - 4 5 . 0 0 - 4 5 . 0 . 0 0 2 . 0 0 4 . 0 0 6 . 0 0 8 . 0 0 1 0 . 0 0 1 2 . 0 0 1 4 . 0 0 1 6 . 0 0 1 8 . 0 0 2 0 . 0 0

Vg ( KV)

Figure 4-2. R e l a t i v e Beam Intensity as F u n c t i o n of Sin# and Vg at 80 KV A c c e l e r a t i n g Voltage

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1 .00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11 .00 15.00 ��-,---,-��-,---,---,-,��--,--,-, 15.00 9.00 3.00 -3. 00 -15.00

w

Z

-21. 00 <( -27.00 -33.00 -J9.00 9.00 3.00 -3. 00 -9.00 -15.00 -21 .00 -27.00 -33. 00 • CONTOUR INTERVAL = 1.0 -39.00 -45. 00 �_.__._..._____._�_,___.._.__...____.__._..._____._�_,___.._.__...___..__.__..._____.___._____.___.____._____,__,...___..__.__..._____.___._____.__.__.____,__,...___..__.__..._, -45. 00 1 .00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11 .00

CHANNEL NUMBER

Figure 4-3. Beam Profile at 80 KV Accelerating Voltage

(V

_g

=

15 KV)

A.r\TM1nt LAJLl:3 Lrn�Aii.Y COLC'ff.tJtOO ?}Cr�OOL cl 11:.INEt

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C h a p t e r V C O M P A R I S O N The p r e d i c t o r m o d e l d e v e l o p e d in p r e v i o u s c h a p t e r is c o m p a r e d w i t h a t h e o r e t i c a l a c c e l e r a t o r d e s i g n p r o g r a m O P T I C I A N [WH87], w h i c h is p r o v i d e d by the same a c c e l e r a t o r manufacturer.

F r o m OPTICIAN, we can g e t x and y c o o r d i n a t e s a f t e r each elem e n t of the accelerator. An overall t r a n s f e r m a t r i x of t h e a c c e l e r a t o r c a n be g i v e n by O P T I C I A N at c e r t a i n o p e r a t i n g condition. T a ble 5-1 shows the output of O P T I C I A N at 100 KV a c c e l e r a t i n g v o l t a g e and 17 KV v o l t a g e of GEL.

A s s u m i n g that the d i s t r i b u t i o n of ions e m i t t e d form the ion s o u r c e is a normal d i s t r i b u t i o n of the e m i t t i n g angle, f i x i n g all o t h e r c o n d i t i o n s at the same, a c o m p l e t e b e a m p r o f i l e can be g e n e r a t e d by u sing OPTICIAN. F i gure 5-1 shows the b e a m p r o f i l e p a t t e r n at 100 KV a c c e l e r a t i n g v o l t a g e and 17 KV v o l t a g e of G E L g e n e r a t e d by u sing OPTICIAN.

The results from the p r e d i c t o r model agree well as the results g i ven by O P T I C I A N both in the shape and the size of b e a m p a t t e r n s in the range of opera t i o n conditions.

The shapes of the b e a m patterns, h a v i n g an e l l i p t i c a l s h a p e in the c o n t o u r plots, are f o u n d e x p e r i m e n t a l l y as shown in Figure 3-7 and t h e o r e t i c a l l y as shown in Figure 4-3

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T a b l e 5-1. List Output of O P T I C I A N at V a = 100 KV and V g = 17 KV

File: COPARISON Title: COPARISON

Created: Jun 5, 1990 3:33:15

Ion source 1 M o m e n t u m = 6.104 MeV/c Mass Focal len. Magnet Accel tube Focal len. Drift Inj energy X Focal L. Energy = Radius = Betal = Energy = Leng t h = Charge state Ent lens X Focal L. Energy = Length = Energy = 020 MeV, Current = 1.000 Charge .300mA = 1 . .000m. .020 MeV .229m. . 000 .02 OMeV .600m. 1. 1 .200m. .12 0 MeV 1.500 m. .12 0 MeV Y Focal L. 1.000m. Bend angle Beta2 = Field index Ent dia = Inj energy Exit lens Y Focal L. 90.00 Fringe fid: .00900 .000 .000 Field = .08891 T .070m. V o l t a g e = .100MV .02OMeV 1 1.200m.

