A Simple Collisional-Radiative Model Applicable to Argon Arcjet

Transcription

1 A Smpl Collsonal-Radatv Modl Applcabl to gon cjt IEPC Prsntd at t 33rd Intrnatonal Elctrc Propulson Confrnc, T Gorg Wasngton Unvrsty Wasngton, D.C. USA Octobr 6 10, 013 Su-Rong Sun 1 and Ha-Xng Wang Scool of Astronautcs, jng Unvrsty of Aronautcs and Astronautcs, jng, , Cna Abstract: A smpl collsonal-radatv modl s appld to argon arcjt n ordr to nvstgat t domnant cmcal ractons n t plasma flow. T kntc procsss takn nto account n ts papr nclud spontanous msson, lctron mpact onzaton, tr body rcombnaton, ctaton and dctaton btwn dffrnt ctd lvls, lctron on radatv rcombnaton. T modlng rsults ar t populatons of t varous ctd lvls as a functon of dstanc, and t rlatv contrbutons of dffrnt populatng and dpopulatng procsss for ctd lvls. T man producton and loss procsss dtrmn t ctd argon atoms and ons dnsts ar also prsntd nsd t constrctor and panson porton of t nozzl. J u k = mass dnsty of spcs Nomnclatur = dffuson mass flu dnsty vctor of spcs = mass-avragd vlocty of spcs = undrctonal cmcal rat of cang of f( = lctron nrgy dstrbuton functon = lctron nrgy ( = nlastc collson cross scton n A = numbr dnsts of spcs = cmcal racton rat coffcnt = Enstn coffcnt I. Introducton cjt trustrs av alrady bn succssfully usd for satllt nort-sout staton-kpng for svral dcads [1, ]. In ordr to mprov arcjt ffcncy and tnd t opratng rang, t man pyscal and cmcal kntcs mcansms nsd arcjt sould b amnd n dtal. Du to t small sz of t constrctor and nozzl lngt, t plasma flow nsd arcjt trustr s caractrzd by t trmly g tmpratur and vlocty gradnt. Ovr t past svral dcads, altoug muc ffort as bn dvotd to t dvlopmnt of comprnsv pyscal modls to dscrb t plasma flow nsd arcjt trustr, qustons rman concrnng t plasma racton kntcs faturs of t g vlocty plasma flow wtn arcjt trustrs. In ts papr, a zro-dmnsonal collsonal-radatv modl s proposd to study cmcal ractons n plasmas systm ncountrd n arcjt trustr. T collsonal-radatv modl allows t dntfcaton of t man procsss rsponsbl of t ctd atom concntratons. 1 Graduat Studnt, sunsurong@sa.buaa.du.cn. Profssor, w@buaa.du.cn. 1 Octobr 6 10, 013

2 T classcal approac to collsonal-radatv modls (CR Modl s t quas-statonary stat appromaton ntroducd by ats t al. [3]. Ts modl s basd on t assumpton tat t rlaaton tms of ctd lvls ar ordrs of magntud sortr tan onzaton / rcombnaton ons. In ts condtons t lvl dstrbutons ar statonary wt rspct to lctron and ground stat populaton dnsts, smplfyng t soluton of t problm. Latr, t tm-dpndnt soluton of kntc quatons s dvlopd for stuatons caractrzd by vry sort macroscopc rlaaton tms. Numrous modls [4-7] av bn prsntd for varous atoms calculatng tmdpndnt solutons of collsonal-radatv modls. T ntrst of a tm-dpndnt approac s t possblty to follow t tmporal rlaaton of atomc lvl populatons and tn to study t valdty of t quas-stady-stat ypotss. Tus t collsonal-radatv modl allows for t calculaton of global rat coffcnt: t rat coffcnts of onzaton, rcombnaton or dssocaton. In t prsnt papr, w