optimum operating conditions for a laser

7/25/2019 Optimum Operating Conditions for a Laser

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O P T I M U M O P E R A T I N G C O N D I T I O N S F O R A L A S E R

U R A N I U M E N R I C H M E N T P L A N T

KIMIO YAMADA an d NORIHIKO OZAKI

Atomic Energy Research Laboratory, Hitachi Ltd, Ozenji, Tama-ku,Kawasaki, Kanagawa Japan)

a n d

MANABU YAMAMOTO an d KI ICHI UEYANAGI

Central Research Laboratory, Hitachi Ltd, Higashi-Koigakubo, Kokubunji, Tokyo Japan)

S UMMA R Y

Operating conditions o f the laser uranium enrichment plant to obtain cheaper enriched

uranium are optimised by using the standard optimisation procedure. A simple kinetic

model is given to obtain the ion production rate as a function of the laser energy

density, ultraviolet light energy density, atomic density and depth and height of the

reaction region. The unit cost of enriched uranium is chosen as a value imction instead

of the unit cost of the separative work. The construction cost is expressed by means of

an exponential fi~nction to take the scale merit into account.

Two numerical results are given. In case 1, the laser power and efficiency are subject

to the restraints determined by the present technical levels and in case

2,

they arej}'ee.

The unit cost of the enriched uranium is higher than those of the gaseous dijfitsion and

gas centrifuge methods by a factor of 2 ~ 11. Results indicate that laser uranium

enrichment is probably competitive with the other uranium enrichment methods,

provided that the laser efficiency is improved by up to 1 and the laser lijetime is

extended several times.

1 . I N T R O D U C T I O N

Th e t ech n i q u e fo r l a s e r i s o t o p e s ep a ra t i o n h as b een d ev e l o p ed an d r ecen t l y t h e

sepa ra t ion o f u ran ium i so top es wa s ach ieved by the se lect ive two-s tep

pho to ion i sa t ion p rocess , in the Uni ted S ta tes .1

A po in t c om m on to the laser iso top e separa t ion i s to use i so tope sh if t , and exc ite

select ively specif ic iso top es with the laser . La ser iso t op e sepa rat io n involves va rious

methods , depend ing on the d i f fe rences in separa t ion , such as two-s tep

287

Applied Energy ( 3 ) ( 1 9 7 7 ) - - A p p l i e d S c i e n c e P u b l i s h e r s L t d , E n g l a n d , 1 9 7 7

P r i n t e d i n G r e a t B r i t a i n


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KIMIO YAMADA, NORIH IKO OZAKI, MANABU YAMAMOTO, KI1CHI UEYANAGI

p h o t o i o n i s a t io n , p h o t o d e fl e c ti o n , p h o t o d i s s o c i a t i o n a n d p h o t o c h e m i s t r y . T h e

t w o - s te p p h o t o i o n i s a t i o n m e t h o d f o r t he u r a n i u m a t o m is t he m o s t p r o m i s i n g o f

t h e se m e t h o d s . T h e r e a s o n s a r e : ( 1) th i s m e t h o d h a s a l r e a d y a c h i e v e d su c c es s o n a

l a b o r a t o r y s c a l e; (2 ) t h e u r a n i u m a t o m h a s w el l k n o w n a n d r e s ol v e d is o t o p e s h i ft s i n

e l e c t ro n i c l ev e ls i n c o m p a r i s o n w i t h u r a n i u m m o l e c u l e s .

T h e p u r p o s e o f t h is p a p e r is t o d is c u s s th e o p t i m u m c o n d i t i o n s f o r th e l a s e r

u r a n i u m e n r i c h m e n t p l a n t. T h e t w o - s t e p p h o t o i o n i s a t i o n m e t h o d o f t he u r a n i u m

a t o m i s s e le c te d , a n d t h e C o m p l e x m e t h o d 2 is e m p l o y e d a s a n o p t i m i s a t i o n

p r o c e d u r e . T h e o p t i m u m c o n d i t i o n s f o r t w o t y p ic a l c a s e s a r e s u r ve y e d . I n ca s e 1 , t h e

l a s er p o w e r a n d e ~ c i e n c y a r e s u b j e c t t o r e s t r a in t s d e t e r m i n e d b y th e p r e s e n t

t e c h n i c a l l ev e ls , a n d i n c a s e 2 t h e y a r e f r e e f r o m t h e t e c h n i c a l r e q u i r e m e n t s ; i .e . n o

t e c h n i c a l r e s t r i c t i o n s w e r e p u t o n t h e m .

2.

LASER ISOTOPE SEPARATION PROCESS AS APPLIED TO URANIUM ENRICHMENT

2 1 Uranium energy levels

E n e r g y l ev els f o r t h e u r a n i u m a t o m e m p l o y e d i n th e s e l ec ti ve t w o - s t e p

p h o t o i o n i s a t i o n p r o c e s s a r e s h o w n i n F i g . 1 . T h e f a i r l y s t r o n g t r a n s i t i o n ( 7s ) 2 5 L 6

I

E

4 x 1 0 4

e--

2 x 1 0 4

X

I J . J

0

1 s t i o n i z a t i o n l e v e l

U V L i g h t

_ ~ ~ 3 1 0 0

E x c i t e d l e v e l

Is o to p e h i ft ~ ~ k

\ 0 . 0 8 A ) J

L a s e r l i g h t / / ~ 7 p 7 M 7

s 9 1 5 4 U G r o ,u n d l e v e l

i t s ) 2 5 L 6

6

In

4 a ~

-

_ t

O

o i

2 . ~ -

X

0

Fig. 1. U ra ni um energy levels for the selective two-step photoionisation proces s. The

235U

atom is

selectively excite d to the 7s7p7Mr level with dye las er light of wavelength 5915-4A. The excited atom is

successively ionised by the ultraviolet light o f wavelength between 2000 and 3100A.


