U(z) -U0+E2z / i r

KFKI 8 / 1 9 6 9

ION OPTICS OF A HOMOGENEOUS ACCELERATOR TUBE WITH QUADRATIC ENTRANCE

L. Varga

HUNGARIAN ACADEMY OF SCIENCES CENTRAL RESEARCH INSTITUTE FOR PHYSICS

BUDAP ES T

;c г 6

2017

L . Yarga

C e n tr a l R esearch I n s t i t u t e f o r P h y s i c s , B u d a p est, Hungary

A b s tr a c t

A method i s d e s c r ib e d f o r im proving th e io n o p t i c a l p r o p e r t i e s vb f a hompgeneoub a c c e l e r a t o r tube by a p p r o p r ia t e ly m o d ify in g i t s e n tr a n c e

a p e r tu r e . I t i s shown t h a t a low m a g n if ic a t io n can be en su red by s im p le means w ith o u t p r e - a c c e l e r a t i o n .

1 . I n tr o d u c tio n

The e s s e n t i a l i n v e s t i g a t i o n s on th e io n o p t i c s o f homogeneous a c c e l e r a t o r tu b e s had b e e n made by M. E lk in d 1 more th a n t e n y e a r s a g o . E ver s i n c e t h a t tim e h i s work has u n d e r la in th e design, c o n c e p ts f o r tu b e s

o f t h i s t y p e . In th e y e a r s p a s t c o n s id e r a b le p r o g r e s s was made i n im p ro v - in g t h e c a l c u l a t i o n m ethods p a s w e ll a s i n d e v e lo p in g new m atching s e c t i o n s b etw een t h e io n sou rce and th e tube^ * , t o com pensate th e thousand tim e sx 4 d i f f e r e n c e betw een th e e n e r g ie s o f p a r t i c l e s e x i t i n g from th e so ru ce and t h e t u b e , The m atching h a s t o m e e t some m e c h a n ic a l, e l e c t r i c a l and o p t i c a l r e q u ir e m e n ts such a s a c c u r a c y , h ig h b r e a k in g s t r o n g t h , low a b e r r a t io n s , lo w m a g n if ic a t io n , r e g u l a b i l i t y , and, i f p o s s i b l e , s e l f - f o c u s i n g . The sim u lta n e o u s s a t i s f a c t i o n o f t h e s e r eq u irem en ts b u t d i f f i c u l t , and m ost o f su ch sy stem s have room f o r im provem ent. At p r e s e n t th e system d e v e lo p e d by Johnson e t a l^ seems t o be th e b e s t , f o r t h i s system how ever, h i g h - - l e v e l t e c h n i c a l m eans, and tu b e s w ith low lo a d in g a re n eed ed . Owing t o th e r a p id in c r e a s e i n m a g n if ic a t io n i n term s o f th e en ergy m u l t i p l i c a t i o n o f th e a c c e l e r a t o r , o b s e r v a b le f o r a l l o f th e c u r r e n t ly u se d t h r e e -

- e le m e n t tu b e s 1 , p r e a c c e le r a t io n i s i n e v i t a b l y n e e d e d . K eeping th e o v e r - - a l l en erg y m u l t i p l i c a t i o n u n a lte r e d , th e n e t m a g n if ic a t io n can be remark­

a b ly d e c r e a se d by m o d ify in g th e a x i a l f i e l d d i s t r i b u t i o n by u s in g th e c o m b in a tio n o f an im m ersion l e n s , and a th r e e -e le m e n t tu b e in s t e a d o f a s im p le th r e e -e le m e n t tu b e .

- 2 -

The a x i a l f i e l d o f th e e l e c t r o s t a t i c g e n e r a to r '’, ty p e EG-2 o f our I n s t i t u t e h a s been m o d ifie d t o e n a b le u s t o o p e r a te th e so u rce and th e a c c e l e r a t o r w ith o u t any p r e a c c e l e r a t i o n . The o p t ic a l p aram eters o f an ac**

c e l e r a t o r tu b e depend m a in ly on th e a p e r tu r e a t i t s e n tr a n c e , t h u s , in v e s ­ t i g a t i o n s were made on th e v a r i a t i o n s i n o p t i c a l p r o p e r t ie s w ith m o d ific a ­ t i o n s in th e i n i t i a l E^~Eg t r a n s i t i o n . S u f f i c i e n t l y lo w m a g n if ic a t io n i s o b ta in a b le by adequate m o d if ic a t io n o f th e a x i a l f i e l d - d i s t r i b u t i o n even f o r a few th o u sa n d tim e s energy m u l t i p l i c a t i o n , and th e io n so u rce can be mounted d i r e c t l y a t th e upper tu be en d , w ith o u t any m a tch in g elem en t betw een them .

