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ELECTRON MOLECULE COLLISION
FREQUENCIES FROM BREAKDOWN DATA IN A CROSSED MAGNETIC FIELD FOR ETHANE GAS
A.E.D. Heylen
To cite this version:
A.E.D. Heylen. ELECTRON MOLECULE COLLISION FREQUENCIES FROM BREAKDOWN
DATA IN A CROSSED MAGNETIC FIELD FOR ETHANE GAS. Journal de Physique Colloques,
1979, 40 (C7), pp.C7-143-C7-144. �10.1051/jphyscol:1979770�. �jpa-00219476�
JOURNAL DE PHYSIQUE CoZZoque C7, suppZ6ment au n07, Tome 40, ~ u i Z Z e t 1979, page c7- 143
ELECTRON-MOLECULE COLLISION FREQUENCIES FROM BREAKDOWN DATA
IN
A CROSSED MAGNETIC FIELD FOR ETHANE GASA.E.D. Heylen.
Department of EZectricaZ and EZectronic Engineering, The University of Leeds, Leeds LS2 9JT West Yorkshire.
INTRODUCTION
The author has shown t h a t f o r n i t r o g e n l , argon and hydrogen2, breakdown voltages3 i n a crossed mag- n e t i c f i e l d can be s u c c e s s f u l l y analysed and p r e d i c t e d u s i n g the electron-molecul e c o l 1 is i o n frequencies d e r i v e d from t h e e u i v a l e n t gas pres- sure times gap d i s t a n c e method
9 .
A common f e a t - u r e o f these gases i s t h a t f o r each gas a s i n g l e c o l l i s i o n frequency was adequate t o cover he widea
range o f e q u i v a l e n t reduced e l e c t r i c f i e l d
,
( E / P ) ~ , used. An exception t o t h i s general r u l e i s ethane gas2 f o r which t h e use o f t h e d e r i v e d s i n g l e electron-molecule c o l l i s i o n frequency3 d i d n o t a l l o w good p r e d i c t i o n o f the breakdown charac- t e r i s t i c s . Since then t h e work o f watts5 has revealed c o l l i s i o n frequencies i n ethane d i f f e r e n t from those obtained by Dargan and Heylen3, b u t even t h e use o f an average o f Watt's lower c o l l i s - i o n frequency values d i d n o t produce good agree- ment between theory and experiment.
I t i s thus concluded t h a t i n ethane gas the c o l - l i s i o n frequency i s n o t single-valued, b u t i s a f u n c t i o n o f ( E / P ) ~ , H/p and p o s s i b l y even gas pressure, p . Th-~s i s borne o u t by t h e a n a l y s i s o f breakdown data presented i n t h i s paper.
THEORY AND PROCEDURE
The breakdown v o l a e, VS, i n a crossed magnetic f i e l d i s given byf.9
vs
= B pd seceRn lp(d-a)sece(
+
Rn A Rn(l+l/~H)where A and B a r e the Townsend gas constants, pd i s the gas pressure times gap spacing, 8 i s t h e angle the e l e c t r o n avalanche makes w i t h t h e e l e c - t r i c f i e l d ,
a
i s the gap d i s t a n c e r e q u i r e d f o r t h e e l e c t r o n s t o reach e q u i l i b r i urn energy and yH i s the secondary i o n i z a t i o n c o e f f i c i e n t i n a crossed ma n e t i c f i e l d . I n equation ( I ) , sece i s givenby
4
F -7 1sece =
I
1+
(-~ -
-)J ~ ~ ~ J ~
where e/m i s t h e e l e c t r o n i c charge t o mass r a t i o , vo i s t h e electron-molecule c o l l i s i o n frequency a t 1 t o r r and H/p t h e reduced magnetic f i e l d ; a l s o
where V i i s t h e i o n i z a t i o n p o t e n t i a l o f t h e gas and
i n which yo i s the secondary i o n i z a t i o n c o e f f i c - i e n t i n t h e absence o f a magnetic f i e l d . This l a t t e r formula i s due t o Somervi l l e 6 and has been shown t o apply2.
By rearrangement o f equation ( 1 ) as f o l l a r s an(+
+
-) 1 exp( pd sec8)= A p(d-a) sece ( 5 )YH "s
and u s i n g equations (2) t o ( 4 ) , i t i s p o s s i b l e t o d e r i v e a value o f v o t o f i t t h e experimental break- down data. As no e x p l i c i t expression f o r v i s a v a i l a b l e , a computer s o l u t i o n was used whicR i n v o l v e d a simple search and b i s e c t i o n technique.
The values o f y o were obtained from the breakdown data3 u s i n g equation ( 1 ) w i t h zero magnetic f i e l d . The va ues o f A and
3
B are those obtained by Heylen f o r ethane gas and correspond t o those of propane i n t h i s h i g h E/p range.RESULTS AND DISCUSSION
From the breakdown data f o r ethane gas3 and w i t h the a i d o f equations (1 ) t o ( 5 ) , t h e v o values were obtained as o u t l i n e d above and are shown i n F i g 1. I t i s seen t h a t f o r each gas pressure used, t h e c o l l i s i o n frequency decreases w i t h increase i n (F/p) b u t t h e values do n o t coincide.
