Mean absorption coefficients of air plasmas

Transcription

1 Jounal of Physcs: Confeence Sees Mean absopton coeffcents of a plasmas o cte ths atcle: N Bogatyeva et al 0 J. Phys.: Conf. Se Vew the atcle onlne fo upates an enhancements. Relate content - Raatve emsson fom a themal plasmas wth vapou of Cu o W V Aubecht M Batlova an O Coufal - Mean absopton coeffcents of He/A/N/(Cxy Nx Coy) themal plasmas fo CN synthess D Salem R Hannach Y Cessault et al. - Net emsson coeffcent of CO -Cu themal plasmas: ole of coppe an molecules. Blloux Y Cessault V F Boetsj et al. Recent ctatons - Enegy tanspot of lase-ven movng optcal schage n a Chen Chen et al - Raatve popetes an aatve tansfe n hgh pessue themal a plasmas B Peyou et al hs content was ownloae fom P aess on 3//08 at :00

2 th Euopean Confeence on Hgh-echnology Plasma Pocesses (HPP ) Jounal of Physcs: Confeence Sees 75 (0) 0009 o:0.088/ /75//0009 Mean absopton coeffcents of a plasmas N Bogatyeva M Batlova an V Aubecht Bno Unvesty of echnology Faculty of Electcal Engneeng an Communcatons echnca Bno Czech Republc E-mal: batlova@feec.vutb.cz Abstact. Mean absopton coeffcents of a (both Planc an Rosselan mean) have been compute fo ffeent splttng poceues of the whole fequency nteval (0 3 6x0 5 s - ) an vaous tempeatues ( K). Results have been compae an scusse to fn the optmal values of mean absopton coeffcents fo the multgoup metho of soluton of the equaton of aaton tansfe.. ntoucton he popagaton of aaton though plasma s an ntegal pat of the escpton of the plasma. n the escpton of aaton tansfe mathematcal moelng s of geat mpotance. Howeve the nonlneaty of the equatons escbng the aaton fel an the stong epenence of the paametes an coeffcents on the aaton fequency maes mathematcal plasma moels vey complcate. heefoe vaous appoxmate methos ae use (metho of net emsson coeffcent [-3] metho of patal chaactestcs [4 5]). One of the poceues fo hanlng the fequency epenence of the coeffcents n the equaton of tansfe s the multgoup metho whch assgns a gven photon to one of G fequency goups. All photons wthn a gven goup ae teate n the same way assgnng aveage popetes such as the absopton coeffcent to that goup. n pactce the aveage absopton coeffcent s geneally taen as ethe a goup Rosselan o goup Planc mean (epenng on the absopton popetes of the meum fo the gven fequency goup). n ths pape attenton has been gven to the absopton popetes of a at the pessue of atm an n the tempeatue ange ( K). Both Rosselan an Planc aveages have been compute fo ffeent splttng poceues of the whole fequency nteval (0 3-6x0 5 s - ).. Raaton tansfe he man quantty escbng the aaton tansfe s the aaton ntensty. t s efne as the aaton powe pe unt sol angle an unt aea of a suface that s place nomal to the ays. We stngush between spectal an total ntensty an espectvely:. () ( ) ( ) 0 Hee s a poston vecto fxng the locaton of a pont n space an a unt ecton vecto. n case of themoynamc equlbum the aaton ntensty s ecton-nepenent an gven by the Planc functon Publshe une lcence by Lt

