CURRENT STATUS OF CALCULATIONS AND
MEASUREMENTS OF ION STOPPING POWER IN
ICF PLASMAS
T. Mehlhorn, J. Peek, E. Mcguire, J. Olsen, F. Young
To cite this version:
T. Mehlhorn, J. Peek, E. Mcguire, J. Olsen, F. Young. CURRENT STATUS OF CALCULATIONS AND MEASUREMENTS OF ION STOPPING POWER IN ICF PLASMAS. Journal
de Physique Colloques, 1983, 44 (C8), pp.C8-39-C8-66. <10.1051/jphyscol:1983804>. <jpa00223311>
HAL Id: jpa-00223311
https://hal.archives-ouvertes.fr/jpa-00223311
Submitted on 1 Jan 1983
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JOURNAL
DE PHYSIQUE
Colloque C 8 , supplement au nO1l, T o m e 44, novembre 1983
page C8-39
CURRENT S T A T U S OF C A L C U L A T I O N S AND MEASUREMENTS OF I O N S T O P P I N G POWER
I N I C F PLASMAS
T.A. Hehlhorn, J.M. Peek, E.J. McGuire, J.N. Olsen and F.C. youngs
Sandia NatioraZ Laboralorie;, ,llbuqv.erque, R.X. 8 7 1 9 5 , u.S.11.
*filavaZ Research I ~ b o r a t o r yidaskington,
,
D. C., U.S.A.
RESUME
En fusion inertielle conduite par les ions, on 6prouve actuellement la n6c6ssit6 de perfectionner les modeles de ralentisscment.
L16volution des recherches montre que les lois d16chelle approch6es
ne sont plus suffisantes pour extrapoler les modsles actucllemcnt utilis6s. On se propose de predire, 3 10 % pres, les parcours ioniques
dans les cibles ICF. On expose le modsle du gaz d161ectrons libres,
ainsi que les profils de densit6 de charge atomique du type HartreeFock-Slater pour dgterminer l'ionisation moyenne I(Z,q,E) d'une cible
d16lectrons. Cette rn6ttiode est syst6matiquement exp1ori.e afin de
mettre en Gvidence les insuffisances de la physique sous-jaccnte,
particulisrement pour de faibles vitesses des projectiles. Des modsles
alternatifs sont 6galement d6velopp6s par d'autrcs auteurs 3 la Sandia.
Des mesures exp6rimentales de pouvoir dtarr6t, amplifi6 dans les
plasmas de fusion, ont 6t6 observ6es dans lc domainc 0,3 T W / C ~au
~
Naval Research Laboratory. Les exp6rimentateurs de la Sandia Ctendent
actuellement ces donn6es 3 des 6tats d'ionisation plus 6lCvPe et 3
des cibles 3 Z plus grand, avec l'aide de l'accCl6rateur PROTO-1
(1 ,2 ~ ~ / c m * )
.
More p r e c i s e s t o p p i n g power models f o r use i n ICF t a r g e t d e s i g n
need t o be developed. The l i g h t i o n beam ICF program i s now moving
i n t o a phase where "ad hoc" s c a l i n g of c e r t a i n key p h y s i c s p a r a m e t e r s
Our g o a l i s t o
i n t h e s t o p p i n g power models i s no l o n g e r s u f f i c i e n t .
A verified
p r e d i c t i o n ranges i n ICF t a r g e t s t o w i t h i n about 10-205.
s t o p p i n g power model i s a l s o e s s e n t i a l i n d i a g n o s i n g t a r g e t
i r r a d i a t i o n i n t e n s i t i e s ; such d a t a can o n l y be i n f e r r e d by t a r g e t
r e s p o n s e . P r e s e n t l y , our a r e a of primary c o n c e r n i n v o l v e s
c a l c u l a t i n g t h e s t o p p i n g power of t h e bound e l e c t r o n s of p a r t i a l l y
i o n i z e d atoms. One bound e l e c t r o n s t o p p i n g power model t h a t we a r e
i n v e s t i g a t i n g u s e s t h e l o c a l o s c i l l a t o r model along w i t h E a r t r e e Fock-Slater atomic charge d e n s i t y p r o f i l e s t o c a l c u l a t e I ( Z , q . E ) , a
g e n e r a l i z e d average i o n i z a t i o n p o t e n t i a l f o r t h e t a r g e t e l e c t r o n s .
T h i s method i s b e i n g s t u d i e d s y s t e m a t i c a l l y t o l o o k f o r d e f i c i e n c i e s
i n t h e u n d e r l y i n g p h y s i c s model, e s p e c i a l l y a t low p r o j e c t i l e
v e l o c i t i e s . Another p r o c e d u r e u s e s t h e G e n e r a l i z e d O s c i l l a t o r
S t r e n g t h model t o c a l c u l a t e t h e bound e l e c t r o n s t o p p i n g .
Experimental measurements of enhanced s t o p p i n g power i n ICF plasmas
a t t h e 0.3 lW/cm l e v e l have been r e p o r t e d by t h e Naval Research
Laboratory.
F u r t h e r experiments a t Sandia a r e aimed a t e x t e n d i n g
t h i s d a t a base b o t h t o h i g h e r i o n i z a t i o n s t a t e s and t o higher-Z
t a r g e t s u s i n g a 1.2 lWIcm2 p r o t o n beam on t h e PROTO-I a c c e l e r a t o r .
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983804
JOURNAL DFI PHYSIQUE
The i m p l i c i t g o a l of o u r work o v e r t h e p a s t few y e a r s h a s been t o
d e v e l o p t h e c o m p u t a t i o n a l a b i l i t y t o a c c u r a t e l y s i m u l a t e t h e s t o p p i n g power
of any a r b i t r a r y i o n i n a t a r g e t of a r b i t r a r y composition, t e m p e r a t u r e ,
d e n s i t y , and d e g r e e of i o n i z a t i o n .
p r o g r e s s towards t h i s goal;
We have r e c e n t l y made s i g n i f i c a n t
however, much work s t i l l remains b e f o r e even t h e
more modest needs of S a n d i a ' s l i g h t i o n beam f u s i o n program a r e a d e q u a t e l y
met.
T h i s workshop p r e s e n t s a good forum from which t o i s s u e a c a l l t o t h e
i n t e r n a t i o n a l p h y s i c s community t o j o i n i n an a t t e m p t t o d e v e l o p more
a c c u r a t e and more g e n e r a l s t o p p i n g power models t o be used i n i o n - d r i v e n
ICF.
The key h e r e i s t h e accuracy.
Many u s e f u l models t h a t p r e d i c t g e n e r a l
t r e n d s and t h e approximate s c a l i n g of s t o p p i n g powers f o r ICF plasmas
a l r e a d y e x i s t ; most of them a r e mentioned i n S e c t i o n 4.
However, now i s t h e
time t o a t t e m p t t o make t h e s e models more a c c u r a t e by r i g o r o u s l y comparing
them w i t h t h e l a r g e body of c o l d m a t t e r s t o p p i n g power d a t a and t h e n
e x t e n d i n g them t o t h e more demanding regime of p a r t i a l l y i o n i z e d m a t t e r .
S i n c e i t i s r e l a t i v e l y easy t o perform good s t o p p i n g power e x p e r i m e n t s f o r
c o l d t a r g e t s t h e r e h a s been a tendency t o t r e a t t h e i m p o r t a n t p h y s i c a l
q u a n t i t i e s t h a t c o n t r o l t h e m a t e r i a l and p r o j e c t i l e dependencies of t h e
s t o p p i n g p r o c e s s a s e m p i r i c a l p a r a m e t e r s t h a t a r e o b t a i n e d through b e s t f i t s
t o experimental data.
Good e x p e r i m e n t a l measurements of ion s t o p p i n g powers
i n p a r t i a l l y i o n i z e d ICF p l a s m a s a r e n o t p a r t i c u l a r l y "easy" t o do.
Moreover, t h e d a t a w i l l p r o b a b l y n o t be o b t a i n e d w i t h a s high a p r e c i s i o n a s
c a n be a c h i e v e d w i t h c o l d t a r g e t s .
Therefore,
t h e s t o p p i n g power models
t h a t must be developed f o r t h e d e s i g n of r e l i a b l e , and e f f i c i e n t ICF t a r g e t s
w i l l need t o be more h i g h l y developed and i n t e r n a l l y c o n s i s t e n t .
Experiments a r e n e c e s s a r y t o v e r i f y t h e models, b u t t h e d a t a i s l i k e l y t o be
t o o s p a r s e and t o o u n c e r t a i n t o r e l y on d e t e r m i n i n g e m p i r i c a l p a r a m e t e r s
from t h e measurements.
T h i s u n c e r t a i n t y i s a g g r a v a t e d by t h e f a c t t h a t f o r
most e x p e r i m e n t s now e n v i s i o n e d one c a n o n l y v e r i f y t h e d e p o s i t i o n package
i n c o n j u n c t i o n w i t h a hydrodynamics package; i t might be i m p o s s i b l e t o t e s t
t h e s t o p p i n g power models s e p a r a t e l y .
We have t h e r e f o r e f o r m u l a t e d a n e i g h t
p o i n t p l a n f o r d e v e l o p i n g a n a c c u r a t e and g e n e r a l s t o p p i n g power model f o r
u s e i n ion-beam ICF t a r g e t d e s i g n and t a r g e t d i a g n o s t i c s :
1 ) Develop c a n d i d a t e s t o p p i n g power models f o r hydrogenic p r o j e c t i l e s
(e.g.
protons, deuterons,
tritons - hereafter referred t o generically
a s p r o t o n s f o r s i m p l i c i t y ) emphasizing t h e atomic p h y s i c s of t h e low t o
i n t e r m e d i a t e energy regimes.
( I n Bethe formalism t h i s i s e q u i v a l e n t t o
a c c u r a t e l y c a l c n l a t i n g t h e a v e r a g e i o n i z a t i o n p o t e n t i a l and t h e s h e l l
corrections.)
2 ) T e s t t h e s e models a g a i n s t t h e l a r g e amount of c o l d t a r g e t d a t a f o r
p r o t o n s t o p p i n g powers f o r e l e m e n t s a c r o s s t h e p e r i o d i c t a b l e .
3 ) Compare t h o s e models t h a t a r e s n c c e s s f u l i n S t e p 2 w i t h a v a i l a b l e
p r o t o n s t o p p i n g power d a t a f o r p a r t i a l l y i o n i z e d t a r g e t s .