2 . Q u ad ratic o p t ic s

A lthough th e ru n n in g - up o f f i e l d s tr e n g h t i s ad lib it u m v a r i ­ a b le , in th e p r e s e n t pap er a q u a d r a tic i n i t i a l p o t e n t i a l d i s t r i b u t i o n i s c o n s id e r e d . T h is i s c o n v e n ie n t f o r d e s ig n and an e x a c t s o l u t i o n o f th e p a r a x ia l r a y e q u a tio n can be o b t a in e d . In th e i n t e r e s t o f g e n e r a l i t y i n th e i n i t i a l E^-Eg t r a n s i t i o n E g ^ O , th u s n o t a t h r e e - b u t a fo u r - elem en t tu b e i s d is c u s s e d / F i g . l / , where th e e le m e n ts are a s f o l l o w s :

1 / A p erture w ith t r a n s i t i o n from E-^ = 0 t o Eg=^ 0 2 / Q u ad ratic s e c t i o n w ith p o t e n t i a l d i s t r i b u t i o n

U(z) -U0+E2z / i r

where i s th e q u a d r a tic s e c t i o n le n g h t . 3 / Homogeneous s e c t i o n w ith f i e l d s t r e n g t h E^.

4 / A perture a t th e lo w er tu b e -e n d w ith t r a n s i t i o n from E^=^0 t o E^ = 0 . The f o l l o w i n g i s t o p r e s e n t t h e t r a n s i t i o n m a t r ic e s o f th e fo u r

e le m e n ts .

2 .1 The o p t i c a l p aram ters o f th e f i r s t a p ertu re w ere o b ta in e d i n th e same way a s in 1 / , how ever, i n th e i n t e r e s t o f h ig h e r a c c u r a c y , f in 1 / was com pleted by a t e r p in v o l v in g th e a p e r tu r e deam eter in s t e a d o f th e f a c t o r ^ . The D /f v a lu e c a lc u la t e d by n u m e ric a l i n t e g r a t i o n in

r e f , 6 , can be w e l l approxim ated by

D _ ± \n &-C, J_D , & -E, f

f ' 4 L U0 \3,1 U0 }

th e form u la b e in g j used, in s t e a d o f i n r e f . ' 1'.

n J u ( E i - t i l / on f 4 Uo

For L / < ---- 4 ---

Z U

U

r e l a t i v e t o th e P / f v a lu e s o b ta in e d by nu m erical i n t e g r a t i o n and

p r e s e n t e d i n r e f . 6 . Assuming th e p r i n c i p a l planeB o f th e a p e r tu r e le n s t o c o in c id e i n th e a p ertu re p la n e , th e t r a n s i t i o n m a t r ix * can be

g iv e n , a s

M- 7 o\

i

U0 5 \Uo)

2 ,2 Q u ad ratic s e c t i o n . R e p la ic in g ray e q u a tio n t a k e s th e form

r . U f - 0

dx

d z

Г

5

[L/fzJJ th e p a r a x ia l

/ у where th e d o ts and p r in e s d en o te d i f f e r e n t i a t i o n s w it h r e s p e c t t o X and z , r e s p e c t i v e l y . S u b s t it u t in g Eq / 1 / in t o Eq. / 4 / , th e d i f f e r e n t t i a l form , d e s c r ib in g th e t r a j e c t o r y i n th e second o p t i c a l e le m e n t, i s

Г -h E i z E z

41 ^■Г

The s o l u t i o n o f Eqs, / 4 а / i s

where

r(z)=r0cosQ(z)+ró-2

in Q(z)

r'(z)~-4? i^'S in 9 (z)+ -r0 [JJo.cosQ(z)

2 \ U(z)

U(z)

1 Utz)+f2U(z)-U' 9 ( z ) ^ l n j — o W ,

/ 5 /

The t r a n s i t i o n m a tr ix i s determ ined by where '

Гп

Г0

- 4- -

l e t Ъе - I

- L - Л - , — - ?

я

E3 c ' К A) К ] U0

The t r a j e c t o r y p a ra m eters a t

Z ” l

t

/ cos 9(X) XÍ2 I sin 0 ft/

Г л ] . I _____________ . c o s O i l )

*- -I s i n 9 (a) j h i f . (t+6)(N-t) / 7 /

" A

1 2

о / , I ?

2 . 3 The p a r t i c l e e x i t i n g t h e . q u a d r a tic s e c t i o n i e p a sse d t o th e homo­

g en eo u s s e c t i o n w ith E , f i e l d . From t h e l i n e a r r e l a t i o n s h i p b etw een

_ _ I P

p a ra m eters

I

, f0

J;

,o H i j Ä r f

where

2 . 4 On p a s s in g th rou gh t h e output th e beam e n t e r s th e f i e l d cs 0 . T h is t r a n s i t i o n i s c o n s id e r e d c o rresp o n d in g t o 1 / .

