STUDIES OF PHYSICAL MECHANISMS IN LASER ENHANCED IONIZATION IN FLAMES

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STUDIES OF PHYSICAL MECHANISMS IN LASER ENHANCED IONIZATION IN FLAMES

P. Schenck, J. Travis, G. Turk

To cite this version:

P. Schenck, J. Travis, G. Turk. STUDIES OF PHYSICAL MECHANISMS IN LASER EN- HANCED IONIZATION IN FLAMES. Journal de Physique Colloques, 1983, 44 (C7), pp.C7-75-C7-84.

�10.1051/jphyscol:1983707�. �jpa-00223264�

J O U R N A I DE PHYSIQUE

Colloque C7, supplkment au n O 1 l , Tome 44, novembre 1983 page C7-75

STUDIES OF PHYSICAL MECHANISMS I N LASER ENHANCED IONIZATION I N FLAMES P.K. Schenck, J.C. Travis and G.C. Turk

National Measurement Laboratory, National Bureau o f Standards, Washington, DC 20234, U. S.A.

R6sum6 : Les m6canismes de l ' i o n i s a t i o n augment6e p a r e x c i t a t i o n l a s e r qui aboutissent 2 un i m p o r t a n t d6peuplement l o c a l des atomes n e u t r e s dans l a flam- me, sont pr6sent6s. En plus, c e t t e p e r t u r b a t i o n l o c a l e dans l e t a u x d ' i o n i s a - t i o n de l a flamme p e u t e t r e observge p a r imagerie successive. Deux modGles thgoriques du dgplacement physique des 6 l e c t r o n s e t des i o n s correspondants a u s i g n a l LE1 dans l a flamme sont pr6sentbs a i n s i que l e u r a p p l i c a t i o n 2 des observations expgrimentales.

A b s t r a c t : Laser enhanced i o n i z a t i o n (LEI) mechanisms which r e s u l t i n l o c a l l y l a r g e n e u t r a l atom d e p l e t i o n s i n flames a r e discussed. I n a d d i t i o n , t h i s r e - s u l t s i n a l o c a l l y l a r g e p e r t u r b a t i o n o f t h e i o n i z a t i o n r a t e o f the flame can be observed by an imaging technique. Two t h e o r e t i c a l models o f the p h y s i c a l motion o f t h e LE1 e l e c t r o n s and i o n s i n t h e flame and t h e i r a p p l i c a - b i l i t y t o experimental observations a r e discussed.

I. I n t r o d u c t i o n : Laser enhanced i o n i z a t i o n (LEI) i s understood t o proceed by a sequential process o f o p t i c a l e x c i t a t i o n and thermal i o n i z a t i o n from the l a s e r - populated s t a t e . C a l c u l a t i o n s using measured cross sections f o r o p t i c a l e x c i t a t i o n and c o l l i s i o n a l i o n i z a t i o n i n d i c a t e a v a r i e t y o f c o n d i t i o n s under which n e a r - t o t a l i o n i z a t i o n o f atoms passing through the l a s e r i n t e r a c t i o n zone may be achieved w i t h e i t h e r pulsed o r CW l a s e r s . An independent v e r i f i c a t i o n o f t h i s c a p a b i l i t y has been made u s i n g a b s o r p t i o n experiments t o measure t h e d e p l e t i o n o f n e u t r a l atoms which accompanies n e a r - t o t a l i o n i z a t i o n . Space and t i m e r e s o l v e d s t u d i e s o f t h e depleted atom volume a l s o y i e l d i n f o r m a t i o n about t h e d i f f u s i o n and convection of n e u t r a l atoms i n t h e flame.

The d i f f u s i o n and convection o f laser-produced ions, as we1 l as t h e i r f i e l d - i n d u c e d motion, may be observed by an i o n imaging technique. Results observed w i t h p a r a l l e l p l a t e electrodes and a hydrogenlair flame i l l u s t r a t e t h e dominance o f e l e c t r i c f i e l d e f f e c t s over o t h e r physical mechanisms i n t h e flame. The i o n imaging tech- nique can be used t o study n o t o n l y t h e l o c a l l y h i g h i o n i z a t i o n from LE1 b u t a l s o t h e height-dependence o f t h e background flame i o n i z a t i o n r a t e .

The temporal p r o f i l e s o f LE1 s i g n a l c u r r e n t pulses have been analyzed using a n a l y t i - c a l and numerical t h e o r e t i c a l models. The a n a l y t i c a l p o i n t charge model i s useful f o r d e s c r i b i n g t h e gross f e a t u r e s o f t h e c u r r e n t pulse components due t o the e l e c - t r o n s and i o n s i n a h i g h l y i d e a l i z e d flame environment. The numerical model i n - cludes d i f f u s i v e e f f e c t s , and i s amenable t o more r e a l i s t i c treatments o f flame background c o n d i t i o n s . The l a t t e r model has been used t o generate a "motion p i c - t u r e " i l l u s t r a t i n g t h e s p a t i a l and temporal e v o l u t i o n o f t h e excess i o n and e l e c t r o n charge d i s t r i b u t i o n s f o l l o w i n g t h e i r production by LEI.