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OPERATING CONDITIONS FOR URANIUM ENRICHMENT

289

7 s 7 p 7 M 7 , 2 = 5 9 1 5 . 4 A , i s c h o s e n f o r i s o t o p e s p e c if i c e x c i t a t i o n , b e c a u s e t h i s

le ve l h a s a r e m a r k a b l e i s o t o p e s h i ft , a p p r o x i m a t e l y 0 -0 8 A , a n d a f a i r l y s t r o n g

a b s o r p t i o n c r o s s - s e c t i o n . A l s o t h e e x c i t a t i o n e n e r g y o f t h i s l e v e l a g r e e s w i t h t h e

w a v e l en g t h o f th e m a x i m u m o u t p u t p o w e r o f t h e d y e l as er . T h e i o n i s a t io n l im i t f r o m

t h is e x c i t a ti o n l e v e l i s 3 1 0 0 A f o r a si ng le q u a n t u m p h o t o i o n i s a t i o n . T h e l o w e r l im i t o f

w a v e l e n g t h t o p r e v e n t d i r e ct i o n i s a t i o n f r o m t h e g r o u n d s t a te is 2 0 0 0 A . T h e

u l t r a v i o l e t li g h t in th i s w a v e l e n g t h r a n g e i s o b t a i n a b l e b y f r e q u e n c y d o u b l i n g o f

v i s ib l e l a se r l i gh t such a s the Ar ion l a se r l i ne s .

T h e 7 s 7 p 7 M 7 e x c i t e d le v el o f 2 3 5U a t o m i s s p l i t i n t o e i g h t h y p e r f i n e s t r u c t u r e s d u e

t o t h e i n t e r a c t i o n b e t w e e n s p i n s o f t h e e l e c t r o n s a n d n u c l e u s . I n t h e s e l e ct iv e t w o - s t e p

p h o t o i o n i s a t i o n p r o ce s s , o n l y o n e c o m p o n e n t o f t h e h y p e r fi n e s tr u c t u re is us e d .

2 .2 .

h o t o i o n p r o d u c t i o n r a t e

I n t h i s s e c t io n , a s i m p le k i n e t ic m o d e l t o c a l c u l a te t h e p h o t o i o n p r o d u c t i o n r a t e i s

g iv e n . T h e t h e r m a l i s a t i o n p r o c e s s e s to b e c o n s i d e r e d a r e i l l u s tr a t e d i n F i g. 2 . M a j o r

t r a n s i t i o n p r o c e s s e s a r e r e s o n a n t e x c it a t i o n , p h o t o i o n i s a t i o n , i n d u c e d e m i s s i o n a n d

t h e r m a l r e l a x a t io n . T h e r e s o n a n t e x c i t a t io n a n d p h o t o i o n i s a t i o n t a k e p l ac e w h e n

t h e a t o m a b s o r b s a p h o t o n w i t h e n e r g y h v= a n d h v r e sp e c ti v el y .

I f w e n e g l ec t c h a r g e t r a n s f e r a n d e n e r g y t r a n s f e r b e t w e e n 235U i n t h e g r o u n d s t a te ,

s t i o n i z a t io n C h a r g e t r a n s f e r

l a v e l / / ~ / / ~ , ~ ~ / ~ ~ / / ~ ~

Vi

E x c i te d l e v e l

W i

E n e r g y t r a n s f e r

l 1 V e

p o n t a n e o u s d e c a y

I n d u c e d e m i s s i o n

W e

G r o u n d l e v e l

35U 38u

Fig. 2. A three-levelsystem llustrating a selective wo-step photoionisationprocess. M ajor transition

processes are resonan t excitation, photoionisation, induced emission and thermal relaxation.


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3.

O P T I M I S A T I O N P R O C E D U R E

3 1 Op t imisat ion calculat ion

T h e c o m p l e x m e t h o d 2 w a s u s e d a s t he o p t i m i s a t i o n p r o c e d u r e . I n o r d e r t o

o p t i m i s e w i t h t h i s m e t h o d , t w o p r e r e q u i s i t e s a r e i n g e n e r a l n e c e s s a r y . F i r s t l y , o n e

h a s t o d e f in e t he i n d e p e n d e n t v a r i a b l e s o f t h e o p t i m i s a t i o n p r o b l e m . T h e n e c e s s a r y

c o n d i t i o n s f o r i n d e p e n d e n t v a r i a b l e s a r e : ( 1) t he e f f ec t u p o n t h e v a l u e f u n c t i o n is

g r e a t a n d ( 2) th e y h a v e f in i te o p t i m u m v a l u e s. S e c o n d l y , a s u i t a b l e v a l u e f u n c t i o n h a s

t o b e d ef in e d . O p t i m i s a t i o n o f t h e o p e r a t i n g c o n d i t i o n s o f th e l a s er u r a n i u m

e n r i c h m e n t p l a n t m e a n s t h e d e t e r m i n a t i o n o f t h e o p t i m u m c o m p o s i t i o n s a n d t he

s p e c i fi c a ti o n s w h i c h m i n i m i s e t h e u n i t c o s t o f e n r i c h e d u r a n i u m . I t is th e r e f o r e

d e s i r a b l e t o c h o o s e t h e u n i t c o s t o f e n r ic h e d u r a n i u m i n s t ea d o f t h e u n i t c o s t o f

s e p a r a t i v e w o r k a s a v a lu e f u n c t i o n . T h e v a l u e f u n c t i o n is , o f c o u rs e , e x p r e s s e d a s a

f u n c t i o n o f th e i n d e p e n d e n t v a r i a b le s .