COORDINATES AT END OF EACH ELEMENT: X

---After element X mm. , X'mrad Y mm. Y 'mrad DeltaP/P % DeltaL Ion source 1 E n v . 1.0 20. 0 1.0 20.0 . 00 . 0 Focal len. 2 Env. 1. 0 20.0 1.0 20.0 . 00 ' . 0 Magnet 3 Env. 4 . 6 4 . 3 7 . 3 22 . 6 . 00 4 . 7 Accel tube 4 Env. 2 . 6 3 . 1 10. 5 7 . 6 . 00 11-.4 Focal l e n . 5 Env. 2 . 6 3 . 8 10. 5 1.4 . 00 11. 4 Drift 6 Env. 4 . 7 3 .8 8.8 1. 4 . 00 11.4

DISTANCE TO NEXT WAIST TIME

\_\ \. _/

After element Xdist m Ydist m X mm. , Y mm. microsec Ion source 1 . 00 . 00 1.0 1.0 . 0000 Focal len. 2 . 00 . 00 1.0 1.0 . 0000 Magnet 3 -.08 -.32 4 . 6 . 9 . 1831 Accel tube 4 -.02 -1.37 2 . 6 1.1 .3602 Focal len. 5 . 39 6.23 2.2 5.8 . 3602 Drift 6 -1. 10 4 . 74 2 . 2 5.9 . 6719 OV E R A L L T R A N S F E R MATRIX: -3.2594 .1692 . 0000 . 0000 . 6159 . 0000 -1.0802 .1811 . 0000 . 0000 . 1059 .0000 . 0000 . 0000 -1.0188 .4386 .0000 . 0000 . 0000 . 0000 -.7977 -.0572 . 0000 .0000 . 0000 . 0000 . 0000 . 0000 . 1667 . 0000 1.9222 . 5626 . 0000 . 0000 1.7198 2.4495

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(

m

)

- 2 0 . 0 0 - 1 5 . 2 0 - 1 0 . 4 0 - 5 . 6 0 - 0 . 8 0 4 . 0 0 8 . 8 0 13.60 18.40 . 60 . 60 5 . 1 6 5, 16 3. 44 >-- 3 . 4 4 - 3 . 44 - 5 . 1 6 - 5 . 1 6 * CONTOUR INTERVAL = __ 6 0 1 M I I I I I I I I I I I I I I I I 1 M H r - K l I A 1 A I I I I I I I I I I I 1 1 I I I I I I ' - 2 0 . 0 0 - 1 5 . 2 0 - 1 0 . 4 0 - 5 . 6 0 - 0 . 8 0 4 . 0 0 8 . 8 0 13.60 18.40 . 60

X ( mm)

F i g u r e 5-1. Beam P r o f i l e G e n e r a t e d by O P T I C I A N at 100 KV A c c e l e r a t i n g V o l t a g e and 17 KV V o l t a g e of G E L

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and Figure 5-1. The y - s e m i a x i s b is b i g g e r than x - s e m i a x i s a of the ellipse. We also found that b is more s e n s i t i v e than a w h e n the a c c e l e r a t i n g v o l t a g e and the v o l t a g e of G E L were c h a n g e d .

The sizes of the b e a m p a t t e r n s g i v e n by the p r e d i c t o r m o d e l a n d O P T I C I A N a r e a b o u t t h e s a m e . A t 100 K V a c c e l e r a t i n g voltage, the beam spot, g iven by the p r e d i c t o r model, is about 0.96 cm x 1.41 cm and about 0.94 cm x 1.76 cm g i v e n by OPTICIAN.

F r o m the a bove facts, we c o n c l u d e that the p r e d i c t o r model is a useful tool to predict the shape and the size of b e a m p a t t e r n s w h i c h is a p p r o x i m a t e l y as good and relia b l e as t h e b e a m o p t i c s r e s u l t of the G e n e r a l I o n e x M o d e l 1545 L i n e a r Parti c l e Accelerator.

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[B A 6 6 ] [C E 8 9 ] [GA8 9 ] [G A 8 4 ] [ G E 8 2 ] [L I 6 9 ] [ W H 8 7 ] R E F E R E N C E CITED M. Bandford, "The T r a n s p o r t of C h a r g e d P a r t i c l e Beam", Spon Books Ltd., London (1966).

F. E. Cecil, Private Communications.

A. Gaviria, "Beam P r o file M o n i t o r for a 150 KeV Linear Accelerator", Senior Thesis, D e p a r t m e n t of Physics, C o l o r a d o S c h o o l of Mines, G o l d e n , CO 80401 (1989).

J. E. G a l v i n and I. E. Brown, "Ion Beam P r o f i l e Monitor", Rev. Sci. I n s t r . , 55(11), (1984) 1866 - 1867.

"Air I n s u l a t e d A c c e l e r a t o r S y s t e m M o d e l 1545: T e c h n i c a l S p e c i f i c a t i o n s " , G e n e r a l I o n e x Corporation, 19 Graf Road, Newburyport, M A 01950

(1982) .

