Cost analyses of uranium enrichment by laser isotope separation process

COST

ANALYSES OF URANIUM ENRICHMENT LASER ISOTOPE SEPARATION PROCESS

BY

NORIHIKO OZAKI and KIMIO YAMADA

Atomic Energy Research Laboratory, Hitachi Ltd, Ozenji, Tama-ku, Kawasaki, Kanagawa (Japan) and MANABUYAMAMOTO,SHUNSUKETOMIYAMAand KIICHI UEYANAGI

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

SUMMAR Y

The probability of the selective two-step photoionisation of 2a5U atoms by laser and ultraviolet radiations is estimatedfrom the rate equations for uranium atoms with two isotopes with three levels. The population of 2aS U ions is obtained by linearising the rate equations. We have calculated the ion production ratesfor three cases in which the laser and ultraviolet powers are changed while the atom density is kept constant. The power consumption and the capital investment required for the large-scale laser enrichment plant conceptionally designed based upon the above results, and consequently the unit cost of separative work, are estimated. It is concluded that the laser isotope separation process could be competitive with the conventional gaseous diffusion and gas centrifugal methods.

NOMENCLATURE

Ajk

d El(I), El(II), Et(III ) Eu(I), Eu(II), Eu(III) h l

Spontaneous transition probability of 235U atom for the transition j ~ k. Subscripts j and k represent the ionised state i, excited state m and ground state g. Thickness of thermal insulator. Electric power consumed by lasers for cases I, II and III, respectively. Electric power consumed by ultraviolet light sources for cases I, II and III, respectively. Characteristic length of high temperature oven. Length of uranium beam in the direction of laser light. 279

Applied Energy (2) (1976)--© Applied Science Publishers Ltd, England, 1976 Printed in Great Britain

280 ni(I), ni(II), ni(III) N(I), U(II), N(III) N o

Ui, U'~, U~ N~, N~8, N~8

U~ Nu P q~ q~

Qt(I), Q,(II), Q,(III) Q~(I), Q~(II), Q,(III) S

S T

Tm, Ti r.,~ro, Tw 1)

wjk

fl 6T 2

Zs, Z8 (7 O"c O"i

~b.~,

N O R I H I K O OZAKI e t al.

Numbers of 235U ions flowing into ion collector for cases I, II and III, respectively. Numbers of separation units for cases I, II and III, respectively. Density of uranium atom at the entrance of reaction region. Populations of ground, excited and ionised 235U atoms, respectively. Populations of ground, excited and ionised 2 3 8 U atoms, respectively. Number of ion collectors. Nusselt number. Vapour pressure of uranium. Heat loss transferred to air from outer surface of thermal insulator. Heat energy necessary to maintain the vapour pressure of uranium at 10 -2 Torr at reaction region. Total amounts of heat loss from ovens for cases I, II and II1, respectively. Heat energy for vaporisation of uranium for cases I, II and III, respectively. Electrode distance of ion collector. Surface area of high temperature oven. Temperature of uranium. Lifetimes of excited and ionised states of uranium atom. Temperatures of nth thermal shield, of oven and of wall. Average velocity of uranium atom. Induced transition probability of 235U atom for the transition j --, k. Subscripts j and k represent the ionised state i, excited state m and ground state g. Concentration of 2 3 5 U atoms. Heat transfer coefficient between air and surface. Temperature difference between air and surface. Emissivity of thermal shield. Thermal conductivity of thermal insulator. Macroscopic charge exchange cross-sections of 235U and 238U atoms, respectively. Stefan-Boltzmann constant. Charge exchange cross-section. Photoionisation cross-section of excited z35U atom. Flux of ultraviolet radiation.

COST ANALYSES OF URANIUM ENRICHMENT

1.