4 ) Develop a n e f f e c t i v e p r o j e c t i l e charge model f o r higher-Z
ions t h a t i s
c o m p a t i b l e w i t h t h e p r e v i o u s p r o t o n model and i s u s e f u l f o r a r b i t r a r y
d e g r e e s of t a r g e t i o n i z a t i o n .
5 ) Compare t h i s combined model w i t h a c t u a l e x p e r i m e n t a l measurements of
high-Z p r o j e c t i l e s t o p p i n g powers i n c o l d t a r g e t s .
6 ) Compare t h e combined model w i t h a v a i l a b l e s t o p p i n g power d a t a f o r
p a r t i a l l y ionized targets.
7 ) V e r i f y t h e dense plasma s t o p p i n g power models a s t h e a v a i l a b l e
i n t e n s i t y and energy on t a r g e t s i n c r e a s e s .
8) Continue t o s t u d y whether plasma i n s t a b i l i t i e s a t h i g h i n t e n s i t i e s
might l e a d t o anomalous s t o p p i n g powers o r o t h e r b e h a v i o r damaging t o
o p t i m a l t a r g e t performance L1.21.
T h i s p r o g r e s s i o n i s l o g i c a l i f somewhat obvious, b u t i t i s meant t o
p o i n t o u t t h a t a c a r e f u l l y c o n s t r u c t e d and v e r i f i e d model w i l l become
i n c r e a s i n g l y i m p o r t a n t t o t h e a c c u r a t e c a l c u l a t i o n of i g n i t i o n c o n d i t i o n s
of ion-driven
ICF t a r g e t s .
independent and s e q u e n t i a l .
Note a l s o t h a t t h e s e s t e p s a r e n o t n e c e s s a r i l y
To q u a n t i f y o u r accuracy r e q u i r e m e n t s , w e
e s t i m a t e t h a t e v e n t u a l l y we w i l l want t o be a b l e t o p r e d i c t i o n r a n g e s i n
ICF t a r g e t m a t e r i a l s t o w i t h i n a b o u t 1 0 5 .
I m p l i c i t i n t h i s agenda f o r
d e v e l o p i n g a n a c c u r a t e t h e o r e t i c a l model f o r i o n s t o p p i n g power i n p a r t i a l l y
i o n i z e d m a t e r i a l i s t h e need t o have a p a r a l l e l experimental e f f o r t t o
p r o v i d e t h e d a t a n e c e s s a r y t o v e r i f y o r d i s p r o v e t h e models.
certainly a non-trivial
This i s
t a s k and i t would be u s e f u l t o s h a r e i d e a s about how
t o o b t a i n such d a t a a t t h i s meeting.
I n c o n j u n c t i o n w i t h t h e i d e a of d e v e l o p i n g e x p e r i m e n t s f o r measuring
on s t o p p i n g powers a t ICF-level
beam i n t e n s i t i e s , we would emphasize t h e
JOURNAL DE PHYSIQUE
C8-42
interdependence of t h e a b i l i t y t o r e l i a b l y p r e d i c t t h e s t o p p i n g power of an
i o n beam and t h e a b i l i t y t o r e l i a b l y "measure" t h e beam i n t e n s i t y i n c i d e n t
on a t a r g e t a t ICF o r near-ICF c o n d i t i o n s .
That i s , a l l p r e s e n t t e c h n i q u e s
f o r i n f e r r i n g t h e power and c u r r e n t d e n s i t y i n c i d e n t on a n ICF t a r g e t
i n v o l v e coupled depositionlhydrodynamic s i m u l a t i o n of t h e t a r g e t i n t e r a c t i o n
process.
T h e r e f o r e , a v e r i f i e d depositionlhydrodynamic s i m u l a t i o n
c a p a b i l i t y i s e s s e n t i a l t o i n t e r p r e t these diagnostics correctly.
The next s e c t i o n of t h i s paper i s i n t r o d u c t o r y i n n a t u r e and g i v e s a n
overview of t h e combined S a n d i a beam-target
i n t e r a c t i o n model, of which t h e
i o n s t o p p i n g power model i s o n l y a p a r t a l t h o u g h perhaps t h e most
s i g n i f i c a n t one. The t h i r d s e c t i o n w i l l d i s c u s s some of t h e work b e i n g done
a t Sandia on computing t h e c o n t r i b u t i o n of bound e l e c t r o n s t o t h e s t o p p i n g
power of p r o t o n s i n p a r t i a l l y i o n i z e d plasmas.
The n e x t s e c t i o n d i s c u s s e s
t h e p r e s e n t e x p e r i m e n t a l u n d e r s t a n d i n g of i o n s t o p p i n g powers under ICF
conditions.
Both t h e p a s t work a t NRL a s w e l l a s experiments p r e s e n t l y
underway a t Sandia w i l l be d e s c r i b e d .
Moreover, t h e unique e x p e r i m e n t a l
problems and c a l c u l a t i o n a l r e q u i r e m e n t s i n v o l v e d i n making such s t o p p i n g
power measurements w i l l a l s o be d i s c u s s e d .
The main p o i n t s of t h i s paper
w i l l be summarized i n t h e l a s t s e c t i o n .
2 BASIC SANDIA TABOET-INTBBACTION WDRL
A diagram showing t h e i m p o r t a n t components of t h e Sandia beam-target
i n t e r a c t i o n model i s shown i n F i g u r e 1.
The ray t r a c k i n g module i n t e r f a c e s
w i t h t h e hydrodynamic code and c o n t r o l s t h e s t o p p i n g power c a l c u l a t i o n s .
T h i s module t r a c k s t h e i o n t r a j e c t o r i e s through t h e t a r g e t geometry,
informs
t h e d e p o s i t i o n module of t h e p r o j e c t i l e and t a r g e t c o n d i t i o n s , and t h e n
t r a n s l a t e s t h e c a l c u l a t e d AE d e p o s i t e d o v e r d i s t a n c e Ax i n t o a z o n a l energy
MODULE
I4
Fig.
1.
SOLVE
7
Block diagram of Sandia beam-target
i n t e r a c t i o n model.
source term f o r use i n t h e temperature e q n a t i o n of t h e hydro code.
Furthermore, beyond simply c o n t r o l l i n g t h e d e p o s i t i o n r o u t i n e s , t h i s module
i s i n h e r e n t l y important s i n c e r e 1 i a b l e t a r g e t d e s i g n and s i m u l a t i o n a l s o
r e q u i r e s t h e a b i l i t y t o a c c u r a t e l y model t h e s p a t i a l and angul a r dependence
of t h e i n c i d e n t i o n beam.
i n a two-dimensional
As d e p i c t e d i n F i g u r e 2, t h i s i o n " r a y t r a c k i n g "
g r i d can e i t h e r occur along g r i d l i n e s (however, t h e s e
g r i d l i n e s d i s t o r t a s t h e implosion p r o g r e s s e s so t h i s i s not an a t t r a c t i v e
o p t i o n ) , along 2-d r a y s a l l of which pass through t h e a x i s of symmetry, o r
a l o n g 3-d r a y s whose apparent p a t h s i n 2-d p r o j e c t i o n a r e h y p e r b o l i c .
SYMMETRY
Fig.
2.
P r o j e c t i o n of two- and three-dimensional r a y p a t h s through a
c y l i n d r i c a l l y symmetric two-dimensional g r i d .
The d e p o s i t i o n c a l c u l a t i o n i s based on a n e f f i c i e n t and a c c u r a t e
i n t e g r a t i o n of a Bethe-type
s t o p p i n g p o r e r equation.
We expect t h a t t h i s
b a s i c numerical frame-work w i l l remain unchanged i n t h e f u t u r e .
Rather, more
s o p h i s t i c a t e d p h y s i c s w i l l be i n c l u d e d a s new s c a l i n g p a r a m e t e r s i n t h e
Bethe-based model.
For example, a s w i l l be d i s c u s s e d l a t e r , we have
computed a new s e t of e f f e c t i v e average i o n i z a t i o n p o t e n t i a l s <I>f o r
allrminnm u s i n g t h e modified-LOM model
131.
These new v a l u e s were t h e n
i n c o r p o r a t e d i n t o t h e a p p r o p r i a t e p h y s i c s s u b r o u t i n e , but t h e c a l c u l a t i o n a l
a s p e c t s of t h e o v e r a l l model remained unchanged.
New plasma s t o p p i n g power
p h y s i c s o r a l t e r n a t e e f f e c t i v e charge models f o r heavy i o n s could l i k e w i s e
be i n c o r p o r a t e d i n t h e a p p r o p r i a t e p h y s i c s s u b r o u t i n e s w i t h o u t a f f e c t i n g t h e
numerical a l g o r i t h m s .
Therefore, by using t h i s e f f e c t i v e parameter
technique t h e speed and accuracy of t h e numerical a l g o r i t h m s c a n remain
optimized w h i l e i n c r e a s i n g l y more s o p h i s t i c a t e d p h y s i c s i s simulated.
T h i s f i n a l module i n our beam-target
i n t e r a c t i o n model c a l c u l a t e s
JOURNAL D€ PHYSIQUE
i n f l i g h t r e a c t i o n r a t e s and y i e l d s .
Nuclear and atomic p r o c e s s e s t h a t
g e n e r a t e d e t e c t a b l e r a d i a t i o n y i e l d s c a n e i t h e r be u s e d t o p r e d i c t c u r r e n t
d e n s i t y on t a r g e t o r be used t o i n f e r a c t u a l s t o p p i n g power i n f o r m a t i o n
under ICF c o n d i t i o n s .
The primary atomic d i a g n o s t i c used i n ion-driven
i s measurement of c h a r a c t e r i s t i c x-ray
ICF
e m i s s i o n due t o d i r e c t i n n e r - s h e l l
i o n i z a t i o n caused by t h e i n c i d e n t charged p a r t i c l e s (41.
T h i s technique.
which h a s been t h e o r e t i c a l l y i n v e s t i g a t e d by Nardi and Zinamon 151, h a s t h e
advantage t h a t i t c a n be imaged t o p r o v i d e s p a t i a l i n f o r m a t i o n about t h e
deposition region.
However, i t s use i s l i m i t e d t o low i n t e n s i t i e s because
i o n i z a t i o n of t h e t a r g e t changes t h e b a s i c c r o s s s e c t i o n s .