propos to focus our attnton on t kntcs mcansms nsd arcjt. So t stady stat soluton of ctd stats kntcs as bn laboratd wtout calculatng drctly t tm voluton of t spcs only du to t varous cmcal procsss nvolvd. T plasma flow paramtrs nsd an arcjt (lctron dnsty, lctron tmpratur, prssur and avy partcl tmpratur dstrbutons ar obtand from nonqulbrum modlng of t plasma flow nsd arcjt trustr [8]. T rsults of t kntc procsss av bn prsntd along t nozzl as and radal drcton. II. Caractrstc Tm Scals of Plasma Flow Insd cjt Snc t plasma flow troug t constrctor and nozzl wt a g vlocty, t flud dynamcal tm scals ar comparabl to t cmcal racton tm scals [9, 10]. Hr w compar t typcal cmcal racton tm scals wt tos for convcton and dffuson to analyz t adaptablty of stady stat soluton of CR modl for ts cas. T tm scal for spcs dnsty cangs du to flud panson or contracton s 1 t (1 u T convctv tm scal s dfnd as T tm scal for dffuson of spcs s dfnd as T local cmcal tm scal for t racton k s wr t c t d t k ( u (3 J k (4 s t mass dnsty of spcs, u s t mass-avragd vlocty of spcs, flu dnsty vctor of spcs, k s t undrctonal cmcal rat of cang of. J s t dffuson mass Octobr 6 10, 013

3 Tm (s convctv flud panson dffuson dctaton Aal dstanc (m Fgur 1. Tm scals for dctaton along t constrctor as Fgur 1 sows t tm scals of varous procsss n plasmas along t constrctor as. T tm scals of transport procsss ar sn to b largr tan t tm scals of d-ctaton procss along t as, wr t dctaton racton s lctron mpact mtastabl stat d-ctaton. Trfor, nglctng t ffcts of convctv and dffuson transport on t spcs dstrbuton and cmcal racton procss n CR modl s rasonabl for ts cas. Altoug t dscrpancs may st btwn calculatd and practcal populaton numbr dnsts, t cmcal racton mcansm nsd arcjt can b clarly clarfd. III. Collsonal Radatv Modl T systm studd n ts work s a plasma formd by atomc argon ncludng ground stat and ctd stats (, argon atomc ons (, argon molcular ons (, argon cmr molculs ( and lctrons. W assum tat t plasma s lctrc nutralty. T plasma as bn consdrd optcally tn (poton absorpton and potoonzaton av bn nglctd. T dstrbutons of nrgs of partcls ar assumd Mawllan. A. Elctron Inducd Procsss T lctron nducd procsss nclud lctron mpact ctaton and dctaton procsss, lctron mpact onzaton and tr body rcombnaton procsss. Racton rat coffcnts for lctron nducd procsss ar calculatd from lctron nrgy dstrbuton functons (EEDF usng t quaton: C j Emn f v d wr f rprsnts t EEDF, v t vlocty of t lctron of kntc nrgy and E mn t trsold nrgy of t procss. T prmnt masurmnt of ctaton cross scton as bn usd nstad of tos from t mprcal formula [11, 1]. T rat coffcnts of nvrs procsss ar calculatd by t prncpl of dtald balancng. T domnant ctaton procsss ar takn from t ltratur [13]. t cross scton of t transton btwn atomc lvls and j,. Radatv Rcombnaton Only t transtons stragtforward to t ground stat and t 3p 5 4s lvls ar consdrd n ts study. T radatv rcombnaton procss s nglctd for g lyng ctd stats snc t radatv rcombnaton cross scton dpnds on n wr n s t ffctv quantum numbr [14]. T plasma s assumd to b optcally 3 tn to t contnuum radaton du to rcombnaton procsss. T rcombnaton rat coffcnt to t ground stat s drvd from t ltratur [15]. T radatv rcombnaton cross scton adoptd for otr procsss s gvn n t rfrnc [11]. C. Spontanous Emsson (5 3 Octobr 6 10, 013