281

INTRODUCTION

The recent developments in tunable lasers have made it possible to carry out systematic research on the selective action of laser radiation. A variety of methods has been proposed for utilising the selective action of laser radiation to separate isotopes and some of these methods have been demonstrated. 1"2 The principal requirements for the successful application of the selective process are: (1) a wellresolved isotope shift in the absorl~tion spectra of the element or one of its compounds; (2) a high monochromatic and tunable laser radiation and (3) a physical or chemical process conserving the induced selectivity and separating excited atoms from unexcited ones. The photochemical isotope separation process is capable, at least in theory, of very large separation factors similar to those obtained by the electromagnetic process. Considerable effort was expended, mainly in the United States, to apply the photochemical separation process to uranium enrichment during and following World War II. 3 While some enrichment was obtained in the laboratory, the great success of gaseous diffusion cause~l the effort to be dropped. Recently, a successful experiment on uranium isotope separation using the selective two-step photoionisation~of 235U atoms in an atomic beam of uranium was reported at the 8th International Quantum Electronics Conference. 4 This experiment shows the applicability of the laser isotope separation process in the large-scale production of enriched uranium. However, the economic problems of laser enrichment have remained unsolved. It is the purpose of this paper to review uranium isotope separation using selective two-step photoionisation and to evaluate its present potential to the uranium enrichment industry. The reasons that we restrict our study to the selective two-step photoionisation of uranium atoms are: (1) no other useful photochemical separation process has as yet been devised and (2) we find the remarkable isotope shift only in the absorption spectrum of uranium atoms. In the absorption spectrum of a uranium compound such as uranium hexafluoride, the vibration-rotation bands of an isotopically substituted uranium molecule overlap those of the abundant one. 3

2.

TWO-STEP P H O T O I O N I S A T I O N OF U R A N I U M

(a) Efficiency of selective two-step photoionisation There are numerous conceivable methods for realising separation following selective excitation of an atom. In the selective two-step photoionisation scheme which has been employed by the Lawrence Livermore Laboratory, a excited 235U atoms are selectively produced by laser light and then photoionised by an intense ultraviolet

282

N O R 1 H I K O O Z A K I et al.

light beam while 238U atoms remain unexcited. The ionised 235U atoms are separated electrostatically. We assume that a similar scheme is employed for the separation unit of the large-scale enrichment plant conceptionally designed in this study. The uranium atoms, emanating from a high temperature oven, are irradiated from the side by a tunable laser beam whose wavelength is tuned to the excitation energy of a 235U atom. From the top, ultraviolet radiation irradiates the uranium atoms to photoionise them. The ionised 2asU atoms thus generated are then electrostatically collected by the ion collector located downstream at the reaction region. The photoionisation probability of 2asU atoms can be obtained by solving the rate equations for the uranium atom with two isotopes (235U and zaau; these are designated by subscripts 5 and ~8, respectively) with three levels (ground, excited and ionised states; these are designated by superscripts g, m and i, respectively). Neglecting the ionised and excited z 38U atoms produced by the charge exchange and resonance energy transfer collisions of Z3au atoms with ionised and excited 23SU atoms, respectively, in comparison with the ground 238U atoms, and assuming that the population of the 238U atoms in the ground state is constant with respect to time, the rate equations for 238U atoms are as follows:

dN~5_ dt

dN°5 _ dt

Wo,.NO5 WomNOs+

W,.o + W,., + ~--£ + A~ o N~5

(1)

W,.O +-T-£ + A,. o N~5 +-~i Ni5 ~.

Here, Wik and Ajk are the induced and spontaneous transition probabilities of 235U atoms for the transitionj --. k and N°a/TI and N~/T m are the transition rates due to charge exchange and resonance energy transfer processes, respectively. Using the initial conditions that at time t = 0, the populations N~s = N~5 = 0, N~ = aN o and N~ = (1 - a)No, where a is the concentration of 2asU atoms and N o the density of uranium at the entrance of the reaction region, we can obtain the population of the ionised 2asU atom as a function of time as follows: ( 1 e 'It e '2' ) N~5 = ac~N° 7~-72 + ~1(71 - Y2) + Y2(~2 ~ Y l ) where: )q.2 = ½[-(b + c + d) _ x/(b + c + d) z - 4(bc + c d + b d - ce)] (l -.-~- W m i

b

N°"

L

(2)

COST ANALYSES OF URANIUM ENRICHMENT

283

c = I'Vgr,

Ul

d = W,.g+ W.,i+~=+A,.g

Ul

e= W,.o +-T~ + A,. o Now, we can evaluate the efficiency of the two-step photoionisation when we are given the atomic quantities of uranium, the density of the atom and the intensities of the laser and ultraviolet radiations.

