W hile stu d y in g th e electrical conductivity of io n ised a ir, L am b a n d Lin (1957) m ad e th e o b serv atio n t h a t th e io n isatio n r a te w as co n sid erab ly fa s te r b e h in d th e shock w ave th a n h a d b een expected. T he io n isatio n r a te o b se rv e d by P e ts c h e k a n d B y ro n (1957) fo r shock w a v es of
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co m p arab le s tre n g th in argon, w as sev eral o rd ers of m a g n itu d e slow er th a n L am b a n d L in h a d observed; even allow ing for th e difference in th e io n is a tio n p o te n tia ls b e tw e e n th e sp ecies o f a rg o n a n d th o se c o n s titu e n ts of a ir. D u rin g th e ir in v e s tig a tio n , P e ts c h e k a n d B yron em p lo y ed a sh o ck re fle c tio n te c h n iq u e t h a t d e te r m in e d th e local electro n n u m b e r d e n sity by c o rre la tin g i t to th e in te n s ity of th e visible lig h t e m itte d by th e shock h e a te d gas.
N ib le tt a n d B lack m an (1958) trie d to em ploy th e tec h n iq u e of P etsch ek a n d B y ro n to d e te rm in e th e io n is a tio n re la x a tio n tim e b e h in d shock w aves in a ir. A h y d ro m ag n e tic shock tu b e w as em ployed to produce shock w aves w ith M ach n u m b ers from 11 to 17 tra v e llin g in to 133 P a of air. T he a ssu m p tio n w as m ad e t h a t th e lu m in o u s reg io n follow ing th e shock fro n t w as due to p ro cesses in v o lv in g free ele ctro n s. H ow ever, w hile th e v isib le ra d ia tio n in sh o ck -h eated a rg o n is d u e p rim a rily to free -free a n d free -b o u n d c o n tin u u m ra d ia tio n , th e v isib le ra d ia tio n from sh o c k -h e a te d a ir h a s b e e n found to be d u e to m o le c u la r b a n d system s (P en n er, 1959). As p o in ted o u t by L in et al (1962), th e p o in t of o n set of in te n se ra d ia tio n b e h in d th e shock w ave w as m o st likely due to th e a r r iv a l o f th e c o n ta m in a te d d r iv e r g a s fro m th e e le c tric a l d isch arg e, a n d w as n o t due to th e io n isatio n as N ib le tt a n d B lack m an h a d a s s u m e d . T h ese lu m in o s ity m e a s u r e m e n ts , p e rh a p s w ro n g ly in te r p r e te d , w ere re p o rte d as b e in g ab le to d e m o n s tr a te t h a t th e io n is a tio n tim e d e crea se s w ith in c re a sin g M ach n u m b e r.
A m eth o d , b a sed on th e m e a su re m e n t of th e a tte n u a tio n of m icrow aves to d e te rm in e th e electron d e n sities a n d io n isatio n ra te s in shock-heated air, w as em ployed by M a n h eim er-T im n at an d Low (1959). Shock w aves in th e M a c h n u m b e r r a n g e fro m 8.2 to 10.4 fo r a ir; a n d for
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n itro g e n /o x y g e n m ix tu re s (99.75% / 0.25% by v o lum e) in th e M ach n u m b e r ra n g e from 7.4 to 8.8, b o th in p re s s u re s ra n g in g from 0.13 to 1.33 k P a, w ere stu d ied . T he a u th o rs show ed th e re w as good a g re e m e n t b e tw ee n th e e x p e rim e n ta lly d e te rm in e d e le ctro n n u m b e r d e n s ity an d th e o re tic a l calcu latio n s b a se d on a th erm o d y n am ic e q u ilib riu m m odel. E ig h t r e a c tio n s e q u e n c e s w e re c o n s id e re d in t h e i r m o d el, tw o d isso c ia tio n re a c tio n s , one fo rm a tio n re a c tio n ( th a t of N O ) a n d five io n isin g reactio n s. M icrow ave tec h n iq u e s te n d to suffer a fu n d a m e n ta l lim it, n am ely , poor s p a tia l re so lu tio n , w hich is a co n seq u en ce of th e long w av ele n g th s. T h is te n d s to m ak e good s p a tia l re s o lu tio n w ith in th e r e la x a tio n zone d iffic u lt. M a n h e im e r-T im n a t a n d Low h a d a r a t h e r sm a ll (12.7 m m d ia m e te r) t e s t se ctio n a n d a s su c h , th e ir m icrow ave a tte n u a tio n sig n al w as p ro b ab ly re la te d to th e p resen c e of shock w aves in th e w aveguide th a n to an y io n isatio n re la x a tio n b eh in d th e shock w ave in th e te s t section.