The f o u r t h m a trix

1 0

^ - 1 ___ N -1 . / 9/

2XN C-7+2/A '

inhere th e sym bols are k e p t u n a lte r e d ,

2 . 5 The produ ct o f th e fo u r m a tr ic e s e q u a ls th e m a trix tO] o f th e w hole o p t i c a l sy ste m , where th e elem en ts

0 ij

Qí" ^I2^2l+(^12 + $12 $22^^21 0 ,2 ^ 1 2 + $12^22

°2I

$210 U $22^21^22^21^

^22"$21^12* $22 $$22

r e s p e c t i v e l y .

/Ю /

The elem en ts o f m a tr ix t0] determ in ed n u m e r ic a lly f o r v a r io u s N,

A,

/ i . e . by a f a c t o r o f 5/ th e in c r e a s e in 0 ^ and °21 i s o n ly 5 p e r c e n t f o r N=1000,

£

£ s , th e e f f e c t produced by D/K i s sm a lle r s i n c e f o r sm a ll £ s th e q u a d r a tic s e c t i o n i s dom inant a s compared w ith th e a p e r tu r e .

On co m p letin g th e o p t i c a l sy stem w ith two f i e l d - f r e e s e c t i o n s / F i g . 1 / p r e c e d in g and s u c c e e d in g i t / s = €>.K and p=q.K s in c e th e o b j e c t and image d is t a n c e s measured i n t u b e - le n g h t u n i t s a re

6

CO,2

é

C02 2

co/ 2 - 6 0 ^ * 0 ^

q ( 6 0 21+ 0 22)

/ 1 1 /

J21

I f th e ’o b jec t* v e c t o r i s a t a d is t a n c e

б

K, = -js = 7 (0 11 + q021) + t[6011+0,2+q(ő021+ 022j]

w ith s lo p e

/ 1 2 /

к'-то21+((е!02+о22)

6 -

2 , 6 A lthough t h e s e r e s u l t s a r e enough t o p r e d ic t p o i n t s X , k ’ a s s o c i a t e d w ith g iv e n p o in t s

X

I

O ii+ qO ii \/-

6 0 , f 0 , + q ( 0 0 j 0 22) K 00„+0,/q(002l+0!2) m /

E v id e n t l y , a l l o f th e p o i n s t s T , t ’ , t h a t l i e w i t h i n th e e m itt a n c e -

—diagram /h o l d in g a t a d is t a n c e б К from th e tu b e e n t r a n c e / on th e s t r a i g h t l i n e d e f in e d by

t

Ж

■о d 0 „ + 0 12+ q ( ó O ^ Ö J

“ a

0„* aO ;

Y— 6 0 1<+ 012 ^{hi + i} 'Q((^02 ^{...Я ул _ j} +022)

a re tra n sfo rm ed in t o th e same X / F i g . 2 / . I f t h i s l i n e h a s no common p o in t w ith th e e m itta n c e -d ia g r a m , a t X cannot he a p o in t o f any p a r t i c l e t r a j e c t o r y . . The m argin al p o in t s X -j and X 2

^he beam

i n a p la n e - o f - o h s e r v a t io n / a t d is t a n c e qK from, t h e tu b e -e n d / can be d eterm in ed by fra m in g th e diagram w ith two s t r a i g h t l i n e s t a n g e n t ia l

t o i t a t

X

V(ó,Hí 0],q)

f o r g iv e n v a lu e s o f

d

L et th e f u n c t i o n У

(d,

Q)

a / b o th i t s num erator and denom inator has a z e r o p o i n t , i . e .

Y-0 ±f

О21

/ I V

o f which

and

Y

n -~ -On.. Ä + Q ß /Q v.

/ 1 5 /

°21 0+022ll0:

* N otes In g e o m e tr ic a l o p t i c s - O^^/Opl d eterm in es t h e second f o c a l p o i n t , w h ile “ °2 2 ^ 021 tiie ^i r s "t one o f th e o p t i c a l Systeme [0]

Ь / i f Q * ± o o , t h e n У — * Уоо ’ —7РГ~ *»е»

T o o S O i f

U 21

с /

-^— —

d / ( 7 = q 0 =

^

i v e í b th e вате a s t h a t o f Cj-z-Q ^

j

The s ig n o f é + 0 2 2 /Op/cLepends on t h a t th e ’ o b j e c t ’ p o in t i s b e­

f o r e o r behind t h e ’f o c a l ’ p o in t / 1 5 а / . These two v e r s io n s a re shown i n F i g . 3 . A lth ough qQ can be e i t h e r p o s i t i v e o r n e g a t iv e , i t s

p r a c t i c a l v a lu e s f o r th e o p t i c a l system under i n v e s t i g a t i o n were found t o be l e s s th an z e r o . /S e e i n A p p en d ix // From / 1 2 / we have

