THEORETICAL ANALYSIS OF 16-µm CO2GASDYNAMIC LASER

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THEORETICAL ANALYSIS OF 16-µm

CO2GASDYNAMIC LASER

S. Saito, K. Suzuki, M. Obara, T. Fujioka

To cite this version:

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JOURNAL DE PHYSIQUE CoZZoque C9, suppZ6ment au nOZ1, Tome 41, novembre 1980, page C9-167

THEORETICAL ANALYSIS OF

16-Pm

C02 GASDYNAMI

C LASER

S. Saito, K. Suzuki, M. Obara and T. Fujioka

Department o f ElectricaZ Engineering, Keio U n i v e r s i t y , 3-14-1, Hiyoshi, ~ o h o k u - k ~ , Yokohama-ski, 223, Japan.

Abstract.- The possibility of obtaining high-power 16-um radiation from a conventional C02 gasdynamic laser (GDL) has been evaluated theoretically by means of a modified ~nderson's time-dependent method. In this simulation, the rate equations with the energy of the vibrational mode or the PoPu-

lation of the each vibrational level are used. The analysis showed that the 16-pm pulse of 25~J/pulse/cm3 extractable energy and 4.2 kW maximum power can be achieved on the P(15) line of the (0200)-

(010) transition by injecting a fast 9.4-vm pulse at a position 15 cm dotmstream oof the nozzle thro- at to populate the upper laser level. For a gas miiture of CO : N2 : H2

-

20 : 13 :

7

(%) and a nozzle area ratio of 100, the optimum reservoir temperature an3 pressure were calculrited to be

1200 K and 15 atm, respectively. Because of its high repetition rate and high aveikge-pbwer capabi- lities, such a conventional GDL can easily provide the power levels required fot- ifitidstrial applica- tion of 16-urn laser radiation.

I. INTRODUCTION

Recently, 16-pm l a s e r ~ ' - ~ h a v e become of i n t e r e s t a s p o t e n t i a l l i g h t s o u r c e s f o r uranium i s o t o p e s e p a r a t i o n 6 - 8 . The high e f

-

f i c i e n c y , powerful performance and well-de- veloped technology of t h e C 0 2 l a s e r make it an a t t r a c t i v e c a n d i d a t e f o r t h e 1 6 - p m l i g h t source. For o b t a i n i n g a 16-pm l a s e r emis- s i o n , t h e v i b r a t i o n a l t r a n s i t i o n between

0

t h e (02 0) and (010) l e v e l s o f C02 i s used and t h e c o o l i n g of C02 gas f o r g r e a t l y r e - ducind

kk

lower l e v e i l s p o p u l a t i o n

is

i n - &.spendable. I n t h i s tk$atd, the most proper

melifis

t 6

d gisaynamic i a s ~ r iifiifig adiabatic-

isxpansiun

whibh can pkaduck

h i g h

power be-

cistiks

o t

..if.$

..

.,

+.

high

.

%.

veio+ty

,..,.. A

$id

~ i $ ~ r a t i r j r i parameter. I n a d d i t i o n , o p e r a t i o n a t a high r e p e t i t i o n r a t e i s p o s s i b l e .

Recently, Wexler e t a l . have performed a C02 16-pm l a s e r experiment w i t h an a f t e r - mixing-type e l e c t r i c d i s c h a r g e gasdynamic l a s e r (EDGDL) 5. However, e x t r a c t a b l e l a s e r

i s l i m i t e d mainly by t h e capabbey of t h e e l e c t r i c a l d i s c h a r g e power. A

CDL

o p e r a t i n g a t high r e s e r v o i r p r e s s u r e and temperature which i s r e a l i z a b l e by combugtion must be a more a t t r a c t i v e c a n d i d a t e t h a n t h e EDGDL i n terms of s p e c i f i c e x t r a c t a b l e l a s e r power. Therefore, we have t h e o r e t i c a l l y s i m u l a t e d 16-pm l a s e r performance i n o r d e r toes-* 16-pm l a s e r emissioA with ii cbnventional GDL having a n o z z l e of

large

area

r a t % o .

