Figure 1 .- Setup for solar-simulator-pumped laser experiment. The photon flux on ..... R + I + R I. 1 + 1 + 1 2. R + R I + R 2 + 1. R + I* +- R I. I* + I. R I + R I + R2 +.
NASA Technical
. .. .
.
-i
Paper
2241 February 1984
Threshold Kinetics of a Solar-Simulator-Pumped Iodine Laser John W. Wilson, Yeungg-rl Lee, Willard R. Weaver, Donald H. Humes, and Ja H. Lee LO7AN COPY: RETURN TO AFWL TECHNICAL LIBRARY KIRTLAND AFB, N.li4. 87117
NASA Technical Paper 2241 1984
Threshold Kinetics of a Solar-Simulator-Pumped Iodine Laser John W. Wilson Langley Research Center Hampton, Virginia
Yeunggd Lee Hampton Institute Hampton,Virginia
Willard R. Weaver and Donald H. Humes Langley Research Center Hampton, Virginia
Ja H. Lee Vanderbilt University Nashville,Tennessee
National Aeronautics and Space Admtnistration
Scientific and Technical Information Branch
.............................................. ........................................................ ..................................................... .............................................................. ............................................................
ENERGY LEVELS AND REACTION PRODUCTS
Molecular Fragmentation Photodissociation Products P r i m a r yR e a c t i o n s Secondary R e a c t i o n s
Reaction Rate f o r R
+
R + R2
for R
+
I += R I
Reaction R a t e f o r I
+
I + I2
Reaction R a t e f o r R
+
R I + R2
for R
+
I* + R I
R e a c t i o nR a t e
R e a c t i o nR a t e
................................................... ................................................... ................................................... + .............................................. .................................................. I
....................................................... Reaction R a t e f o r R I + R I R2 + ............................................ Reaction R a t e f o r + .................................................. Reaction R a t e f o r R + R I R2 + ............................................. Reaction R a t e f o r + R I R I ; ................................................ ........................................................... O t h e rR e a c t i o nR a t e s ............................... SPECTRUM AND G A I NC O E F F I C I E N TO FM E T A S T A B L EI O D I N E B r o a d e n i n g of S p e c t r a l L i n e s ................................................... Reaction R a t e f o r I* + I
+
I*
I + I2 +
I*
G a i n a n dS t i m u l a t e d
P H O T O L Y S I SO F
I2
I*
+
E m i s s i o nC r o s s
ALKYL I O D I D E S
Section
.....................................
......................................................
iii
7 8 9 10
13
14
15 15 15 16 16 17 17 17 17 18 18 20 22
25
INTRODUCTION The atomic i o d i n e laser based o n t h e p h o t o d i s s o c i a t i o n of a l k y l i o d i d e g a s e s w a s among t h e f i r s t p r o p o s e d f o r d i r e c t solar-to-laser e n e r g y c o n v e r s i o n i n space (ref. 1 ) The f i r s t s o l a r - s i m u l a t o r d e m o n s t r a t i o n b e i n g a c h i e v e d (ref. 2 ) , more a t t e n t i o n i s now g i v e n t o s y s t e m r e q u i r e m e n t s o f c h e m i c a l r e v e r s i b i l i t y a n d l a s a n t r e p r o c e s s i n g i n s c a l i n g t o l a r g e space systems. Such a s c a l i n g r e q u i r e s a n a d e q u a t e processes p r e s e n t i n t h e g a s d u r i n g laser o p e r a t i o n knowledgeofthechemical a p r e l i m i n a r yc h e m i c a lk i n e t i cm o d e l is presented ( r e f .3 ) . The developmentof comparison t o s o l a r s i m u l a t o r e x p e r i m e n t s ( r e f . 4). e l s e w h e r ew i t hl i m i t e d
.