Moreover, a
f a i r l y s o p h i s t i c a t e d t r e a t m e n t of t h e vacancy p r o d u c t i o n c r o s s s e c t i o n s ,
f l u o r e s c e n t y i e l d s [61, and subsequent t r a n s p o r t of t h e l i n e - r a d i a t i o n
through t h e t a r g e t m a t e r i a l a s a f u n c t i o n of d e n s i t y , temperature,
i o n i z a t i o n s t a t e i s r e q u i r e d t o f u l l y u t i l i z e t h i s technique.
and
Such models
a r e b e i n g s y n t h e s i z e d from t h e a v a i l a b l e atomic p h y s i c s d a t a base (e.g.
r e c e n t work a t Sandia on p r e d i c t i n g t h e observed s p e c t r a from M-shell
i o n i z a t i o n of g o l d [71) and w i l l c o n t i n u e t o be of d i a g n o s t i c importance.
D e t e c t i o n of c h a r a c t e r i s t i c r a d i a t i o n from n u c l e a r r e a c t i o n s h a s been
f r e q u e n t l y used i n d i a g n o s i n g beam c o n d i t i o n s i n ICF L8.91.
Figure 3
summarizes t h e r e a c t i o n r a t e e q u a t i o n and a l s o c a t a l o g s some of t h e n u c l e a r
r e a c t i o n s t h a t have been s u c c e s s f u l l y u t i l i z e d f o r ICF d i a g n o s t i c s .
The
model e q u a t i o n p o i n t s o u t t h e interdependence of t h e beam c u r r e n t and t h e
s t o p p i n g power model.
The c o n s t a n t "C" i n f r o n t of t h e i n t e g r a l c o n t a i n s
t h e i n s t a n t a n e o u s v a l u e of t h e i n c i d e n t c u r r e n t ; t h u s , t h e r e a c t i o n r a t e , P,
i s p r o p o r t i o n a l t o t h e i n s t a n t a n e o u s c u r r e n t and i n v e r s e l y p r o p o r t i o n a l t o
t h e s t o p p i n g power.
T h e r e f o r e , a c c u r a t e knowledge of one of t h e s e
q u a n t i t i e s p e r m i t s c a l c u l a t i o n of t h e o t h e r .
s e c t i o n s of i n t e r e s t t o ICF.
F i g u r e 4 i l l u s t r a t e s two c r o s s
Note t h a t t h e energy dependence of d i f f e r e n t
c r o s s s e c t i o n s c a n v a r y so a s t o e f f e c t i v e l y change t h e d e t e c t o r response.
For example, t h e v e r y narrcnr Breit-Wigner
resonance i n t h e l i t h i u m c r o s s
s e c t i o n makes t h i s m a t e r i a l a v e r y s e n s i t i v e d e t e c t o r of p r o t o n s slowingdown through t h e 440 keV peak, b u t h a s v i r t u a l l y no response t o lower energy
protons.
I n c e r t a i n s p e c i a l c a s e s we might need t o become concerned w i t h o t h e r
p r o c e s s e s such a s &-ray t r a n s p o r t , knock-on p r o d u c t i o n and t r a n s p o r t , and
the like.
For example, i n a s e r i e s of D-T f u e l e d exploding p u s h e r t a r g e t s
s h o t on t h e PROTO-I a c c e l e r a t o r , we confirmed t h e s u s p i c i o n [l01 t h a t t h e
main n e u t r o n y i e l d d i d n o t come from thermonuclear r e a c t i o n s b u t r a t h e r from
t h e beam f u s i o n r e a c t i o n s of knock-on d e u t e r o n s and t r i t o n s [ I l l .
These
knock-ons where produced by l a r g e - a n g l e R u t h e r f o r d and n u c l e a r s c a t t e r i n g of
t h e p r o t o n beam by t h e f u e l ions.
A s p e c i a l s e t of r o u t i n e s t o s i m u l a t e
t h i s p r o c e s s were w r i t t e n and i n c o r p o r a t e d i n t o our g e n e r a l i n t e r a c t i o n
model.
An example of t h e agreement found between experiment and c a l c u l a t i o n
f o r t h i s p r o c e s s i s found i n F i g u r e 5 .
Fig.
3.
Smnmary of i n f l i g h t r e a c t i o n model e q u a t i o n . Also shown a r e some
of t h e n u c l e a r r e a c t i o n s t h a t have been used i n ion-driven ICF
diagnostics.
'L~(~.Y)"B~
?O
I
j
b
1
h,
1
20
Fig.
4.
100
Energy (KeV)
l000
100
1000
Energy (KeV)
Sample energy dependent c r o s s s e c t i o n s f o r ( d , t ) f u s i o n r e a c t i o n
and ( L i , p ) gamma producing r e a c t i o n .
JOURNAL DE PHYSIQUE
I
I
I
X-RAY PULSE
0.0
0.4
I
14 MEV NEUTRONS
0.8
1.2
1.6
2 .O
TIME (IO-'SEC)
Fig.
5.
Comparison of d e t e c t o r response and c a l c u l a t i o n f o r p r o d u c t i o n of
1 4 MeV n e u t r o n s from e x p l o d i n g p u s h e r t a r g e t ( P r o t o - I Shot
# 3121).
The b a s i c p r o t o n s t o p p i n g power e q u a t i o n s [ l 2 1 used i n t h e S a n d i a beamt a r g e t i n t e r a c t i o n model c a n be summarized a s :
where:
i s Avogadro's number, p i s t h e t a r g e t d e n s i t y , A , Z and q a r e t h e
0
atomic weight, n m b e r and i o n i z a t i o n s t a t e of t h e t a r g e t atom, < I >i s t h e
and N
average i o n i z a t i o n p o t e n t i a l , Ci i s t h e s h e l l c o r r e c t i o n f o r t h e ith s h e l l ,
ye i s t h e r a t i o of t h e i o n v e l o c i t y t o t h e e l e c t r o n thermal v e l o c i t y , w
t h e plasma frequency,
definitions.
P
is
and t h e remaining symbols have t h e i r u s u a l
The u s e of t h e B e t h e e q u a t i o n f o r t h e bound e l e c t r o n s and t h e
u s e of a s e p a r a t e term f o r t h e plasma e l e c t r o n s i s common both t o t h i s work
and t o t h a t of Nardi, P e l e g and Zinamon 1131. k s h e r 1141. Bangerter 1151,
and Beynon 1161.
We p r e s e n t l y assume t h a t our dense plasma, f r e e e l e c t r o n
s t o p p i n g power models a r e adequate and t h a t our major u n c e r t a i n t y i s i n o a r
modeling of t h e bound e l e c t r o n s t o p p i n g power of p a r t i a l l y i o n i z e d atoms.
P r e s e n t experimental d a t a s u g g e s t s t h a t t h i s i s a v a l i d assumption.
Within
t h e Bethe e q u a t i o n formalism, an u n c e r t a i n t y i n t h e bound e l e c t r o n s t o p p i n g
power f o r p r o t o n s can be d i r e c t l y r e l a t e d t o p h y s i c s u n c e r t a i n t i e s i n our
c a l c u l a t i o n of t h e average i o n i z a t i o n p o t e n t i a l .
shell-correction
terms, C..
< I > ,and i n t h e r e l a t e d
Once a g a i n , our r e s t r i c t i o n h e r e t o p r o t o n s i s
t o allow u s t o i g n o r e e f f e c t i v e charge e f f e c t s and t o only s t u d y t h e
v a r i a t i o n of <I> and Ci w i t h i o n i z a t i o n .
A b r u t e f o r c e c a l c u l a t i o n of <I>i s s t i l l p r o h i b i t i v e l y d i f f i c u l t f o r
a r b i t r a r y ions;
t h e formal d e f i n i t i o n of < I >i n t h e Bethe theory being:
where E a r e a l l p o s s i b l e p o s i t i v e energy t r a n s i t i o n s of t h e t a r g e t atom,
n
fn
a r e t h e corresponding d i p o l e o s c i l l a t o r s t r e n g t h s , and (Z-q) i s t h e number
of e l e c t r o n s .
of i n t e r e s t .
For ICF we need < I ( Z , q ) > f o r b o t h n e u t r a l s and f o r a l l i o n s
To complicate m a t t e r s f u r t h e r ,
g i v e optimal beam-target
conpling.
i o n e n e r g i e s of a few MeVIamn
I n t h i s energy regime, s h e l l c o r r e c t i o n s
and t h e d e t a i l s of t h e low energy s t o p p i n g power p l a y an e s s e n t i a l r o l e i n
energy d e p o s i t i o n and range c a l c n l a t i o n s .
T h e r e f o r e , what we r e a l l y need
f o r a11 atoms and t h e i r a s s o c i a t e d i o n s i s b o t h an average i o n i z a t i o n
p o t e n t i a l and a s e t of energy-dependent
shell corrections.
Alternatively,
we can g e n e r a l i z e t h e d e f i n i t i o n of t h e average i o n i z a t i o n p o t e n t i a l such
t h a t i t i s now energy dependent: I ( Z , q , E ) , where E i s t h e i o n energy.
normal d e f i n i t i o n t h e n t a k e s t h e form I ( Z , q ) = I(Z,q,E->W)).
(The
Thus, our g o a l
of developing a n a c c u r a t e atomic s t o p p i n g power model h a s now become t h e
g o a l of a c c u r a t e l y c a l c u l a t i n g t h e f u n c t i o n I (Z, q, E).
I n many of t h e a r t i c l e s c i t e d above,
some b a s i c s c a l i n g formula f o r
I ( Z , q ) i s proposed based e i t h e r on f i t s t o approximate c a l c u l a t i o n s o r on
simple, a n a l y t i c , p h y s i c a l models.
For example, our o r i g i n a l s c a l i n g
e s t i m a t e s took t h e form I121 :
i n our p r e s e n t n o t a t i o n .
q=Z-l,
T h i s formula i s a c c u r a t e i n two l i m i t s , q=O and
t h e n e u t r a l atom and hydrogenic limits.
Such v a l u e s , I ( Z , q ) ,
attempt
t o approximate t h e h i g h energy l i m i t of t h e average i o n i z a t i o n p o t e n t i a l and
JOURNAL DE PHYSIQUE
CA-48
t h e y can be u s e f u l i n e l e c t r o n t r a n s p o r t o r approximate high energy i o n beam
transport calculations.
However, an a s s o c i a t e d s e t of energy-dependent
s h e l l corrections a r e required f o r l i g h t ion fusion simulation.
Moreover,
experiments show t h a t such s c a l i n g i s adequate only f o r hydrocarbon
compounds and o t h e r low-Z t a r g e t s .
T h e r e f o r e , more a c c u r a t e models f o r
c a l c u l a t i n g I ( Z . q) a r e needed.