I n o u r s i i n u l a t i o n ; $dr t h e ~ o n d i t i o n

b e f o r e i n j e c t i o n o f 9.4-pni

beain,

we

solved

a set of conventional r a t e e q u a t i o n s

w i t h

energy of each mode. For t h e conditictk aft&? i n j e c t i o n of 9.4-pm pumping beam, we

an&-

iykea it

ior

t w b

cases

thak

(11

6'9

.i-vm

p u l s e i s very i n t e n s e , ( 2 ) i n t e n s i t y of t h e ~ u m p i n g p u l s e i s v a r i a b l e . I n c a s e o f (21, we e s t i m a t e d g a i n o f t h e 16-prn and t h e 16- IIm o u t p u t power by s o l v i n g a s e t of r a t e e q u a t i o n s w i t h p o p u l a t i o n of each v i b r a - t i o n a l l e v e l . 12

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C9-168 JOURNAL DE PHYSIQUE

II

.

SIMULATION MODEL [A]

To produce t h e p o p u l a t i o n i n v e r s i o n f o r t h e 16-ym t r a n s i t i o n , an i n t e n s e s a t u r a t i n g l a s e r p u l s e o f 9.4-pm r a d i a t i o n must be i n - j e c t e d t o depopulate t h e ( 0 0 1 ) l e v e l and t o 0 p o p u l a t e t h e (02 0). l e v e l a s shown i n Figs.1 and 2. Therefore, we considered how t o pop- u l a t e t h e (001) l e v e l a s a f i r s t s t e p and

0

how t o populate t h e (02 0) l e v e l by depopu- l a t i n g t h e (001) l e v e l a s a second s t e p . The f i r s t s t e p can be d e s c r i b e d by Anderson's time dependent method9 u s i n g r a t e e q u a t i o n s with t h e v i b r a t i o n a l energy of C02 mlecules. The second s t e p depends t o a c o n s i d e r a b l e degree on both t h e i n t e n s i t y and t h e tempral width of t h e s t i m u l a t i n g 9.4-pm p u l s e t o 0 pump t h e (02 0) l e v e l v i a t h e induced t r a n - 0 s i t i o n from (001; t o (02 0 ) . Therefore, i f t h e 9.4-pm l a s e r p u l s e i s i n t e n s e and s h o r t 0

enough t o pump the (02 0 ) l e v e l w i t h i n i t s d e - e x c i t a t i o n time, t h e t r a n s i t i o n between

0

t h e (001) and (02 0 ) l e v e l s i s s a t u r a t e d completely and t h e i n f l u e n c e of de-excita- t i o n r e a c t i o n s i s p r a c t i c a l l y a v o i d a b l e . Under t h e s e c o n d i t i o n s , t h e p o p u l a t i o n of 0 t h e (02 0) l e v e l can become e q u a l t o t h a t of t h e (001) l e v e l , and i s a v a i l a b l e a s upper l e v e l p o p u l a t i o n f o r 16-pm t r a n s i t i o n . Then we analyzed t h e small s i g n a l g a i n o f 16-pm on t h i s assumption.

The v i b r a t i o n a l energy model u s e d i n our s i m u l a t i o n i s shown i n Fig. 2. I t i s a s - sumed t h a t t h e i n d i v i d u a l i n t r a v i b r a t i o n a l c o l l i s i o n p r o c e s s e s a r e s o f a s t t h a t e a c h

i

o f them forms a Boltzmann d i s t r i b u t i o n d e f i n e d by t h e r e s p e c t i v e v i b r a t i o n a l t e m -

p e r a t u r e . I n Fig. 2, t h e v1 and t h e v2 m&s,

d e f i n e d a s Mode I , afre a s s u m e d ~ b e c o u p l e d

s t r o n g l y by t h e Fermi resonance so that their v i b r a t i o n a l temperature may be defined by TI. The important r e a c t i o n p r o c e s s e s u s e d i n t h e p r e s e n t a n a l y s i s and their rate constants compiled by Tylor e t a l . are sham i n Table I.