J. J. Livingood, "The Optics of Dipole Magnets", Acad. Press, N e w York (1969).

N. R. White, " C o m p u t e r s and T h e D e s i g n of Ion Beam Optical System", N u c l . Instr. and Meth., B21

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S E L E C T E D BIBLI O G R A P H Y

[1] J. F. Ziegler and R. F. Level, eds., "Ion I m p l a n t a t i o n E q u i p m e n t and Techniques:, North H o l l a n d (1985).

[2] J. F. Ziegler, ed., "Ion I m p l a n t a t i o n : S c i e n c e and Technology", 2 e d . , Acad. Press (1988).

[3] J. Keller, "Beam O p tics D e sign for Ion I m p lantation", N u c l . Instr. and M e t h . , 189 (1981) 7-14.

[4] H. F. G l a v i s h , " M a g n e t O p t i c s for B e a m T r a n s p o r t " , Nucl. Instr. and Meth., 189 (1981) 43-53.

[5] A. Septier, e d . , "Focussing of C h a rged Part i c l e s V o l .1 and V o l . 2", Acad. Press, N e w Y o r k (1967).

[6] A. Septier, ed., " A p p l i e d C h a r g e d P a r t i c l e Optics: Part C", Acad. Press, New York (1983).

[7] H. W o l l n i k , " O p t i c s of C h a r g e d P a r t i c l e s " , A c a d . Press, New York (1987).

[8] A. J. Boerboom, " Ion O p t i c s of M u l t i p o l e s " , Nucl. Instr. and Meth., A258 (1987) 426-430.

[9] K. Oide, "A Final Focus S y stem for F l a t - B e a m Linear C o l l i d e r s " , N u c l . I n s t r . a n d M e t h . , A 2 7 6 (1989) 427-432.

[10] M. Baril and M. Noel, " M o d i f i c a t i o n of an A c h r o m a t i c M a s s S p e c t r o m e t e r to I n c l u d e T r a n s v e r s e F o c u s i n g " , Nucl. Instr. and Meth., A258 (1987) 318-322.

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[11] N. R. W h i t e and K. H. Purser, "The D e s i g n of M a g n e t s w i t h N o n d i p o l e F i e l d C o m p o n e n t s " , Nucl. Instr. and Meth., A258 (1987) 437-442.

[12] H. Wollnik, J. Brezina and M. B e r z , " G i o s - B e a m Trace: A P r o g r a m P a c k a g e to D e t e r m i n e O p t i c s P r o p e r t i e s of I ntense Ion Beams", Nucl. Instr. and Meth., A258 (1987) 408-411.

[13] G. W. G r i m e a n d J. T a k a c s , "An I o n A c c e l e r a t o r F a c i l i t y for The P r e p a r a t i o n of N u c l e a r B o m b a r d m e n t Targets", Nucl. Instr. and Meth., 189 (1981) 199-203. [14] T. Wada, N. T a k a h a s h i and I. Yamamoto, " E l e c t r o n Beam

P r o f i l e M e a s u r e m e n t by U s i n g T L Sheets", Nucl. Instr. and Meth., A261 (1987) 368-372.

[15] R. R. Silbar, " B eam E l l i p s e M a t c h i n g : W a i s t - t o - W a i s t Transport", Nucl. Instr. and Meth., 87 (1970) 221-227. [16] K. S. Krane, " I n t r o d u c t o r y N u c l e a r Physics", Wiley, New

Y o r k (1987).

[17] J. D. Jackson, " C l a s s i c a l E l e c t r o d y n a m i c s " , 2nd e d ., Wiley, N e w York (1975).

[18] R. W a l p o l e and R. Myers, " P r o b a b i l i t y and S t a t i s t i c s for Engin e e r s and Scientists", 4th e d . , Macm. Pub. Co, N e w Y o r k (1989).

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A p p e n d i x A N O R M A L D I S T R I B U T I O N

T he N o r m a l D i s t r i b u t i o n is t h e m o s t f r e q u e n t l y u s e d c o n t i n u o u s p r o b a b i l i t y d i s t r i b u t i o n in the e n t i r e field of statistics. Its g r a p h c a lled the normal curve, is the bell shaped curve of Figure A-l.

Figure A-l. Normal Curve

A c o n t i n u o u s r a n d o m v a r i a b l e X h a v i n g the b e l l - s h a p e d d i s t r i b u t i o n of F i g u r e A - l is c a l l e d a n o r m a l r a n d o m v a r i a b l e . T h e m a t h e m a t i c a l e q u a t i o n for t h e p r o b a b i l i t y d i s t r i b u t i o n of t h e n o r m a l v a r i a b l e d e p e n d s on the two p a r a m e t e r s ji and a, its m e a n and s tandard d e v i a t i o n

O nce fj, and a are specified, the normal c u r v e is c o m p l e t e l y

X