(b) Ion production rate in the plant We assume that the tunable lasers and ultraviolet light sources with the specifications shown in Table 1 are employed in the plant conceptionally designed in this study. The specifications of the tunable lasers are different for three cases while those for the ultraviolet light sources are the same in all cases. At the present time, tunable lasers such as those shown in Table 1 "are not available, but we may reasonably expect that the operating performance and cost would be achieved in the near future due to technical improvement and cost reduction by mass production. On the other hand, the data of the ultraviolet light sources, for instance the highpressure mercury l a m p , are already realised and we cannot expect great improvements in the future. TABLE l SPECIFICATIONS OF TUNABLE LASER AND ULTRAVIOLET LIGHT SOURCES

Source T u n a b l e laser Ultraviolet light source

Wavelength

Output

(A)

[ W(cw)]

5915.4

10 20 100 100

2100 ~ 3100

Efficiency (per cent) 0-02 0.02 0"02 2.0

Cost ($)

Case

5000 10000 50000 500

I II III I ~ III

The photoionisation cross-section of the uranium atom is 1.25 x 10_ 14 cm 2 for one of eight hyperfine components in an absorption spectrum. 4 The photoionisation cross-section of the excited uranium atom is roughly estimated at 1.5 x 10-17 cm 2 for a hydrogen-like atom approximation, s The charge exchange and resonance energy transfer cross-sections of the ionised and excited 23sU atoms with 23~U atoms are assumed to be 10-13 cm 2, based upon the results of the experimental and theoretical investigations on those of the inert gases and alkali atoms. 6 We have no reliable data on the uranium atoms. A schematic view of the reaction region is shown in Fig. 1. The uranium atoms, whose density is 1013/cma, are produced by the high temperature oven and come into the reaction region with the Maxwellian velocity distribution of the most probable

284

NORIHIKO OZAKI

et al.

velocity of 450 m/s. The atomic beam is 500cm wide and 1 cm deep. The laser radiation, with a cross-section of 1 cm wide and 1 cm deep, comes into the reaction region, perpendicular to the atomic beam. The wavelength is tuned to the excitation energy of 235U atoms in order to excite 235U atoms selectively whilst leaving 23aU atoms unexcited. The ultraviolet radiation of 500cm long and 1 cm wide meets orthogonally the atomic beam and the laser radiation at the.reaction region. The

U~ItravioletRadiation ReactionRegion

Uranium

Atom

LaserRadiation Fig. 1. Schematic view of the reaction region of a separation unit. Uranium atoms emanating from a high-temperature oven are irradiated by laser and ultraviolet radiations at the reaction region.

length of the atomic beam in the direction of the laser light is chosen to be one half of the mean free path of photons in the atomic beam of natural uranium whose density is 1013/cm a (concentration of 235U in natural uranium is 0-72 per cent). The ultraviolet radiation, on the other hand, is scarcely absorbed in the 1 cm deep atomic beam since the photoionisation cross-section is extremely small compared with the photoexcitation cross-section and the density of the excited 235U atom is much lower than that of the ground 235 U atom. It is assumed that we can use the ultraviolet light 1000 times without an appreciable amount of attenuation loss. It is desirable for the efficient utilisation of the laser power that all of the atoms excited by laser radiation should be ionised before they return to the ground state

COST ANALYSES OF U R A N I U M ENRICHMENT

s p o n t a n e o u s l y . F o r this p u r p o s e the p h o t o i o n i s a t i o n s h o u l d be .chosen as: ~b=, >

Arag =

flux

2 x 10 22

of

the

285

ultraviolet

radiation

for

( p h o t o n / c m 2 s)

(7i

= 1"3 × l0 4

( W / c m 2)

w h e r e ~b=v a n d a i are respectively t h e flux o f the u l t r a v i o l e t p h o t o n a n d t h e p h o t o i o n i s a t i o n c r o s s - s e c t i o n o f the e x c i t e d 2 3 5 U a t o m . W e a s s u m e t h a t the field s t r e n g t h s o f t h e u l t r a v i o l e t r a d i a t i o n are 10 3 W / c m 2 f o r case I, 2.5 x 10 3 W / c m 2 f o r case II a n d l0 4 W / c m 2 f o r c a s e III.

'S

1.0

lo-1

:~

ld 2

/

LO ¢d

0 10-3 o~

,.o

tg

2

Q. C: 10 ~

N o~ c

.~0 10.==

I

16 15 7

16 6

Irradiation

I

16 5

Time

15 4.

15 3

(sec)

Fig. 2. lonisation probability of 2asU atoms as a function of irradiation time for case I1. Approximately 50 per cent of the incident 235U atoms are ionised at the exit of the reaction region shown in Fig. I.

286

NORIHIKO OZAKI

et al.