11. Neutral Atom Depletion by LEI: LE1 o f an atom A i n a flame takes place by a two step process o f o p t i c a l e x c i t a t i o n by a tunable l a s e r t o an e x c i t e d s t a t e :

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983707

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followed by c o l l i s i o n a l i o n i z a t i o n o f t h e e x c i t e d atoms by the background gases o f the flame:

The l a s e r e x c i t a t i o n described by ( 1 ) competes w i t h quenching, r a d i a t i v e emission, and s t i m u l a t e d emission i n determining t h e f r a c t i o n o f t h e n e u t r a l atoms maintained i n the e x c i t e d s t a t e . With CW l a s e r sources i t i s f a i r l y common t o maintain a few percent o f the atoms i n an e x c i t e d s t a t e i n our t y p i c a l l a b o r a t o r y flames. Using pulsed l a s e r sources t h e o p t i c a l t r a n s i t i o n of (1) can r e a d i l y be s a t u r a t e d so t h a t t h e f r a c t i o n o f atoms i n t h e e x c i t e d s t a t e can t y p i c a l l y be 50 percent ( t h e case f o r equal g - f a c t o r s ) .

With e x c i t e d s t a t e p o p u l a t i o n s ranging from a few t o tens o f percent, i t i s p o s s i b l e t o a l t e r t h e n e u t r a l atom d e n s i t y i f t h e i o n i z a t i o n r a t e o f t h e e x c i t e d atom i n ( 2 ) i s on t h e order o f t h e r e c i p r o c a l l a s e r i n t e r a c t i o n time. The LE1 volume i o n i z a t i o n r a t e o f A i n e l e c t r o n / i o n s produced per cm3 per S can be erpressed as:

where nA* i s t h e c o n c e n t r a t i o n o f species A i n an e x c i t e d s t a t e , and ki i s the e x c i t e d s t a t e i o n i z a t i o n r a t e constant. ki i s expressed i n Arrhenius from [l]:

where ko i s t h e ground s t a t e i o n i z a t i o n r a t e , E i s t h e energy o f the e x c i t e d s t a t e , k i s t h e Boltzman constant, and T i s t h e absolute temperature. Tn our t y p i c a l ex- perimental c o n d i t i o n s o f Na atoms i n a C2H2/air flame, ko = 87 S - ' , kT = 0.215 eV (T = 2500 K), and E(3P) = 2.104 eV. This value o f ko was e x p e r i m e n t a l l y determined and i s much h i g h e r than what gas k i n e t i c c a l c u l a t i o n s o f ko g i v e . T h i s discrepapcy has been explained by Hollander e t a l . [2] and w i l l n o t be discussed here. (ko) can be i n t e r p r e t e d as t h e mean time r e q u i r e d f o r i o n i z a t i o n o f a n e u t r a l atom o f species A i n t h e flame. The Boltzman f a c t o r i n ( 4 ) f o r t h e Na 3P3/, l e v e l i s 1.78 X 104 g i v i n g a mean time t o i o n i z e o f 0.647 ps from t h i s e x c i t e d s t a t e . If the CW l a s e r maintains t h r e e percent o f t h e n e u t r a l sodium atoms i n t h e 3P l e v e l , they w i l l be i o n i z e d w i t h a time constant o f 20 us. I n t h i s b r i e f a n a l y s i s we have neglected recombination and dwell time e f f e c t s . Recornbi~ation is a r e l a t i v e l y slow t h r e e body process w i t h a time orders o f magnitude slower than i o n i z a t i o n . I n our experiments t h e l a s e r was focused t o between 0.1 and 1 mm r e s u l t i n g i n a dwell time o f 10 t o 100 us, comparable t o our estimated time f o r i o n i z a t i o n .

The experimental apparatus t o study LE1 n e u t r a l atom d e p l e t i o n i s shown i n f i g u r e 1.

I t c o n s i s t s o f a modulated pump beam derived from a CW tunable dye l a s e r t o produce the n e u t r a l atom depletion, and a counter-propagating probe beam d e r i v e d from t h e same l a s e r . The probe beam was raster-scanned through t h e flame using r e f r a c t o r p l a t e s mounted on stepper motors. The beam could scan an area about 2 mm by 4 mm w i t h 0.1 mm r e s o l u t i o n . With no pump beam, t h e r e l a t i v e background Na d e n s i t y was measured by a s p i r a t i n g d i s t i l l e d water and then a s o l u t i o n c o n t a i n i n g 20 ppm Na.