The Local O s c i l l a t o r Model of Lindhard and Winther [ l 7 1 h a s been
f r e q u e n t l y used f o r d e t e r m i n i n g t r e n d s i n I ( Z ) f o r n e u t r a l s [181, f o r
c a l c u l a t i n g approximate shapes t o t h e s t o p p i n g power curve [191, e t c .
This
method h a s a l s o been c a l l e d t h e F r e e E l e c t r o n Gas Model, t h e Local Density
Approximation, and t h e l i k e .
These names a r e s u g g e s t i v e of t h e f a c t t h a t
t h i s model t r e a t s t h e r a d i a l e l e c t r o n charge d e n s i t y about a n atom a s a
l o c a l l y uniform, d e g e n e r a t e f r e e e l e c t r o n g a s w i t h a unique l o c a l plasma
frequency.
The s t o p p i n g power of a f a s t i o n i s t h e n g i v e n by t h e
p o l a r i z a t i o n d r a g o f t h e e l e c t r o n gas on t h e i o n a s i t p a s s e s through t h e
atom.
Within t h e Lindhard formalism t h e average i o n i z a t i o n p o t e n t i a l i s
defined a s [l71
where p ( r ) i s t h e s p h e r i c a l l y averaged e l e c t r o n charge d e n s i t y of t h e atom
o r ion, w
i s t h e e l e c t r o n plasma freqnency. and y i s a n e m p i r i c a l c o n s t a n t
P
t h a t approximates e l e c t r o n b i n d i n g e f f e c t s and h a s a nominal v a l u e of &.
The a t t r a c t i v e n e s s of t h i s approach i s t h a t one a p p a r e n t l y need only
c a l c u l a t e t h e r a d i a l d e n s i t y p r o f i l e p ( r ) t o s u c c e s s f u l l y apply t h i s method.
However, i t h a s been h a s r e c e n t l y e s t a b l i s h e d t h a t t h e LOM model f o r t h e
average i o n i z a t i o n p o t e n t i a l does not s c a l e p r o p e r l y t o t h e hydrogenic l i m i t
That i s , I(Z,Z-l)
1201.
should.
scales a s z''~I(I,o)
rather than a s ~'1(1,0) a s i t
Thus t h e LOM model, which does a r e a s o n a b l e j o b of c a l c u l a t i n g
average i o n i z a t i o n p o t e n t i a l s and s t o p p i n g powers f o r n e u t r a l atoms, w i l l be
p r o g r e s s i v e l y more i n e r r o r a s t h e i o n i z a t i o n s t a t e of a n i o n i s i n c r e a s e d .
An a t t e m p t h a s been made t o augment t h e LOM t h e o r y by g e n e r a l i z i n g t h e
e m p i r i c a l c o n s t a n t y i n t o a simple f u n c t i o n of q and Z t h a t would g i v e t h e
c o r r e c t o n e - e l e c t r o n l i m i t [211.
I n developing t h i s f u n c t i o n , p u b l i s h e d GOS
( G e n e r a l i z e d O s c i l l a t o r S t r e n g t h ) r e s u l t s f o r alnminum i o n s 1221 were used
a s a benchmark.
The GOS model i s based on t h e plane wave Born approximation
(FWBA). The s t r e n g t h
of t h i s method i s t h a t i t i s r e l a t i v e l y simple t o use,
p e r m i t s t h e c a l c u l a t i o n of a l l r e l e v a n t p r o c e s s e s ,
energy range [231.
and i s v a l i d over a l a r g e
For p r o t o n s t o p p i n g power c a l c u l a t i o n s i t s major
drawback i s t h a t t h e PWBA method i s n o t v a l i d n e a r t h e e l e c t r o n i o n i z a t i o n
and e x c i t a t i o n t h r e s h o l d s .
T h i s t h r e s h o l d roughly corresponds t o p r o t o n
e n e r g i e s of between 100 and 200 keV.
Below t h i s energy t h e method i s n o t
v a l i d , and n e a r t h e t h r e s h o l d t h e method t e n d s t o o v e r - p r e d i c t
power c r o s s s e c t i o n s .
t h e stopping
The GOS method h a s been s u c c e s s f u l l y compared w i t h
e l e c t r o n impact i o n i z a t i o n c r o s s s e c t i o n s f o r both n e u t r a l and i o n i z e d
t a r g e t s ( i n c l u d i n g g o l d i o n s ) and i s c o n t i n u a l l y b e i n g compared t o
e x p e r i m e n t a l d a t a f o r o t h e r p r o c e s s e s a s i t becomes a v a i l a b l e .
I-values,
T h i s s e t of
c a l c u l a t e d u s i n g t h e GOS model, almost c e r t a i n l y r e p r e s e n t s t h e
most a c c u r a t e v a l u e s t h a t have been p u b l i s h e d t o d a t e .
Using t h i s d a t a ,
good agreement was o b t a i n e d between t h e LOM and GOS I - v a l u e s f o r t h e
alrminum s e r i e s of i o n s when t h e c o n s t a n t y was g e n e r a l i z e d t o t h e f u n c t i o n
[ZOl :
F i g u r e 6 d e m o n s t r a t e s t h e agreement o b t a i n e d between t h e LOM and GOS models
when t h i s g e n e r a l i z e d f u n c t i o n i s used t o c a l c u l a t e t h e s t o p p i n g power.
The
o r i g i n a l model along w i t h t h i s g e n e r a l i z e d d e f i n i t i o n of 7 h a s been termed
t h e augmented-LOM (A-MM) model.
As w i l l be d i s c u s s e d f u r t h e r i n t h e next
s e c t i o n , t h e s e augmented-LOMIGOS-equivalent
s t o p p i n g powers seem t o
correspond v e r y w e l l w i t h t h e enhanced d e u t e r o n s t o p p i n g powers measured i n
the ~
1 plasma
+ ~ of t h e NRL s t o p p i n g power experiment C241.
Energy k W
Fig.
6,
Comparison of p r o t o n s t o p p i n g power i n aluminum a s a f u n c t i o n of
energy: Augmented-MM model ( s o l i d l i n e ) , GOS model (diamonds),
Z i e g l e r a n a l y t i c f i t t o expgriment ( d o t t e d l i p ? ) . P l o t A f o r
n e u t r a l a l m i n u m , B f o r A1
plasma, C f o r A 1
, and D f o r A1
plasma.
+,,
JOURNAL DE PHYSIQUE
We nor seemingly have a f a i r l y r e l i a b l e s e t of asymptotic I-values f o r
t h e i o n i c s e r i e s of a l m i n u m ; but what about t h e g e n e r a l i z e d v a l u e s I(Z.q,E)
t h a t we need t o compute a c c u r a t e s t o p p i n g powers f o r e n e r g i e s of about 5
Mev/amu and below?
The procedure t h a t r e followed t o g e n e r a t e t h e v a l u e s
I ( 1 3 , q , E ) u s i n g t h e A-UIM method can be summarized a s f o l l o w s .
F i r s t we
g e n e r a t e d t h e s t o p p i n g number p e r e l e c t r o n , L, u s i n g t h e A-UIM model a s
g i v e n by t h e e q u a t i o n :
The r a d i a l charge d e n s i t y p ( r ) was c a l c u l a t e d u s i n g f r e e atom w a v e f u n c t i o n s
o b t a i n e d from a s t a n d a r d Herman-Skillman
code l251; ground s t a t e o r b i t a l s
were used throughout. The f u n c t i o n c(p,E) is t h e Lindhard-Winther
stopping
f u n c t i o n f o r a z e r o temperature Fermi d e g e n e r a t e e l e c t r o n gas ( y = l ) .
Approximations t o t h i s f u n c t i o n have been t a b u l a t e d and p u b l i s h e d by many
a u t h o r s [17,191.
Having v e r i f i e d t h e s e v a l u e s a g a i n s t t h e GOS r e s u l t s ( a s
d i s c u s s e d above), t h e A-MM s t o p p i n g n m b e r s were t h e n equated t o t h e formal
d e f i n i t i o n of t h e L-value
i n Bethe theory, and a s e r i e s of I-values.
I(13,q.E)
These I-values were t h e n f i t t o polynomials f o r
r e r e computed.
use i n t h e s t a n d a r d beam-target
i n t e r a c t i o n package d e s c r i b e d i n S e c t i o n 3.
The v a l u e s 1 ( 1 3 , q , E ) g e n e r a t e d by t h i s procedure a r e shown i n F i g u r e 7.
Proton Energy W V )
Fig.
7.
V a r i a t i o n of t h e average i o n i z a t i o n p o t e n t i a l f o r aluminmu i o n s a s
Lowest c u r v e f o r n e u t r a l atom, h i g h e s t
o f u n c t i o n ogl9nergy.
c u r v e f o r A1
ion.
The p r o t o n r a n g e s i n a l u m i n m p r e d i c t e d by t h e s e I - v a l u e s a r e
s u b s t a n t i a l l y d i f f e r e n t from t h o s e o b t a i n e d w i t h our o r i g i n a l s c a l i n g
formula (Eq. 3 ) .
F i g u r e 8 s h o r s t h e range of a 1.6 MeV p r o t o n i n a n
aluminum plasma a s a f u n c t i o n of t a r g e t i o n i z a t i o n .
(The t a r g e t i o n i z a t i o n
was o b t a i n e d v i a a Saha e q u a t i o n by assuming a c o n s t a n t d e n s i t y o f . O 1 t i m e s
s o l i d and t h e n v a r y i n g t h e t e m p e r a t u r e . )
The most s t r i k i n g f e a t u r e of t h i s
p l o t i s t h a t t h e p r o t o n range h a s a p l a t e a u a t q=3.
t h e c l o s e d - s h e l l c o n f i g u r a t i o n of t h e neon-like
T h i s f e a t u r e i s due t o
l ion.
+
~
~
We f i n d t h a t on a
s u b s h e l l b a s i s t h e s t o p p i n g power of t h e t i g h t l y bound neon-like
changes v e r y l i t t l e between i o n i z a t i o n s t a t e s q=2 and q=3.
e l e c t r o n i n t h e sodium-like
core
Likewise,
the 3 s
c o n f i g u r a t i o n i s so weakly bound t h a t i t i s
v i r t u a l l y i n d i s t i n g u i s h a b l e from t h e f r e e plasma e l e c t r o n s i n i t s s t o p p i n g
power.