The ionisation probability of the 235 U atom as a function of irradiation time can be estimated from eqn. (2) and an example of case II is shown in Fig. 2. The absorption of the laser light along its path is taken into account in this calculation. The irradiation time at the exit of the reaction region is approximately 2 × 10- 4 sec. Hence, the flux of the ionised/3sU atom is estimated at 1015/cm2 s from Fig. 2. The loss of the/3SU ions due to the charge exchange collisions with Z3SU atoms when they are collected by the ion collector located downstream of the reaction region is roughly evaluated as follows. The decrease of the ion density is determined only by the deflection distance from its original path provided that the electrode distance is sufficiently small and the ions are trapped by the collector as soon as they enter into its electric field. The number of z 35 U ions flowing into the ion collector per unit time n i is therefore: n i = vN c I' [ - N ~ ( x ) [ 1 - e x p . ( - 2 8 s ) ] + N~ (x)

J0[_

(,,

- ~[1-

exp(-Y~sS)]

)]

d.~;

where v is the average velocity of the uranium atom, N c the number of collectors, l the length of the uranium beam in the direction of the laser beam and s the electrode distance. The macroscopic charge-exchange cross-sections are defined as: Z 5 = ~Noa c

X8 = ( l - ~ ) N o a

c

For case I, the number of 235U ions collected per unit time becomes: ni(II) ~ 3 × 1 0 1 7

(ions/s)

About 40 per cent of the Z35U ions are lost when they are collected. Similar results for the various cases, including cases 1 and III, are shown in Fig. 3. The 23~U ion production rates for these cases are: ni(l) ~- 6 x 1 0 1 6 ni(lll) -~ 6 x 10 iv

(ions/s) (ions/s)

The saturation of the ion production rate in the relatively high power region of the laser radiation and ultraviolet radiation shown in Fig. 3 is due partly to: (i) the low atom density in a beam in comparison with the density of photons and (ii) the increase of the induced transitions from excited state to ground state owing to the enhancement of the excited atoms.

3.

E N E R G Y C O N S U M P T I O N IN TH E P LA N T

(a) Laser and ultraviolet light sources

As the model for the study of the large-scale production of the enriched uranium, we chose a 8750 ton SWU/y plant designed for 4 per cent product and 0-25 per cent

COST ANALYSES OF URANIUM ENRICHMENT

287

1019

UV P o w e r case"[ ~.__--~ ~--case 11

-.-- 10 18

f

C 0 ,(~

. _ _ - - ~ 103

case I

10 17

(w/cm2) lO4

n,,

C

/ 1 0

.2 ~

2

1019

e

/ 1 0 1

E

1015

i

1

1014

101

I 10 2

I 10 3

104

Laser Power ( W / c m 2 ) Fig. 3.

Ion production rate

versus

laser power. Ultraviolet power is chosen as a parameter.

waste. 7 Supposing that we would get 1500 ton/y of 4 per cent product by blending the natural uranium with 60 per cent enriched uranium which could be achieved by the laser isotope separation process considered in the previous section, we should produce. 60 per cent enriched uranium at the rate of 80ton/y or 23sU atoms at 3 × 1021/s. Suppose that a unit isotope separator is composed of a tunable laser system, an ultraviolet light source system and a high temperature oven for producing the atomic beam. The number of units is: N(I) = 3 x

1021/ni(I)

~ 5 × 104

N(II) "-- 104 N(III) -~ 5 × 103 The corresponding numbers for ultraviolet light sources are 25 × 104 for case I, 13 × 104 for case II, and 25 × 104 for case III.

288

N O R I H I K O OZAK1 et al.

The electric power c o n s u m e d by the lasers E t and by the ultraviolet light sources E, is: 10 - x 5 x 1 0 4 = 2"5 x 10 9 Et(I) - 0.0002 20 x 1 0 4 = 10 9 El(II) - 0"0002 100 - x E~(III) -- -0'002 E,(I) =

100 0.02

5 x 103=2'5

(W}

(W)

x 108

x 25 × 104 = 12-5 × 108

100 E.(II) = 0.02 × 13 x 1 0 4 = 6'5 x 108 100 E,(III) = 0 ~ 0 2 x 25 x 104 = 12"5 x 10 s

(W)

(W)

(W)

(w)