Since t h e l a s e r bandwidth was narrow compared t o the Na a b s o r p t i o n i n t h e flame t h e r e l a t i v e number d e n s i t y i s simply:

where I, i s the no-Na probe l a s e r i n t e n s i t y as recorded by the PM tube and I i s t h e t r a n s m i t t e d l a s e r i n t e n s i t y w i t h Na present i n t h e flame. Repeating t h e experiment w i t h the pump beam a l l o w s us t o map o u t t h e d e p l e t i o n o f n e u t r a l Na atoms by LE1 along t h e l i n e - o f - s i g h t o f t h e probe l a s e r i n t h e burner flame.

I n p r a c t i c e , t h e pump l a s e r beam was modulated two d i f f e r e n t ways. I n the f i r s t experiments the l a s e r was chopped a t 2 kHz and phase s e n s i t i v e d e t e c t i o n was used t o m o n i t o r t h e pump beam induced changes i n t h e t r a n s m i t t e d probe beam i n t e n s i t y .

Figure 1. LE1 n e u t r a l atom d e p l e t i o n apparatus. M, m i r r o r ; BS, beam s p l i t t e r ; AOM;

acousto-optic modulator; A, aperature; L, lens; B, burner; Sv and SH are r e f r a c t o r p l a t e s ; F, l i n e f l i t e r ; and PM, p h o t o m u l t i p l i e r tube.

These changes i n absorbance were converted i n t o r e l a t i v e d e p l e t i o n s and a r e shown i n t h e contour p l o t o f f i g u r e 2A. Although the maximum measured n e u t r a l atom d e p l e t i o n was 74 percent, o n l y the lower d e p l e t i o n contours are drawn f o r c l a r i t y . The contour p a t t e r n i s c o n s i s t e n t w i t h d i f f u s i o n from a l i n e source i n a f l o w i n g medium 131. D i f f e r e n c e s can be accounted f o r due t o t h e divergence and r e s i d u a l turbulence o f the flame f l o w o f t h e c a p i l l a r y burner used i n these studies.

A second s e r i e s o f experiments was c a r r i e d o u t w i t h t h e pump l a s e r pulsed on f o r about 20 vs, the estimated mean time t o i o n i z e , a t a p u l s e r a t e o f about 1 kHz. I n these experiments the pump-laser-induced change i n t h e probe beam absorbance was recorded a t each r a s t e r p o i n t w i t h a s i g n a l averager. The r e s u l t o f t h i s was t o o b t a i n the r e l a t i v e n e u t r a l atom d e p l e t i o n a t each p o i n t as a f u n c t i o n o f time r e l a t i v e t o t h e pump l a s e r pulse. The data from t h i s experiment was e q u i v a l e n t t o more than 40,000 absorption measurements made w i t h 0.1 mm s p a t i a l r e s o l u t i o n and 5 vs temporal r e s o l u t i o n . Figure 2B shows d e p l e t i o n contours every 10 vs f o l l o w i n g t h e pump l a s e r e x c i t a t i o n . The n e u t r a l atom d e p l e t i o n , o r hole, can be seen t o d i f f u s e o u t i n t o the background p o p u l a t i o n o f t h e flame and r i s e w i t h t h e flame f l o w v e l o c i t y .

The c y l i n d r i c a l symnetry o f these l i n e - o f - s i g h t experiments allows us t o s o l v e the d i f f u s i o n equaticn:

where N i s the d e n s i t y ( o f t h e h o l e ) and D i s t h e d i f f u s i o n c o e f f i c i e n t , i n two d i - mensions. The r e s u l t i n g s o l u t i o n w i t h a f l o w i n g background i s :

N(x, Y, t ) ^% exp[-(x2 + ( y - ~ t ) ~ / ( w ~ + 4 D t ) l

(w' + 4Dt) ( 7 )

where i s t h e c o n v o l u t i o n o f the Gaussian s p a t i a l widths o f t h e pump and probe beams, and v i s t h e flow v e l o c i t y of t h e flame. An a n a l y s i s o f the centers of the contour p a t t e r n s y i e l d s a flow v e l o c i t y of v = 14 m/s f o r the c a p i l l a r y burner.

The widths o f t h e contours g i v e s an estimate o f the d i f f u s i o n constant of D = 14 cm2/s. The flow v e l o c i t y i s c o n s i s t e n t w i t h t h e burner s i z e , gas f l o w r a t e s , and flame temperature. This k i n d o f a n a l y s i s i s t h e basis f o r a flame f l o w v e l o c i - meter r e p o r t e d elsewhere [4]. The d i f f u s i o n c o e f f i c i e n t i s h i g h e r than r e p o r t e d values 151 and may r e f l e c t t h e r e s i d u a l turbulence, edge e f f e c t s , and f l o w divergence.

