ALIGNMENT, ORIENTATION AND THE BEAM FOIL INTERACTION

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Submitted on 1 Jan 1979

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ALIGNMENT, ORIENTATION AND THE BEAM FOIL INTERACTION

R. Schectman, L. Curtis, H. Berry

To cite this version:

R. Schectman, L. Curtis, H. Berry. ALIGNMENT, ORIENTATION AND THE BEAM FOIL INTERACTION. Journal de Physique Colloques, 1979, 40 (C1), pp.C1-289-C1-294.

�10.1051/jphyscol:1979160�. �jpa-00218440�

JOURNAL DE PHYSIQUE Colloque C1, supptkment au n ^O 2, Tome 40, fkvrier 1979, page C1-289

ALIGNMENT, ORIENTATION AND THE BEAM FOIL INTERACTION*

R. M. Schectman and L. J. C u r t i s The U n i v e r s i t y o f Toledo, Toledo, Ohio 43606

and H. G. B e r r y

The U n i v e r s i t y o f Chicago and Argonne National Laboratory

Risumi

-

Nous p r i s e n t o n s l e s r i s u l t a t s d'un c e r t a i n nombre de mesures rgcentes de battements quantiques, d'alignements e t d ' o r i e n t a t i o n s pour une v a r i e t i de systemes atomiques. On en d i s c u t e l a s i g n i f i c a t i o n dans l e b u t de comprendre l e processus d ' i n t e r a c t i o n e n t r e l e s i o n s e t l a lame.

A b s t r a c t

-

We present here t h e r e s u l t s o f a number o f r e c e n t measurements o f quantum beats, alignment and o r i e n t a t i o n f o r a v a r i e t y o f atomic systems. The s i g n i f i c a n c e o f these r e s u l t s i n understanding t h e i o n - f o i l i n t e r a c t i o n process i s discussed.

I. INTRODUCTION

The nature of t h e beam-foil i n t e r a c t i o n has long been a s u b j e c t o f much i n t e r e s t . For t h e p a s t several years we have been c a r r y i n g o u t an e x t e n s i v e program o f experiments aimed a t probing t h i s i n t e r a c t i o n , and we w i l l d e s c r i b e here some r e c e n t r e s u l t s which shed some l i g h t on t h e n a t u r e o f t h e processes concerned.

The general aim o f any s t u d y o f t h e i o n - f o i l i n t e r a c t i o n i s two-fold: ( 1 ) t o p r o v i d e as complete as p o s s i b l e a d e s c r i p t i o n o f t h e s t a t e o f t h e outgoing beam produced when i o n s a r e trans- m i t t e d through t h i n f o i l s and ( 2 ) t o c o n s t r u c t a p h y s i c a l model o f t h e i n t e r a c t i o n process which can e x p l a i n these r e s u l t s . I n c o n s t r u c t i n g such a model i t i s i n s t r u c t i v e t o c o n s i d e r t h r e e d i s t i n c t classes o f i n t e r a c t i o n one c r a l l o f which may con- t r i b u t e t o t h e phenomena observed: (1 ) e x c i t a t i o n by t h e bulk, (2) e l e c t r o n capture--both a t o r near t h e s u r f a c e and o f secondary e l e c t r o n s t r a v e l l i n g w i t h t h e emerging beam and ( 3 ) i n t e r a c t i o n w i t h t h e surface and w i t h surface e l e c t r i c f i e l d s . . I n terms o f these processes, one can attempt t o assess t h e r e l a t i v e importance o f b u l k and s u r f a c e i n t e r - a c t i o n s i n determining t h e p r o p e r t i e s o f t h e observed o u t g o i n g beam, as w e l l as t r y t o determine t h e r e l a t i v e importance o f c o l l i s i o n processes v i s a v i s e l e c t r o n capture. I t i s a l s o o f g r e a t

*blork supported i n p a r t by t h e U.S. National Foundation and Department o f Energy

importance t o d i s c o v e r whether t h e r e a r e s i g n i f i - c a n t e f f e c t s o f s u r f a c e e l e c t r i c f i e l d s and--if so--what t h e strength, range and t i m e dependent c h a r a c t e r i s t i c s o f these f i e l d s are. The r e s u l t s t o be presented here f u r n i s h much d e s c r i p t i v e i n - f o r m a t i o n concerning t h e n a t u r e o f t h e i n t e r a c t i o n , b u t do n o t u n i q u e l y determine t h e d e t a i l s o f a complete model o f t h e i n t e r a c t i o n process. They do, however, suggest an important r o l e f o r s u r f a c e e f f e c t s , and a r e s t r o n g l y suggestive o f an impor- t a n t r o l e i n these processes f o r e l e c t r o n capture.