T h e s t a n d a r d d e v i a t i o n o f i n d e p e n d e n t v a r i a b l e s is a p p l i e d t o a c o n v e r g e n c e

j u d g e m e n t in th e o p t i m i s a t i o n c a l c u l a t io n . T h e c o n v e n t i o n a l j u d g e m e n t f o r

c o n v e r g e n c e i s t o c o m p a r e t h e s t a n d a r d d e v i a t i o n o f th e v a l u e f u n c t i o n w i th a s m a l l

p o s i ti v e n u m b e r . H o w e v e r , it is d e s ir a b l e t o u s e t h e s t a n d a r d d e v i a t io n o f t h e

i n d e p e n d e n t v a r i a b l e s a s a j u d g e m e n t c o n d i t i o n f o r c o n v e r g e n c e in c a se o n e i s

i n t e r e st e d in t h e c o n v e r g e n c e v a lu e s o f th e i n d e p e n d e n t v a r ia b l e s.

l

S ~ l o n c o lle c to r

R e a c t i o ne g i o n

S l i t

ruc ib le

Fig. 3. The schem aticview of the isotope separation region. The uranium atom evaporating from the

high temp erature crucible is irradiated by laser light and ultraviolet light in the reaction region , and

ionised 235U atoms are collected by the ion collector electrodes. Distance a = 50mm .


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2 9 2 KIMIO YAMADA, NORIHIKO OZAKI, MANABU YAMAMOTO, KIICHI UEYANAGI

3.2.

ndependent variables

Figure 3 shows the schematic view of the isotope separation region. The

arrangement of the laser, ultraviolet light and atomic beam and the related

independent variables are shown in Fig. 4. The isotope separation region is

composed of a crucible for making the uranium vapour, a slit for the atomic beam

collimation and ion collector. The uranium metal in the crucible is heated using the

electron gun. The uranium atoms evaporating from it enter the reaction region with

a cross-section ofSuv cm in width and 1 cm in depth, and are irradiated by laser and

ultraviolet beams. The laser light, being perpendicular to the atomic beam, is Suv cm

in width and Sa cm in height. The ultraviolet light with cross-section of 1 cm in

depth and S a cm in height meets orthogonally both the atomic beam and the laser

light. The

235U

ions are selectively produced in the reaction region and are collected

by the ion collector located downstream of the reaction region.

Five independent variables are selected according to the reasons described in

section 3.1 ; these are laser energy density, ultraviolet light energy density, atomic

density, depth 1 and height S, of the reaction region. The important variables which

might have influence on the unit cost of enriched uranium besides the independent

variables are distance between the crucible and the reaction region, gap o f the ion

collector electrodes and width Su~ of the reaction region. It is, of course, desirable for

React ion region

W i d t h

t y = P i

Laser l i gh t

E n , r . d . , . , = p , )

tomic beam

( n e n s i t y = N o )

F i g . 4 . T h e i n d e p e n d e n t v a r i a b le s f o r o p t i m i s a t i o n o f l as er u r a n i u m e n r i c h m e n t p l a n t . T h e u r a n i u m

atom is i r rad ia ted by laser l i gh t and u l t rav io le t ] i gh t w i th energy dens i t i es Pc and P~ , respec t i ve ly .


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a t o m i c d e n s i t y t o r e d u c e t h e d i s t a n c e b e t w e e n t h e c r u c i b le a n d t h e r e a c t i o n r e g i o n .

H o w e v e r , i t i s n e c e s s a r y fo r t h e t h e r m a l s h i el d a n d c o l l i m a t i n g sl it to s e p a r a t e t h e m

b y a t l e a st 5 c m . T h e d e n s i t y o f 2 3 5U i o n s d e c r e a s e s b y c h a r g e t r a n s f e r a s t h e y g o

a c r o s s th e a t o m i c b e a m t o t h e i o n c o l le c t o r . T h e r e f o r e , th e s m a l l e r g a p o f t h e i o n

co l l ec to r e l ec t r o d es i s d e s i r a b l e . T h e w id th S uv o f t h e r e a c t i o n r eg io n i s 1 cm . Th e

u l t ra v i o l e t l ig h t e n e r g y d e n s i t y d if fe r s o n b o t h s id e s o f t h e r e a c t i o n r e g i o n b e c a u s e o f

t h e a b s o r p t io n o f th e e xc it e d u r a n i u m a t o m s . H o w e v e r, th e a m o u n t o f a t t e n u a t i o n

lo s s w i ll s c a r ce ly b e n o t i c ed s i n ce t h e p h o to io n i s a t i o n c r o s s - s ec t i o n o f u l t r a v io l e t

l ig h t is e x t r e m e l y s m a l l. A s l o n g a s t h e a m o u n t o f a t t e n u a t i o n l os s c a n b e n e g l e c te d ,

u l t r a v io l e t l i gh t m a y b e u s ed . A s a r e s u l t , i t is p o s s ib l e t o u s e u l t r a v io l e t li g h t a t l e a s t

500 t imes.

3.3.

Value un ction

(1) Prod uction rate o f enricheduranium.

T h e c o n c e n t r a t i o n o f 2 35 U i o n s d e c r e a se s

b y c h a r g e t r a n s f e r c o l l is i on s b e t w e e n z 3 5U i o n s a n d 2 3 8 U a t o m s w h e n i o n s a r e

s e p a r a t e d f r o m t h e n e u t r a l b e a m b y t h e s t a t ic e l e ct ri c fi el d. T h e n u m b e r o f z 35 U i o n s

co l l e c t ed b y t h e i o n co l l e c to r p e r u n i t t im e i s g iv en b y t h e f o l l o w in g eq u a t io n ( s ee

A p p e n d i x ) :

n

1 1 0 )

n

~ S, . S..V(N~5 + N~) - A , (11)

A s = n

1

w h e r e n i s t h e n u m b e r o f d i vi s io n s o f d e p t h S Z n t h e r e a c t i o n r e g i o n , N d a n d d a r e t h e

n u m b e r a n d t h e g a p o f t h e i o n co l l e c to r e l ec t r o d es , r e sp ec t iv e ly , v i s t h e a v e r a g e

t h e r m a l v e l o c i ty o f t h e a t o m i c b e a m , a n d a r~ is t h e c h a r g e t r a n s f e r c ro s s -s e c t io n .