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(A) l

^{5 u s e c}

0

IL

^{- 1 0 1}

2: 35 u s e c

1 :

-1 0 1

65 u s e c

- 1 0 l

2F

^{95 u s e c}

l

^{15 u s e c 25 u s e c}

l

^{75 u s e c}

l

^{85 u s e c}

-1 0 1 -1 0 l

2: ₁₀₅ usec 2. . ₁₁₅ u s e c

1. \ c

L--'

Figure 2. Neutral atom d e p l e t i o n contours (1 percent through 10 percent) f o r Na i n a C2H2/air burner. (A) 200 mW l a s e r chopped a t 2 kHz (steady s t a t e ) and ( B ) tjme r e s o l v e d c m t o u r s f o l l o w i n g 20 usec l a s e r pulse.

The n e u t r a l atom d e p l e t i o n by LE1 s t u d i e d here may h e l p i n t h e i n t e r p r e t a t i o n o f e a r l i e r experimental r e s u l t s o f van Di j k e t a l . [6] and Mu1 l e r e t a l .

171.

^{I n}

t h e i r experiments t h e l a s e r induced fluorescence o f sodium was seen t o decrease f a s t e r than the l a s e r pulse i n t e n s i t y d u r i n g a 1 us dye l a s e r pulse. A comparison o f t h e c o l l e c t e d i o n / e l e c t r o n s i g n a l and the measured d e p l e t i o n o f n e u t r a l atoms as w e l l as t h e p e r s i s t e n c e o f LE1 induced d e p l e t i o n f a v o r i o n i z a t i o n over l a s e r induced chemistry as the source o f our observations.

111. I o n i c Imaging i n Flames: As described above, LE1 s i g n a l s r e s u l t from dramatic increases i n the i o n i z a t i o n r a t e o f t h e l a s e r - e x c i t e d atoms. Consistent w i t h t h e observation o f n e u t r a l atom d e p l e t i o n i s t h e observation o f l o c a l increases i n the r a t e o f i o n i z a t i o n i n t h e flame. I n order t o observe t h e laser-induced changes i n flame i o n i z a t i o n rates, t h e t r a d i t i o n a l LE1 spectrometer was m o d i f i e d as shown i n f i g u r e 3A. I n s t e a d o f t a k i n g t h e LE1 s i g n a l from one o f t h e p l a t e electrodes, a l mm tungsten r o d was mounted h o r i z o n t a l l y , j u s t i n s i d e t h e low v o l t a g e e l e c t r o d e , and connected t o t h e e l e c t r o n i c s . Under c o n d i t i o n s o f h i g h enough v o l t a g e the

c u r r e n t drawn through t h e flame s a t u r a t e s [8] and the s a t u r a t i o n c u r r e n t d e n s i t y is (A cm-2) i s given by:

5 10 15 20 25 30 35 40 Height (mm)

Figure 3. (A) Electrode configuration and e l e c t r i c a l connections f o r i o n i z a t i o n imaging. (B) DC-coupled i o n i z a t i o n r a t e image f o r H2/air burner with 1 ppm Na s o l - ution a s p i r a t e d , and 15 mV l a s e r i r r a d i a t i o n a t 589 nm 19 mm above t h e burner.

i s = erd

where e i s t h e charge on t h e e l e c t r o n , r i s the volume i o n i z a t i o n r a t e , and d i s t h e width o f t h e flame. [For ( 8 ) t o be s t r i c t l y v a l i d , the p l a t e s m u s t be i n f i n i t e and t h e flame must f i l l t h e i n t e r - e l e c t r o d e space.] The actual c u r r e n t received by a portion of t h e p l a t e s , i . e . , t h e rod, i s given by i s times t h e r o d ' s l a t e r a l a r e a . I f r i n equation ( 8 ) i s a f u n c t i o n of height i n t h e flame, t h e probe c u r r e n t should manifest t h e v e r t i c a l dependence of t h e i o n i z a t i o n r a t e . Figure 3B shows t h e s a t u r a t i o n c u r r e n t monitored by t h e probe a s a function of height f o r a hydrogen/