1

X / 9 - J - T

Det fOl

О г/б Ю ггря)

i n d i c a t i n g t h a t any t r a j e c t o r y p a s s in g th rou gh X / q ^ / h a s th e same i n i t i a l c o o r d in a te T a t 6 , in d e p e n d e n tly o f i t s in d iv id u a l s l o p e . S in ce °2 1 0 , / s e e i n A ppendix/ th e s ig n s o f K / l « / and

can be e i t h e r i d e n t i c a l or d i f f e r e n t depending on t h a t th e

6

X / q Q/ can be d eterm ined by th e e q u a tio n

x f a j — / 17/

where the sign of X /q _ / i s the same as th at of t * .

From th e A ppendix and / 1 7 / . i t can be see n t h a t X /q Q/ c o n tin u o u s ly d ic r e a s e s w ith in c r e a s in g en erg y m u l t i p l i c a t i o n / a t l e a s t f o r N’ s up t o th e o r d e r o f 1 0 ^ /. U sin g th e r e s u l t s o b ta in e d from a n a ly z in g t h e q -d e - pendence o f

'f

e m itta n ce-d ia g ra m i s known. In r e f / ' an io n so u r ce i s d e s c r ib e d which has b een d e sig n e d f o r u se w ith th e a c c e l e r a t o r co m p lete w ith th e io n o p t i c a l system d e s c r ib e d h e r e . The -ein ittan ce diagram o f t h i s so u r ce / s e e th e d o tte d l i n e i n F i g . 4 / can be tra n sfo rm ed i n t o a form fram ab le by two s t r a ig h t l i n e s p a r a l l e l t o th e a x i s t ’ , and s im p li f y th e t r e a t ­ ment l e t th e diagram be com pleted t o a r e c ta n g u la r / s e e th e s o l i d l i n e i n F i g . 4 / by two s t r a ig h t l i n e s p a r a l l e l to th e a x i s T . T h is can be done w ith o u t in t r o d u c in g any s i g n i f i c a n t e r r o r . Assuming t h i s c o r r e c te d diagram to p r e s e n t th e beam’ s c r o s s - s e c t i o n a t f> , i t s two p a r a l l e l ta n g e n t s j determ in e th e p o in t s

X

whose i n t e r s e c t i o n s w ith th e p la n e - o f - o b s e r v a t io n a t q a re t h e m arginal p o in t s o f th e beam’ s c r o s s - s e c t i o n i n t h a t p la n e .

B e s id e s th e above s t r i g h t l i n e s w ith s lo p e У / q /= 0 and W d o o A o o any o th e r l i n e w ith s lo p e — o o —

^(Q) +

+ Xmi +

q ^00 < q -= о from th e tu b e -e n d co rresp o n d t o p o in t s

r ^

^22^^21

w h ile f o r any o th e r q ’ s th e i n i t i a l param eters -

X

+ T m? - t j ’ . I f qQ < q < q ^ , th e m a rg in a l t r a j e c t o r i e s a r e s t a r t e d from p o in t s - T : +t* And + - t ’ , w h ile f o r q ’ s o u t s id e t h i s i n t e r v a l th e t r a j e c t o r i e s s t a r t e d fr^m th e o th e r two c o r n e r s a re m a r g in a l. E v id e n t ly , th e m arginal t r a j e c t o r i e s a r e th e same i n each c a s e , i n th e f i r s t one w it h o u t , in t h e second w ith c r o s s - o v e r w ith in th e i n t e r v a l qQ- t o - q ^ , V a r ia tio n s i n th e beam d ia m eter f o r q ’ s w it h in th e i n t e r v a l q0- t o ~ q o o were fo u n d to be l e s s t h a t t h o s e f o r

q ’ s O u tsid e o f i t .

The q-dependence o f th e beam d ia m eter f o r g iv e n [0] and v a r io u s 6 f s h a s b een so f a r c o n s id e r e d . I t i s how ever, o f much more p r a t i c a l im portance t o a d j u s t th e N i n an o p t i c a l system w ith g iv e n e m itt a n c e ,

é 0, t

<60 ,

) =/=

б'; у 4’

60

, d 1 )

I f th e form o f diagram shown i n F i g . 4 co rresp o n d s t o t h e e m itta n c e a t

6 0

±

( б . - é . )

6, .

К (б 0) (6,).