11. PHENOMENOLOGY

The most complete d e s c r i p t i o n o f t h e beam which emerges from t h e f o i l i s contained i n t h e s p e c i f i c a t i o n o f t h e d e n s i t y m a t r i x o f t h i s system, and t h e experiments described here a r e de- signed t o measure p a r t s o f t h i s d e n s i t y m a t r i x . Since these experiments have been c a r r i e d o u t u t i - l i z i n g r a d i a t i o n which has been wavelength s e l e c t e d e i t h e r by use o f a monochromator o r an i n t e r f e r e n c e f i l t e r , a s i n g l e measurement p r o v i d e s no informa- t i o n on t h e d i s t r i b u t i o n o f charge states, n o r upon t h e d i s t r i b u t i o n o f , and p o s s i b l e coherence between s t a t e s . o f d i f f e r e n t p r i n c i p a l quantum number; i n a d d i t i o n i n f o r m a t i o n upon s t a t e s v a r y i n g i n o r b i t a l quantum number a a r e obtained here o n l y f o r t h e hydrogenic atoms described i n S e c t i o n I V . While r e c e n t work has shown t h a t p r e s e n t experiments do n o t r e q u i r e t h e i n t e r a c t i o n process t o be

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979160

C

1-290 JOURNAL DE PHYSIQUE

spin-independent [I] a l l experiments are, i n f a c t , compatible w i t h such an assumption and--since theo- r e t i c a l arguments g e n e r a l l y a l s o l e a d t o t h i s assumption--it has been adopted i n t h e a n a l y s i s o f o u r r e s u l t s , where t h e p o r t i o n t o t h e d e n s i t y m a t r i x s t u d i e d i s presented i n t h e I L PIL> r e p r e -

s e n t a t i o n . For s t a t e s o f L 5 1, t h e o p t i c a l measurements c a r r i e d o u t determine t h e e n t i r e den- s i t y m a t r i x b l o c k as, e.g., was presented i n o u r e a r l i e s t work d e s c r i b i n g t h e o r i e n t a t i o n produced by transmission o f i o n s through t i 1 ted f o i 1 s. 1.21 For l a r g e r L, f i e l d f r e e measurements determine o n l y combinations o f d e n s i t y m a t r i x elements and i t i s convenient t o c a r r y o u t a s p h e r i c a l t e n s o r expansion o f p, i n terms o f which t h e expansion co- e f f i c i e n t s pkq w i t h k 5 2 a r e then u n i q u e l y

determined by our experiments. [3] An e q u i v a l e n t p a r a m e t e r i z a t i o n o f t h e outgoing beam which can p r o v i d e a d i r e c t p h y s i c a l i n t e r p r e t a t i o n has been g i v e n by Fano and Hacek,[4] who i n t r o d u c e t h e a1 ignment (A) and o r i e n t a t i o n (0) parameters:

(Here t h e z a x i s l i e s along t h e beam.) I t i s c l e a r t h a t t h e r e i s a one-to-one correspondence between t h e a l i g n m e n t / o r i e n t a t i o n parameters and t h e p k q ' s i n t r o d u c e d e a r l i e r , so t h a t measuring t h e a l i g n - ment and o r i e n t a t i o n i s e q u i v a l e n t t o s p e c i f y i n g t h e accessible p a r t o f t h e d e n s i t y m a t r i x . A g e n e r a l i z a t i o n o f t h e approach o f Fano and llacek t o t h e case o f mixed p a r i t y coherences and r a d i a t i o n e m i t t e d i n t h e presence o f electromagnetic f i e l d has been c a r r i e d o u t by Gabrielse, [S] and i s par- t i c u l a r l y u s e f u l i n d e s c r i b i n g hydrogenic systems.

