EFFICIENCY OF EXCITATION OF ROTATIONAL AND VIBRATIONAL LEVELS IN A NITROGEN MOLECULE

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JOURNAL DE PHYSIQUE CoZZoque C7, suppZ6ment au n07, Tome 4 0 , JuiZZet 1979, wpe C7- 29

EFFICIENCY OF EXCITATION OF ROTATIONAL AND VIBRATIONAL LEVELS IN A MTROGEN MOLECULE

J.I. Londer, L.P. Menahin, K.N. Ulyanov.

AZZ-Union EZectrotechnicaZ I n s t i t u t e , Moscow U.S.S.R.

1 , Energy l o s s e s due t o e x c i t a t i o n o f e l e c t r o n s l e v e l s i n c o l l i s i o n s o f e l e c - t r o n s w i t h molecules may be n e g l e c t e d i n an e l e c t r i c a l ?ischarge i n N2 a t F/N l e s s o r about 4.10'0 V-cm m.3nergy s u p p l i e d t o 2 N2 i s transformed i n t o h e a t through e x c i - t a t i o n and r e l a x a t i o n of r o t a t i o n a l and v i b r a t i o n a l l e v e l s i n molecules, and a l s o through e l a s t i c c o l l i s i o n s o f charged par- t i c l e s w i t h molecules,

If

gv

i s a f r a c t i o n of energy consumed t o e x c i t a t e v i b r a t i o n a l l e v e l s ,

Ze -

t o e x c i t a t e r o t a t i o n a l l e v e l s and

fie

is t h e energy, d i s s i p a t e d through e l a s t i c c o l l i s i o n s , we have following expression:

C h a r a c t e r i s t i c r e l a x a t i o n time f o r v i b r a - t i o n a l l e v e l s i n N2 i s much g r e a t e r than t h a t f o r r o t a t i o n a l l e v e l s . Therefore hea- t i n g of n i t r o g e n t a k e s place i n two ways:

t h e r a p i d way by e l a s t i c c o l l i s i o n s ^{a n d} r o t a t i o n a l r e l a x a t i o n , and t h e slow way due t o v i b r a t i o n a l r e l a x a t i o n .

2 , Experimental d e t e r m i n a t i o n of t h e f r a c t i o n of energy consumed by t h e r a p i d h e a t i n g processes was r e o r t e d i n [2]1vhen E N was v a r i e d from 10-1' t o 4 * 1 0 - ~ ~ ~ * c m ? I n our paper measurements were made when E/R was v a r i e d from t o

loeJ6

V-om. 2

Experiments were performed i n e x t r a pure n i t r o g e n i n :; pulsed d i s c h a r g e , genera- t e d by an e l e c t r o n beam. The dimensions of t h e discharge chamber were 9.4x2.8x2.4 cm3 and a l l measurements r e l a t e d t o a con- s t a n t volume and g a s d e n s i t y . When energy i s absorbed,pressure i n t h e chamber chan- g e s accordingly. P r e s s u r e v a r i a t i o n s were recorded by a f a s t - response t e n s o m e t r i c gaude. Typical o s c i l l o g r a m of a tensomet- r i c s i g n a l i s given i n f i g . 1 . The envelo-

pe shows t h e temporal p r e s s u r e v a r i a t i o n s . Two s e c t i o n s of t h i s curve can be d i s t i n - guished: t h e i n i t i a l s e c t i o n w i t h a s t e e p

slope,which corresponds t o r a p i d r e l a x a - t i o n and a f l a t s e c t i o n , vrhich begins a f - t e r t h e end of t h e pumping p u l s e and which corresponds t o v i b r a t i o n a l r e l a x a - t i o n .