\ v * ( * , ) \ - y t J 6

m

X m[ 6 j

" X ( q r]

- ( 0 „ + q ^ 0 2, ) - M

4

i . e . X /q ^ y / i s th e p ro d u ct o f

X /

6

=

T / fj

Г / 4 ,

6

6

6

- 8 -

For s p e c i a l p ara m eters o f e m itta n c e i t may th u s o ccu r t h a t th e minimum sp o t d ia m eter a t qT i s o b ta in e d f o r a v a lu e o f N o th e r th a n t h a t r e q u ir e d t o image th e minimum c r o s s - s e c t i o n o f th e s o u r c e ’ s o u t­

put beam onto th e t a r g e t .

The dependence o f th e o p t i c a l system under i n v e s t i g a t i o n o n th e param eters i s n u m e r ic a lly i l l u s t r a t e d a l s o in F i g . 6 where q = 1 and N i s c o n s ta n t.

Mounting th e so u r ce d i r e c t l y on th e upper tu b e en d , E ,

€

2 ,7 Making u se o f th e f o c u s in g proced ure d e s c r ib e d i n 2 . 6 i n v e s t i g a ­ t i o n s were made on th e broad en in g o f th e beam d ia m eter d u rin g a c c e le r a ­ t i o n . In a th r e e -e le m e n t tu b e th e beam d ia m eter i s th e g r e a t e s t a t th e e n tr a n c e , however i n our c a se a s i g n i f i c a n t b ro a d en in g i n th e q u a d r a tic s e c t i o n has t o be c o n s id e r e d . E v id e n t ly , th e maximum d ia m eter must be w it h in th e i n t e r v a l A s in c e e x i t i n g from th e r e th e beam i s s u b j e c t t o no more f o c u s in g w it h in th e t u b e , "r" i n / 5 / i s a p e r io d ic f u n c t io n o f z and may h ave extrem e v a lu e / o r v a l u e s / a t Z_ determ in ed from r * /z / = 0 by s o lv in g

Making xxse o f , t h e p r e v io u s sym b ols, and assum ing [0] t o image th e c r o s s o w e r 'a t

6

a p o i n t , w hith r ’ = we have

/ 1 9 / and from / 7 /

/ 2 0 /

- 10 -

The maximum b ro a d en in g o f beam r e l a t i v e t o i t s e n tr a n c e d ia m eter f o r g iv e n v a lu e s o f A and

€

f(N) - 60[u tg 2e ( z j] c o s Q (zJ /

/

On t h e b a s i s o f data i n th e Appendix f / N / was c a l c u l a t e d a ls p num eric c a l l y f o r q = 1 and v a r io u s a s s o c i a t e d v a lu e s o f A and

€

35, F i e l d d i s t r i b u t i o n

The a x i a l p o t e n t i a l d i s t r i b u t i o n co rresp o n d s t o / 1 / i f

U(r,z) -U0+E2 z * ■

P r e s e n t form o f U / r , z / s a t i s f i e s th e L a p la c e -e q u a tio n .

35.1 L et th e e l e c t r o d e s be spaced by d a lo n g th e a x i s z / F i g . 8 / .

O b v io u s ly , th e e le c r r o d e s must be convex i n d i r e c t i o n - z , such t h a t th e c e n t r e o f th e one mounted a t z = n .d sh o u ld be a t d is t a n c e d above t h e e le c t r o d e p la n e . L et th e e le c t r o d e shape f i t th e e q u ip o t e n t ia l p a s s in g th rou gh t h e p o in t г = 0 , z = d /n / and c r o s s th e p lan e

z = nd a t th e r = d. f2* / F i g . 8 / ,

A lth o u g h r = d

f2

\

e f f e c t produced by g e o m e tr ic a l e r r o r / t h e e le c t r o d e d e t e r i o r a t e s t o a p l a n e , in th e s u b s e c t io n ’ r =- d. i 2 / .

C orresp onding t o t h e s e p r e m isse s we have

U[r-0; z-cl (n -(n)]-U(r-d{2; z-nd)

z - n

2

wherefrom

f

fn C 1

can be determ in ed by / 2 2 / , a s

±

d H d

^{- 1}

where th e sym bols are a s b e f o r e , and t o e lim in a t e

ß 1

C l

V =

1 -C d

+n

th e f u n c t io n

^(\>)

£

For s m a lle r v v a lu e s a s p h e r ic a l su r fa c e i s th e most ad va n ta g eo u s t o approxim ate th e i d e a l e q u i p o t e n t i a l . The r a d iu s o f cu r v a tu r e f o r th e s p h e r ic a l s u r fa c e p a s s in g through th e c i r c l e o f r = d.