T h o u g h h i g h e n r i c h m e n t is o b t a i n e d a t t h e i o n c o l l e c to r , t h e e n r i c h m e n t r e q u i r e d

f o r t h e f u e l u s ed i n a n u c l ea r p o w e r p l a n t i s a b o u t 3 % . Th e r e f o r e , i t i s n ece s s a r y t h a t

h i g h l y e n r i c h e d u r a n i u m i s b l e n d e d w i t h n a t u r a l u r a n i u m t o f o r m a n u c l e a r f u e l. T h e

q u a n t i t i e s o f 3 % p r o d u c t a n d n a t u r a l u r a n i u m f o r b l e n d i n g c a n b e w r i t t e n a s :

M s M s A s ( I - ~ e) - ~ e ( 3 M s A s +

M~A8)

w . = 1 2 )

N a[M sM s(~ e - ce .) - 9a . ae]

M s A 5 + M s A s

W e = W n + (13)

N ,

w h e r e W . a n d /,Iz a r e t h e q u a n t i t i e s o f n a t u r a l u r a n i u m a n d 3 % p r o d u c t

r e sp e c ti v el y , M s a n d M s t h e m a s s n u m b e r s o f 2 3 sU a n d z 3 s u r e sp e c ti v el y , a e t h e

e n r i c h m e n t o f t h e u r a n i u m o b t a i n e d , ~ , th e n a t u r a l a b u n d a n c e r a ti o o f u r a n i u m a n d

N a A v o g a d r o ' s n u m b e r .


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(2 ) O p e r a t i n g c o s t . T h i s i n c l u d e s c o s t s f o r m a i n t e n a n c e , e m p l o y m e n t , m a t e r i a l s

a n d e l e ct r ic p o w e r . T h e e q u i p m e n t t o b e m a i n t a i n e d i n c lu d e s t h e d y e l a se r ,

u l t r a v i o le t la s e r a n d e v a c u a t i o n s y s t e m s . T h e m a i n t e n a n c e c o s t c a n b e w r i t te n a s

m r = s t C l / t l + ~;,vCuv/tuv + ~vCv/tv (14 )

w h e r e C , 5, t a r e r e s p e c t i v e l y u n i t c o s t , t h e r a t i o o f m a i n t e n a n c e c o s t t o i n i ti a l c o s t

a n d t h e l i f e t im e o f t h e e q u i p m e n t : t h e s u b s c r i p t s 1, u v , v r e p r e s e n t t h e d y e l a s e r,

u l t r a v i o l e t l a s e r a n d e v a c u a t i o n s y s t e m s , r e s p e c t i v e l y .

I t is a s su m e d t h a t t h e e m p l o y m e n t c o s t is p r o p o r t i o n a l t o t h e n u m b e r o f l as er s. A s

a l a s e r i r r a d i a t e s t h e a r e a o f S a x S a a t t h e r e a c t i o n r e g i o n , t h e n u m b e r o f l a s er s is

g iven a s

N , = [ S , / ( . a p ) ]

+ [Suv/Sa] (15)

I[ 1]: ga uss sy m bo l

w h e r e AD is t h e n u m b e r o f r e - u t il i s a ti o n s o f th e u l t r a v i o l e t l a se r , W i t h t h e n u m b e r o f

l a se r s , th e e m p l o y m e n t c o s t c a n b e w r i t t e n a s :

G e m : A e m N l + B e rn (16)

w h e r e

Aem

a n d

Bern are

c o n s t a n t .

A m a t e r i a l c o s t is g i ve n b y n a t u r a l u r a n i u m q u a n t i t i e s p a s s in g t h r o u g h t h e

r e a c t i o n r e g i o n a n d t h a t f o r b l e n d i n g a s :

C m a = U m ( W n -'~ M s N o V S r / N ~ ) (17)

w h e r e IV , is t h e n a t u r a l u r a n i u m q u a n t i t y f o r b l e n d i n g c a l c u l a te d f r o m e q n . ( 1 2) , U m

t h e u n i t c o s t o f n a t u r a l u r a n i u m a n d S r t h e c r o s s - s e ct i o n o f t h e a t o m i c b e a m .

T h e e l e c t r i c p o w e r c o s t i s

E p : U p P e S e / ~ e + P i S i / t ] i A p ) + E g + O r ) (18)

w h e r e P a n d S a r e e n e r g y d e n s i t y a n d i r r a d i a t i o n a r e a r e s p e c ti v e ly , q t h e l a s e r

e f f ic i e n c y , s u b s c r i p t s e a n d i r e p r e s e n t t h e d y e l a s e r a n d u l t r a v i o l e t l a s e r r e s p e c ti v e l y ,

U p t h e u n i t c o s t o f e l ec t ri c it y , E g t h e p o w e r c o n s u m e d b y t h e e l e c t r o n g u n a n d O t t h e

e l e c tr i c p o w e r c o s t in c l u d i n g t h a t f o r e v a c u a t i o n a i r c o n d i t i o n e r a n d c o o l i n g w a t e r

s y s t e m s .