4 T rat of radatv dcay s gvn by t Enstn transton probablty, multpld by an scap factor, dscrbng t ffct of radaton trappng. T transton probablts wr adoptd from mor rcnt rsults of Ws t al. [16] as basc data. W assum t scap factors to b qual to 1 (.., 100% scap of radaton, no radaton trappng. D. Inlastc Atom-Atom Collsons For t atom mpact ctaton procsss, t modls rtand by rfrnc [13] ar usd. T racton rat coffcnts of nvrs procsss ar calculatd by t prncpl of dtald balancng. For ground stat atom onzaton procss, t onzaton cross scton masurd by Haugsjaa and Amm [17] s usd. For atom mpact tr body rcombnaton procss, t racton rat coffcnt s takn from t ltratur [18]. E. Otr Procsss Fnally, som addtonal procsss wr ncludd n t modl. Ts procsss nclud pnnng onzaton of argon 1s stats, t tr-body collsonal assocaton to form cmrs and molcular ons, t lctron-mpact dssocaton of cmrs and molcular ons, t atom-collson dssocaton of cmrs and molcular ons, t lctron collsonal rcombnaton for molcular ons. T racton rat coffcnts for cmrs and molcular ons ar takn from t rfrnc [14, 19, 0]. F. Mastr Equaton Takng nto account t dffrnt lmntary procsss mntond abov, t rat quatons for t producton of an ctd atom on t lvl n stady stat can b wrttn as at rc rc ds at ds n n n n A n n n n n n n n n y y n n y y n y n y pnn y, y T rat balanc quaton of n g n n n g y y n n n on y at g y y n pnn, 3 body T rat balanc quaton of n n g n n ds T rat balanc quaton of : n 3body : n n n n n n T lctrcal nutralty of t plasma: n T stat quaton: p n g : y y y A gs n n n 3body g, pnn n n n on at ds n A y y ds n on n n on pnn, g 4 Octobr 6 10, 013 n n n n n pnn, n n g n k T n n k T n k T pnn, n rc gs rc n at ds n pnn, rc A n n on mtamta n n (10 g k T n k T n n k T k T Hr n rfrs to t lctron dnsty, n g s t gas dnsty and t otr subscrpts of n (, y,,, (6 (7 (8 (9 (11 dnot t ctd or onzd partcls. s t racton rat coffcnt and A s t Enstn coffcnt. In ac st of calculatons, T, T and p ar constant.

5 IV. Computatonal Rsults G. Cmcal kntc procsss nsd constrctor Fg. sows t aal profls of argon atom ground stat, argon atom ctd stats, cmrs, argon ons and molcular ons numbr dnsts along t as of t constrctor. It can b sn from ts fgur tat t numbr dnsty of ons s lowr tan tat of ground stat of argon atom wl gr tan t numbr dnsts of otr partcls, and som of ons ar onzd to produc. T numbr dnsts of argon cmrs and molcular ons can b nglctd n t cntr of constrctor. Fgur 3 sows dffrnt onzaton and rcombnaton mcansms along t constrctor as. It s sown tat lctron mpact g lyng ctd stats onzaton s domnant onzaton procss, wl lctron mpact ground stat onzaton procss s wakr tan g lyng ctd stats onzaton. Atom mpact onzaton ractons play a mnor rol n total onzaton mcansms. T domnant rcombnaton procss