IflT

f

z =

R -d

w hich te n d s t o 2 d . V f o r v ^ 2 . T h is a p p ro x im a tio n i s good enough e v en f o r V = 2 / t h e e r r o r i s about 5 p er c e n t / . Care must be ta k en i n th e ca se o f £ = 0 and n = 1 . Now £ = 1 , hen ce z - 0 , and th e s p h e r ic a l s u r fa c e i s d e f in a b le b u t a b e t t e r a p p ro x im a tio n can be o b ta in e d by d i r e c t c o n s id e r a t io n s wi-th th e use o f / 2 2 / , Owing t o

£

f p ' f ’ - f - 1 ?

i . e . t h e f i r s t e le c t r o d e h a s t o be a . cone w ith o p en in g o f 2 ? = 109o28*

and w ith i t s peak a t th e p o in t z =, 0 .

3 .2 There must be determ in ed th e d iv i d e r su p p ly in g th e o p e r a tio n a l v o l t a g e f o r th e geom etry d is c u s s e d a b o v e . Comparing th e p o t e n t i a l d i f ­ f e r e n c e betw een th e n - t h and / п - l / t h e le c t r o d e s w ith th a t betw een th e n = (

i / d-l )

I /

c u r r e n t , the, r e s i s t a n c e s i n th e d iv id e r w i l l be o b ta in e d r e l a t i v e to th e l a s t r e s i s t o r ’ s v a lu e .

- 12 -

The r e l a t i v e r e s i s t a n c e s to be u se d in t h e n - t h s e c t i o n can be d eterm in ed from

Rn A U( n ) 2 £ ± ^ H ^ 2 n z l2

Rmax A U O f -1)

i ~ - ( 1 - £ )

E v id e n t ly th e v a lu e s a re l i n e a r l y i n c r e a s i n g .

N otes

I t . i s a q u e s t io n , w hether th e lo a d in g a f f e c t s th e v o lt a g e s e t by th e d i v i d e r . In our o p in io n th e lo a d in g a f f e c t s t h e end f a c e r a th e r th a n th e a c c e le r a t o r e l e c t r o d e s . From th e l i n e a r in c r e a s e i n f i e l d s tr e n g h t i t f o l l o w s t h a t th e i n i t i a l s e c t i o n o f th e a c c e l e r a t o r tu b e can n o t be e n t i r e l y u t i l i z e d f o r en ergy m u l t i p l i c a t i o n , a lth o u g h th e l o s s o f le n g h t ^ ^

i s a c c e p t a b ly sm a ll /a b o u t 5 p e r cen t i n p r a c t i c e / . As r eg a rd s th e b r e a k in g s t r e n g t h , i t i s a d v a n ta g eo u s t h a t th e lo a d in g i s r e l a t i v e l y sm a ll a t th e tu be e n tr a n c e where th e c o llim a t e d , f a s t n e u t r a l beam o r i g i n a t i n g from th e so u r ce has not y e t b een d i s t r i b u t e d .

Acknowledgments

Thanks a r e due t o M iss E. H aviár f o r h e r h e lp i n n u m erica l

e v a lu a t i o n s a s w e ll a s t o Mr. L. K ir á ly h id i fo p th e tan k t e s t s co n c er n in g th e s o l u t i o n o f problem s i n f i e l d d i s t r i b u t i o n .

Appendix

Л = О

С

К ° П о 1—1 см

°21 °22

80 - 2 .5 5 1 2 .0 1 1 10“ 1 - 2 .4 4 3 1 .6 1 4 ю “ 1

160 - 5 .6 2 0 1 .4 6 5 ю “ 1 - 3 .3 9 2 1 .1 5 4 ю “ 1

520 - 5 .1 3 7 1 .0 5 8 ю - 1 - 4 .5 2 0 8 .2 2 9 ю “2

640 - 6 .7 6 4 7 .6 0 5

см1о1—1 - 5 - 7 2 4 5 .8 5 1 ю “2

1280 - 8 ,1 0 2 5 .4 3 8 10 2 - 6 .7 0 2 4 .1 5 3 10~2

2560 - 8 .1 9 5 3 .8 7 5 10-2 - 6 .7 3 7 2 .9 4 5 10~2

Л = 0 ,0 5

£

N “ 1

°11 °12 °21 °22

80 - 1 .9 1 6 1 .5 8 2 10“ 1 - 2 .1 2 1 1 .1 6 8 10"1

160 - 2 .5 9 7 9 .5 9 4 ю “2 - 2 .5 9 3 6 .5 3 6 10“2

520 - 3 .1 7 9 5 .1 8 0 ю “ 2 - 2 .9 6 0 3 .0 6 6 ю “ 2

640 - 3 .5 9 7 2 .2 6 5 10“2 - 3 .1 7 6 9 .0 1 7 ю “3

1280 - 3 .8 1 1 4 .9 7 4 ю “5 - 3 .2 1 1 - 3 .1 4 1 . 1 0 -5 25 6 0 - 3 .8 0 0 - 4 .5 9 2 ю " 5 - 3 .0 5 8