(3 ) P l a n t c o n s t r u c t i o n c o s t a n d c a p i t a l c o s t. T h e c o n s t r u c t i o n c o s t h a s t o b e d e f in e d

a s a f u n c t i o n o f t h e i n d e p e n d e n t v a r ia b l e s . F o r t h i s p u r p o s e , w e e x p r e s s t h e

c o n s t r u c t i o n c o s t b y m e a n s o f a n e x p o n e n t i a l f u n c t i o n

Cj = A j (DPj)kJ (19)

I n t h i s e x p r e s s i o n , t h e c o s t e x p o n e n t k j is a d i m e n s i o n l e s s q u a n t i t y b e t w e e n z e r o a n d

u n i t y w h i c h d e t e r m i n e s t h e v a r i a t i o n s i n t h e c o s t o f c o n s t r u c t i o n w i th t h e s i ze o f t h e

c o m p o n e n t . B o t h A j a n d k j m u s t b e d e t e r m i n e d e m p i r ic a l ly b y m e a n s o f c o s t


9/20

OPERATING CONDITIONS FOR URANIUM ENRICHMENT 2 9 5

e v a l u a t i o n s t u d ie s . T h e d e s i g n p a r a m e t e r s , DPj a r e q u a n t i t ie s c h a r a c t e r i s i n g t h e c o s t

o f t h e i n d iv i d u a l c o m p o n e n t s a n d m u s t t h em s e l ve s b e th e i n d e p e n d e n t v a ri a b le s o r

f u n c t i o n s o f t h e m .

F i g u r e 5 s h o w s t h e e m p i r i c a l c o s t f u n c t i o n s w h i c h a r e u s e d t o d e s c r i b e t h e

c o n s t r u c t i o n c o s t s o f th e v a r i o u s p l a n t c o m p o n e n t s . T h e a b s c is s a e in d i c a t e t h e

d e si g n p a r a m e t e r o f t h e c o n s t r u c t i o n c o s t f u n c t i o h ; t h e o r d i n a t e s s h o w t h e c o st o f

c o m p o n e n t s . T e n d i f f e re n t c o s t f u n c t i o n s a r e c o n t a i n e d i n F ig . 5 , e a c h o f t h e m

d e r i v e d b y t h e u s e o f g o o d s o n t h e m a r k e t . H o w e v e r , t h e e x p o n e n t k j o f th e e le c t ri c

p o w e r s o u r c e a n d c o o l i n g w a t e r s y s t em w a s q u o t e d f r o m a p a p e r b y M .

M ~t r t ensson . 3

A s s u m i n g t h e p l a n t l i f e ti m e a n d a n n u a l c a p i t a l c h a rg e , w e c a n d e d u c e t h e c a p i ta l

c o s t f r o m t h e c o n s t r u c t i o n c o s t.

( 4 ) The unit cost of enriched uranium. T h e u n i t c o s t o f e n r i c h e d u r a n i u m is

o b t a i n e d f r o m t h e c o s t d e s c r i b e d a b o v e a s f o l l o w s :

U = (Cop + Cp /We (20)

w h e r e C op i s t h e o p e r a t i n g c o s t a n d C v t h e c a p i t a l c o s t .

4 .

CASESTUDY

T a b l e 1 s h o w s t h e p a r a m e t e r s u s e d t o o p t i m i s e t h e o p e r a t i n g c o n d i t i o n s o f t h e la s e r

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

e m p l o y e d i n t h is c a l c u l a t io n , b u t s o m e o f t h e m p o s s e ss t h e p o s s i bi l it y o f c h a n g i n g t o

TABLE

PARAMETERS USED IN THE COMPUTATION

No tatio n xplanation Value

Ap

Up

Um

i

T

T I

T u v

? v

The number o f re-utilisations of the ultraviolet laser

Unit cost of electricity, S/kWh

Unit cost of natural uranium, /kg

Fixed charge rate,

Lifetime, years

Dye laser

Ultraviolet laser

Evacuation systems

500

0.017

33

10

0.5

0-5

2

m o r e f a v o u r a b l e v a l u e s in t h e f u t u r e . F o r e x a m p l e , i t is p o s s i b le t o e x t e n d t h e l if e ti m e

o f a l a s e r b y a f a c t o r o f 5 if t h e l a s e r t u b e i s i m p r o v e d . H o w e v e r , th e u n i t c o s t s o f

e l e c t ri c i ty a n d n a t u r a l u r a n i u m r is e g r a d u a l l y , a n d t h e r is e s i n th e s e p ri c es h a v e

m i n o r i n fl u en c e s u p o n t h e u n i t c o s t o f en r i c h e d u r a n i u m .


10/20

2 9 6 K I M I O Y A M A D A , N O R I H I K O O Z A K 1 , M A N A B U Y A M A M O T O , KII CH 1 U E Y A N A G I

106

10s

Dye laser

k= 0.67

J

I

J

J

/

101 102 103

Dye lase r po w er ( w )

105

1 4

J

i

U ltrav io le t I ~ ' ~

k -0 .67

f

1 2 1 3 1 4

Ultrav io le t l as e r pow er ( w )

F i g . 5 . T h e e m p i r i c a l c o n s t r u c t i o n c o s t f u n c t i o n s . I n t h e fi g u r e s, t h e a b s c i s s a i n d i c a t e s t h e d e s i g n

p a r a m e t e r o f t h e c o n s t r u c ti o n c o s t f u n c t io n . T h e o r d i n a t e s h o w s t he c o s t o f c o m p o n e n t s i n d ol la r s.


11/20


297

10 5

10 4

E l e c t r i c p o w e r s o u r c e

k = 0 . 6

/

/

/

/

/

I

w

10 6 10 7 10 8

T o ta l e l e c tr ic p o w e r ( w )

B u i l d i n g

k = 0 . 8

10 3

10 2

/

/

J

10 0

/

J

f

101

F loo r space ( m 2 )

10 2

Fig.

5 contd.


12/20

7

z

~

e

o

2

,

o

i

~

0

~

I

-

7

o

e

I

i

A

v

I

-

7

.

E

~

x

O

0

,

z 0

0 0

> z> >

> 0

o

m

>

z> 0


13/20


2 9 9

1

10 3

Vacuum vessel

k = 0 . 4 J

~P

f

10 0 101 10 2

Vo lume in vacuum v ess e l (m 3 )

E vacuatio n s y s t ~

10 4

J

10 3

10 0 101 10 2

Volume in vacu um vess e l ( m 3 )

Fig.