s lctron mpact tr body rcombnaton to g lyng ctd stats. T radatv rcombnaton and atom mpact tr body rcombnaton procsss av a small nflunc on total rcombnaton mcansms n /g (m (gs (1s (p Ionzaton rat (m - 3 s As dstanc (m Fgur. Aal profls of plasma composton along t constrctor as. (3p (p (1s (1s(1s Rcombnaton rat (m -3 s (3p (p (1s As dstanc (m As dstanc (m (a (b Fgur 3. Aal profls of onzaton (a and rcombnaton (b mcansms along t constrctor as. Fgur 4 sows t aal profl of plasma composton along t nnr wall of constrctor. It s found tat dffrnt from t composton along t as, t argon molcular ons and cmrs play an mportant rol. It sould b notd tat t numbr dnsts of ons ar lowr tan tat of molcular ons. Wt t ncras of tmpratur along t wall, t numbr dnsts of argon ctd stats ncras. Fgur 4 also sows aal profls 5 Octobr 6 10, 013

6 of producton and loss rat of argon cmrs along t constrctor wall. It can b sn tat argon cmrs ar cratd by argon atom tr-body collsonal assocaton procss. caus of t g numbr dnsts of argon atom, t atom-collson dssocaton of cmrs s domnatng loss cannl. Radaton of cmrs also contrbuts to t loss mcansm. Pnnng onzaton of argon cmrs and lctron-mpact onzaton racton av a small nflunc on t loss mcansms. Fgur 5 furtr sows t aal profl of producton and loss rat of molcular ons along t wall. It s sn tat t ons ar manly cratd by atomc ons to molcular ons convrson, wras mtastabl-mtastabl assocatv onzaton and pnnng onzaton of argon cmrs sm to play only a mnor rol at t wall. Loss of ts ons s causd prmarly by t dssocatv rcombnaton to t ground stat, but lctron mpact dssocaton n t plasma plays also a sgnfcant rol, spcally at t downstram of wall. Atom mpact dssocaton procss can b nglctd. n / g (m (1s (p (gs Varaton rat of molcul (m -3 s (1s (1s (gs(1s (1s Producton rat of molcular ons (m -3 s As dstanc (m Aal dstanc (m (a (b Fgur 4. Aal profls of plasma composton (a and producton and loss rat of argon cmrs (b along t constrctor wall (1s(1s (1s Octobr 6 10, 013 As dstanc (m As dstanc (m (a (b Fgur 5. Aal profls of producton (a and loss (b of molcular ons along t constrctor wall. Fgur 6 sows radal profls of plasma composton along t constrctor outlt. T numbr dnsts of atomc ons gradually dcras from t cntr to wall. T numbr dnsts of molcular ons frstly ncras, tn dcras to t wall. Molcular ons bcom mor mportant at t constrctor wall. T ctd stats av t sam trnd bcaus of t dcrasd tmpratur. Fgur 7 sows radal profls of producton and loss procsss of mtastabl stat (1s 5 along t constrctor outlt. T man producton procsss of 1s 5 stat ar lctron mpact p lvls dctaton and lctron mpact rsonanc stat dctaton at t bgnnng of constrctor as, tn atom collson dssocaton of cmrs and atom mpact p lvls dctaton bcom mor and mor mportant at t Loss rat of molcular ons (m -3 s (gs(gs (1s(gs