V

- 8 .8 9 5 10“ 5

зл -

Л = 0 ,0 5 6 = 0 .1

N °11 012 °21 °22

80 - 1 .8 6 3 1 .6 5 6 10"1 - 2 . 070 1 .2 4 0 ю “ 1

160 - 2 .5 2 3 1 .0 6 0 д о - 1 - 2 .5 2 3 7 .4 7 4 ю - 1

520 - 3 .0 9 6 6 .4 1 6 ю “2 - 2 .8 8 3 4 .1 6 9 10“2

64Ó - 3 .5 5 6 3 .6 4 8 ю “2 - 3 .1 1 4 2 .0 9 5 10~2

1280 - 3 .8 1 8 1 .9 2 7 10“ 2 - 3 .2 0 3 8 .8 5 0

10~3

2560 - 3 .9 5 8 9 .2 2 9 ю “ 5 - 3 .1 5 2 2 .3 6 9 10“ 5

Л = 0 .0 5 6 = 0 .2

N °11 012 °21 °2 2

80 - 1 .8 3 9 1 .7 2 0 10"1 —2 ,0 4 4 1.3.04 10“ 1

160 - 2 .5 1 2 1 .1 4 2 ю “ 1 - 2 .5 0 6 8 .2 4 5 10~2

320 - 3 .1 5 3 7 .3 5 1 ю “2 - 2 .9 0 1 5 .0 2 2 10"2

640 - 3 .6 7 0 4 .6 2 1 ю “ 2 - 3 .2 0 6 2 .9 6 1 10“2

1280 - 4 .1 0 7 2 .8 6 3 ю - 2 - 3 .4 1 4 1 .6 9 9 10~2

2560 - 4 .4 3 4 1 .7 6 3 ю “ 2 - 3 .5 2 4 9 .5 6 1 IO"?

Л, = 0 .1 £ = 0

N °11 012 °21 °22

80 - 1 .4 7 5 1 .4 1 7 ю - 1 - 1 . 7 6 7 ' 9 .4 1 0 10~2

160 - 1 .9 2 8 8 ; 144 10“2 - 2 .0 4 4 4 .5 3 6 ю “2

'' 320 - 2 .2 7 9 4 .0 3 6 ю “2 - 2 .2 1 3 1 .4 6 7 ю -2

640 - 2 .5 0 0 1 .4 4 2 10“2 - 2 .2 5 5 - 2 .7 9 7 10“5

1280 - 2 .5 7 5 - 4 .9 1 2 ю “4 - 2 .1 6 3 - 1 .1 2 7 1—1 о см1

2560 - 2 .4 9 1 - 7 .9 2 4 ю “ 5 - 1 .9 4 2 - 1 .4 1 0 10“2

Л = 0 ,1 £ = 0 .1 N

1 о и н см1—1о 1—1смо

022

80 - 1 .4 3 5 1 .5 4 3 10“ 1 - 1 .7 2 0 1 .0 7 0 10“ 1

160 - 1 .8 8 8 9 .7 1 6 i o - 2 - 1 .9 9 3 6 .0 7 4 10“2

320 - 2 .2 6 2 5 .8 2 8 н о А)