3 th Euopean Confeence on Hgh-echnology Plasma Pocesses (HPP ) Jounal of Physcs: Confeence Sees 75 (0) 0009 o:0.088/ /75// h B ( ). () h c exp A lght beam tavelng though a gas laye of thcness s loses ntensty by absopton an by scatteng of photons. he attenuaton of aaton s popotonal to the magntue of the ncent enegy (ntensty ) an to the length of the path s. (3) κ Because scatteng of photons by molecules an atoms s always neglgble fo heat tansfe the popotonalty constant κ epesents the absopton coeffcent. n the local themoynamc equlbum the followng elaton hols between the emsson an absopton coeffcents ε B. (4) κ he complete statonay equaton of aaton tansfe fo an absobng an emttng meum s ga κ ( B ). (5) s 3. Absopton popetes of plasmas Raaton n ac plasmas epens beses othes physcal quanttes on the concentatons of all chemcal speces n the plasma. n the calculaton of the plasma a y a composton was assume at the pessue of atmosphee consstng of N O A an CO. he equlbum composton of the a plasma was compute usng mgas coe [6]. Atoms an up to the tple ons of N O A C an atomc molecules O N N + NO NO + CO CO + an CN wee assume to be pesent. When a photon nteacts wth a gas molecule atom o on t may be absobe asng the patcles enegy level. Convesely a gas patcle may spontaneously lowe ts enegy level by the emsson of an appopate photon. hee ae thee ffeent types of aatve tanstons that lea to a change n the enegy level of a gas patcle by photon emsson o absopton: tanston between non-ssocate ( boun ) atomc o molecula states calle boun-boun tanstons (bb) tanstons fom a boun state to a fee (ssocate) one (absopton) o fom fee to boun (emsson) calle boun-fee tanstons (bf) tanstons between two ffeent fee states fee-fee tanstons (ff) he total absopton coeffcent s gven as the lnea sum of all thee pocesses mentone above ff bf bb ( p) κ ( p) + κ ( p) κ ( p) κ +. (6) he calculaton of the absopton coeffcent epesents a fomable tas when expemental ata s lacng snce the aal wave functons of all fee an boun electonc states must be nown. Howeve smplfcatons can be mae by usng vaous sem-empcal methos an hyogenc appoxmatons 3.. Contnuous aaton he aaton contnuum may be ve nto photon emsson fom fee-boun (ecombnaton) aaton an fee-fee (bemsstahlung) aaton.

4 th Euopean Confeence on Hgh-echnology Plasma Pocesses (HPP ) Jounal of Physcs: Confeence Sees 75 (0) 0009 o:0.088/ /75//0009 Snce the netc enegy of fee electon s not quantze ts ecombnaton wth postve on of a chemcal speces a leas to contnuous aaton. hus fo ecombnaton aaton a a h meve + E E. (7) Hee s the fequency of ecombnaton aaton h Plancs constant v e the velocty of fee a a electon E the onzaton potental of the atom o on E the enegy of the -th electonc enegy state whee the electon s captue. he spectal absopton coeffcent of pocess (7) s elate to the photon absopton coss a secton σ by bf a a κ σ. N (8) a whee N s the populaton ensty of the -th electonc state of the absobng speces a. Neutal atoms an up to the tple ons of N O A C elements wee consee. Photo-onzaton coss sectons fo the goun states of neutal atoms an ons of N O A an C wee calculate usng analytc fts of theoetcal coss sectons fom the Opacty Poject [7]. he coss sectons fo excte levels of neutal atoms wee calculate usng the quantum efect metho of Buges an Seaton [8]; ths was apple to oxygen 3s 3p 4s an 4p states ntogen 3s an 3p states cabon 3s 3p 4s an 4p states. All othe excte states of N O A C wee teate usng the Coulomb appoxmaton fo hyogen-le speces [9]. he enegy levels tabulate n [0] wee use fo all atoms an ons une conseaton. We have taen nto conseaton almost 600 enegy levels. he hyogen-le appoxmaton was use fo the teatment of fee-fee tanstons too. n contast to boun electons of a gven level fee electons contbute to the absopton coeffcent at all fequences. he elatve mpotance of boun-fee an fee-fee absopton epens on the state of onzaton. At low tempeatues thee ae vey few fee electons an boun-fee absopton omnates. At vey hgh tempeatues most electons ae fee an fee-fee absopton s omnant. 3.. Dscete aaton Quantum mechancs postulates that the enegy levels fo atomc o molecula electon obt as well as the enegy levels fo molecula otaton an vbaton ae quantze;.e. electon obts an otatonal an vbatonal fequences can only change by cetan scete amounts. heefoe n boun-boun tanstons photons must have a cetan fequency (o wavelength) n oe to be captue o elease esultng n scete spectal lnes fo absopton an emsson hc h mn Em En (9) λ mn fo the tanston fom the state m to the state n. Howeve no spectal lne can be tuly monochomatc; athe absopton o emsson occus ove a tny but fnte ange of wavelengths. he esults ae boaene spectal lnes that have the maxma at the wavelength pecte by equaton (9). Numeous phenomena cause boaenng of spectal lnes. he most mpotant ae natual lne boaenng Dopple boaenng Sta boaenng esonance boaenng an Van e Waals boaenng. Absopton coeffcent κ bb fo scete spectum must tae account of all ovelappng spectal lnes of all atoms an ons of the plasma. he absopton coeffcent of an solate lne of speces a s [9] κ ( p) cf a a π N ( p) P ( p) bb a 0 mn n (0) 3