I t w a s shown i n a p r e v i o u s r e p o r t ( r e f . 4 ) t h a t t h e laser o u t p u t c o n s i s t s o f a transientpulseregionfollowed by a c o n t i n u o u s wave ( c w ) r e g i o n i n w h i c h t h e laser power o u t p u t i s p r o p o r t i o n a l t o t h e power absorbed. A t l a t e times, t h e cw r e g i o n i s terminated as a result of quenching by t h e i o d i n e m o l e c u l e w h i c h f o r m e d t h r o u g h three-bodycollisionof t w o ground-stateiodineatomswithanalkyliodidemolecule. The I 2 f o r m a t i o n c r i t i c a l l y d e p e n d s o n t h e r e a c t i o n rates o ft h ea l k y li o d i d e recombination
R
+
I +RI
andthree-bodyformation
of I 2 a s
where R d e n o t e st h ea l k y lr a d i c a l . I t was d e t e r m i n e d( r e f . 4 ) t h a t some of t h e r a t e constants for these reactions in the literature a r e n o tc o m p a t i b l ew i t hL a n g l e y experiments. Inthepresent report, t h e k i n e t i c f a c t o r s i n v o l v e d i n r e a c h i n g laser t h r e s h o l d a r e e x a m i n e d .I np a r t i c u l a r ,t h ee f f e c t so fg a sd i f f u s i o n ,h y p e r f i n es p l i t t i n g ,a n d gain length scaling are t r e a t e d i n d e t a i l .
SOLAR S IMULATOR
The s o l a r - s i m u l a t o r l i g h t s o u r c e i s a n a r c d i s c h a r g e a c r o s s a n 8-mm g a p s t a b i The l i g h t o u t p u t i s r e f l e c t e d by a h i g h l i z e d by a 1030-kPa (10.2-atm) X e f l o w . q u a l i t y e l l i p t i c a l reflector and focused in the chopper plane as shown i n f i g u r e 1 . The r e f l e c t o r h a s a v a p o r - d e p o s i t e d aluminum f r o n t s u r f a c e p r o t e c t e d by a MgF2 coati n g t o p r e v e n ts u r f a c eo x i d a t i o na n da b r a s i o n . !&e s p e c t r a l c o n t e n t of t h e a r c plasma o u t p u t c o r r e s p o n d s t o b l a c k b o d y e m i s s i o n a t 6000 K a t t h e f o c u s of t h e e l l i p tical reflector. The d i v e r g e n t l i g h t beam l e a v i n g t h e f o c u s i s c o l l e c t e d by a 7075 aluminum a l l o y 25O c o n e w i t h a p o l i s h e d i n t e r i o r s u r f a c e a n d MgF2 c o a t i n g . me l i g h t beam i s a g a i n f o c u s e d o n t h e c o n e a x i s , w h i c h is aligned with the optical a x i s of t h es y s t e m . Three d i f f e r e n t c o n e s i z e s were u s e d t o g a i n s c a l i n g i n f o r m a t i o n f o r m o d e lt e s t i n g .
50 k W
Solar Sirnulalor
Exposed Region Laser Tube
I-cl Mirror
Detector
ical Coll ector
Figure 1
.-
Setup for solar-simulator-pumped
The p h o t o nf l u xo n the w a v e l e n g t hi n t e r v a lb e t w e e n b l a c k b o d yr a d i a t o r a t a temperature T is
4 exp(hc/UtT) h
i s t h ev e l o c i t yo fl i g h t , The e x p o n e n t i a la r g u m e n t
where c constant.
A
and
A
+
dh
e m i t t e d by a
dh
2m
=
l a s e r experiment.
1
h i s P l a n c k ' cs o n s t a n t , i s g i v e n as
and
k
i s Boltzmann's
hc 1.44 " khT -
hT
f o r h i nc e n t i m e t e r sa n d T i nk e l v i n . The l i g h t i s r e f l e c t e df r o mt h ec o n i c optical c o l l e c t o r w i t h a r e f l e c t a n c e R h a t e a c hw a v e l e n g t hb e f o r er e a c h i n gt h e axis. The l i g h t i n t e n s i t y a t t h e o p t i c a l a x i s i s r e l a t e d t o t h e g e o m e t r yo ft h e arc p l a s m aa n dt h er e f l e c t o ra n d c o l l e c t o r s u r f a c e s ,d e n o t e d by t h e f u n c t i o n M ( r , R ) , as
1 (r,R) d h = M ( r , R )
h
where
E
me
h
R E
h h
@ ( A ) dh
i s t hpe h o t o enn e r g y .