a i r flame supported on a s l o t burner head. A 1 ppm s o l u t i o n of Na was a s p i r a t e d i n t o the burner. A -500 V p o t e n t i a l was more than s u f f i c i e n t f o r c u r r e n t s a t u r a t i o n . A weak (c15 mV) CW l a s e r was tuned t o t h e Na 3P,/, t r a n s i t i o n and d i r e c t e d horizon- t a l l y through t h e flame. The ion "image" of t h e excess i o n i z a t i o n i s c l e a r l y v i s i b l e a t about 19 mm above t h e burner head. The normal background i o n i z a t i o n and t h e high i o n i z a t i o n of t h e r e a c t i o n zone a r e a l s o e v i d e n t i n f i g u r e 3B. The width of t h e l a s e r induced i o n i z a t i o n image i s s l i g h t l y wider than t h e convolution of the l a s e r width and probe diameter. When 200 mW of l a s e r power was used t h e LE1 image dominated t h e background, demonstrating t h e a b i l i t y t o l o c a l l y p e r t u r b t h e ion d e n s i t y i n t h e flame. The e f f i c i e n c y of t h e probe i n i n t e r c e p t i n g the l o c a l ioniza- t i o n r a t e was measured t o be >95 percent [g] by monitoring t h e "shadow" of t h e probe on t h e low voltage e l e c t r o d e by taking t h e LE1 signal from t h e low voltage p l a t e .

A t s u b s a t u r a t i o n voltages t h e d i f f u s i o n and convection of t h e l a s e r produced ions were monitored by t h i s technique. An a n a l y s i s [g] of t h i s d a t a i n d i c a t e s t h a t e l e c t r i c f i e l d e f f e c t s a r e more important than d i f f u s i o n , convection, and recombina- t i o n which might be expected t o reduce the LE1 signal s t r e n g t h s .

IV. Temporal P r o f i l e s of LE1 Current Pulses: The p o i n t charge model [ l 0 1 f o r t h e temporal behavior of LE1 c u r r e n t pulses ignores d i f f u s i o n and s e l f-coulombic e f f e c t s o f t h e l a s e r generated ions and e l e c t r o n s . The negative and p o s i t i v e charges a r e assumed t o be p o i n t charges which indeperdently i n t e r a c t with t h e e l e c t r i c f i e l d e s t a b l i s h e d by t h e e l e c t r o d e s . Figure 4 shows t h e e l e c t r o d e geometry used i n t h e one-dimensional point charge model. In a n a l y t i c a l a p p l i c a t i o n s t h e burner most o f t e n supports an C2H2/air flame. The high i n h e r e n t i o n i z a t i o n o f t h i s flame r e s u l t s i n a sub-saturated f i e l d and charge d i s t r i b u t i o n a s described by Lawton and Weinberg [8]. The e l e c t r i c f i e l d i s a maximum a t t h e cathode and f a l l s l i n e a r l y t o zero a t t h e sheath edge a s shown i n f i g u r e

4.

The sheath i s a p o s i t i v e ion space charge due t o t h e low m o b i l i t y of t h e ions. The e l e c t r o n s t r a v e l much f a s t e r than t h e p o s i t i v e i o n s and a l a r g e imbalance i n the number d e n s i t i e s i s required t o

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0 X (cm> W

CATHODE ANODE

Figure 4. Point charge model geometry.

SIGNAL

3-

Figure 5. Point charge model c a l c u l a t e d pulse p r o f i l e s f o r ( A ) e l e c t r o n s and ( B ) ions f o r 2 cm e l e c t r o d e spacing, -1500 V applied p o t e n t i a l , and l a s e r 0.5 cm from cathode.

-

TIME (usec)

I l I

1 0 - -

-

1 -

8.0

510 1d.0 15.0 20.0

TIME (usec) Figure 6. Experimental pulse shape p r o f i l e s under conditions of f i g u r e 5.

e q u a l i z e t h e removal r a t e s o f i o n s and e l e c t r o n s a t s t e a d y s t a t e .

I n t h e p o i n t charge model t h e LE1 c u r r e n t i s o b t a i n e d by c a l c u l a t i n g t h e induced charge on t h e anode b y t h e i o n and e l e c t r o n charges i n t h e flame. The sheath boundary i s t h e e f f e c t i v e anode i n t h i s s i t u a t i o n s.o t h a t t h e induced charge qA i s :

where q+ and q- a r e t h e induced charges f r o m t h e i o n s and e l e c t r o n s r e s p e c t i v e l y . Xg, X- and X+ a r e t h e sheath edge, e l e c t r o n p o s i t i o n , and i o n p o s i t i o n as shown i n f i g u r e 4. The LE1 c u r r e n t i i s o b t a i n e d by d i f f e r e n t i a t i n g e q u a t i o n ( 9 ) w i t h r e s p e c t t o t i m e :