T h e r e f o r e , both t h e t o t a l s t o p p i n g power and t h e r e b y t h e range of a
1.6 MeV p r o t o n changes v e r y l i t t l e between charge s t a t e s q=2 and q=3 i n a n
The maximum d e v i a t i o n between t h e LOH/GOS r e s u l t and t h a t
aluminum plasma.
g i v e n by Eq. 3 o c c u r s f o r q=3.
Fortnitonsly, t h i s i s the ionization s t a t e
t h a t was r e a c h e d a t peak power i n t h e NRL s t o p p i n g power experiments.
i t was r e l a t i v e l y easy t o s e e t h a t t h e
Thus,
r e s u l t s w e r e much c l o s e r t o t h e
s t o p p i n g powers measured i n t h e experiments t h a n t h o s e c a l o a l a t e d u s i n g
Eq. 3.
l0
Scaled-Bethe Model
.-.-.----.
LOMIGOS Model
0-
-
-
6-
. . . . . . . . . . . . . . . . . . . . . . .
4
0
1
2
3
4
6
~
7
8
O
l
O
l
l
P
Ionization State
8.
Fig.
Range of 1.6 MeV p r o t o n i n a l o l i n u m a s f u n c t i o n of t h e d e g r e e of
i o n i z a t i o n of t h e t a r g e t .
Scaled B e t h e model (Eq. 3 ) and LOMIGOS
r e s u l t s shorn. Note t h e marked d i f f e r e n c e i n t h e two models f o r
ZBAR=3.
We have t r i e d t h i s g e n e r a l i z e d 7 f u n o t i o n f o r a g o l d t a r g e t t o s e e i f
t h e same good agreement e x i s t s between t h e LOM and t h e GOS models f o r high-Z
atoms.
U n f o r t u n a t e l y , t h e agreement was n o t n e a r l y a s good a s f o r aluminum
JOURNAL D€ PHYSIQUE
atoms, e s p e c i a l l y a t low e n e r g i e s ( s e e F i g u r e 9 ) . T h i s s u g g e s t s t h a t t h e y
function i s not universal.
Furthermore, even though we could p o s s i b l y
g e n e r a t e a n o t h e r unique f u n c t i o n f o r gold, t h i s i s n o t l e a d i n g t o t h e
g e n e r a l i t y t h a t we a r e seeking.
Moreover, i t i s p a r t i c u l a r l y d i s t r e s s i n g
t h a t even t h e n e u t r a l atom r e s u l t s prove t o be a r e l a t i v e l y bad f i t t o b o t h
t h e GOS and t h e t a b u l a t e d e x p e r i m e n t a l r e s u l t s .
Energy MeV)
Fig.
9.
Comparison of p r o t o n s t o p p i n g power i n g o l d a s a f u n c t i o n of
energy: Augmented-MM model ( s o l i d l i n e ) , GOS model (diamonds),
Z i e g l e r a n a l y t i c f i t t ~ ~ g x p e r i m e n(td o t t e d I d n e ) . P l o t A f g s ,
plasma, C f o r ~ l +
n e u t r a l gold, B f o r An
, and D f o r A1
plasma.
A t present,
it seems u s e f u l t o s u b j e c t t h e LOM model t o f u r t h e r s t u d y
and a t t e m p t t o i s o l a t e any p h y s i c s d e f i c i e n c i e s i n i t s approach.
Therefore,
r e a r e b e g i n n i n g t o s y s t e m a t i c a l l y study t h e v a r i o u s a s p e c t s o f , and
approximations made i n t h e s e c a l c u l a t i o n s .
T h i s means f i r s t r e t u r n i n g t o a
s t u d y of n e u t r a l atoms t o f a c i l i t a t e comparison w i t h e x p e r i m e n t a l d a t a .
The
f i r s t s t e p i n t h i s p r o c e s s i s t o i n v e s t i g a t e t h e s e n s i t i v i t y of t h e
c a l c u l a t i o n s t o t h e e x a c t d e t a i l s of t h e charge d i s t r i b u t i o n ,
F i g u r e 10
d e m o n s t r a t e s t h e d i f f e r e n c e between t h e c a l c u l a t e d charge d i s t r i b u t i o n f o r
a n i s o l a t e d atom (denoted HFS f o r Harttee-Fock-Slater)
atom i n a s o l i d - s t a t e
l a t t i c e a s t a b u l a t e d i n Ref. 26.
and t h a t of t h e same
F i g u r e 11 shows t h e
r e l a t e d change i n t h e c a l c u l a t e d p r o t o n s t o p p i n g power a s compared t o
experiment u s i n g t h e s e two d i s t r i b u t i o n s .
(Note t h a t t h e i n t e r s t i t i a l
e l e c t r o n s not included i n t h e tabulated s o l i d - s t a t e d i s t r i b u t i o n a r e
i n c l u d e d a s d e s c r i b e d i n Ref. 2 7 ) .
s t o p p i n g power i s o v e r - p r e d i c t e d
We see t h a t w h i l e t h e low energy
f o r i s o l a t e d atoms, i t i s someahat under-
p r e d i c t e d when t h e more r e a l i s t i c s o l i d - s t a t e
d i s t r i b u t i o n i s used.
(We
a l s o see t h e o v e r - p r e d i c t i o n of t h e GOS model n e a r t h r e s h o l d a s p r e v i o u s l y
noted.)
As a numerical check of our p r o c e d u r e s we have compared our
I - v a l u e s w i t h t h o s e r e p o r t e d by Z i e g l e r [191.
For n e u t r a l atoms w i t h y=l
o u r numerical p r o c e d u r e s s h o u l d be e q u i v a l e n t a s s u b s t a n t i a t e d by t h e good
agreement shown i n T a b l e I.
Note t h a t u s i n g t h e c a n o n i c a l v a l u e y=J& t h e
c a l c u l a t e d I - v a l u e s f o r t h e two d i s t r i b u t i o n s a r e : HFS
-
1 2 4 eV, MTW
-
1 3 8 eV.
T h i s i s t o be compared w i t h t h e a c c e p t e d e x p e r i m e n t a l v a l u e of
1 6 2 eV.
Thus, t h e s o l i d s t a t e d i s t r i b u t i o n does g i v e a b e t t e r e s t i m a t e t o
I(13.0).
but a s u b s t a n t i a l d i s c r e p a n c y s t i l l e x i s t s .
Our hope i s t h a t by
u s i n g t h e b e s t a v a i l a b l e d a t a f o r p ( r ) f o r v a r i o u s n e u t r a l atoms ( i n c l u d i n g
high-Z atoms such a s g o l d ) we c a n i s o l a t e and c o r r e c t any i n a c c u r a c i e s or
omissions i n t h e i n t e r a c t i o n function I(p,E).
We a r e c u r r e n t l y p r e p a r i n g t o
perform s i m i l a r comparisons between i s o l a t e d and s o l i d - s t a t e d i s t r i b u t i o n s
f o r copper (2=29) and s i l v e r (2=47).
We w i l l a t t e m p t t o e s t a b l i s h whether a
t r e n d towards i n c r e a s i n g e r r o r s w i t h i n c r e a s i n g Z e x i s t s ,
and t o q u a n t i f y
how much of t h e s e d e v i a t i o n s a r e due t o i n a c c u r a c i e s i n t h e charge
distribution.
Fig. 1 0 .
Radial charge d e n s i t y p r o f i l e s f o r n e u t r a l aluminurn atoms.
R e s u l t s f o r f r e e atoms (=F-S) and atoms w i t h i n a s o l i d - s t a t e
I n t e r s t it i a l s included i n sol id-state
l a t t i c e (M-J-W) a r e shown.
d i s t r i b u t i o n u s i n g c o n t i n u o u s o p t i o n a s d i s c u s s e d i n Ref. 26.
JOURNAL DE PHYSIQUE
Energy Mev)
Fig. 11.
Comparison of p r o t o n s t o p p i n g power i n n e u t r a l almuinum a s a
f u n c t i o n of energy: Free-atom LOM-calculation ( s o l i d l i n e ) , WS
r e s u l t s (diamonds), e x p e r i m e n t a l d a t a (dashed l i n e ) , and s o l i d s t a t e L O E c a l c u l a t i o n (chain-dot l i n e ) . Notice t h e change i n t h e
LOM-computed c u r v e s w i t h d i f f e r e n t charge d i s t r i b u t i o n s .
TABLE I
Comparison of average i o n i z a t i o n p o t e n t i a l s c a l c u l a t e d i n t h i s s t u d y
w i t h t h o s e r e p o r t e d by Z i e g l e r [191. E-F-S d e n o t e s H a r t r e e F o c k - S l a t e r
e l e c t r o n d i s t r i b u t i o n s f o r f r e e atoms. M-J-W d e n o t e s s o l i d - s t a t e
d i s t r i b u t i o n s f o r atomic e l e c t r o n s a s t a b u l a t e d i n Ref. 26. The c o n t i n u o u s
and d i s c o n t i n u o u s sub-headings r e f e r t o t h e way t h a t t h e i n t e r s t i t i a l
e l e c t r o n s not included i n t h e solid-state tabulations a r e joined t o t h e
sol id-state distribution.
M-J-W
U-F-S
Discoatinaous
Continwus
T h i s Stndy
106.8
118.9
119.2
Ziegler
106.3
118.7
---
At t h i s p o i n t , a p a r t i a l l i s t of q u e s t i o n s r e l a t e d t o t h e LOM model
and i t s l o n g term a p p l i c a b i l i t y f o r o u r modeling c a n be compiled:
1)
What i s t h e most a p p r o p r i a t e p ( r ) t o use i n t h e s e c a l c u l a t i o n s f o r
n e u t r a l atoms?
a ) Thomas Fermi
b ) Hartree-Fock
C) Solid-state
2)
What i s t h e most a p p r o p r i a t e p ( r ) f o r i o n s ?
3)
W i l l a r e l a t i v i s t i c atomic s t r u c t u r e code (e.g.
Liberman [281) g i v e
b e t t e r r e s u l t s f o r high-Z atoms and i o n s such a s gold?
c a l c u l a t i o n s s u g g e s t t h a t t h i s i s o n l y a 10-2M
4)
(Sample
e f f e c t [291).
I s t h e low energy regime p r o p e r l y t r e a t e d w i t h i n t h e Lindhard-Winther
i n t e r a c t i o n model?
a)
What about charge exchange energy l o s s ? 1301
b)
Momentum t r a n s f e r ?
c)
Does t h e e f f e c t i v e charge of a p r o t o n e n t e r i n ?
d)
What i s t h e magnitude of More's o r b i t c o r r e c t i o n [31J?