3. Methods o f e s t i m a t i n g t h e energy consumed f o r r a p i d h e a t i n g of n i t r o g e n a r e based on t h e ener<?y conservation l o a f o r g a s e s a t c o n s t a n t d e n s i t y :

Here Bv 5s t h e v i b r a t i o n a l enersy densi- t y , W i s power d e n s i t y absorbed by t h e g a s , i s a d i a b a t i c index. By inte:;rstin;

( 2 ) from 0 t o

rp

^(where

rp

i s t h e pulse d u r a t i o n ) we o b t a i n :

-

U

Here

A P

i s t h e p r e s s u r e increment per pulse. Expression f o r Ev may be w r i t t e n i n followin, form:

Here

, Z,

i s t h e c h a r a c t e r i s t i c r e l a x n t i o n

. .

time r e l a t e d t o v i b r a t i o n a l e n e r , g . If

rp<< rvr ^,

we may o b t a i n by i n t e g r a t i n g (4) :

t ) ( - ; t<$'<qr

^(5,

A f t e r t h e end of t h e pumping p u l s e r a p i d recombination of plasma talces place.Pres- s u r e and temperature v a r i a t i o n s r r i l l be dependent upon r e l a x a t i o n of v i b r a t i o n a l l e v e l s . This process i s d e s c r i b e d by equa- t i o n s ( 2 ) and ( 4 ) vrhere W = 0 . The system of e q u a t i o n s ( 2 ) - ( 5 ) can be reduced t o two e q u a t i o n s f o r

2,

^and ^{T V T}

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979714

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Worn (6) we derive:

Expressions (7)

-

⁽⁹⁾allov? to compute

z,,

,.&f$/ and from the measured

values of

AP

^and

^p' .

Energy input density can be determinated from the mean discharge current and voltage.The cathode drop vrhich has a value 4 2 0 5 5 0 ~ at

P

=380 torr and 550f50V at P =760 torr should be substracted.

In our experiments the value

Wvr

^did

not exceed 1:'0 hence the equations (8) and ( 9 ) may be simplified as follows:

(9a) Fraction of energy absorbed from electrons through elastic collisions is given by:

Here %d is frequency of elastic collisions

-

(per one molecule),

Ge

-mean energy of electrons, -drift velocity of electrons, e- electron charge, m,M-electron and molecule

N

masses respectively. Dependences of

%e,y

and on E/N were taken from [I]

.

^fic-

cording to 3 (10)

zef -

^10%^at^E/IV=IO^-172

V* cn' and

ps8

^eE" 2% at

x/~=Io-'

V

.

cm

.

Pig.2 shows the dependence of

.gv and fc on E/?J, plotted with the use of expressions EL), (9a) and ^(10).In the same f i m r e the experimental data from[2,3] for

f p at hicher values are given. It can be seen that our results are in coo& a&

xeement with [2,3] at x/H=Io-~~ v;cmP.

If B/N decreases,

, ,

decreases markedly and

2%

rapidly increases.

4. A systematical error vrhich has been made in our experiments in the determina-

tion of

2,

,and

gz

is due to presence of a buffer volume in the discharge chamber (-10%) and inaccurate assessment of catho-

de d r o p vnlue(f50~),This inaccuracy leads

to error in the value of

y,,

which is -10% nhe* ~/1=1.5*10-'~ and ~ 1 . 5 % when

~:/N=Io-'~ V. cxn2 at P=380 torr. fit P 1760 torr the error is less. 'Ye consider the accuracy of our results to be N 15%.

iin envelope of signals from the tdnso- metric censor Tias found to be modulated by 2.5 l a x . This oscillations modulation r a s connected with the generation of acoustic oscillations in the resonator,formed by the walls of the discharge chamber.%- timation of fraction of energy consumed by this oscillations, shows that their mean enerej density is less than I O - ~ J / C ~ . 2 This is by 2 or 3 orders less t h m the to- tal energy input density.lherefore the ener$yy of acoustic oscillations in the energy balance was not taken into account.

Methods described above were tested In a mixture C02:B2=1 :3 (P=380 torr) for which the vibrational energy relaxation time is knovm. Tensometric neasurenents of pressur.e variations performed with an accuracy of flO% coincided with those, computed from the energy input density for constant volume conditions.

Fig. 1 Fig. 2

References

I . h. G.Engelhardt

,

A.V.Phelps, C. G.Risk.

Phys.Rev., 135,6A,p. 1566 (1964).

2.8. P.Napartovich,V.G.Naumov,V.fbT. Shashkov D l 3 SSSR v.232 p.570 (1977).

3. R.W.Crompton,D,J,Sutton. Pros. Roy.

Soc.A, v.A215, p.467 (1952).