7 wall. Elctron collsonal rcombnaton for molcular ons plays also an non- nglgbl rol. T man loss procsss ar lctron mpact ctaton to p lvls and rsonanc lvls, tn argon atom tr-body collsonal assocaton racton bcoms t domnatng loss cannl wn approacng t wall. Fgur 8 sows radal profls of producton and loss procsss of rsonanc stat (1s 4 along t constrctor outlt. Elctron mpact p lvls dctaton and lctron mpact ground stat and mtastabl stat ctaton ar t domnatng producton procss at frst, tn atom collson dssocaton of cmrs and lctron mpact ground stat ctaton and atom mpact p lvls dctaton bcom t man producton cannl at t vcnty of wall. T domnatng loss procsss of 1s 4 stat ar lctron mpact ctaton to p lvls at frst, radaton of 1s 4 stat bcoms man loss procss and atom mpact tr-body collsonal assocaton racton plays also a sgnfcant rol nar t constrctor wall n / g (m (1s (p (gs Radal dstanc (10-4 m Fgur 6. Radal profls of plasma composton along t constrctor outlt Producton rat of 1s 5 (m -3 s (1s 5 (p(1s 5 (1s 4 (1s 5 (1s (1s 5 (p(1s 5 (1s 5 (p(1s 5 (1s Loss rat of 1s 5 (m -3 s Radal dstanc (10-4 m Radal dstanc (10-4 m (a (b Fgur 7. Radal profls of producton (a and loss (b of 1s5 stat along t constrctor outlt (1s 5 (1s 5 (p (1s 5 (1s 4 (1s 5 (1s (1s 5 (3p (1s 5 (1s 5 7 Octobr 6 10, 013

8 10 3 Producton rat of 1s 4 (m -3 s (1s 4 (p(1s 4 (1s 5 (1s 4 (1s 3 (1s 4 (p(1s 4 (1s 4 (p(1s 4 (1s Loss rat of 1s 4 (m -3 s Radal dstanc (10-4 m Radal dstanc (10-4 m (a (b Fgur 8. Radal profls of producton (a and loss (b of 1s4 stat along t constrctor outlt (1s 4 (1s 4 (p (1s 4 (1s 5 (1s 4 (1s 3 (1s 4 (1s 4 (1s 4 H. Cmcal kntc procsss nsd panson porton of t nozzl Fgur 9 sows aal profls of plasma composton along arc attacmnt zon. In t frst part of arc attacmnt, t numbr dnsts of molcular ons ar gr tan tat of atomc ons. T numbr dnsts of ctd stats ncras wt lctron tmpratur and t numbr dnsts of mtastabl stat ar t gst n ts rgon. In t last part of arc attacmnt, t numbr dnsts of atomc ons bcom t gst. T numbr dnsts of molcular ons and ctd stats gradually dcras and t numbr dnsts of cmrs can b nglctd. Fgur 10 sows aal profls of onzaton and rcombnaton mcansms along arc attacmnt zon. At t bgnnng of arc attacmnt, lctron mpact ground stat atom onzaton s t domnatng onzaton cannl, wras pnnng onzaton of mtastabl stat as also an mportant nflunc on total onzaton mcansms. Atom mpact trbody rcombnaton s t man rcombnaton cannl, and radatv rcombnaton plays a mnor rol. In t last part of arc attacmnt, lctron collson g lyng ctd stats s t domnatng onzaton mcansm, wras pnnng onzaton of mtastabl stat can b nglctd. Atom collson tr body rcombnaton s stll t man rcombnaton mcansm, but lctron mpact tr body rcombnaton to gly ctd stats bcom mor and mor mportant. Fgur 11 sows aal profls of producton and loss rat of molcular ons along arc attacmnt rgon. At t bgnnng of arc attacmnt, ons ar manly producd by atomc to molcular ons convrson, and anotr mportant producton procss s t mtastabl-mtastabl assocatv onzaton. ons ar manly dstroyd by t lctron mpact dssocaton to produc atomc ons, wras dssocatv rcombnaton also as an nflunc on total loss mcansm. In t last part of arc attacmnt, atomc to molcular ons convrson bcom t most mportant producton procss. Otr producton procsss can b nglctd r. T loss of ons s manly du to t drct lctronc collson dssocaton. 8 Octobr 6 10, 013