A l l experiments t o be described here i n - v o l v e d e t e c t i o n o f r a d i a t i o n e m i t t e d by t h e beam subsequent t o t r a v e r s i n g t h e f o i l . I n some cases, quantum beats were measured; i n o t h e r cases, t h e d e t a i l e d p o l a r i z a t i o n s t a t e o f t h e e m i t t e d l i g h t ( s p e c i f i e d py t h e t h r e e r e l a t i v e Stokes parameters H/I, C / I and S / I ) were determined--sometimes as a f u n c t i o n o f t h e azimuthal angle o f observation,

@.

I n a l l cases, d e t e r m i n a t i o n o f t h e d e n s i t y m a t r i x

d e s c r i b i n g t h e emergent beam was t h e aim o f t h e measurements.

I V . RESULTS FOR HYDROGEN

A ) n = 2

I n t h i s case, p i s s p e c i f i e d by f i v e p a r a - meters. The r a t i o pp,/pp, has been c a r e f u l l y measured over a wide energy range by Winter

& fl

[6] and we have c a r r i e d o u t measurements i n p a r a l l e l and a n t i p a r a l l e l e l e c t r i c f i e l d s , as o r i g i n a l l y

suggested by Eck,[7] t o determine t h e o t h e r f o u r elements o f p over t h e energy range 30 KeV

-

1 MeV.

[8] P a r t i c u l a r c a r e has been p a i d t o e f f e c t s o f h y p e r f i n e i n t e r a c t i o n , experimental e f f i c i e n c y and l o c a t i o n o f t h e f o i l p o s i t i o n , r e v i s i n g and ex- tending t h e p r e l i m i n a r y work of Gaupp e t a1

[91

and S e l l i n

g

fl.[10] The d e t a i l e d r e s u l t s w i l l be described elsewhere i n these proceedings by Gabrielse. [ll]

A v e r y slow v a r i a t i o n o f t h e parameter w i t h energy i s observed and p S i s observed t o exceed b o t h ppl and p over t h e e n t i r e energy range studied. PO

B) n=3

F i e l d f r e e measurements p r o b i n g t h e d e n s i t y m a t r i x f o r t h i s system have been c a r r i e d o u t by Wells,[12] extending t h e 250 KeV measure- ments of Denis e t a1 [ I 3 1 t o a v a r i e t y o f o t h e r energies down t o 94 KeV. Again, here,only a v e r y slow v a r i a t i o n o f d e n s i t y m a t r i x elements w i t h energy was observed, and again s - s t a t e s a r e g r o s s l y over-populated compared w i t h t h e i r s t a t i s t i c a l weights.

V. RESULTS FOR THE 3p l P and 4d LEVELS OF HE I

A) F o i l s Perpendicular t o t h e I n c i d e n t and Outgoing Beams

I n t h i s case, o n l y a s i n g l e pkq. p i

( p r o p o r t i o n a l t o a s i n g l e r e l a t i v e Stokes para- meter, M/I) i s non-vanishing, and Figures 1 and 2 show t h e v a r i a t i o n o f t h i s parameter w i t h energy f o r t h e two s t a t e s studied. Note t h a t p i i s a l - ways p o s i t i v e and t h a t , i n b o t h cases, i t o s c i l l a t e s w i t h energy. A noteworthy aspect o f Figures 1 and 2 i s t h e beam c u r r e n t d e n s i t y dependence of t h e alignment,[14] which occucs i n b o t h cases, and i t s e l f o s c i l l a t e s w i t h energy as shown i n F i g u r e 3.

Figure 1 - The l i n e a r polarization f r a c t i o n M/I f o r the 3p

l P

level of He I a s a function of energy.

+ current density 30 ua/cm2

zero current density extrapolation For t h i s case, : A

=

-2/3 M/I.

BEAM ENERGY (MeV)

Figure 2 - The l i n e a r polarization f r a c t i o n

lI/I

f o r t h e 4d level of He I a s a function of energy.