l i g h t i n t e n s i t y i s measured by a calorimeter a n d r e p r e s e n t e d
[ (:: $1
C ( r , R ) = CA exp -2.77
2
(31
-+-
by
where CA i s t h ep e a ki n t e n s i t yo ft h e arc image, L i s t h ef u l ll e n g t h a t half maximum l i g h t i n t e n s i t y a l o n g t h e t u b e a x i s , R is t h ef u l lw i d t h a t h a l f maximum t o t h et u b ea x i s , R i s t h ed i s t a n c ea l o n gt h et u b ea x i s , l i g h ti n t e n s i t yt r a n s v e r s e The s i z e of t h e a r c imagedependsonthe and r i s t h ed i s t a n c e from t h et u b ea x i s . s i z e of t h ec o n e c o l l e c t o r a n d i t s d i s t a n c ef r o mt h ef o c u s . It i s c l e a r t h a t
calorimeter d a t a .S i n c em o s to ft h e t o be d e t e r m i n e df r o mt h e which a l l m s M ( r , R ) energy i s i n t h e v i s i b l e r e g i o nw h e r e R h i s n e a r l yc o n s t a n t ,e q u a t i o n ( 5 ) may be w r i t t e n w i t h t h e h e l p of e q u a t i o n ( 4 ) a s
where R h i s r e p l a c e d by t h ec o n s t a n t R V i S , s i n c em a i n l yv i s i b l er a d i a t i o nc o n t r i b u t e st ot h ec a l o r i m e t e rm e a s u r e m e n t s .E x p r e s s i n gt h en u m e r a t o ra n dd e n o m i n a t o ri n u n i t s of t h e s o l a r c o n s t a n t y i e l d s
C 0 e x p [-2.77(I2/L2
M(r,R) =
~
_"
"___
R
+
r2/R2)]
v is
where i t i s f o u n d f r o m t h e c a l o r i m e t e r d a t a t h a t
co -
L =
R =
2.72
+
(1
(4
+
X
lo4
0.375m)
1.5m)(m 8
2
+
5)
2.192 + 0.824111 5 + m
and m i s a p a r a m e t e ra s s o c i a t e dw i t ht h e d i f f e r e n ta p e r t u r e s . (See t a b l e I. 1
s c a l e of t h e t h r e e
c o l l e c t o r c o n e sw i t h
3
TABLE I.- SCALE PARWTERS FOR COLLECTOR
Aperture diameter,
cm
D i s t a n c ef r o m
focus, c m
m
CONES
L, cm
CO
solar constants
R,
mm ~~
9.6 16.6 23.6
7.0 15.2 24.5
0.5 2.0 2.5
3.2719288 6.1 3 7.27
8 881 7 245 ~~
4.73 5.49 5.67
. . .
A comparisonbetweenmeasurementsofintensityalongthe optical axis and the i s shown i n f i g u r e 2. m o d e lf u n c t i o n of e q u a t i o n ( 4 ) i n u n i t s o f t h e s o l a r c o n s t a n t Measurements i n t h e r a d i a l d i r e c t i o n f o r t h e c o n e w i t h a n a p e r t u r e d i a m e t e r o f 16.6 c m a t a l o c a t i o n 3 c m a l o n g t h e o p t i c a l a x i s f r o m t h e p e a k i n t e n s i t y a r e shown i n f i g u r e 3 i n c o m p a r i s o nw i t h a t h e o r e t i c a l c u r v e b a s e d o n e q u a t i o n ( 4 ) .
Distance, cm
F i g u r e 2.- I l l u m i n a t i o n o n a x i s o f l a s e r t u b e as a f u n c t i o n o f d i s t a n c e i s b a s e do ne q u a t i o n( 4 )a n d t a b l e I. Dots b e h i n dc o n ef a c e .C u r v e a r e experimentalmeasurements of A p r i l 13,1981 ( a p e r t u r e w i t h 9.6-cm a r e e x p e r i m e n t a lm e a s u r e m e n t so fJ u l y 30, 1981 d i a m e t e r ) .T r i a n g l e s ( a p e r t u r ew i t h 16.6-cm d i a m e t e r ) .S q u a r e s a r e experimentalmeasurements o f March 25,1981 ( a p e r t u r ew i t h 23.6-cm d i a m e t e r ) .