5)
Do h i g h e r o r d e r Z-proj e c t i l e e f f e c t s p l a y a r o l e i n t h i s modeling?
6)
What impact does t h e f i n i t e - t e m p e r a t u r e
e x t e n s i o n of t h e Lindhard
i n t e r a c t i o n model of Maynard and Deutsch L321 have on t h e s e problems?
Perhaps some of t h e s e q u e s t i o n s can be a t l e a s t p a r t i a l l y answered a t t h i s
workshop.
The f i n a l r e s u l t of i n t e r e s t i n t h e a r e a of bound e l e c t r o n s t o p p i n g
powers f o r i o n i z e d m a t t e r i s t o d i r e c t l y s t u d y t h e GOS r e s u l t s f o r g o l d
133.341.
model.
We have i n c o r p o r a t e d t h e t a b u l a t e d GOS v a l u e s i n t o our d e p o s i t i o n
Low energy v a l u e s a r e i n t e r p o l a t e d u s i n g a s q u a r e r o o t of energy
scaling.
F i g u r e 1 2 d e m o n s t r a t e s t h e v a r i a t i o n of t h e range i n g o l d w i t h
i o n i z a t i o n f o r p r o t o n s of v a r i o u s e n e r g i e s .
Eq. 3 s c a l i n g a r e shoan.
GOS r e s u l t s and t h o s e u s i n g
As i n t h e c a s e of aluminum, t h e range i s p r e d i c t e d
t o d e c r e a s e more slowly w i t h i o n i z a t i o n when t h e b e t t e r atomic p h y s i c s (GOS)
i s used.
The new and s u r p r i s i n g r e s u l t i s t h a t t h i s model p r e d i c t s t h a t t h e
range f o r h i g h energy p r o j e c t i l e s 0 5 MeV/amu) c a n i n i t i a l l y i n c r e a s e w i t h
i o n i z a t i o n of t h e atom.
T h i s r e s u l t seems t o have been a n t i c i p a t e d by
Brueckner [351, although t h e mechanism he invokes f o r t h i s anomaly does n o t
seem t o be v a l i d h e r e .
Such range l e n g t h e n i n g seems t o occur only f o r
high-Z m a t e r i a l s , and we b e l i e v e t h a t t h i s r e s u l t c a n be d e s c r i b e d i n t e r m s
of t h e d i f f e r e n c e s i n t h e i n t e r a c t i o n v e l o c i t i e s of t h e t a r g e t e l e c t r o n s
when t h e y a r e i n t h e i r bound and t h e i r f r e e s t a t e s .
bound,
When t h e e l e c t r o n i s
i t s c h a r a c t e r i s t i c v e l o c i t y i s determined by quantum s t a t i s t i c s and
i s e s s e n t i a l l y g i v e n by t h e l o c a l Fermi v e l o c i t y .
Looking a t a
A U + ~ plasma,
where t h e e f f e c t i s maximized, we f i n d t h a t t h e plasma t e m p e r a t u r e
C8-56
JOURNAL DE PHYSIQUE
a s s o c i a t e d w i t h t h i s i o n i z a t i o n i s about 11 eV.
Therefore, the f r e e
e l e c t r o n i n t e r a c t i o n v e l o c i t y w i l l c o r r e s p o n d t o t h e thermal v e l o c i t y of an
e l e c t r o n i n a n 11 eV plasma.
r e l e v a n t Fermi v e l o c i t y ,
Since t h i s v e l o c i t y i s l e s s t h a n one-half
the
t h e bound e l e c t r o n i n t e r a c t s more s t r o n g l y with t h e
f a s t p r o t o n throughout most of i t s range t h a n t h e f r e e one does.
Moreover.
s i n c e t h e i o n range i s p r i m a r i l y determined by t h e h i g h energy s t o p p i n g ,
t h i s means t h a t t h e range of a s l i g h t l y i o n i z e d i o n c a n i n c r e a s e o v e r t h a t
of t h e n e u t r a l atom u n t i l t h e plasma thermal v e l o c i t y becomes comparable t o
o r g r e a t e r t h a n t h e r e l e v a n t Fermi v e l o c i t y .
l i m i t e d t o high-Z
T h i s e f f e c t i s probably
t a r g e t s because t h e peak atomic d e n s i t i e s and t h e i r
corresponding Fermi v e l o c i t i e s a r e roughly an o r d e r of magnitude l a r g e r t h a n
T h i s i s a new and i n t e r e s t i n g r e s u l t t h a t needs
t h o s e f o r low-Z m a t e r i a l s .
t o be v e r i f i e d e x p e r i m e n t a l l y .
We r e i t e r a t e t h a t t h e s e GOS r e s n l t s a r e t h e
T h e r e f o r e , i t may
b e s t d a t a t h a t i s c u r r e n t l y a v a i l a b l e f o r t h e s e problems.
become advantageous t o automate t h e COS c a l c u l a t i o n a l p r o c e s s t o o b t a i n
s i m i l a r i n f o r m a t i o n f o r o t h e r atoms i f no o t h e r model proves t o be e a s i e r t o
use.
l4
36
l2
30
10
26
B
20
E' 1006
16
N
-
E
2
400
L
0
m
G
a
86
360
70
300
W
260
40
200
0
6
l0
16
20 0
6
C
Ionization State
12.
10
16
20
d
V a r i a t i o n of p r o t o n range i n g o l d a s a f u n c t i o n of i o n i z a t i o n
s t a t e of t h e t a r g e t : GOS r e s u l t (diamonds), scaled-Bethe r e s n l t s
( c i r c l e s ) . Dashed l i n e s i g n i f i e s c o n s t a n t range.
Plot A f o r 1
MeV p r o t o n s , B f o r 2 MeV p r o t o n s , C f o r 4 MeV p r o t o n s , and D f o r
Note t h e range l e n g t h e n i n g a t low i o n i z a t i o n
1 0 MeV p r o t o n s .
s t a t e s f o r h i g h e r energy p r o t o n s .
OF ION STDPPING POW= AT ICF
4
INmsrrIEs.
Within t h e p a s t two y e a r s l i g h t i o n beam i n t e n s i t i e s on t a r g e t have
reached l e v e l s where i n t e r e s t i n g beam-target
performed.
i n t e r a c t i o n s t u d i e s can be
Moreover, s i n c e f u l l - s c a l e ICF t a r g e t experiments a r e scheduled
t o b e g i n w i t h i n t h e n e x t y e a r , i t i s e s p e c i a l l y important t o a t t e m p t t o
o b t a i n e x p e r i m e n t a l d a t a and v e r i f y t h e i o n s t o p p i n g powers used i n t a r g e t
d e s i g n and s i m u l a t i o n codes.
The f i r s t such measurements w e r e made a t t h e Naval Research
L a b o r a t o r y 1241.
concepts.
F i g u r e 13 shows s c h e m a t i c a l l y t h e s a l i e n t e x p e r i m e n t a l
A l MeV, 200 M d e u t e r o n beam from t h e G-LE-I1
f o c u s s e d o n t o a composite,
sub-range
produced by a p i n c h - r e f l e x
diode.
i n t e n s i t y of about 50 kA/cm
2
'
diagnostic target.
a c c e l e r a t o r was
The i o n beam was
Using a p l a n a r anode, a f o c u s s e d
was d e l i v e r e d t o t h e t a r g e t a t a n average a n g l e
2
'
of i n c i d e n c e of about 5 d e g r e e s from normal.
I n t e n s i t i e s up t o 200 M l c m
were reached w i t h a s p h e r i c a l ( f o c u s s i n g ) anode; t h e average a n g l e of
i n c i d e n c e f o r t h a t anode was about 20 degrees.
t h e pinch-reflex
A more d e t a i l e d schematic of
diode a s w e l l a s a r e p r e s e n t a t i v e GAMBLE-I1 v o l t a g e and
c u r r e n t waveforms a r e s h m n i n F i g u r e 1 4 .
CD2 cooted
onode foil
,
,cathode
Torget Detail
/
0.3pm
CD,
Fig. 1 3 .
'
6.4pm
MYLAR
or AI
\
Ipm
CD,
Schematic of NRL enhanced d e u t e r o n s t o p p i n g power experiment.
JOURNAL DE PHYSIQUE
TIME (NS)
Pig. 14.
Schematic of NRL Pinch R e f l e x Diode and sample GAMBLE11 v01 tage
and c u r r e n t wavef orms.
R e f e r r i n g once a g a i n t o F i g u r e 1 3 , we s e e t h a t t h e d i a g n o s t i c t a r g e t
was a sandwich s t r u c t n r e ; t h e s t o p p i n g f o i l of i n t e r e s t was l o c a t e d between
two t h i n l a y e r s of d e u t e r a t e d p o l y e t h e l e n e (CD,).
Deuterons a c c e l e r a t e d
l
o n t o t h e t a r g e t t h e n underwent d ( d , u ) Be r e a c t i o n s i n both t h e f r o n t and t h e
r e a r CD, l a y e r s and t h e n e u t r o n s were energy analyzed v i a t i m e o f - f l i g h t
(TOP) measurements.
Note t h a t t h e r e a r l a y e r was t h r e e times t h i c k e r t h a n
t h e f r o n t t o compensate f o r t h e d e c r e a s e i n c r o s s s e c t i o n w i t h lower
i n c i d e n t d e u t e r o n e n e r g i e s a f t e r energy l o s s i n t h e s t o p p i n g f o i l .
noted, both Mylar and a l m i n u m stopping f o i l s were analyzed.
d e t e c t o r s i g n a l i s shown i n F i g u r e 1 5 .
As
A t y p i c a l TOF
Careful experiments were conducted
t o v e r i f y t h a t t h e f i r s t peak was indeed due t o d e u t e r o n s i n c i d e n t on t h e
f r o n t CD, l a y e r w h i l e t h e second peak was due t o n e u t r o n s from D-D r e a c t i o n s
on t h e r e a r CD, t a r g e t .
The e s s e n t i a l f e a t u r e s used i n t h e coupled deposition/hydrodynamic
s i m u l a t i o n of t h e experiment c a n be summarized a s f o l l o w s .
Since t h e beam
c r o s s s e c t i o n a l a r e a was l a r g e compared t o t h e t a r g e t dimensions, t h e onedimensional hydrodynamics of a p l a n a r expansion were adequate t o d e s c r i b e
t h e t a r g e t motion.