5 th Euopean Confeence on Hgh-echnology Plasma Pocesses (HPP ) Jounal of Physcs: Confeence Sees 75 (0) 0009 o:0.088/ /75//0009 whee 0 s the electon aus c the velocty of lght a f mn the absopton oscllato stength of the spectal lne fo electonc tanstons between the m an n enegy states. ( p) ensty of the lowe electonc enegy state an P ( p) N a n s the populaton s the nomalze lne shape. bb o calculate the absopton coeffcent κ a of the -th spectal lne t s necessay to etemne ts half-wth δ spectal shft an the absopton oscllato stength a f mn. he values of absopton oscllato stength ae tabulate fo a lot of spectal lnes of atoms an the ons n Kuucz Atomc Lne Database []. he lne shapes n ou calculatons ae gven by a convoluton of Dopple an Loentz pofles esultng n smplfe Vogt pofles. he fne multplet stuctue an the possble ovelap of lnes have also been taen nto account. Fo each spectal lne we have calculate paametes efnng the half-wths an shfts. Sem-empcal fomulas gven n [9] wee use. We have taen nto conseaton moe than spectal lnes Molecula absopton atomc molecules Changng the obt of an electon eques a elatvely lage amount of enegy esultng n absoptonemsson lnes at shot wavelengths between the ultavolet an the nea nfae (between 3x0 5 s - an x0 4 s - ). Changes n vbatonal enegy level eque somewhat less enegy so that the spectal lnes ae foun n the nfae (between x0 4 s - an 0 3 s - ) whle changes n otatonal enegy levels call fo the least amount of enegy an otatonal lnes ae foun n the fa nfae (beyon 0 3 s - ). Changes n vbatonal enegy levels ae often accompane by otatonal tanstons leang to closely space goups of spectal lnes that may patly ovelap an lea to so-calle vbaton-otatonal bans. hus the molecula spectum s much moe complcate then that of monatomc gases. Fo electonc tanstons no selecton ules fo vbaton quantum numbes exst.e. tanstons between abtay vbaton levels of the uppe an lowe electonc states ae possble. he theoetcal bacgoun fo the vbatonal stuctue analyss s the Fanc-Conon pncple [] that maes t possble to pect the stbuton of vbatonal ban ntenstes. Relatve lne ntenstes n the electonc-vbatonal specta ae etemne by the Fanc-Conon factos [ v ψ v τ ] qv v ψ. () Hee ψ v an ψ v ae the vbatonal wave functons of the lowe an hghe electonc states espectvely. he boun-boun absopton coeffcent fo a tanston between two vbatonal levels v v of two electonc states can be expesse n the fom v v κ π cn f () 0 v v v whee 0 enotes the electon aus c the spee of lght N v the numbe ensty of the lowe vbatonal state an f v v the ban oscllato stength efne by [3] f v v Re v v qv v 3R c g (3) whee R s the Rybeg constant g the weghtng facto of the lowe level v v the fequency at whch the tanston occus an R gves the ntensty stbuton n electonc stuctue. Fo e appoxmate calculaton of aatve popetes t s useful to efne the spectal absopton coeffcent fo the ban system aveage ove the otatonal spectum an also patally smeae out ove the vbatonal stuctue Re κ Nσ ( ) Nπ 0 qv v wv. (4) 3R g Δ v v 4