(b) High-temperature oven The heat loss from the high temperature ovens for the production o f the atomic beam is considered in this section. To produce an atomic beam o f 1013/cm3 density, the density o f the a t o m at the exit slit o f the high temperature oven (which is located 10 cm upstream o f the reaction region) is 3 × 1014/cm3, that is, approximately equal to 10-2 Torr. F r o m the experimental formula for the v a p o u r pressure o f uranium: 8 logP-

23300 - +8.58 T

where P is the v a p o u r pressure in T o r r and T t h e temperature in K; it is known that the oven is required to be kept at 2200 K. The heat energy necessary to maintain the v a p o u r pressure at 10 -2 T o r r is estimated from the heat capacity and conversion energy o f uranium, 8 that is: qv = 2'2 × 10 3

(Joule/g)

The total a m o u n t o f u r a n i u m v a p o u r emanating out per unit time from the exit slit, with the aperture o f 0 . 5 c m x 500cm, is 1.3g/s and then the heat energy Q,, for vaporisation of the u r a n i u m is: Q~,(I) = q,, x 1.3 × N(I) = 15 × 10 v Qv(II) = q~, × 1-3 x N(II) = 3 × 107 Q~(III) = q,, × 1.3 × N(III) = 1.7 x 107

(W) (W) (W)

COST ANALYSES OF U R A N I U M E N R I C H M E N T

289

The heat transferred to the air from the high temperature ovens is calculated as follows. We assume that the plant is composed of a number of separating Nodules operated in parallel to achieve the desired product flow rate. Each module is composed of ten separation units. Each unit is made up o f a high temperature oven, a tunable laser system and ultraviolet light sources. The ultraviolet light sources are c o m m o n to 1000 separation units. The high temperature ovens mounted in a module 10cm apart from one another are surrounded with the multi-layered thermal shielding metal plates and, outside them, a thermal insulator. The heat loss q,, transferred to air from the outer surface of the thermal insulator located horizontally and cooled by natural convection, is:

qt "~ N u ~ 6 T S where Nu is the Nusselt number, fl the heat transfer coefficient (W/m C ) , h the characteristic length (m), 6 T the temperature difference between air and the surface (~C) and S the surface area (upper and lower) of the insulator (m2). If we reduce the wall temperature (by using the thermal shields and insulator) to 1 0 0 C , we can suppress the heat loss from the separation module to be as low as: qt = 9 x 10 3

(W)

The number of thermal shields and the thickness of the thermal insulator necessary to suppress the wall temperature below 100 '-C is calculated by solving the equations: 2 err q' = 71(T" - Tw)S =--(T°~n - T"4)S where ). is the thermal conductivity, d the thickness of the insulator, e the emissivity of the thermal shield, a the Stefan-Boltzmann constant, n the number of the thermal shields and T,, T u, and T Othe temperature of the nth thermal shield, of the wall (in this case, 100°C) and of the oven (2200K), respectively. For the typical case, the thickness of the insulator is of the order of a metre and a large number of thermal shields are necessary. The total amount of the heat loss from the ovens becomes: Q,(I)=q, x

N(I) 10 - 5

x 107

(W)

Q,(II)=q, x

N(II) 10 - 8

x 106

(W)

- 5 x 106

(W)

u(nI)

Q,(III) = q, x - 10

Thus the total amount of power required for the high temperature ovens is the sum of the heat for vaporisation Qv and the heat transferred to the air Q,; that is, 2 x 108 W

290

NORIHIKO OZAKI et aL

for case I, 3.8

x 107

W for case II, and 2.2 x l0 T W for case III.

4.

UNIT COST OF SEPARATIVE WORK

The various costs of producing separative work may be divided into three categories: capital, power and operating. The capital cost is an annual cost converted from the capital investment by applying an appropriate annual capital charge. Operating cost includes all annually incurred cost, exclusive of power.

(a) Capital cost The separation unit is composed of a tunable laser system, the ultraviolet light sources which are common to 1000 separation units, and a high temperature oven. Each separation module (which consists of ten separation units) is equipped with a vacuum tank and an evacuation system for the reaction regions and the ion collector systems. The plant is provided with the process support systems which include process ventilation, fire protection and cooling water and also such facilities as administration building, technical service building and maintenance building, and the instrumentation and control systems. TABLE 2 CAPITAL COST ESTIMATION

Number o/' systems

Capital investment (MS)

System Case 1 T u n a b l e laser Ultraviolet light source Uranium vapour production Evacuation Process s u p p o r t I n s t r u m e n t a t i o n a n d control Civil Total

5 25 5 5

× 104 × 104 x 103 × 103 1 1 1

Case 11 104 13 × 104 103 103 1 1 I

Case 111 5 25 5 5

X 10 3.