L in et a l (1962) u s e d m a g n e tic -in d u c tio n a n d m icro w av e re fle c tio n p robes in a 600 m m d ia m e te r shock tu b e to in v e s tig a te th e io n is a tio n profile b e h in d stro n g shock w aves in a ir w ith M ach n u m b e rs ra n g in g from 14 to 20 a t in itia l p re s s u re s of 2.6 to 26 P a . U sin g te c h n iq u e s sim ila r to th o se u se d by L in & Kivel (1959) a n d M a n h e im e r-T im n a t & Low (1959), th e y o b se rv ed th e p o w er re fle c tio n co efficien t of th e m icrow ave probe in o rd er to deduce th e electro n n u m b e r d e n sity (m ore p re c ise ly , th e e le c tro n d e n s itie s d e d u ce d fro m p ro b e s of d iffe re n t fre q u e n c ie s u n d e r s im ila r e x p e rim e n ta l co n d itio n s w ere co m p ared ). In co njunction w ith th is e x p e rim e n ta l tech n iq u e, L in et al em ployed a m ag n etic-in d u ctio n process sim ila r to th a t u sed by L am b a n d L in (1957) to m e a su re th e electrical conductivity d istrib u tio n b e h in d shock w aves
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in a ir w ith a s p a tia l reso lu tio n com parable to th e effective w id th of th e a p p lie d m a g n e tic field . T h e m a in r e s u lt o f th is w o rk w a s th e o b s e rv a tio n t h a t fo r th e ra n g e of sh o ck s tr e n g th s co v ered (shock v e lo c itie s fro m 4.5 k m s '1 to 7 kms*1), th e io n is a tio n d is ta n c e w as ap p ro x im ately 10 to 40 tim es th e m ea n free p a th of th e u n d is tu rb e d gas a h e a d of th e shock fro n t a n d th a t th e electron n u m b e r d en sity ap p ea re d to o v ershoot th e e q u ilib riu m v alu e, by a facto r of b etw een 2 a n d 3, for som e d is ta n c e b e h in d th e shock fro n t before re la x in g b a c k to w a rd s e q u ilib riu m .
In a c o m p le m e n ta ry p a p e r to t h a t of L in, N e a l a n d Fyfe (1962), an e x te n siv e th e o re tic a l in te r p r e ta tio n w as m ad e o f th e e x p e rim e n ta l re s u lts o b tain ed in th e afo rem en tio n ed w ork by L in a n d T eare (1963). A c ritic a l e x a m in a tio n w a s m a d e of th e v a rio u s io n is in g r e a c tio n sequences. E le ctro n im p a c t a n d ion im p a c t io n isatio n , p h o to io n isatio n , ch arg e exchange, e le ctro n a tta c h m e n t a n d io n is a tio n by n e u tr a l ato m a n d m o lecu lar im p a c t w ere th e io n is a tio n p ro cesses considered. R ate e q u a tio n s w ere d eriv e d for th e s e re a c tio n s a n d solved b y n u m e ric a l in te g ra tio n . S ince th e low io n is a tio n reg im e w as s tu d ie d , L in an d T e a re u se a ‘one-w ay co u p lin g ’ a p p ro x im a tio n b e tw e e n d isso ciatio n , io n is a tio n a n d ra d ia tiv e e x cita tio n . O ne-w ay co u p lin g re fe rs to th e tech n iq u e w h ereb y th e te m p e ra tu re , d e n sity a n d species co n cen tratio n s a re i n itia lly c a lc u la te d in d e p e n d e n t of io n is a tio n a n d r a d ia tiv e e x citatio n , a n d th e n u se d to d e te rm in e th e r a te s for th e s e processes. U pon n u m e ric a l in te g ra tio n , th e y produced, as a fu n ctio n of d istan c e b e h in d th e shock fro n t, a n in s ta n ta n e o u s electron p ro d u ctio n r a te plus electron a n d positive ion d en sities. As a re su lt, a d e ta ile d b reak d o w n of specific io n is a tio n r a t e s for th e v a rio u s io n is a tio n p ro c e sse s w as
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com piled. T he d o m in a n t io n isa tio n reactio n s in th e ir a n aly sis w ere th e a to m -a to m re a c tio n s follow ed by p h o to io n is a tio n , e le c tro n -im p a c t, a to m -m o le c u le a n d m o le c u le -m o le c u le c o llis io n a l io n is a tio n ; th e im p o rtan c e of each re a c tio n b ein g a fu n ctio n of shock velocity. L in an d T eare stre s s e d t h a t th e electro n im p a ct reactio n s c o n trib u te little to the io n isa tio n a t shock velocities below a b o u t 5 kms*1 b u t m ay becom e th e d o m in a n t io n is in g re a c tio n a t v elo cities g r e a te r t h a t 9 kins*1. The d o m in a n t ato m -ato m process in th e low velocity reg im e w as considered to be th e associative io n isatio n reactio n
N + O <=» N O + + e~. ...(R l)
T he n e t en erg y re q u ire d for th is io n isin g re a c tio n is c o n sid erab ly less th a n th e full io n isatio n p o te n tia l of NO, as chem ical en erg y is rele ased by th e a sso c ia tio n of th e N a n d O. O n c o m p a rin g th e ir th e o re tic a l m odel w ith th e e x p e rim e n ts of L in et a l, L in a n d T e a re d e m o n s tra te d