Our two-dimensional
i o n r a y t r a c e package was nsed t o
s i m u l a t e t h e a n g l e of incidence of t h e beam w i t h r e s p e c t t o t h e t a r g e t (up
t o 15'
a t 250 ~ l c m ' ) . The GAMBLE-I1 v o l t a g e and c u r r e n t waveforms were
nsed t o reproduce t h e beam time h i s t o r y .
However, t h e peak v o l t a g e was
s c a l e d t o t h e d e u t e r o n energy a s determined from n e u t r o n TOF because t h e
energy of t h e d e u t e r o n s on t h e l a y e r e d t a r g e t i s s i g n i f i c a n t l y l e s s t h a n t h e
diode v o l t a g e 1361.
We a l s o s i m u l a t e d a 50/50 mixture of p r o t o n s and
d e u t e r o n s i n t h e beam s i n c e t h i s f r a c t i o n was e x p e r i m e n t a l l y determined.
Note t h a t t h i s h a s a s i g n i f i c a n t e f f e c t on t h e c a l c u l a t i o n because a 1.0 MeV
p r o t o n w i l l d e p o s i t l e s s energy i n t h e s t o p p i n g f o i l t h a n a 1.0 MeV
d e u t e r o n , t h u s r e s u l t i n g i n a lower temperature (and p o s s i b l y a lower
i o n i z a t i o n s t a t e ) a t peak power t h a n f o r a p u r e d e u t e r o n beam.
We t h e n
t a b u l a t e d t h e d e t a i l e d energy l o s s of t h e d e u t e r o n s i n t h e beam a t peak
power t o compare w i t h t h e e x p e r i m e n t a l l y measure v a l u e .
The c a l c u l a t e d
energy l o s s a t peak power was t h e d e s i r e d q u a n t i t y f o r comparison w i t h
experiment because t h e n e u t r o n o u t p u t i s maximm a t t h i s time.
Moreover,
t h e a b r u p t d e c r e a s e i n t h e diode v o l t a g e ( s e e F i g u r e 1 4 ) due t o f l a s h o v e r of
t h e i n s u l a t o r on t h e g e n e r a t o r r e s u l t e d i n a s h a r p drop-off
i n t h e nentron
s i g n a l which h e l p e d i n l o c a t i n g t h i s t i m e on b o t h n e n t r o n peaks.
TIME
Fig. IS.
(0s)
Sample n e n t r o n TOF d e t e c t o r s i g n a l response measured w i t h a Mylar
s t o p p i n g f o i l and s p h e r i c a l anode.
F i g u r e 16 shows t h e measured and c a l c u l a t e d r e s u l t s f o r t h e s e
experiments.
For MyIar f o i l s a t t h e 50 kAlcm
enhancement of t h e s t o p p i n g power was seen.
2
c u r r e n t d e n s i t y no
T h i s was a l s o t h e p r e d i c t i o n of
t h e coupled d e p o s i t i o n / h y d r o d y ~ m i c ss i m u l a t i o n .
T h i s s h o t g i v e s us
confidence t h a t t h e t e c h n i q u e i s v a l i d s i n c e i t r e p r o d u c e s t h e known n e u t r a l
atom r e s u l t w i t h i n e r r o r b a r s .
The v e r t i c a l e r r o r b a r s r e f l e c t t h e
u n c e r t a i n t y i n measuring t h e time-difference
between t h e two peaks i n t h e
n e u t r o n s i g n a l ( t y p i c a l l y about 3 n s ) w h i l e t h e h o r i z o n t a l e r r o r b a r s
r e p r e s e n t t h e u n c e r t a i n t y i n t i m i n g t h e n e n t r o n s i g n a l s r e l a t i v e t o t h e peak
JOURNAL DE PHYSIQUE
C8-60
3
i o n power ( t y p i c a l l y about 4 u s ) .
I n f o c u s s i n g geometry (250 M/cm ) , t h e s e
e r r o r b a r s a r e i n c r e a s e d due t o a n a d d i t i o n a l u n c e r t a i n t y r e l a t e d t o t h e
s p r e a d i n a n g l e of i n c i d e n c e of t h e d e u t e r o n beam.
This uncertainty i n the
a n g l e i s p r o p a g a t e d i n t o a n u n c e r t a i n t y i n t h e d e u t e r o n energy through t h e
D-D r e a c t i o n kinematics.
Note t h a t f o r t h e p l a n a r anode t h e e r r o r b a r s a r e
much s m a l l e r t h a n f o r t h e f o c u s s i n g anode.
T h i s d i f f e r e n c e i s due t o t h e
l a r g e r s p r e a d i n t h e a n g l e of i n c i d e n c e f o r t h e f o c u s s i n g anode.
The
p l o t t e d c i r c l e s on t h e s e e r r o r b a r s r e p r e s e n t t h e most p r o b a b l e experimental
v a l u e s a s determined f o r t h e cross-section-weighted
average a n g l e of
incidence.
m-oe
j
L
10
12
14
38
1NC:OihT OEUTEROV CNERGY IhfeV1
Pig. 16.
i
4 0 0 ~ - -:L
:3
L
12
14
'NCIOENT DEUTEROS ENERGY I M e V l
Comparison of energy-loss measurements f o r ( a ) and ( b ) p l a n a r and
( C ) and f d ) s p h e r i c a l d i o d e s w i t h energy-loss c u r v e c a l c u l a t e d f o r
s o l i d targets.
The t r i a n g l e s a r e hydrocode r e s u l t s .
Solid l i n e
s h o r s t a b u l a t e d c o l d t f r g e t v a l u e s . Note t h a t p l a n a r d i o g e s
c o r r e s p o n d t o 50 U / c m and s p h e r i c a l d i o d e s t o 250 kA/cm
.
The experiments where d e u t e r o n s were f o c u s s e d t o a c u r r e n t d e n s i t y of
about 250 M/cm
2
shorped a d e f i n i t e enhancement i n i o n s t o p p i n g power a s
compared t o t h a t of a n e u t r a l , c o l d t a r g e t .
These measurements r e p r e s e n t
t h e f i r s t c l e a r evidence t h a t "range s h o r t e n i n g " i n p a r t i a l l y i o n i z e d m a t t e r
does occur.
For t h e lor-Z p l a s t i c t a r g e t we achieved good agreement between
experiment and c a l c u l a t i o n simply by u s i n g t h e average i o n i z a t i o n p o t e n t i a l
s c a l i n g g i v e n by Eq. 3.
(We a t t r i b u t e t h i s t o t h e dominance of t h e hydrogen
atoms i n t h e s t o p p i n g power of Mylar).
i o n s t o p p i n g power f o r t h e 50 Mlcm
a
There i s a s l i g h t enhancement of t h e
beam on aluminum case.
The e a r l i e r
o n s e t of enhancement f o r aluminum a s compared t o Mylar i s r e l a t e d t o t h e
lower i o n i z a t i o n p o t e n t i a l of t h e o u t e r e l e c t r o n s of aluminum which r e s u l t s
i n a l a r g e r amount of thermal i o n i z a t i o n a t a g i v e n t e m p e r a t u r e .
Mlcm
f
With 200
i n c i d e n t on a l m i n u m we once a g a i n s e e a d r a m a t i c enhancement of t h e
i o n s t o p p i n g power.
T h i s experiment demonstrated t h a t t h e average
i o n i z a t i o n p o t e n t i a l s c a l i n g g i v e n by Eq. 3 was i n a d e q u a t e f o r a n y t h i n g b u t
low-Z p l a s t i c s .
Table 11 t a l l i e s t h e v a r i o u s hydrodynamic and d e p o s i t i o n
q u a n t i t i e s t h a t a r e o b t a i n e d u s i n g b o t h I-values
g i v e n by Eq. 3 and t h e
I ( Z , q , E) v a l u e s t h a t a r e o b t a i n e d u s i n g t h e augmented-LOM model.
We s e e
t h a t t h e energy l o s s of 685 keV a t peak power computed w i t h t h e LOM model
corresponds w e l l t o t h e e x p e r i m e n t a l l y measured v a l u e .
However, t h e simple
s c a l i n g f o r m u l a gave a n energy l o s s of 1.06 MeV f o r t h e same i n p u t
parameters.
T h i s approximately 50% l a r g e r p r e d i c t e d energy l o s s i s n o t even
w i t h i n t h e e x p e r i m e n t a l e r r o r b a r s and we can conclude t h a t t h e LOM-values
a r e c l e a r l y i n b e t t e r agreement w i t h experiment.
t h i s s e t of I-values
We have t h e r e f o r e adopted
a s t h e s t a n d a r d o p t i o n i n t h e d e p o s i t i o n package t h a t
i s found i n o u r v a r i o u s hydrodynamic s i m u l a t i o n codes.
TABLE I1
Comparison of hydrodynamic and d e p o s i t i o n r e s u l t s from s i m u l a t i o n of
NRL aluminum s t o p p i n g power experiment u s i n g average i o n i z a t i o n p o t e n t i a l
s c a l i n g from both LOM r e s u l t s and Eq. 3 s c a l i n g . All q u a n t i t i e s t a b u l a t e d
a t time of peak power (36.5 n s ) .
l o s s ( M ) was about 700 KeV.
Note t h a t measured e x p e r i m e n t a l energy
Eq. 3 S c a l i n g
LOM Re s a l t
Energy A v a i l a b l e
4.42 KJ
4.42KJ
F r a c t i o n Absorbed
84.7 %
60.7 k
K i n e t i c Energy
.73 KJ
.53 KJ
2.46 KJ
1.79 KJ
Ion Energy
.25 KJ
.21 KJ
R a d i a t i o n Loss
.l4 K J
.04 KJ
AJl ( c a l c u l a t e d )
1058 KeV
685 KeV
E l e c t r o n Energy
A new experiment aimed a t expanding t h i s d a t a base i s p r e s e n t l y b e i n g
f i e l d e d on t h e PROTO-I a c c e l e r a t o r a t Sandia (371. While t h e NRL
2
e x p e r i m e n t s on GAMBLE-I1 were performed a t approximately 0.3 Wlcm
the
PROTO-I a c c e l e r a t o r u s i n g t h e applied-B diode [381, i s c a p a b l e of d e l i v e r i n g
JOURNAL DE PHYSIQUE
about 1 TWIcm
a
A m o d i f i e d time-resolved
on t a r g e t .
electric-magnetic
a n a l y z e r L391 i s b e i n g used i n c o n j u n c t i o n w i t h R u t h e r f o r d s c a t t e r i n g f o i l s
t o perform a time-dependent
a n a l y s i s of t h e energy l o s s p r o c e s s .
p r i n c i p l e t h e experiment i s q u i t e s t r a i g h t f o r w a r d .