III. RESULTS AND DISCUSSIONS [MODEL[A]] To reduce t h e v i b r a t i o n a l temperature of Mode I a s w e l l a s t o maintain t h e h i g h v i b r a t i o n a l temperature of Mode I1 i s indis- pensable f o r 16-pm l a s i n g . Therefore a nozzle w i t h a l a r g e a r e a r a t i o i s d e s i r a b l e t o meet t h e above requfrments. However, it i s d i f - f i c u l t t o d e s i g n and c o n s t r u c t a nozzle w i t h l a r g e a r e a r a t i o , and it may cause f l o w s e p a r a t i o n a t t h e nozzle e x i t . Therefore, i n t h i s s i m u l a t i o n , an a r e a r a t i o of 100 .,.was chosen a s a s t a n d a r d v a l u e which i s

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t h e g a i n a t t a i n e d a t t h e p l a c e where t h e r e a c t i o n of t h e ( 0 2 0 0 ) l e v e l i s very f a s t , 9.4-ym p u l s e i s i n j e c t e d . Therefore 16-pm and parameters of 9.4-urn beam meeting such g a i n can n o t be o b t a i n e d simultaneously over

every p o i n t along t h e downstream shown i n Fig. 3. A s can e a s i l y be seen from Fig. 3, 16-ym g a i n i n c r e a s e s s h a r p l y and i s maximized, t h e n g a i n c l o s e t o t h e maximum v a l u e remains a l o n g t h e downstream d i r e c t i o n . T h i s means t h a t one can p u t a c a v i t y n o t o n l y

a t

t h e p o i n t g i v i n g maximum g a i n b u t a l s o i t s downstream. Figure 4 shows t h e e f f e c t o f r e s e r v o i r p r e s s u r e Po on both 10.6-pm and 16-pm g a i n s a t a p o i n t 12 cm downstream from t h e t h r o a t . The 16-pm g a i n , as w e l l a s t h e 10.6-ym g a i n , i n c r e a s e s a s Po d e c r e a s e s u n t i l around Po = 15 atm, a t which t h e maximum g a i n i s given.

I t i s b e i l v e d t h a t t h e p r e s s u r e of t h @ cavity i n c r e a s e s w i t h Po, r e s u l t i n g i n t h e de-pop- u l a t i o n of t h e (001) l e v e l . I n t h i s way, t h e a n a l y s i s showed t h a t a maximum 16-pm g a i n of 2.5 % cm'l can be o b t a i n e d f o r parameters o f r e s e r v o i r tem- p e r a t u r e To of 1200 K , r e s e r v o i r p r e s s u r e Po o f 15 a h , gas mol f r a c t i o n o f C02: N2: H 2 = 20 : 73 : 7 ( % ) and with a nozzle a r e a

r a t i o of 100. A l l o f t h e s e parameters can e a s i l y be r e a l i z e d by experiment.

IV

.

SIMULATION MODEL [BJ

F u r t h e r t h e o r e t i c a l i n v e s t i g a t i o n of performance of 16-pm r a d i a t i o n by

a

conven- t i o n a l C02 GDL h a s been made based upon the r e s u l t s o b t a i n e d by Model [A]. For t h e

s i m -

0

u l a t i o n o f p o p u l a t i n g t h e (02 0) l e v e l ,

a

s t r o n g and s h o r t 9.4-pm p u l s e enough t o i n - s t a n t a n e o u s l y s a t u r a t e 9.4-ym t r a n s i t i o n

is

assumed i n Model [A]

.

However, &-tation

. . . . . ~ . an assumption a r e n o t c l e a r . Therefore, f o r understanding t h e s t a t e a f t e r i n j e c t i o n o f 9.4-pm r a d i a t i o n , a s e t of r a t e e q u a t i o n s w i t h p o p u l a t i o n of each v i b r a t i o n a l l e v e l i s newly i n t r o d u c e d h e r e t o examine t h e time and s p a t i a l b e h a i v i o r s of v i b r a t i o n a l e x c i t a t i o n by 9.4-ym p u l s e . I n t r o d u c t i o n of t h e new r a t e e q u a t i o n model a l s o e n a b l e s us t o e s t i m a t e . a d e t a i l e d s p e c i f i c 16-pm output power, an e x t r a c t a b l e energy and p u l s e pro- f i l e a g a i n s t t h e parameters of t h e 9.4-pm s t i m u l a t i n g beam.