5 contd.


14/20

300

K I M I O Y A M A D A , N O R I H I K O O Z A K I , M A N A B U Y A M A M O T O , K II C HI U E Y A N A G I

1 4

103

; C o o l i n g w a t e j

system

k=0.78 J

J

i f

1 5 1 6 1 7

Power of cooling wa ter pum p(w )

105

1 4

f

Electron g u n j

k=0.68

. /

/

f

105 10 6

Electric gun power ( w

J

10 7

Fig .

5 contd.


15/20

O P E R A T IN G C O N D I T I O N S F O R U R A N I U M E N R I C H M E N T

301

Table 2 shows the physical quantities used in the optimisation programme. The

excitation cross-section of uranium is from the paper by Tvccio

e t a l 1

The

photoionisat ion cross-section is the one approximated to theoretically. The charge

transfer cross-section is estimated from the experimental values of the other

elements. 4 The energy transfer cross-section is the calculated value f rom those of

inert gases. These values are possibly overestimated, and this has a minor influence

on the unit cost of enriched uranium.

T A B L E

P H Y S I C A L Q U A N T I T I E S

npu t da ta N um e r i c a l v a lue

C r o s s - s e c t i o n , c m z

Ex c i t a t i on 1 .3 x 10 ~4

l o n i s a t i o n 1 . 5

x 1 0 - 1 7

C h a r g e t r a n s f e r 1 .3 x 1 0 13

E n e r g y t r a n s f e r 1 . 0 x 1 0 13

W a v e l e n g t h , A

D y e l a s e r 5 9 1 5 . 4

U l t r a v i o l e t l a s e r 2 6 0 0

E

. ,m

m

e-

,,-=

e-

e-

F.

2 5 0 0

2 3 0 0

2 1 0 0 ,

T

1 0 - 2 1 0 -1 1 0 0

E f f ic i e n c y o f d y e l a s e r ~ x

F i g . 6 . T h e u n i t c o s t o f e n r i c h e d u r a n i u m p l o t t e d a s a f u n c t i o n o f d y e l a s e r e t ~c i en c y . T h e u n i t co s t o f

e n r i c h e d u r a n i u m i s o p t i m i s e d v i a t h e f iv e i n d e p e n d e n t v a r i a b l e s . T h e u l t ra v i o l e t l a se r et ~ c ie n c y is t a k e n a s

5 x 1 0 - 2 % .


16/20

3 0 2 KIMIO YAMADA, NORIHIKO OZAKI, MANABU YAMAMOTO, KIICHI UEYANAGI

F i g u r e 6 s h o w s th e u n i t c o s t o f e n r ic h e d u r a n i u m a s a f u n c t i o n o f t h e d y e la s e r

e f fi c ie n c y , a n d F i g . 7 s h o w s t h e u n i t c o s t o f e n r i c h e d u r a n i u m v e r s u s u l t r a v i o l e t l a s e r

e f f i c i e n c y . O n t h i s c a l c u l a t i o n , a n y t e c h n i c a l r e s t r i c t i o n s a r e n o t i m p o s e d o n t h e

i n d e p e n d e n t v a r i a bl e s . T h e u n i t c o s t o f e n r i c h e d u r a n i u m d e c r e a s e s e x p o n e n t i a l l y as

l a s e r e f fi c ie n c y i n c r e a s e s t o 1 ~o w h e r e i t t a k e s t h e a s y m p t o t i c v a l u e . I t m i g h t b e s a i d

t h a t t h e e f f o r t s t o i m p r o v e t h e l a s e r e t fi c ie n c y a b o v e 1 ~o a r e r a t h e r f r u i tl e s s f o r

i s o t o p e s e p a r a t i o n .

H o w e v e r , t e c h n i c a l r e s t r i c t i o n s e x i s t w i t h r e s p e c t t o l a s e r e n e r g y d e n s i t y a n d

e f fi c ie n c y . F o r e x a m p l e , t h e u l t i m a t e v a l u e o f th e d y e l a s e r e ff ic i en c y i s a b o u t

2 x 10-3~o , a n d t h e u l t r a v i o l e t l a s e r e f fi c ie n c y i s a b o u t 3 x 1 0 - 2 ~ o f o r t h e

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

e n r i c h m e n t t o i m p r o v e t h e l a s e r e f fi c ie n c y u p t o o n e p e r c e n t .

= 6 0 0 0

4 0 0 0

C

2 0 0 0

0

E

1 0 2 1 0 1 1 0 0

E f f i c i e n c y o f u l t r a v i o l e t l i g h t s o u r c e I ~

Fig. 7. The un it cost of enriched uranium plotted as a func tion of ultraviolet laser efficiency.A un it cost

of enriched uranium is optimised by the five ndepen dent variables. The dye las er efficiency s taken a s 2-5

10 2~, .

O p t i m i s a t i o n o f t h e o p e r a t i n g c o n d i t i o n s is p e r f o r m e d f o r tw o c a s es : c a s e 1, t h e

l a s e r e n e r g y d e n s i t y a n d e f fi c ie n c y a r e s u b j e c t t o r e s t r a i n t s d e p e n d i n g o n t h e p r e s e n t

t e c h n i c a l l e v e ls ; w h e r e i n c a s e 2 t h e r e i s n o r e s t r i c t i o n . I n c a s e 2 , t h e e f fi c ie n c i e s o f t h e

d y e l a s e r a n d t h e u l t r a v i o l e t l a s e r a r e c h o s e n a s 1 ~,,, a c c o r d i n g t o t h e r e s u l ts