0

0.2..

0.4 0.6 0.8 1.0

BEAM ENERGY (MeV)

Figure 3 - The r a t e of current density dependence of t h e l i n e a r polarization S j

=

A ( M / I ) / A ( ~ ) f o r the 3p

1P

level of He I a s a function of energy.

B )

T i l t e d Foils

Here, f i e l d f r e e measurements can deter- mine the 4 p k q i s with

k 5

4 ( i . e . , t h e four

Fano-Hacek parameters). Measurements a t one detec- tion position

( 0 ,

4) provide three r e l a t i v e Stokes parameters and f o r e

=

~ / 2 ,

4 =

0, these h s ~ ~ e been measured between 0' and 60" i n 5" increments over the e n t i r e energy range 30-1000 KeV f o r both t h e 2s - ^3p

^{l P}

t r a n s i t i o n a t 4016 and the 2p

I P

- 4d t r a n s i t i o n a t 4922 1. The r e s u l t s f o r t h e l a t t e r t r a n s i t i o n f o r a t i p angle

a =

45"

a r e shown i n Figure 4. From these measurements, the alignment and orientation parameters

A; - C/I and

a r e d i r e c t l y determined; however, only the com- bination

(A:

+

A: cos

6 )

- ^M/I

i s obtained. We have therefore carried out a num- ber of measurements of M/I versus

4

f o r t h e 5016 i?

t r a n s i t i o n , with the r e s u l t s f o r

cx =

45' shown i n Figure

5.

Similar measurements f o r the 4922 j, t r a n s i t i o n a r e in progress.

-0.1

_{l a l , l 8 l S 1 '}

0 0.2 0.4

0.6

0.8

1.0

BEAM ENERGY (MeV)

Figure 4 - Relative Stokes parameters M/I

(+),

CII

(K)

and SII

( 0 )

f o r the 4d

ID

l e v e i a s a function of energy.

Comparison of Figure 1 and 5 shows t h a t

p i

i s e s s e n t i a l l y unchanged by rotating t h e f o i l through 45"; other measurements suggest t h a t the angular dependence of t h e other

p kq

s i s a1 so energy i n - dependent. I t thus seems l i k e l y t h a t , a good approximation, one can write

k k

r k q (E.a)

=

g (El

f

( a ) . ⁽³⁾

This i s we71 i l l u s t r a t e d , f o r example in Figure 6

where a l l of t h e measured values of

p:

f o r t h e

C 1-292 JOURNAL _DE PHYSIQLE

I d 1D l e v e l , measured between 100 KeV and 425 KeV a r e p l o t t e d as a f u n c t i o n of t h e f o i l t i p angle a f t e r f a c t o r i n g o u t the energy dependence measured f o r a t i p angle of a = 45" (data f o r 3p IP corres- ponding t o F i g u r e 4. These r e s u l t s agree v e r y well w i t h a s i n g l e u n i v e r s a l - - h e r e l i n e a r - - c u r v e repre-

a p h y s i c a l model o f t h e i n t e r a c t i o n process.

Nevertheless, t h e r e s u l t s presented here do p r o v i d e a number o f h i n t s a t t h e d i r e c t i o n i n which a suc- c e s s f u l model must proceed and we wish t o here discuss t h e i m p l i c a t i o n s o f t h e r e s u l t s so f a r obtained.

s e n t i n g t h e observed angular v a r i a t i o n . For a l l cases measured t o date, such an approximation seems v a l i d and t h e r e s u l t i n g f q ( a ) a r e k

f$

-

constant f o r 3p 1P

f f

-

l i n e a r f o r b o t h 3p I P and 4d I D f $

-

q u a d r a t i c f o r 3p I P

f ]

-

l i n e a r f o r 3p IP, q u a d r a t i c f o r 4d I D

TILT ANGLE, CY

I

¹ 0 ^{I I I}

0 0.2 0.4 0.6

BEAM ENERGY (MeV)

F i g u r e 5

-

Alignment and o r i e n t a t i o n parameters f o r t h e 3p 1P l e v e l o f He I vs energy:

A;

(+I,

^{A;O(%). AC}

(01,

0;

(*I .