I n t h i s model c a l l e d Model [Bl

,

6 levels of C02 up t o and i n c l u d i n g t h e (001) l e v e l w i t h o u t t h e (110) and t h e (030) l e v e l s , and N ₂( v = l ) l e v e l a r e taken i n t o account. a s

showninFig.5. The r a t e e q u a t i o n w i t h 16-pm~ photon f l u x is added t o a s e t of rate equations with v i b r a t i o n a l p o p u l a t i o n s . Since t h e pop- u l a t i o n o f t h e (110) and t h a (030) l e v e l s

i s n e g l i g i b l e

a t

about 200 K , t h e s e two l e v e l s a r e n o t taken i n t o consideration he=. Then, we solved t h e s e e q u a t i o n s on t h e as-

sumption t h a t t h e r o t a t i o n a l p o p u l a t i o n s always form Boltzmann d i s t r i b u t i o n d e f i n e d by a g i v e n t r a n s l a t i o n a l temperature, 9.4- pm beam w i t h r e c t a n g u l a r p u l s e p r o f i l e aria

Gaussian i n t e n s i t y d i s t r i b u t i o n i s i n j e c t e a i n t o t h e s t r e a m t r a n s v e r s e l y 15 down- s t r e a m from t h e n o z z l e t h r o a t a s shown

in

Fig. 1. The r e a c t i o n s c o n s i d e r e d and t h e i r r a t e c o n s t a n t s a r e l i s t e d i n Table

II. I n

t h e a n a l y s i s Of 16-pm t r a n s i t i o n , most

in-

p o r t a n t r e a c t i o n s a r e r e a c t i o n s w i t h t h e

0

(02 0) l e v e l , e s p e c i a l l y t h e e f f e c t $ of r e a c t i o n ( 5 )

-

(10 i n Table I1 , a,re cxmsidergd

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JOURNAL DE PHYSIQUE

t o be? l a r g e .

I n

r e a c t i o n s

( 8 ) ,

( 9 ) and

( l o ) ,

t h e ]:ate c o n s t a n t s f d r helium a r e tenl:ative- l y uhed i n s t e a d o f t f i e s e f o r H 2 , becauise t h e r a t e c o n s t a n t s f o r H Z ake nbC c l e a r . A s mol f r a c i t i o n o f H2 i s

$ m a l l ,

a l a r g e e r r o r seems t o bb a v o i d a b l e .

. ,

A s t h e i n i t i a l v a l u e QE t h e popu3,ation o f ehch v i b r a t i o n a l l e v e l , t h e v a l u e s c a l - c u l a k e d by Using t h e Model [ A ] aye usetd: a gak m i x t u r e

of

C02

r

N2 : H2 = 20 : 7 3

i

7 ($1, a . r e ! s e r v o i r t e n p e r a t a r e o f i200

K,

a a:eser- v o i r p r e s s u t e o f 1 5 & t m , and a n o z z l e a r e a r a t i b of 100, These p a r a m e t e r s a r e tui:ned o u t 'to be optimum v a l u e s £02 s m a l l s i g n a l g a i n a t 16-urn.

V. F&SULTS

AND

DISCUSSIDNS [MODEL [B]

1

F i g u r e 6 shows h e ~ n a x i n u n 16-yin s m a l l s i g n h l g a i n a g a i n s t t h e 9.4-pm i n p u t power. Wten a 9.4-pm i n p u t bower i n e x c e s s of' h u t 1 m l ( s p o t s i z e = 8 mtn d i a . , w i d t h = 100 h s e c )

i s

i n j e c t e d , a g a i n o f 16-1~mf~(15)) i s maximized, d n d i c a t i n g t h a t t h e 9.4j-vm 0 t r a n s i t i o n bettieen t h e (001) and t h e (02 0 ) l e v e l s i s s a t u r a t e d ~ o m p l e t e l y . The te'lnporal b e h a v i o r o f t h e e a c h l e v e l p b p u l a t i o n w i t h - o u t 16-um o s c i l l a t i o n i s s h o r n i n F i g . 7. The 9.4-ym Snput power i s