17/20

OPERATING CON DITIONS FOR URAN IUM ENRICHMENT

303

TABLE 3

TECHNICALRESTRICTIONS

A s s u m p t i o n C a s e 1 C a s e 2

Power density, W /cm 2

Dye laser 200 free

Ultrav iolet laser 4000 free

Efficiency, %

Dye laser 2 10 -3 1

Ultraviolet laser 3 x 10 -2 1

TABLE 4

OPTIMUM OPERATINGCONDITIONSAND CONSEQUENTCOSTS

R e s u l t s C a s e 1 C a s e 2

Optimum values

Dye laser power density, W /cm 2 200 314

Ultraviolet laser power density, kW /cm 2 4.00 16.7

A tom ic density, cm -3 7-83 x 1013 8.23 x 1013

De pth Sj, cm 511 510

Height S a cm 1.02 0-998

3 % uraniu m prod uction , kg/year 998 2470

To tal electricity, M W 26.0 3.06

Co nst ruct ion cost, $/kg 197 132

Electric power cost, $/kg 3830 182

Ma intenance cost, $/kg 462 359

M ate rial cost, $/kg 888 395

U nit cost of enriched uranium, $/kg 5380 1070

m e n t i o n e d a b o v e . T h e t e c h n i c a l r e s t r ic t i o n s i m p o s e d o n t h e la s e r e n e r g y d e n s i t y a n d

e ff ic ie n cy a re s u m m a r i s e d i n T a b l e 3 .

T a b l e 4 s h o w s t h e o p t i m i s e d o p e r a t i n g c o n d i t i o n s o f t h e la s e r u r a n i u m

e n r i c h m e n t p l a n t . T h e a t o m i c d e n s i t y a n d d e p t h S l a n d h e i g h t Sa o f t h e r e a c t i o n

r e g i o n a r e h a r d l y a f f e c te d b y c h a n g i n g t h e l a s e r e n e r g y d e n s i t y a n d e ff ic ie n c y, a n d t h e

e l e c t r ic p o w e r c o s t d e c r e a s e s a s a r e s u l t o f t h e i m p r o v e m e n t o f l a s e r e f fi c ie n c y . T h e

o t h e r r e m a r k a b l e r e s u l t is t h a t t h e e n e r g y d e n s i t y r e q u i r e d b y t h e d y e la s e r a n d

u l t r a v i o l e t la s e r w i t h a n d w i t h o u t t h e r e s t r i c t i o n s a r e n o t a p p r e c i a b l y d if f er e n t. T h e

l a s e r e n e r g y d e n s i t y s h o w n i n T a b l e 4 i s p r o b a b l y r e a l is e d ev e n a t t h e p r e s e n t

t e c h n i c a l l e v e l s, w h e r e a s a t t a i n m e n t o f a l a s e r e f fi c ie n c y o f 1 ~o i s v e r y d i f fi c ul t. A h i g h

m a i n t e n a n c e c o s t e n s u e s i n c a s e 2 b e c a u s e t h e l i f e t i m e o f t h e l a s e r i s r e l a t i v e l y s h o r t .

H e n c e , i t is i m p o r t a n t t o e x t e n d t h e l i f e t i m e o f t h e l a s e r f o r t h e r e d u c t i o n o f th e u n i t

c o s t o f e n r i c h e d u r a n i u m .

T h e o p t i m i s e d u n i t c o s ts o f e n r i c h e d u r a n i u m a r e 5 3 8 0 5 / k g i n c a s e 1 a n d

1 07 0 $ / k g i n c a s e 2. T h e u n i t c o s t o f s e p a r a t i v e w o r k d o n e b y t h e g a s e o u s d i f f u s i o n

a n d g a s c e n t r i f u g a l m e t h o d s i s e s t i m a t e d a t a b o u t 1 00 $ / k g S W U w i t h a p o s s i b l e c o s t

e s c a l a t i o n . S u p p o s i n g t h a t t h e a s s a y i s 0 .3 ~o, w e n e e d s e p a r a t i v e w o r k 3 .5 k g S W U


18/20

304

K I M I O Y A M A D A , N O R I H I K O O Z A K I , M A N A B U Y A M A M O T O , K I 1C HI U E Y A N A G I

and 10 kg of feed material for the production of 1.0 kg of 3.0 ~o product. Then the

unit cost of enriched uranium including the material cost is approximately 500 /kg.

Compared with the costs of the other uranium enrichment methods, the obtained

opt imum values are greater by a factor of 11 in case 1 and by a factor of 2 in case 2.

However, the opt imum value of the unit cost of enriched uranium depends largely on

the unit cost of electricity Up, the lifetime z of the laser and the efficiencies of the

lasers. The electricity cost of 0.017 S/kWh is probably high and the improvement of

the lifetime and efficiency of the laser can reasonably be expected in the near future.

It can be concluded from the results of case 2 that laser uranium enrichment is able to

compete with the other methods.

5 . C O N C L U S I O N

Optimum operating conditions of the laser uranium enrichment plant, in which the

selective two-step photoionisation process of atomic uranium is employed, has been

studied. The unit cost of enriched uranium at present is fairly expensive in

comparison with those by the gaseous diffusion and gas centrifuge methods.

However, we can reasonably say that laser uranium enrichment is competitive with

the other uranium enrichment methods provided that the following requirements

are satisfied:

(1) the laser efficiency is improved to about one percent.

(2) the laser lifetime is extended to about one year.

A C K N O W L E D G E M E N TS

The authors would like to thank Drs K. Taniguchi, S. Yamada and A. Doi of the

Atomic Energy Research Lab orat ory for their constant encouragement throughout

the study.

R E F E R E N C E S

1 . S . A . T v c c I o et al . T w o - s t e p s el ec ti v e p h o t o i o n i z a t i o n o f 235U n u r a n i u m v a p o r , 8th In terna t iona l

ConJerence on Quantum Electronics S a n F r a n c i s c o , U S A ( 1 9 7 4 ) .