Again an unusual Feature o f ethane i s t h a t p a r t i - c u l a r l y a t h i g h (E/p), the c o l l i s i o n frequency a t a given ( E / P ) ~ decreases w i t h increase i n H/p w h i l s t i n o t h e r gases the reverse has been observed8 i n agreement w i t h the theory f o r these gases. T h i s e f f e c t has a l s o been observed i n ethane by watts5 who used a pulsed Townsend technique t o f i n d vo. I n the middle range of (E/p),, i t i s observed t h a t f o r a given ( E / P ) ~ and H/p, where one would expect a s i n g l e value o f vQ, the a c t u a l values o f v o increase w i t h increase i n gas pressure. Although these e f f e c t s a r e d i f - f i c u l t t o account f o r , i t must be remembered t h a t the p r e s e n t method used f o r determining v o values o n l y samples t h e t a i l o f t h e e l e c t r o n energy d i s - t r i b u t i o n f u n c t i o n a t values o f energy above t h e i o n i z a t i o n p o t e n t i a l and small changes i n - t h e o v e r a l l d i s t r i b u t i o n f u n c t i o n have a l a r g e a f f e c t on t h e energy t a i 1.
I t i s g r a t i f y i n g t o see t h a t t h e present v o values tend t o t h e constant value o b t a i n e d by Dargan and Heylen3 a t h i g h gas pressure ( 5 t o 25 t o r r ) and t h a t a t low gas pressure t h e p r e s e n t values e r e i n good agreement w i t h t h e r e c e n t data o f !.latts (1.5 Lo 5 t o r r ) , although h i s values were taken a t H/p ,magnitudes about t e n times l e s s than those o f (Dargan and ~ e y l e n 3 . A feature worth mentioning
i s t h a t v o values obtained i n the r e g i o n o f t h e l e f t hand s i d e of t h e Paschen minimum o f t h e low- e s t t h r e e curves3, were l a r g e and are n o t shown i n F i g 1. This i n d i c a t e s t h a t breakdown data obtained i n t h e apparatus3 are u n r e l i a b l e below t h e Paschen minimum because o f t h e occurence o f l o n g p a t h breakdown.
Using t h e d e r i v e d v o values i n t h e S o m e r v i l l e equation (4), t h e YH values i n t h e presence o f a crossed magnetic f i e l d are shown i n F i g 2. The y~ values a t a given E/p decrease w i t h increase
i n H/p because of t h e i n c r e a s i n g p r o b a b i l i t y o f e l e c t r o n recapture by t h e cathode. A t t h e
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979770
h i g h e s t H/p value used, t h e y value i s reduced by a f a c t o r o f f o u r t e e n times, w l i ch i s s i g n i f i c a n t . However such a l a r g e change i n y has r e l a t i v e l y l i t t l e e f f e c t on the computed vaeues o f v o which, i t has been c a l c u l a t e d , are reduced o n l y by an average o f about 10% a t moderate H/p and 20% a t h i g h H/p when t h e recapture e f f e c t i s n e g l e c t e d i n t h e computation.
CONCLUSIONS
I n ethane gas t h e e l e c t r o n molecule col l i s i o n frequency a t a given e q u i v a l e n t reduced e l e c t r i c f i e l d decreases w i t h increase i n the reduced magnetic f i e l d and i s gas pressure dependent.
Good agreement e x i s t s between present d e r i v e d c o l l i s i o n frequency values and those o b t a i n e d by o t h e r authors.
ACKNOWLEDGEMENT
The author i s i n d e b t e d t o Mr Paul Clark f o r c a r r y i n g o u t t h e computer calculations.;
REFERENCES
1. HEYLEN, A E D, 1978, Proc 5 t h I n t . Conf.
on Gas Discharges, IEE Conf. Publ. No. 165, pp 262-264 .
2. HEYLEN, A E D, 1979, Proc IEE, Feb. 6 p 3. DARGAN, C L, and HEYLEN, A E D, 1968,
Proc IEE,
115,
pp 1034-10444. HEYLEN, A E D, and BUNTING, K A, 1969,
I-
I I I t ~ I I , II n t . J. E l e c t r o n i c s ,
7,
pp 1-12 2 4 (EIP~ 25 . WATTS, 1.1 P, 1977, Fi1.D Tliesis, Z i i i v e r s i t y o f Leeds
6. SOMERVILLE, J N, 1952, Proc Phys SOC,
E,
pp 620-628
FIG 2 Townsend secondary i o n i z a t i o n c o e f f i c i e n t , 7. HEYLEN, A E D, 1975, I n t . J. E l e c t r o n i c s ,
39, ys
function o f the reduced electric f i e l d ,pp 653-660 E7p i n V cm-1 t o r r - 1 , f o r various reduced magnetic
8. H E Y L E N , A E D , a n d D A R G A N , C L , 1 9 7 3 , I n t . J. f - i e l d s t r e n g t h s , H / p i n T e s l a p e r t o r r E l e c t r o n i c s ,
2,
pp 433-451FIG 1 Computed electron-molecule c o l l i s i o n frequency, v o x i n s e c f o r e t h a n e g a s as a f u n c t i o n o f
-
t h e e q u i v a l e n t reduced e l e c t r i c f i e l d (E/p),, i n V cm-1 t o r r - l f o r various reduced magnetic f i e l d , H/p, .in Tesla per t o r r and gas pressures p, i n t o r r . Also shown:t ,
~ a t t s 5 , p = 1.5 t o 5 t o r r ;U--0