S i n c e t h e e l e c t r o n and i o n v e l o c i t i e s a r e s i m p l y g i v e n by t h e p r o d u c t o f t h e e l e c t r i c f i e l d and a p p r o p r i a t e m o b i l i t y , e q u a t i o n ( 1 0 ) can be s o l v e d a n a l y t i c a l l y f o r t h e s u b s a t u r a t i o n case o f t h e l i n e a r l y d e c r e a s i n g e l e c t r i c f i e l d . The r e s u l t i n g c u r r e n t p u l s e s f r o m t h e e l e c t r o n and i o n a r e shown i n f i g u r e s 5A and 5B. The e l e c t r o n i n - duced c u r r e n t decays e x p o n e n t i a l l y w i t h t i m e as i t reaches t h e sheath edge and zero e l e c t r i c f i e l d . The i o n i n d u c e d c u r r e n t i n c r e a s e s w i t h t i m e as i t approaches t h e cathode and maximum e l e c t r i c f i e l d . A t t h e cathode t h e i o n i s c o l l e c t e d / n e u t r a l i z e d and t h e i o n c u r r e n t d r o p s t o zero. The a r r i v a l t i m e o f t h e i o n can be used t o mea- s u r e i t s m o b i l i t y [Ill.

The inadequacy o f t h i s model i n p r e d i c t i n g t h e measured c u r r e n t p u l s e s , shown i n f i g u r e 6, a r i s e s f r o m i g n o r i n g t h e c o l l e c t i v e b e h a v i o r o f t h e i o n s and e l e c t r o n s , as w e l l as t h e t i m e response o f t h e e l e c t r o n i c s . The a d d i t i o n o f d i f f u s i o n and s e l f - c o u l o m b i c e f f e c t s r e q u i r e s an i t e r a t i v e n u m e r i c a l s o l u t i o n t o t h e c o n t i n u i t y e q u a t i o n s f o r t h e e l e c t r o n and i o n d e n s i t i e s i n t h e flame. The one-dimensional f o r m o f t h e c o n t i n u i t y e q u a t i o n i s :

where

nt

i s t h e i o n / e l e c t r o n d e n s i t y , rc i s t h e volume i o n i z a t i o n r a t e , and a i s t h e r e c o m b i n a t i o n c o e f f i c i e n t . The f l u x i n e q u a t i o n ( 1 1 ) i s g i v e n by:

KiEn,

-

D+dn+/dx - - ( 1 2 )

where K, i s t h e m o b i l i t y , E i s t h e e l e c t r i c f i e l d , and D+ i s t h e d i f f u s i o n c o e f f i - c i e n t . C o n v e c t i o n e f f e c t s a r e i g n o r e d s i n c e t h e y a r e n e g l i g i b l e on t h e t i m e s c a l e o f t h e s e experiments. The e l e c t r i c f i e l d i s c a l c u l a t e d f r o m t h e a p p l i e d p o t e n t i a l and Gauss' law:

-).

where E = I E l i s t h e magnitude o f t h e e l e c t r i c f i e l d . The use o f e q u a t i o n ( 1 3 ) i n t h e i t e r a t i v e s o l u t i o n t a k e s i n t o a c c o u n t s e l f - c o u l o m b i c e f f e c t s .

The i t e r a t i v e s o l u t i o n of ( 1 1 ) - ( 1 3 ) t o o b t a i n t h e L E 1 c u r r e n t p u l s e i s accomplished b y s t a r t i n g w i t h t h e s i m p l e Lawton and Weinberg s o l u t i o n and a l l o w i n g i t t o r e a c h a s t e a d y s t a t e s o l u t i o n . D e t a i l s o f t h i s c a l c u l a t i o n depend on t h e magnitude of t h e a p p l i e d v o l t a g e , e l e c t r o d e spacing, and assumed v a l u e s o f rc, a , e t c . The c a l c u l - a t e d charge d i s t r i b u t i o n s n+(x, t ) and n - ( X , t ) a r e used i n t h e e q u i v a l e n t o f equa- t i o n ( 9 ) t o c a l c u l a t e t h e induced charge on t h e anode, f r o m which t h e LE1 c u r r e n t p u l s e i s o b t a i n e d b y d i f f e r e n t i a t i n g w i t h r e s p e c t t o time. An a l t e r n a t i v e t o t h i s i s t o c a l c u l a t e t h e c u r r e n t d e n s i t i e s f r o m t h e f l u x e s a t t h e e l e c t r o d e s . The v o l t - age drops across any b a l l a s t o r l o a d r e s i s t o r s would have t o be t a k e n i n t o account a1 so.

The p r e - l a s e r e l e c t r o n and i o n d i s t r i b u t i o n s and e l e c t r i c f i e l d a r e shown i n f i g - u r e 7A w i t h a p o s t l a s e r s o l u t i o n shown i n f i g u r e 7B. A t t h i s p o i n t , 25 nsec a f t e r

C7-82 JOURNAL DE PHYSIQUE

15 2 15 2 - 0 nsec (/\) r \ \ 30 nsec [Q) f \

f \ /

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3 <r - \ I - -g

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MO j '.