L RW,

s p o t s i z e i s 8 nun d i a . , and w i d t h i s 100 hsec. A f t e r i n j e c t i o n of 9.4-vm X a d i a t i o n , t h e 0 p o p d l a t i o n s ,of t h e (001) a s d t h e (02

D )

l e v e l s become e q u a l w i t h i n 10 n s e c . ~ n d ' a f t e r s t o p p i n g t h e i n j e c t i o n o f 9.4-pm r a - d i a t i o n , t h e p o p u l a t i o n o f t h e (001) l e v e l t e n d s t o r e c o v e r . Although t h e i n i t i a l pop- u l a t i o n d e n s i t y o f t h e (001) l e v e l i s 2.26 x PO 21 m-3, i t becomes 1 . 1 3 x 10 21 m-3 o f 9.4-urn r a d i a t i o n . On t h e c o n t r a r y , t h e (010) l e v e l p o p u l a t i o n h a r d l y i n c r e a s e s . I n t h i s way, i f 9.4-um p u l s e i s i n t e n s e a n d s h o r t , h a l f t h e p o p u l a t i o n o f t h e (001) lev- e l i s a v a i l a b l e a s upper l a s e r l e v e l popu- l a t i o n folt 16-ym t r a n s i t i o n . And. such 9.4-pm & s e l a s e r i s e a s i l y o b t a i n a b l b . Therefore, i t i s b e l i e v e d t h a t t h e assumption i n o u r p r e v i o u s d i m u l a t i o n i s r e a s o n a b l e . F i g u f e 8 shows a t y p i c a l 16-pm p u l s e p L o f i l e o b t a i n e d . F o r an i n j e c t i o n p u l s e o f

l d

MW 9.4-vm i n p u t power, 8 mm d i a . s p o t s i z e , 100 ' n s e c p u l s e w i d t h and a rectangular' p r o f i l e ,

a

16-ym p u l s e o f 25 pJ/pulse/cm 3 e x t r a c t a b l e energy and 4.2 klnl maximum power i s o b t a i n e d w i t h an a c t i v e l e n g t h of 0.1 m.

F i g u r e 8 dhows t h a t t h e second peak a p p e a r 6 & c u t 140 n s e c l a t e r . Because 9.4-vm beam A

forrt!s Gaussian d i s t r i b u t i o n t h e f i k s t peak

t

o f t h e 16-um p u l s e c a n be produced by t h e c a n t e r of t h e beam, and t h e . s e c o n d peak i s

produced by t h e f r i n g e o f t h e beam. B$ i n - j e c t i n g 9r4-um beam wikh uniform i n t e n s i t y

( s u c h a s mulki tfansve2se-mode beam), o n l y t h e s i n g l e peak w i l l a p p e a r . And t h e gas- f l o w v e l o C i t y is 1550

m

sec-'

,

i n d i c a k i l i g t h a t t h e l a s e r i?s t h e o t e t i c a l l y ' a b l e t o op- e r a t e a t &bout 2b0 kHz, ~ h e r e f d r e , t h e av- e r a g e o;tput power o f 4 w/cm3 i s obtdctnabla

(6)

(7)

(8)

9.4 pm INPUT POWER ( KW)

FIG.5. Schematic of t h e energy l e v e l s and t h e

r e a c t i o n s used i n Model [BI

.

FIG.6. The maximum 16-!~m small s i g n a l gain a g a i n s t the 9.4-pm input power.

ihput power pulse wi=dth 1 MW > $ ,

t.

J I 01

0 n ;

W n I

I

no

16 pm Lasing I I 100

200

TIME (

nsec)

FIG.7. Temporal behavior of number d e n s i t y of each v i b r a t i o n a l l e v e l without 16-um o s c i l l a t i o n .

100 200

TIME