× 104 x 102 × 102 1 1 1

Case 1

Case 11

Case 111

250 125 130 500 50 50 30

100 65 25 100 10 10 5

250 125 13 50 5 5 3

1135

315

451

The total plant capital investment is analysed in Table 2. The capital investment for the tunable laser and ultraviolet light source system are estimated from their costs which are shown in Table 1. The capital investment for the other four systems is estimated from those for the gaseous diffusion and gas centrifuge plants and is assumed to be linearly proportional to the scale of plant. If we assume 15 per cent for an annual capital charge, the capital cost of the separative work is $170 million/y for case I, $50 million/y for case II, and $70 million/y for case III, approximately.

COST ANALYSES OF URANIUM ENRICHMENT

291

TABLE 3 POWER COST ESTIMATION Power consumption System Case 1

Case I1

Case 111

Tunable laser (MW) Ultraviolet light source (MW) Vaporisation and heat loss (MW) Miscellaneous (MW)

2500 1250 200 250

1000 650 38 50

250 1250 22 25

Total (MW)

4200

1738

1547

740

300

270

Power cost* (MS/y) * 20 mills/kWh.

(b) Power cost The total amount of electricity used and the consequent power cost in the plant are summarised in Table 3. We assume in this estimation that electric power is bought from an existing utility at a cost of 20 mills/kWh.

(c) Operating cost Costs under this category are based on maintenance, employment and materials for the plant, and do not include provision for research and development activities. Table 4 presents estimated operating costs for the plant. We assume that the maintenance costs of the tunable laser systems and the ultraviolet light sources per annum are 50 per cent of their initial costs.

(d) Unit cost of separative work Unit cost of separative work is the annual cost divided by annual production. Table 5 shows the capital, power and operating costs and the consequent unit cost of separative work. About 10 to 15 per cent of the unit cost of separative work is due to the capital cost, approximately half is due to the power cost and the remaining 20 to 40 per cent is due TABLE 4 OPERATING COST ESTIMATION

Annual cost Case I

Case 11

Case 111

Labour (M S/y) Material Tunable laser (MS/y) Ultraviolet light source (MS/y) Miscellaneous (MS/y)

40

8

5

125 63 2

50 33 2

125 63 2

Total (MS/y)

230

93

195

292

NORIHIKO OZAKI et al.

to the operating cost. The high power cost is attributed partly to the fact that the energy conversion efficiency of the tunable laser is low and partly to the fact that the extremely high ultraviolet radiation field is necessary in order to ionise the excited atoms efficiently. TABLE 5 UNIT COST OF SEPARATIVEWORK Annual cost

Capital cost (MS/y) Power cost (MS/y) Operating cost (MS/y) Total (MS/y) Unit cost of separative work ($/kgSWU)

Case I

Case 11

Case 111

170 740 230 1140

50 300 93 443

70 270 195 535

130

51

61

Comparing the unit cost of case I with that of case II, we can say that as the laser and ultraviolet radiations increase the ion production rate becomes high and, consequently, the unit cost falls. The unit cost of case III is expensive in spite of the fact that the laser and ultraviolet radiations are high compared with those in cases I and II, and, as a result, the ion production rate is high. The expense stems from the inefficient utilisation of the laser and ultraviolet radiations--that is to say, the numbers of lasers and ultraviolet light sources do not decrease, as might be expected from the enhancement of their powers. It might be expected to decrease the unit cost by increasing the atom density in a beam or by increasing an optical depth of a beam in the directions of the laser and ultraviolet sources.

5.

DISCUSSION

The cost analyses of laser uranium enrichment are compared with those of the conventional enrichment m e t h o d s - - t h e gaseous diffusion process and the gas centrifuge method. Table 6 shows the cost data of the gaseous diffusion process, 7 of the gas centrifuge method 9 and of the laser separation process. For all cases the capital cost of the laser enrichment does not exceed those of the gaseous diffusion and gas centrifuge processes. A significant part of the capital cost of the gaseous diffusion process is due to the fact that several thousands of diffusion barriers and gas compressors are necessary owing to its small separation factors. It is possible to reduce the capital cost of the laser enrichment by enhancing the laser power and the atom density in a beam. The cost of the tunable laser systems in the