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0 I—i—i—i—i—i—i—i—i—i—i—UJ—i—i—i / it t—i—i_J 0 0 1—i i i i i ^ ' • • >'^«- • i • i / • ~J - i - i . .1 0

0 10 20 0 10 20 POSITION (mm) POSITION (ram)

Figure 7. Numerical i t e r a t i v e s o l u t i o n f o r the e l e c t r i c f i e l d , ion d e n s i t y , and e l e c t r o n d e n s i t y , (A) before l a s e r p u l s e , (B) 25 nsec a f t e r a 5 nsec l a s e r pulse producing 101 0 i o n / e l e c t r o n p a i r s , a = 10"7s"1cm6, rr = 2 x 101 3s ^ m 3, and V = -1500 V.

1 nsec : 2 nsec : • 3 nsec : • 4 nsec : | 5 nsec :

•\, I I I I "t H, !

.^^-(•/iV t. i ^ n - t - M ' i 11 1•+; i i i r i V-i n i j I-I i t I - M •! F i i i f i \ \ >X> t t-M M - M i; i • • t-i»-t-H N i - M M i i t i 1 i 1; i i i tH^^-Vi i i i i i i 141 i t ;

1 10 nsec : • I 15 nsec : • I 20 nsec \ • 1 25 nsec : ; 1 30 nsec ;

: jy \''\\ ^]> t\ ; ^; "i\ i I k \

\ i t t t y i V i j H I I I ^ I I ; - t - n - t M / i > n i I I I J J I I H i i i i\\ i > r ' i \ i i m » i i - i i ; i m ^ >>-N ' ' i > M i-*\ > t i l U f i I I J W H I M I I ;

1 40 nsec : : | 50 nsec : \ 1 60 nsec : \ I 70 nsec : - I 80 nsec :

:i j | \-'} \) n

• t i t J f W t I I iY+ i i iii i t; •* i t t iyi 4^-< i i i F w r t i n +T i i i i i\i i n i i i i i V i . i ji i i ; i i t r tX \<\ t i i - H ^ Y '⁺- 1 M f i']t 1 f i i t i 1 1 I^M I I ;

\ I 100 nsec ; \ | 150 nsec ; " \ | 200 nsec ; \ i 250 nsec j - \ i 300 nsec ;

1 1 1 1t\ 1 1 i f f n i 1 i\tfi 1 1; 1 n / I \ I 1 1 1 i * i u i y i i 1 1: 1 1 1 f l U < \ \ \ 1 1; 1 1 1 ( i \ J J 1 1 1 i i - f i - i t 1 1; I 1 1 f i \ J^ I f i 4 n 1 r

Figure 8. Iteratively calculated changes in the ion and electron number densities (right scale is -3 x 1 09 to 5 x 1 09 cm"3) for various times. The dashed line is the electric field (left scale 0 to 2200 V/cm). The plate separation is 2 cm. The negative change in the electron density is due to relaxation of the sheath.

the 5 nsec l a s e r pulse, t h e i o n s and e l e c t r o n s a r e w e l l separated and t h e e l e c t r i c f i e l d i s d i s t o r t e d . The sheath edge has a l s o been pushed o u t by the LE1 e l e c t r o n s and ions. The d i f f e r e n c e between t h e pre-laser and p o s t - l a s e r d i s t r i b u t i o n s con- s t i tu t e t h e ac-coupled signal s monitored experimentally. The temporal e v o l u t i o n o f these d i f f e r e n c e s a r e shown i n f i g u r e 8 f o r a s e l e c t i o n o f times. As expected, the e l e c t r i c f i e l d r a p i d l y separates t h e e l e c t r o n s from the ions. The ions o n l y s l o w l y spread o u t and move toward t h e cathode on t h i s time scale. The e l e c t r o n s move r a p i d l y toward t h e sheath edge which has moved o u t from the cathode l e a v i n g a negative d i f f e r e n c e i n the e l e c t r o n d e n s i t y . The "negative d e n s i t y " swallows the e l e c t r o n p u l s e as i t reaches the sheath edge. [This i s c o n s i s t e n t w i t h the use o f t h e sheath edge p o s i t i o n as t h e e f f e c t i v e anode i n equation ( 9 ) o f the p o i n t charge model.] The i o n d i s t r i b u t i o n e v e n t u a l l y reaches the cathode about 10

sec

a f t e r the l a s e r pulse. Since t h e v e l o c i t y o f t h e d i s t r i b u t i o n s a f f e c t s t h e i r c o n t r i b u t i o n t o t h e L E 1 c u r r e n t pulse, i t i s c l e a r t h a t the e l e c t r o n component dominates t h e pulse. The c u r r e n t pulse i s p l o t t e d i n f i g u r e 9 f o r t h e case o f f i g u r e 8.