- 2 .1 7 7 3 .1 3 9

10~2

640 - 2 . 5 4 0 3 .3 2 9 ю -2 - 2 .2 6 0 1 .4 0 6

10~2

1280 - 2 .7 1 6 1 .8 0 6 ю " 2 - 2 .2 4 2 4 .6 1 9 10“5

2560 - 2 . 7 9 4 9 .2 4 4 ю " 5 - 2 .1 3 2 - 1 .8 3 3 1—1 о LPv1

А = 0 .1 £ = 0. 2

N °1 1 °12 °21 022

8 0 - 1 .4 4 2 1 .6 4 2 ю “ 1 - 1 .7 1 4 1 .1 7 6 10“ 1

160 - 1 .9 3 9 1 .0 8 7 ю " 1 - 2 .0 1 9 7 .2 5 2

10~2

320 - 2 . 4 0 0 7 .0 5 9 ю “2 - 2 .2 6 6 4 .3 3 8 1 о“2

640 - 2 .8 1 8 4 .5 2 7 ю “2 - 2 .452 2 .5 3 7 ю “2

.1280 - 3 .1 9 1 2 .8 9 4 ю “2 - 2 .5 7 8 1 .4 6 2 1—) о см1

2560 - 3 .5 0 8 1 .8 5 7 м о 1 го - 2 .6 4 6 8 .3 7 7 IO“5

Л = 0 .2 £ = 0

N °11 °12 °21 022

80 - 1 .3 0 9 1 .2 9 7 10“ 1 - 1 .4 0 6 б .? 9 0 10“2

160 - 1 .3 4 3 7 .2 4 2 1Ö“ 2 - 1 .5 4 3 2 .4 3 8 10~2

320 - 1 .5 6 8 3 .4 3 4

10~2

640 - 1 .6 9 8 1 .0 8 3 10~2 - 1 .5 4 2 - 1 .3 4 3

10~2

1280 - 1 . 7 2 7 - 2 .3 3 8 ю “ 5 - 1 .4 0 0 - 1 .8 0 7

10~2

2560 - 1 .6 5 3 - 8 .6 3 3 10 -5 - 1 .7 5 - 1 .8 0 9

10~2

16

Л = 0 .2 б = 0 .1

N

< t ^П

гН1—1 О см1—1 о

°21 °22

80 - 1 .0 2 7 1 .4 8 5 ю “ 1 - 1 .5 7 1 8 .9 3 8 10“ 2

160 - 1 .3 5 4 9 .4 5 4 ю “ 2 - 1 .5 2 2 4 .7 8 8 10“ 2

320 - 1 .6 3 1 5 .8 2 7 ю ” 2 - 1 .6 0 2 2 .2 9 8 10“ 2

640 - 1 .8 5 2 3 .4 9 8 10“ 2 - 1 .6 1 1 9 .0 9 6 10~5

1280 - 2 .0 1 9 2 .0 5 9 10-2 - 1 .5 5 3 1 .9 9 8 10“ 5

2560 - 2 .1 3 5 1 .1 9 8 10-2 - 1 .4 3 5 - 1 .2 0 0 10~3

А = 0 .2 £ = 0 .2

IT °11 ®12 °21 °2 2

80 - 1 .0 8 3 1 .6 1 9 10“ 1 - 1 .3 9 6 1 .0 5 5 10” 1

160 - 1 .4 8 4 1 .0 9 0 1 0 "1 - 1 .6 0 1 6 .4 4 0 10“ 2

320 - 1 .8 8 3 7 .2 7 0 ю “ 2 - 1 .7 6 9 3 .8 6 1 1 0 "2

640 - 2 .2 8 4 4 .8 2 9 ю “ 2 - 1 .9 0 3 2 .2 9 3 Ю‘~2

1280 - 2 .6 8 7 3 .2 1 5 ю “ 2 - 2 .0 0 8 1 .3 6 2 10“ 2

2560 - 3 .0 7 3 2 .1 5 4 ю " 2 -2. о а \ 8 .1 6 5 10~5

R e fe r e n c e s

1 M.M. E ik in d , R . S . I . 2 4 , 129 / 1 9 5 3 /

2 P.H , R ose, A. G a le js and L. P e c k , R .I.M . j£ l, 262 /1 9 6 4 /

3 C.H. Johnson, J .P . J i d i s h and C.W. Snyder R . S . I . 28_, 942 /1 9 5 7 / 4 V.A Romanov„ A.N. S e r b in o v , P r ih o r i i te c h n ik a E ksperim énta

S , 3 4 / 1 9 6 5 /

5 J . Erő, E. K lo p fe r , P . K ostka, I . K ovács, I . M érey, Ъ. V á ly i, L. Varga. R ep orts o f th e C entral R esearch I n s t i t u t e f o r P h y s ic s . Budapest 1Д, 73 /1 9 6 5 /

6 Zworikin e t a l . E le c t r o n O p tics and th e E le c t r o n M icro sco p e.

/J o h n W iley and S o n s, I n g ., $ew York 1945/p p 413 4 4 4 .f f

7 L, V á ly i, P . Gombos, J , Roósz R ep o rts o f th e C en tra l R esearch I n s t i t u t e f o r P h y s i c s . B udapest, 1 4 , 259 / 1 9 6 6 /

- 18

*

F ig . 2

- 2 0 -

F i g . 4

б

F ig . 5

- 22

F i g . 6

Z .* (n -4 )d

24

Vr

F i g . 8

Г

*

K iad ja a KFKI K önyvtár- é's K iadói O s z t á ly , O v .sd r . Farkas Istv á n n á Peldányszám : 125 Munkaszám: 4-191 B udap est, 1969. január 2 1 , K é sz ü lt a KFKI h á z i s o k s z o r o sító .já h a n , F v .: Gyenes Imre

Szakmai le k t o r : Hrehuss Gyula N y e lv i le k t o r : Kovács Jenőné

6Л. К о у

I