In
A small p o r t i o n of t h e
i o n beam is R n t h e r f o r d s c a t t e r e d through a s e t of a p e r t u r e s i n t o a Thompson
p a r a b o l a where t h e beam i s energy analyzed i n p a r a l l e l E and B f i e l d s .
Because t h e e l e c t r i c f i e l d i s ramped i n time t h e e n e r g i e s a r e l i k e w i s e
determined a s a f u n c t i o n of time.
T h i s t e c h n i q u e f o r measuring i o n beam
energy h a s been used s u c c e s s f u l l y on PBFA-I.
The unique i d e a h e r e i s t o use
two t h i n s c a t t e r i n g f o i l s i n c o n j u n c t i o n w i t h a d u a l a p e r t u r e c o l l i m a t o r
system t o measure t h e i o n energy both e n t e r i n g and e x i t i n g a c e n t r a l
stopping f o i l .
A f e a t u r e of t h i s experiment i s t h a t a complete t i m e - h i s t o r y
of t h e s t o p p i n g power i s o b t a i n a b l e , r a t h e r t h a n a measurement made a t a
s i n g l e p o i n t i n time.
Thus, we a r e a b l e t o t e s t our models through a range
of i o n i z a t i o n s t a t e s w i t h a s i n g l e s h o t .
I n F i g u r e 1 7 C401, we s e e s p e c t r o m e t e r t r a c e s f o r a n aluminam s t o p p i n g
t a r g e t t h a t i n d i c a t e t h a t t h e b a s i c p r i n c i p l e s of t h e experiment a r e sound.
S h m n a r e two p a r a l l e l p a r a b o l i c t r a c e s , t h e one t o t h e r i g h t from t h e i n p u t
beam and t h e o t h e r from t h e o u t p u t beam.
these spectrometers.
Each t r a c e i s c h a r a c t e r i s t i c of
The h o r i z o n t a l displacement i s due t o t h e s t a t i c
magnetic f i e l d and i s a measure of t h e i o n energy, w h i l e t h e v e r t i c a l
displacement i s due t o a t r a n s v e r s e t i m e r a m p e d e l e c t r o s t a t i c d e f l e o t i o n
( p r o v i d i n g t h e time r e s o l v i n g n a t u r e of t h e s p e c t r o m e t e r )
.
Preliminary
a n a l y s i s of t h i s e x p e r i m e n t a l d a t a i n d i c a t e s t h a t t h e r e i s enhanced s t o p p i n g
i n t h e aluminum f o i l .
F u r t h e r d a t a w i l l be t a k e n f o r aluminam and
t h e n we w i l l a t t e m p t t o o b t a i n d a t a f o r n i c k e l and g o l d s t o p p i n g f o i l s .
(Note t h a t GOS d a t a i s p r e s e n t l y a v a i l a b l e f o r alaminnm and g o l d and w i l l
soon be a v a i l a b l e f o r n i c k e l ) .
We w i l l t h e n have experimental d a t a f o r
h i g h e r i o n i z a t i o n s t a t e s of a l u m i n m a s w e l l a s f o r two higher-Z m a t e r i a l s ;
t h e b y h e r e i s t h e i n c r e a s e d i n t e n s i t y and energy a v a i l a b l e i n t h e PROlD-I
beam t h a t makes h i g h e r i o n i z a t i o n s t a t e s a t t a i n a b l e .
F i g u r e 1 8 shows a
sample c a l c n l a t i o n of t h e t a r g e t response and i o n energy l o s s a s a f u n c t i o n
of time f o r a n 7.6 micron t h i c k alnminam s t o p p i n g t a r g e t .
The c a l c n l a t i o n
p r e d i c t s a s i g n i f i c a n t enhancement i n t h e i o n energy l o s s i n t h e f o i l a s t h e
f o i l b e g i n s t o h e a t a s compared t o t h a t f o r c o l d m a t t e r .
We e s t i m a t e t h a t
we a r e r e a c h i n g i o n i z a t i o n s of a t l e a s t s i x t o seven ( a s compared t o t h r e e
f o r t h e NRL e x p e r i m e n t ) .
Such d a t a w i l l s i g n i f i c a n t l y extend t h e a v a i l a b l e
d a t a w i t h which t o t e s t our I-values.
Preliminary c a l c u l a t i o n s using the
GOS model i n d i c a t e t h a t we c a n r e a c h i o n i z a t i o n s t a t e s of a t l e a s t t e n
i n g o l d and t h a t t h e i o n s t o p p i n g power enhancement w i l l be l a r g e enough t o
s e e w i t h t h i s e x p e r i m e n t a l technique.
0,
C
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m
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m c'
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C,
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m a11
L! X
4J
.
mc'
7
cnha
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. E 4
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JOURNAL DE PHYSIQUE
F i g . 18.
Sample c a l c u l a t i o n of expected p r o t o n energy l o s s i n a 7.6
aluminum t a r g e t f o r Sandia s t o p p i n g power experiment.
Shorn a r e
i n p u t energy a s w e l l a s o u t p u t energy assuming b o t h no i o n i z a t i o n
( c o l d ) and t a r g e t i o n i z a t i o n e f f e c t s (MM).
Our work on i o n s t o p p i n g power s i m u l a t i o n f o r ICF a p p l i c a t i o n s a t
Sandia i s moving i n t o a new phase.
We a r e now t r y i n g t o r e p l a c e our e a r l i e r
s c a l i n g r e l a t i o n s of c e r t a i n key p h y s i c s p a r a m e t e r s i n t h e s t o p p i n g power
e q u a t i o n s w i t h r e s u l t s o b t a i n e d from d e t a i l e d atomic p h y s i c s modeling.
In
p a r t i c u l a r , we a r e p r e s e n t l y r e s t r i c t i n g most of our work t o t h e s t u d y of
hydrogenic p r o j e c t i l e s and a r e a t t e m p t i n g t o develop a n a c c u r a t e way of
c a l c u l a t i n g a g e n e r a l i z e d average i o n i z a t i o n p o t e n t i a l I ( Z , q , E) t h a t i s
v a l i d f o r a l l Z ( o r a t l e a s t a r e a s o n a b l e s e t of p o t e n t i a l ICF t a r g e t
materials).
We a r e p r e s e n t l y s t u d y i n g t h e LOM model i n c o n j u n c t i o n w i t h t h e
b e s t a v a i l a b l e atomic charge d i s t r i b u t i o n s i n o r d e r t o i n v e s t i g a t e i t s
s u i t a b i l i t y i n g e ~ e r a t i n gt h e s e I-values.
We have n o t y e t a s c e r t a i n e d
whether some of t h e d e f i c i e n c i e s of t h e LOM model can be overcome - t h i s
work i s c o n t i n u i n g .
A l t e r n a t i v e s t o t h e LOM model a r e a l s o b e i n g s t u d i e d t o
o b t a i n t h i s same d a t a .
In particular,
t h e GOS model p r e s e n t l y r e p r e s e n t s
t h e most r e l i a b l e source of bound s t o p p i n g power d a t a .
I n 1982, t h e f i r s t
s t o p p i n g power r e s u l t s germane t o ICF were o b t a i n e d a t NRL, and good
agreement w i t h our t h e o r e t i c a l models was found.
Experiments a r e p r e s e n t l y
b e i n g performed on S a n d i a ' s P R O W 1 a c c e l e r a t o r i n a n a t t e m p t t o extend t h e
NRL r e s u l t s f o r Mylar and almninum t o h i g h e r i o n i z a t i o n s t a t e s .
u s i n g higher-Z f o i l s (both n i c k e l and g o l d ) a r e a l s o planned.
Experiments
The a u t h o r s would l i k e t o thank J o h n Swegle f o r h i s review of t h e
manuscript.
Thanks a l s o t o Gary Montry f o r h i s a s s i s t a n c e w i t h some of t h e
numerics of t h e f i t t i n g procedure.
a u s p i c e s of t h e U.S.
T h i s work was performed under t h e
Department of Energy.
L
1.
J. A. Swegle, Comments on Plasma P h y s i c s and C o n t r o l l e d F u s i o n
(1982).
141
2.
J. W. Mark, i n P r o c e e d i n g s of t h e Symposium on A c c e l e r a t o r A s p e c t s of
Heavy I o n Fusion, h e l d a t Darmstadt. Germany, (March 2+April 2 , 1982)
G e s e l l s c h a f t f u e r Schwerionenf orschung r e p o r t 82-8.
3.
J. M.
4.
E.J.T. Burns, D.J. Johnson, P.L. Dreike, A.V. Farnsworth,
S l u t z , B u l l . Am. Phys. Soc. 21. p.1120 (1982).
5.
E. Nardi and Z. Zinamon. J. Appl. Phys.
6.
E. J. Mcguire. Sandia Report, SAND-74-032
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G. R.
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F. C. Young, J. Golden, and C.A.
432 (1977).
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R. Leeper, E.J.T.
(1981).
Peek, Sandia N a t i o n a l L a b o r a t o r i e s , P r i v a t e Communication.
and S.A.
52, 7075 (1981).
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Montry, Sandia N a t i o n a l L a b o r a t o r i e s , P r i v a t e Communication.
Burns,
and D . J .
Kapetanakos, Rev. S c i . Instrum..
Johnson. B u l l . Am. Phys.
Soc.
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26, 920
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S l u t z . B u l l . Am. Phys. Soc. 26. 1064 (1981).
11. T.A.
Mehlhorn, and S.A.
1 2 . T.A.
Mehlhorn, J. Appl. Phys.
52.
6522 ( 1 9 8 1 ) .
13. E. Nardi, E. Peleg, and Z. Zinamon, Phys. F l u i d s 2l, 574 ( 1 9 7 8 ) .
1 4 . D. Moshet, Proceedings of t h e ERDA Summer Study of Heavy I o n s f o r
I n e r t i a l Fusion, Lawrence Berkeley Laboratory r e p o r t LBL-5543 (1976).
15. R.O. Bangerter, Proceedings of t h e Heavy-Ion F u s i o n Workshop. Argonne
N a t i o n a l Laboratory Report ANL-79-41, 415 (1979)
.
1 6 . T.D.
Beynon, P h i l . Trans. R.
Soc. Lond. A
m, 613
(1981).
1 7 . J. Lindhard and Aa. Winther. K. Dan. Vidensk S e l s k . Mat.-Fys.
No. 4 (1964).
18. W.K.
Chu and D. Powers, Phys. L e t t . A
*,
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