The one-dimensional model w i t h planar e l e c t r o d e s i s o n l y a crude approximation t o t h e immersed e l e c t r o d e c o n f i g u r a t i o n o f Turk [l

21.

The c y l i n d r i c a l water-cooled

Figure 9. Numer i c a l l

0 50 100 150 200 250 300 TIME _(nsec)

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

0 5 10 15 20

POSITION (mm)

f o r f i g u r e 8.

l ^I

0 100 200 300 400 500 TIME (nsec)

Figure 10. (A) Approximate e l e c t r i c f i e l d from immersed e l e c t r o d e c o n f i g u r a t i o n . (B) Numerically c a l c u l a t e d e l e c t r o n c u r r e n t p u l s e f o r immersed electrode.

C7-84 JOURNAL DE PHYSIQUE

e l e c t r o d e i s immersed i n t h e f l a m e above t h e b u r n e r r e s u l t i n g i n e l e c t r i c f i e l d s [ l 0 1 which a r e p o r e l i k e t h o s e o f a Langmuir probe [8]. F i g u r e 10A shows an a p p r o x i m a t i o n t o t h e measured f i e l d s and 10B i s t h e i t e r a t i v e l y c a l c u l a t e d c u r r e n t p u l s e . O f i n t e r e s t i n f i g u r e 105 i s t h e d o u b l e peak o f t h e c u r r e n t p u l s e due t o t h i s f i e l d . Other causes o f t h i s o f t e n observed double peak may be a m p l i f i e r e f f e c t s [ l 3 1 o r extreme s e l f - c o u l o m b i c e f f e c t s when LEI-induced i o n / e l e c t r o n d i s t r i b u t i o n s dominate t h e e l e c t r i c f i e l d b e h a v i o r .

V. Summary: I n summary, we have s t u d i e d some o f t h e p h y s i c a l mechanisms a s s o c i a t e d w i t h T T h e l o c a l d e p l e t i o n o f n e u t r a l species, o r c o n v e r s e l y t h e l o c a l i n c r e a s e i n i o n s , has been used t o measure f l a m e f l o w v e l o c i t y and d i f f u s i o n c o e f f i c i e n t s . The i o n imaging experiments have h e l p e d t o c o n f i r m t h e i o n i z a t i o n n a t u r e o f t h e o p t o - g a l v a n i c e f f e c t i n f l a m e s as w e l l as v i s u a l i z e t h e l o c a l i o n i z a t i o n r a t e s i n flames.

The t h e o r e t i c a l modeling o f t h e temporal b e h a v i o r o f t h e LE1 c u r r e n t p u l s e s f r o m p u l s e d l a s e r s i s reasonable c o n s i s t e n t w i t h e x p e r i m e n t a l o b s e r v a t i o n .

V I . References

( 1 ) LAWTON J. and WEINBERG F. J., E l e c t r i c a l Aspects o f Combustion, (Clarendon Press, Oxford, 1969) c h a p t e r s two and t h r e e .

( 2 ) HOLLANDER T. J., KALFF P. J., and ALKEMADE C. Th. J., J . Chem. Phys.

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( 3 ) WILSON H. A., Proc. Camb. P h i l . Soc.

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(1904) 406.

( 4 ) SCHENCK P. K., TRAVIS J. C., TURK G. C., and O'HAVER T. C., Appl. Spectrosc 36 (1 952) 168.

( 5 ) ASHTON A. F. and HAYHURST A. N., Trans. Faraday Soc. (1970) 833 ( 6 ) van DIJK C. A. and ALKEMADE C. Th. J., Comb. and Flame

38

(1980) 37.

( 7 ) MULLER C. H. 111, SCHOFIELD K., and STEINBERG M., Chem. Phys. L e t t .

57

(1978) 364;

g

(1979) 2547.

( 8 ) LAWTON J. and WEINBERG F. J., op. c i t . , c h a p t e r s f i v e and e i g h t .

( 9 ) SCHENCK P. K., TRAVIS J. C., TURK G. C., and O'HAVER T. C., J. Phys. Chem.

85

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(10) HAVRILLA G. J., SCHENCK P. K., TRAVIS J . C., and TURK G. C., Anal. Chem. i n p r e s s .

( 1 1 ) MALLARD W. G. and SMYTH K. C . , Comb. and Flame

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( 1 2 ) TURK G. C., Anal. Chem.

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(1981) 1187.

(13) BERTHOUD T . , LIPINSKY J., CAMUS P . , and STEHLE J. L., Anal. Chem.

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