4
-1
0
r, c m Figure 3.- Illumination as a functionofdistancefromconeaxis ( 1 6 . 6 - c m - d i a m e t e ra p e r t u r e ) .C u r v e i s b a s e do ne q u a t i o n (4) a n d t a b l e I. Dots a r e e x p e r i m e n t a lm e a s u r e m e n t so fJ u l y 30, 1981.
A l t h o u g h t h e lamp i n t e n s i t y i s p r e s e n t e d a s a s t a t i c q u a n t i t y , t h e r e a r e , i n f a c t , a number o f p o o r l y u n d e r s t o o d f a c t o r s t h a t a f f e c t t h e i l l u m i n a t i o n o f t h e c e n t r a l r e g i o no ft h e c o l l e c t o r cone.Becausethe lamp e l e c t r o d e s a r e m e c h a n i c a l l yh e l d i n p l a c e , s l o w e r o s i o n w i l l w i d e nt h eg a pa n dc a u s e a less l o c a l i z e d arc. The installation of new lamps w i l l n o t restore t h e m a c h i n e t o i t s i n i t i a l o p e r a t i o n becauseof lamp d i f f e r e n c e s .I na d d i t i o n ,t h e r e a r e unknown f a c t o r sc a u s i n gd a y - t o d a yv a r i a t i o n si nt h em e a s u r e di l l u m i n a t i o n .A s i d ef r o mt h e s el o n g - t e r mv a r i a t i o n s , t h e r e are small t e m p o r a l f l u c t u a t i o n s i n t h e a r c plasma w h i c h c a u s e l a r g e s p a t i a l movements i n t h e a r c i m a g eb e c a u s eo ft h el a r g em a g n i f i c a t i o nf a c t o r s .T h i sp r o d u c e s l a s e r e x p e r i m e n t s ,s i n c et h ei n s t a n t a n e o u s some d i f f i c u l t y i n i n t e r p r e t a t i o n o f t h e pump power i s g e n e r a l l y less t h a n i t s maximum. Onlyby c o n s i d e r i n g many e x p e r i m e n t a l runscantheidealexperimentalresult(that i s , r e s u l t c o r r e s p o n d i n g t o maximumpump power) be i d e n t i f i e d .
The l i g h t i s r e f l e c t e d by t h e c o n i c c o l l e c t o r a n d c o n c e n t r a t e d o n t h e c o n e a x i s w i t hi n t e n s i t yg i v e n by e q u a t i o n ( 3 ) . The l a s e r t u b e i s c e n t e r e d o n t h e c o n e a x i s f o r which the peak light intensity crosses t h e t u b e w a l l a t a n a n q l e o f 46O b e f o r e r e a c h i n gt h el a s a n tg a s .( S e ef i g . 4.) The r e f l e c t i o n loss a t t h et u b ei n t e r f a c e s i s R 3 0.08, a n dt h et r a n s m i s s i o nt h r o u g ht h e I-mm q u a r t zt u b e i s n e a ru n i t y . The t a t t e n u a t i o n of t h e l i g h t i n p a s s i n g t h r o u g h t h e f i l l i n g g a s t o t h e laser tube centerl i n e is
G2 ( x ) = exp[-n o ( h ) x ] R t M ( O , R ) h
Rh @ ( h )d h
(1 1 )
5
I~
laser tub-e
F i g u r e 4.-
Typical light ray reflected into
l a s e r tube.