COST ANALYSES OF URANIUM ENRICHMENT

293

Power consumption of a full-sized diffusion plant is so great that a separate electric power plant is required to operate it. As much as 40 to 50 per cent of the cost of separative work from the diffusion plant is due to power cost. The energy consumption of the gas centrifuge process is about one-tenth that of the gaseous diffusion process due to the remarkably low power requirement of the centrifuge. TABLE 6 A COMPARISON WITH THE COST ANALYSES FOR THE GASEOUS DIFFUSION, GAS CENTRIFUGE AND LASER ENRICHING PLANTS

Laser separation

Capital investment (MS) Annual capital charge (~o) Total electricity consumption (MW) Capital cost (MS/y) Power cost (MS/y) Operating cost (MS/y) Unit cost of separative work ($/kgSWU)

Gaseous diffusion

Gas centrifuge

1200 15 2430 180 117' 14

1490 10 260 149 20t 109

35

32

Case I

Case I1

Case 111

1135 15 4200 170 7405 230

315 15 1738 50 3005 93

451 15 1547 70 270:~ 195

130

51

61

* 5.5 mills/kWh. t 9.0 mills/kWh. $20.0 mills/kWh.

The electricity cost of laser enrichment is a significant portion of the unit cost of separative work. The low conversion efficiency of the tunable laser and the requirement for high power ultraviolet light sources occasioned by the small photoionisation cross-section of the excited 235U atom make the energy consumption large. Hence, it is important for cost reduction to improve the conversion efficiency of the laser and ultraviolet light source and to choose the optimal condition for efficient utilisation of laser and ultraviolet radiations. High operating cost occurs for the gas centrifuge process because every gas centrifuge is replaced by a new one several times during the operating period of the plant. The low operating cost of the gaseous diffusion plant is due to the fact that the diffusion barrier is not renewed once it has been installed. The operating cost of the laser enrichment depends greatly on the lifetime of the tunable laser and the ultraviolet light source. The unit cost of separative work estimated in our study shows that laser enrichment could be competitive to the conventional enrichment processes if the suitable conditions of atom density in connection with the strengths of the laser and ultraviolet radiations are provided. However, we have to emphasiseb that the cost estimation of our study is based on the uncertain data of the atomic and spectroscopic quantities of uranium, and on forecasted laser and electricity costs. Nevertheless, it is clear that improvement in the energy conversion efficiencies of the

294

NORIHIKO OZAK1 et al.

laser and of the ultraviolet light source would be most effective in reducing the unit cost of separative work.

6.

CONCLUDING REMARKS

All the calculations we can make at present show that laser enrichment deserves further consideration. After comparing it with other methods of uranium enrichment, we are encouraged by three particular points: first, low specific requirements for the capital investment; secondly, flexibility of scale combined with the possibility of stepwise expansion of the separative capacity and, thirdly, its development potential. The future development of the laser enrichment process should be focused on improvement in laser efficiency, on the enhancement of the laser and ultraviolet radiation fields and on the extension of the lifetime of the light sources. Another important target of the laser enrichment field is to investigate the accurate transition probabilities of the 235U atoms in the visible region, and find out which level is most suited to the large-scale production of enriched uranium. Greater improvements can be expected for the laser separation process than for the older, more mature diffusion and centrifugation processes.

ACKNOWLEDGEMENTS

The authors would like to express their gratitude to Drs K. Taniguchi, S. Yamada and A. Doi of the Atomic Energy Research Laboratory, and Drs H. Watanabe, J. Kawasaki and I. Miwa of the Central Research Laboratory of Hitachi Ltd for their constant encouragement throughout this study.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9.

R. V. AMBARTZUMIANand V. S. LETOKHOV, Applied Optics, 11 (1972) p. 354. C. B. MOORE, Accounts of Chemical Research, 6 (1973) p. 323. R. L. FARRER, JR and D. F. SMITH,AEC Report K-L-3054 Rev. I1, 1972. S.A. TUCCIO, J. W. DUBRIN, O. G. PETERSON and B. B, SNAVELY,IEEE J. Quantum Electronics, QE10 (1974) p. 790. A. UNSOLD, Physik der Sternatmospharen, Springer Verlag, 1955. S. C. BROWN, Basic data oJplasma physics, John Wiley and Sons, 1959. US AEC: AEC Report ORO-685, 1972. A. HOLDEN, Physical metallurgy of uranium, Addison-Wesley, 1958. H. MOHRHAUER, New Scientist, 56 (1972) p. 12.