2 . M . J . B o x , A n e w m e t h o d o f c o n s t r a i n e d o p t i m i z a t io n a n d a c o m p a r i s o n w i th o t h e r m e t h o d s ,

Co m p u t e r J . , 8 , 42 ( 1965) .

3. M . MARTEr~SSON,S w e d i sh s t u d i e s o n t h e e c o n o m i c s o f u r a n i u m e n r i c h m e n t ,

J . o f the Br i t ish Nuc lear

E n er g y S o c i e t y

10, 191 (1971) ,

4 . B . M. SMIRNOV an d M . 1 . CHIBISOV,R e s o n a n c e c h a r g e t r a n s f e r i n i n e r t g a s e s , S o v i e t P h ys . - Tech .

Phys . 10 , No . 1 , 88 ( 1965) .


19/20

O P E R A T I N G C O N D I T I O N S F O R U R A N I U M E N R I C H M E N T 305

A P P E N D I X

Th e n u m b e r o f 23 5 U io n s co l l e c t ed a t t h e i o n co l l e c to r s i s g iven b y co n s id e r in g t h e

ch a r g e t r a n s f e r co l l i si o n s w h ich t a k e p l a ce w h en th e i o n is ex t r a c t ed f r o m th e n eu t r a l

b ea m . A s t h e r e i s n o ex c i t ed a to m in th e co l l e c t io n r eg io n , th e eq u a t i o n s d e s c r ib in g

t h e p o p u l a t i o n s o f t h e i o n i s a t io n a n d g r o u n d s t a t e s o f u r a n i u m i s o to p e s a s a

f u n c t i o n o f th e d i s t a n c e b e t w e e n t h e i o n a n d i o n c o l le c t o r c a n b e w r i t t e n a s :

dA~ _

d x a r ~(A s A g 5 - A g s A i s ) ( A . I )

d A ~ g i

d x - - a r ~ ( A s A 5 - A i s A ~ )

(A .2 )

d A ~

d x = a r ( A ~ A ~ - A g sA is )

(A .3 )

dAg8

d x - a v ~ (A ~ A ~ - A i s A ~ )

(A .4 )

w h e r e A i s t h e p o p u l a t i o n ( s u b sc r ip t s 5 a n d 8 in d i c a t e t h a t t h e q u a n t i t y b e l o n g s to

2 3 5 U a n d 2 3 S u r e s p ec t iv e ly , s u p e r s c r ip t s g a n d i i n d i ca t e g r o u n d a n d i o n i s a t i o n

s t a t e s r e s p ec t iv e ly ) , a n d x i s t h e d i s t a n ce b e tw een th e i o n a n d i o n co l l e c to r .

F r o m eq n s . ( A . I ) t o ( A . 4 ) , w e h a v e

dA~ dA~ dA~ dA~ dA~ dA~ dA~ dA~

+ - - - - + . . . . 0 (A .5 )

d x d x d x d x d x d x d x d x

Th e s o lu t i o n s o f eq n . ( A . 5 ) is giv en a s :

~ 1~ = A ~ + f l A ~ = 6 - A ~ A . 6 )

w h e r e 7 , fl, 7 a n d 6 a re c o n s t a n t . T h e n , w e o b t a i n t h e f o l lo w i n g e q u a t i o n :

dA~

+ ar~(cc + fl + 27) A~ - crrY(~ + 7) = 0 (A .7)

d x

E l i m i n a t i n g t h e c o n s t a n t s a , f l a n d 7 f r o m e q n . ( A . 7) b y u s i n g t h e s o l u t i o n s (A . 6) a n d

th e i n i t i a l co n d i t i o n t h a t a t x = 0 , t h e p o p u l a t i o n s A ~ = N ~ , A ~ = N ~a, A ~ = N ~ a n d

A ~ = N ~ , w e o b t a in t h e s o lu t i o n o f th e l i n ea r d i f fe r en t i a l eq u a t io n a s f o l lo w s :

A ~ 5 (x ) = N~ol [ ( N ~ N ~ - N ~ N ~ ) e x p ( - a r ~ N o x ) + (U g 5 +

N s ) ( N~ i + N i s ) ] ( A . 8 )

w h e r e N ~, N ~ , N~ a n d N ~ a r e t h e i o n a n d a t o m d e n s i ti e s a f t e r p a s s in g t h r o u g h t h e

r ea c t i o n r eg io n .

A s s u m i n g t h a t t h e d e n s i t y d i s t r i b u t i o n o f t h e i n c i d e n t i o n b e a m t o t h e i o n


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KIM10 YAMADA, NORIHIKO OZAKI, MANABU YAMAMOTO, KI1CH1 UEYANAGI

co l lec to r e lec t rode s is un i fo rm an d the ion ve loc i ty occurr ing f r om the e lec tr i c f ie ld o f

t h e i o n co l le c t o r e l ec t ro d es is m u ch f a s t e r t h an t h e t h e rm a l v e l o c it y o f a t o m i c b eam ,

we h av e t h e t o t a l n u m b er o f 2 3 s u i o n s :

n

2 s f

, t 5 = - ~ V N d A ~ ( x ) d x

0

1

n

= Y / ~ SvNdFNiN~-~NgsNinO L N o a r ~ ( 1 - e x p ( - o r ~ N o d ) ) + N g s + N i s ) N i + N i s ) d ]

(A.9)

wh e re v is th e av e rag e t h e rm a l v e l o c i t y o f t h e a t o m i c b eam , Nd t h e n u m b er o f th e i o n

co l l ec to r e l ec tro d es , d t h e e l ec t ro d e g ap , t h e s u m m a t i o n is b a s ed o n co n s i d e ri n g t h e

d ec reas e o f la s e r en e rg y d en s i t y i n t h e r e ac t i o n r eg i o n an d n is t h e n u m b er o f

d iv i s ions o f the dep th S , o f the reac t ion reg ion .

optimum operating conditions for a laser

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