i s t h es p e c i f i cp h o t o a b s o r p t i o nc r o s ss e c t i o nw i t hp e a k cross s e c t i o n ao, l i n e c e n t e r A,, a n dl i n ew i d t h 6, g i v e ni n t a b l e I1 a c c o r d i n g t o r e f e r e n c e s 5 t o 7. of the photons absorbed in the spectral region of equation (1 2), the absorbing molecules a r e fragmented t oy i e l da t o m i ci o d i n e . The t w o a l k y li o d i d e sa n dp h o t o d i s s o c i a t e @I* o fm e t a s t a b l ei o d i n ew i t hv a l u e so f1 0 0p e r c e n ta n d 51 p e r c e n t , i n t of r a c t i o n s r e s p e c t i v e l y .( S e et a b l e
11. )
TABLE 11.- PHOTOABSORPTION PARAMETERS USED FOR ONE SOLAR CONSTANT EXPOSURE,
n-C3F71 ( r e f .5 )
Parameter
.
........ h . ......... ......... al* ............ ....... ....... f .............. a
0
cm2
I2 ( r e f .7 )
"
7.9
10-19
X
6.2
10-19
X
9.14
10-19
X
nm
272
275
nm
12.7
14.5
23.0
1.0
1.0
0.51
S , sec-1
Rho/Rvis
6
i-C3F71 (ref. 6)
~~~
0
?j0,
THE EQUIVALENT POWER OF 1.4 kW/rn2
3.04
X
10-3
3.37
X
10-3
499
3.38
X
0.8
0.8
1 .o
0.652
0.653
0.673
The r a t e a t which
I*
i s formed i n t h e laser t u b e i s
(1 3)
w i t hG a u s s - H e r m i t eq u a d r a t u r e
which i s e v a l u a t e dt h r o u g ha p p r o x i m a t i o n yie Ids
c(r,R)
= 26 @
I*
0
+
no R R M(r,R) 0 t ho
2.95[@(h
0
E q u a t i o n ( 1 4 ) maynow
+
2.456
0
)
(1.18
(ref. 8 ) a n d
@ ( A o ) exp(-noox)
+ @(A 0 -
2.456
0
)]
exp(-0.223no x ) }
(1 4)
0
be s i m p l i f i e d as
R R
S(r,R)
=
ho R
~
v is
S n [ fe x p ( - n ox )
0
+
(1
- f ) exp(-0.223no 0 x ) ]
C(r,R)
(1 5)
where S (maximum p h o t o d i s s o c i a t i o n r a t e ) and f ( f r a c t i o n a al b s o r p t i o nn e a rl i n e c e n t e r ) are g i v e ni nt a b l e 11. The u s e f u l n e s so ft h e Hermite q u a d r a t u r e i s demons t r a t e d i n f i g u r e 5 w h e r e e q u a t i o n ( 1 5 ) i s compared w i t h a n a c c u r a t e n u m e r i c a l e v a l u (1 3) and the usual exponential approximation. ation of equation
ENERGY LEVELS AND REACTION PRODUCTS
There a r e s e v e r a l c h e m i c a , l / p h y s i c a l p r o c e s s e s i m p o r t a n t t o t h e f o r m a t i o n a n d loss o fe x c i t e di o d i n e . Several r e q u i r e m e n t sm u s t be m e t i n o r d e r t h a t s p e c i f i c r e a c t i o n s may o c c u r . The f i r s t s u c h r e q u i r e m e n t is t h a tt h ec h a n g ei ni n t e r n a l energy. e n e r g y be less t h a n o r o n t h e o r d e r o f t h e a v e r a g e t h e r m a l
7
no x 0
F i g u r e 5.-
R e l a t i v e a t t e n u a t i o n of l i g h t a s a f u n c t i o n of p e n e t r a t i o n i n t ol a s a n tg a s (n-C3F71)-
MolecularFragmentation The approximate b o n d e n e r g i e s of t h e a l k y l i o d i d e c o n s t i t u e n t s a r e g i v e n i n t a b l e 111. These e n e r g i e s a r e mean molecular v a l u e s compiled by Huheey ( r e f . 9 ) .
TABLE 111.- SINGLE- AND DOUBLE-BOND ENERGIES AND DISTANCES OF ALKYL I O D I D E CONSTITUENTS [From r e f . 91
. .
Bond .. -
8
~-
Bond e n e r g y I eV DO I
Bond d i s t a n c e rl pm
c-c
3.58
154
C