6 th Euopean Confeence on Hgh-echnology Plasma Pocesses (HPP ) Jounal of Physcs: Confeence Sees 75 (0) 0009 o:0.088/ /75//0009 Hee N s the molecula numbe ensty the aaton fequency of absobe photon an w v enotes the Boltzman pobablty of the occupaton of the lowe vbatonal level. he sum of Fanc- Conon factos s pefome fo all tanstons v v wth Δ Δ v v + whee Δ s nteval of aveagng aoun. he Fanc-Conon factos ae tabulate fo many molecula tanstons n [4] o they can be calculate by compute coe [5]. Molecula photoabsopton was taen nto account fo selecte electonc tanstons of the followng atomc molecules an electonc tanstons: O O + N N + NO NO + CO CO + an CN. Calculate total absopton coeffcents of aaton as a functon of aaton fequency fo plasma tempeatues of K an K ae plotte n fgue. Molecula speces (electonc tanstons) contbute to the total absopton coeffcents slghtly at lowe tempeatues below K at aaton fequences up to s -. Due to the fequency nteval une conseaton aaton tanstons between otatonal levels wee not taen nto account. Wth nceasng tempeatue the contbuton of scete aaton to the absopton coeffcent nceases. Fgue. he total absopton coeffcent as a functon of fequency fo themal a plasmas at tempeatue of K an K. Dote lnes epesent bounaes between specfc fequency goups fo non-unfom splttng (see table ). 5

7 4. Multgoup metho mean absopton coeffcents One of the methos fo hanlng the fequency epenence n aaton tansfe s the multgoup metho [6]. One assgns a gven photon to one of G fequency goups an all photons wthn a gven goup ae teate the same fom the pont of vew of the absopton popetes of the meum the absopton coeffcent fo gven fequency goup s suppose to be constant wth cetan aveage value ( ) ( ) G... + κ κ. (5) he values of total ntensty ae then gven by ( ) ( ) ( ) ( ) G +. (6) he equaton of tansfe fo the gven fequency goup can be teate as equaton fo gey meum: ( ) ( )) ( ga 4 b π σ κ G (7) whee σ s the Stefan-Boltzmann constant b the facton of 4 π σ lyng wthn the -th goup.e. ( ) ( ) ( ) 4 0 B B B b π σ. (8) Fo the multgoup metho to be useful one must be able to compute o estmate the mean values of absopton coeffcents. Geneally κ s taen as ethe Rosselan o Planc mean. 4.. he Rosselan mean he Rosselan mean also calle the mean fee path of aaton s appopate when the system appoaches equlbum (almost all aaton s eabsobe). he Rosselan mean absopton coeffcent s gven by B B R κ κ ) ( ) (. (9) 4.. he Planc mean he Planc mean s appopate n the case of optcally thn system. he Planc mean absopton coeffcent s gven by v P B B ) ( ) ( κ κ. (0) th Euopean Confeence on Hgh-echnology Plasma Pocesses (HPP ) Jounal of Physcs: Confeence Sees 75 (0) 0009 o:0.088/ /75//0009 6