We have a l s o e x p l o r e d t h e q u e s t i o n o f a p o s s i b l e c u r r e n t d e n s i t y dependence o f t h e r e l a t i v e Stokes parameters f o r t i l t e d f o i l s . Our r e s u l t s show a c u r r e n t d e n s i t y dependence f o r N / I measurement w i t h

a = 45" which again o s c i l l a t e s i n magnitude w i t h energy--closely f o l l o w i n g t h e r e s u l t s obtained f o r a = 0" i n phase, though n o t i n a b s o l u t e value.

The observed c u r r e n t d e n s i t y dependence f o r S/I, on t h e o t h e r hand, shows o s c i l l a t i o n s which a r e approximately o u t o f phase w i t h those i n M/I; i.e., v a r i a t i o n s i n S / I w i t h beam c u r r e n t d e n s i t y a r e l a r g e when those i n I1/I a r e small and v i c e versa.

V I

.

INTERPRETATION

While much progress has c l e a r l y been made i n improving o u r knowledge of t h e n a t u r e o f t h e outgoing beam produced by t h e i o n - f o i l i n t e r - a c t i o n , l e s s progress has been made i n r e a l i z i n g

F i g u r e 6

-

Angular dependence of t h e o r i e n t a t i o n , f : ( a ) f o r t h e 3p P l e v e l o f He I.

One f e a t u r e o f t h e e x c i t a t i o n by f o i l s normal t o t h e beam d i s p l a y e d i n Figures 1 and 2 i s t h a t M / I i s everywhere p o s i t i v e (A: everywhere negative). It should be noted t h a t t h i s i s , indeed, t h e s i g n expected from e l e c t r o n pick-up i n t h e simple model t h a t t h e i o n emerges from t h e f o i l and captures an e l e c t r o n whose v e l o c i t y r e l a t i v e t o t h e f o i l i s small compared w i t h t h a t o f t h e i o n i t s e l f . [ l 5 ] I f one n e x t t u r n s o n e ' s a t t e n t i o n t o t h e observed o s c i l l a t i o n s i n A: w i t h outgoing i o n v e l o c i t y (energy), i t i s tempting t o t r y t o r e l a t e them t o t h e o s c i l l a t o r y e l e c t r o n wake which i s s e t up by t h e i o n ' s t r a v e r s a l through t h e f o i l . [ l 6 ] For a plasma frequency w

-

1015 sec-l, t h e as-

P

sumption o f e l e c t r o n p i c k up from an o s c i l l a t i n g charge d e n s i t y extending sdme few

W

beyond t h e f o i l can g i v e a reasonable f i t t o t h e experimental data.

S c a t t e r i n g from an o s c i l l a t o r y p o t e n t i a l o f s i m i - l a r c h a r a c t e r i s t i c s a l s o would g i v e r i s e t o such o s c i l l a t i o n s i n A:. The c u r r e n t dependence ob- served remains somewhat mysterious. However, o u r r e c e n t measurements p r o v i d e s t r o n g evidence t h a t these changes i n A: a r e c o r r e l a t e d w i t h changes i n f o i l temperature. I n t h i s work [ I 7 1 i t was obser- ved t h a t

: A

increased w i t h f o i l temperature f o r

f i x e d beam c u r r e n t d e n s i t y and t h e r a t e o f increase v a r i e s w i t h beam energy i n e x a c t l y t h e same f a s h i o n as t h e data shown i n F i g u r e 3. Since f o i l temperature i s known t o change t h e secondary e l e c t r o n f l u x , these r e s u l t s can be i n t e r p r e t e d as a d d i t i o n a l c i r c u m s t a n t i a l evidence f o r t h e impor- tance o f e l e c t r o n pick-up.