9 10 6 (1s n / g (m (p (gs As dstanc (m Fgur 9. Aal profls of plasma composton along arc attacmnt rgon Ionzaton rat (m - 3 s (1s(1s (1s (p (3p Rcombnaton rat (m -3 s As dstanc (m As dstanc (m (a (b Fgur 10. Aal profls of onzaton (a and rcombnaton (b mcansms along arc attacmnt rgon. Producton rat of molcular ons (m -3 s (1s(1s (1s Loss rat of molcular ons (m -3 s (1s (p (3p As dstanc (m As dstanc (m (a (b Fgur 11. Aal profls of producton (a and loss (b of molcular ons along arc attacmnt rgon (gs(gs (1s(gs 9 Octobr 6 10, 013

10 Fgur 1 sows aal profls of plasma composton along t arcjt nozzl as. T numbr dnsts of partcls dcras wt t ncras of aal dstanc. T numbr dnsts of molcular ons and cmrs ar too low to b nglctd. Fgur 13 sows aal profls of producton and loss rat of 1s 5 stat along t arcjt nozzl as. T man producton procsss of 1s 5 stat ar du to lctron mpact p lvls and rsonanc lvls dctaton. Elctron collson tr body rcombnaton and atom mpact p lvls dctaton play also a sgnfcant rol at t frst part. Spontanous msson of p lvls plays an mportant rol narby t wall. T man loss procsss of 1s 5 stat ar lctron mpact ctaton to p lvls and rsonanc lvls. In t upstram of nozzl, lctron mpact ctaton rat s gr tan dctaton rat, and lctron mpact tr body rcombnaton rat s lowr tan onzaton rat. In t downstram of nozzl, lctron mpact dctaton rat s gr tan lctron mpact 1s 5 ctaton rat for p lvls. Mantm lctron mpact tr body rcombnaton rat s gr tan onzaton rat (gs n / g (m (1s (p As dstanc (m Fgur 1. Aal profls of plasma composton along t arcjt nozzl as. Producton rat of 1s 5 (m -3 s (1s 5 (p(1s 5 (1s 4 (1s 5 (1s (1s 5 (1s 5 (p(1s 5 (p(1s Aal dstanc (m Aal dstanc (m (a (b Fgur 13. Aal profls of producton (a and loss (b rat of 1s5 stat along t arcjt nozzl as. Loss rat of 1s 5 (m -3 s (1s 5 (1s 5 (p (1s 5 (1s 4 (1s 5 (1s (1s 5 (3p (1s V. Concluson A smpl argon collsonal radatv modl s appld to prdct t populaton dstrbuton and man kntc procsss n dffrnt parts of arcjt. In t constrctor as t plasma s n an onzd stat. Molcular ons and mtastabl stat play an mportant rol at t constrctor wall. Dffrnt kntc procsss st n t arc attacmnt zon. Atom collson procsss and pnnng onzaton av a sgnfcant rol n t bgnnng of arc attacmnt. In t upstram of panson as, t rat of onzaton and ctaton of mtastabl stat s g du to t g 10 Octobr 6 10, 013

11 lctron tmpratur. T dctaton and rcombnaton procsss of mtastabl stat bcom mor and mor mportant wt t ncras of as dstanc. A complt modl ncludng radaton trappng and transport pnomna s undr study to bttr clarfy t mcansm n arcjt. It s mportant tat t ctd lvl populatons obtand allow for a drct and dtald optcal dagnoss of t prmnt n varous parts nsd t arcjt. A study of t prmntally valuatd populatons n arcjt s ndd to valdat t rsults. Acknowldgmnts Ts work was supportd by t Natonal Natural Scnc Foundaton of Cna. (Grant Nos , , Rfrncs 1 Storm, P. V., Cappll, M. A., LIF Caractrzaton of cjt Nozzl