8 th Euopean Confeence on Hgh-echnology Plasma Pocesses (HPP ) Jounal of Physcs: Confeence Sees 75 (0) 0009 o:0.088/ /75//0009 he values of mean absopton coeffcents epen on the choce of the fequency nteval splttng. As example esults fo two ffeent splttng of fequency nteval (0.0 6) 0 5 s - ae pesente. Bounaes between specfc fequency goups of a non-unfom splttng ae gven n table an shown n fgue bounaes between 7 fequency goups of a quasunfom splttng ae gven n table. Values of Planc mean absopton coeffcents fo two ffeent splttng (non-unfom an quas-unfom) ae shown n fgues an 3 espectvely. able. Bounaes between specfc fequency goups ( 0 5 s - ) non-unfom splttng able. Bounaes between specfc fequency goups ( 0 5 s - ) quas-unfom splttng Fgue. Mean absopton coeffcents fo specfc fequency goups non-unfom splttng. 7

9 th Euopean Confeence on Hgh-echnology Plasma Pocesses (HPP ) Jounal of Physcs: Confeence Sees 75 (0) 0009 o:0.088/ /75//0009 Fgue 3. Planc mean absopton coeffcent fo 7 specfc fequency goups the quas-unfom splttng. he Rosselan an Planc mean absopton coeffcents can ffe by an oe of magntue o moe as can be seen n fgue 4 whee compasons of Planc an Rosselan means fo two ffeent fequency goups of the non-unfom nteval splttng ae shown. Fo the goup 7-8 ( ) 0 5 s - both means ffe only slghtly up to the tempeatue K. Geat ffeence fo the goup 9-0 ( ) 0 5 s - appeas ue to stong scete aaton n ths fequency goup whch maes the Planc mean by seveal oes of magntue geate than Rosselan mean. Compasons of Planc an Rosselan means fo all goups of the non-unfom nteval splttng ae shown n fgue. he use of Rosselan an Planc mean absopton coeffcents s only stctly appopate n lmtng ccumstances (absopton omnate o emsson omnate system espectvely). As can be seen n fgues an 4 these two means can ffe vey stongly an thus the esults of the multgoup metho can vay wely epenng upon whch mean s use. n ealty nethe mean s coect n geneal. Anyway the splttng of the whole fequency nteval has to be mae accong to the fequency epenence of the absopton coeffcents. he smplest poceue s then to use the Planc mean fo fequency goups wth low values of absopton coeffcents; fo goups wth hgh values of absopton coeffcents the Rosselan mean s moe sutable. Moe accuate esults bngs the new multgoup metho [6] whch nvolves genealzaton of the Planc an Rosselan means whch occu togethe n the multgoup equatons. 8

10 th Euopean Confeence on Hgh-echnology Plasma Pocesses (HPP ) Jounal of Physcs: Confeence Sees 75 (0) 0009 o:0.088/ /75//0009 Fgue 4. Planc an Rosselan mean fo two ffeent specfc fequency goups of the non-unfom splttng 7-8 an Conclusons Calculatons of the absopton coeffcents fo themal plasma of a have been pefome as a functon of tempeatue n fequency nteval ( ) s - at the pessue of atm. Both Planc an Rosselan means have been compute fo ffeent fequency nteval splttng poceues. Results fo goups of the non-unfom splttng an 7 goups of the quas-unfom splttng have been pesente. he use of Planc o Rosselan means n the multgoup metho of soluton of the equaton of aaton tansfe epens on values of absopton coeffcents. Acnowlegements hs wo has been suppote by the Czech Scence Founaton une poject No. GD0/09/H074 an fom Mnsty of Eucaton Youth an Spots une poject No. MSM Refeences [] Lowe J J 974 JQSR 4 - [] Naghzaeh-Kashan Y Cessault Y an Glezes A 00 J.Phys. D: Appl. Phys [3] Aubecht V an Batlova M 009 Plasma Chem Plasma Pocess [4] Aubecht V an Lowe J J 994 J.Phys. D: Appl. Phys [5] Raynal G an Glezes A 995 Plasma Souces Sc. echnol [6] Coufal O Sezemsy P an Zvny O 005 J.Phys. D: Appl. Phys [7] Vene D A Felan G J an Kosta K 996 Astophyscal Jounal /-49 9

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