The o b s e r v a t i o n f o r t h e 3p l P t h a t A:

does n o t change s i g n i f i c a n t l y when t h e f o i l i s t i l t e d i s a l s o c o n s i s t e n t w i t h t h e simple e l e c t r o n pick-up model described e a r l i e r 1151 where t h e d i r e c t i o n of t h e p r i n c i p a l a x i s f o r t h e alignment i s determined by t h e beam v e l o c i t y . I t i s also, o f course, what would be expected i f t h e alignment were produced i n t h e b u l k . The v a r i a t i o n o f t h e t h r e e a1 ignment parameters w i t h f o i l t i 1 t angle i s n o t what would r e s u l t from a1 ignment produced

-

p a r a l l e l t o t h e t i l t e d f o i l normal. Since capture o f secondary e l e c t r o n s has been suggested above as a s i g n i f i c a n t c o n t r i b u t o r t o our observations, i t i s i n t e r e s t i n g t o observe t h a t measurements o f t h e dependences o f t h e y i e l d o f such e l e c t r o n s upon f o i l t i l t angle [ I 8 1 i s p r o p o r t i o n a l t o l / c o s a, due t o an increase w i t h t i p a n g l e i n t h e num$er o f e l e c t r o n s which can reach t h e f i n a l sur- f a c e w i t h o u t absorption. This same mechanism r e q u i r e s t h a t t h e secondary e l e c t r o n d e n s i t y i s asymnetric about t h e i n c i d e n t beam i n e x a c t l y t h e way r e q u i r e d t o produce o r i e n t a t i o n o f t h e sense observed i n a l l measurements c a r r i e d o u t t o date.

Various t h e o r e t i c a l attempts have been made t o e x p l a i n t h e observed v a r i a t i o n o f t h e alignment and o r i e n t a t i o n w i t h f o i l t i l t angle as due t o t h e e f f e c t s o f surface e l e c t r i c f i e l d s , f o l l o w i n g t h e i n i t i a l suggestion o f Eck.[19] A l l have been successful i n p r e d i c t i n g some p r o p e r t i e s o f t h e measurements, b u t no model i s i n agreement w i t h a l l o f t h e a v a i l a b l e data. The most general o f these models i n terms o f t h e processes i n -

cluded i s t h a t o f Band. [20] T h i s work makes t h e p r e d i c t i o n t h a t p: and p i should be d i r e c t l y pro- p o r t i o n a l t o each o t h e r . As described e a r l i e r , t h i s i s indeed t h e case i n He I f o r t h e 3p I P l e v e l , b u t i s n o t so f o r t h e 4d ID l e v e l . While t h i s model employs several approximations (sudden approximation, power expansion i n terms o f Voa/cos a ) i t may w e l l be t h a t i t s n e g l e c t o f pos- s i b l e o r i e n t a t i o n p r o d u c t i o n by e l e c t r o n c a p t u r e causes i t s f a i l u r e i n t h i s case.

F i n a l l y , we n o t e t h a t t h e l a c k o f o s c i l - l a t i o n s w i t h energy i n measurements o f t h e

o r i e n t a t i o n suggest t h a t t h e mechanism f o r pro- ducing i t may be d i f f e r e n t from t h a t producing t h e alignment. This may a l s o be r e s p o n s i b l e f o r t h e d i f f e r i n g c u r r e n t d e n s i t y dependences observed f o r these two q u a n t i t i e s .

V I I . CONCLUSIONS

I t i s c l e a r t h a t much progess has been made i n l e a r n i n g about t h e n a t u r e o f t h e s t a t e s produced when i o n s t r a v e r s e f o i l s . Somewhat l e s s progress has been made i n c o n s t r u c t i n g a compre- hensive model which czn e x p l a i n a11 of these r e s u l t s , a l t h o u g h many q u a l i t a t i v e f e a t u r e s can be explained by a simple e l e c t r o n pick-up model.

Additi'onal work--both t h e o r e t i c a l and experimen- tal--aimed a t f u r t h e r e l u c i d a t i n g t h i s problem i s underway.

A number o f our colleagues have g r e a t l y a s s i s t e d us i n c a r r y i n g o u t t h i s program o f research. I n p a r t i c u l a r , we wish t o acknowledge t h e c o n t r i b u t i o n s o f S. T. Chen, D. G. E l l i s , G. Gabrielse, T. Gay, R. D. Hight, S. H u l d t and A. E. L i v i n g s t o n .

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