Flows, 3nd AIAA/ASME/SAE/ASEE, Jont Propulson Confrnc and Ebt, AIAA , Lak una Vsta, FL, July, Cappll, M. A., Storm, P. V., Intror Plasma Dagnostcs of cjt Trustrs, Journal of Propulson and Powr, Vol. 1, No. 6, 1996, pp ats, D. R., Kngston, A. E., Mc Wrtr, R. W., Rcombnaton btwn Elctrons and Atomc Ions. I. Optcally Tn Plasmas, Procdngs of t Royal Socty A, Vol. 67, 196, pp Colonna, G., Ptanza L. D., Captll M., Coupld Soluton of A Tm-Dpndnt Collsonal-Radatv Modl and oltzmann Equaton for Atomc Hydrogn Plasmas: Possbl Implcatons wt LIS Plasmas, Spctrocmca Acta Part, Vol. 56, 1997, pp ourdon, A., Vrvsc, P., Tr-ody Rcombnaton Rat of Atomc Ntrogn n Low-Prssur Plasma Flows, Pyscal Rvw E, Vol. 54, No., 1996, pp Lmbaug, C. C., Valdty of t uasstady Stat and Collsonal-Radatv Rcombnaton for Hlum Plasmas. I. Pur Aftrglows, Pyscal Rvw A, Vol. 4, No. 6, Dcmbr 1971, pp Kunc, J. A., Soon, W. H., Collsonal-Radatv Non-qulbrum n Partally Ionzd Atomc Ntrogn, Pyscal Rvw A, Vol. 40, 1989, pp W, F. Z., Wang, H. X., Murpy, A.., Sun, W. P., Lu, Y., Numrcal Modlng of t Nonqulbrum Epanson Procss of gon Plasma c troug A Nozzl, Journal of Pyscs D: Appld Pyscs (submttd. 9 ultl, A., Annaloro, J., Elaboraton of Collsonal-Radatv Modls for Flows Rlatd to Plantary Entrs nto t Eart and Mars Atmosprs, Plasma Sourcs Scnc and Tcnology, Vol., 013, Cang, C. H., Ramsaw, J. D., Numrcal Smulaton of Nonqulbrum Effcts n An gon Plasma Jt, Pyscs of Plasmas, Vol. 1, No. 11, Novmbr 1994, pp Vlck, J., A Collsonal-Radatv Modl Applcabl to gon Dscargs ovr A Wd Rang of Condtons. I: Formulaton and asc Data, Journal of Pyscs D: Appld Pyscs, Vol., 1989, pp ogarts, A., Gjbls, R., Collsonal-Radatv Modl for An gon Glow Dscarg, Journal of Appld Pyscs, Vol. 84, No. 1, July 1998, pp Zu, X. M., Pu, Y. K., A Smpl Collsonal-Radatv Modl for Low-Tmpratur gon Dscargs wt Prssur Rangng from 1 Pa to Atmosprc Prssur: Kntcs of Pascn 1s and p Lvls, Journal of Pyscs D: Appld Pyscs, Vol. 43, 010, pp ultl, A., Ootgm,. Van., ourdon, A., Vrvsc, P., Influnc of n An gon Collsonal-Radatv Modl, Pyscal Rvw E, Vol. 65, 00, pp ond, J. W., Structur of A Sock Front n gon, Pyscal Rvw, Vol. 105, No. 6, Marc 1957, pp Ws, W. L., rault, J. W., Danzmann, K., Hlbg, V., Kock, M., Unfd St of Atomc Transton Probablts for Nutral gon, Pyscal Rvw A, Vol. 39, No. 5, Marc 1989, pp Haugsjaa, P., Amm, R., Ionzaton and Mtastabl Ectaton n Low Enrgy Collsons of Ground Stat gon Atoms, Journal of Cmcal Pyscs, Vol. 5, No. 9, May 1970, pp Dyatko, N. A., Ionk, Y. Z., Koctov, I. V., Marnov, D. L., Mscanov, A. V., Napartovc, A. P., Ptrov, F.., Starostn, S. A., Eprmntal and Tortcal Study of t Transton btwn Dffus and Contractd Forms of t Glow Dscargs n gon, Journal of Pyscs D: Appld Pyscs, Vol. 41, 008, pp Nsr, S., Kunz, T., Langoff, H., A Kntc Modl for t Formaton of Ecmrs, Journal of Pyscs D: Appld Pyscs, Vol. 30, 1997, pp Lam, S. K., Zng, C-E., Lo, D., Dm, yanov, A., Napartovc, A. P., Kntcs of n Hg-Prssur Pur gon, Journal of Pyscs D: Appld Pyscs, Vol. 33, 000, pp Octobr 6 10, 013