A HYBRID METHOD TO SIMULATE AN INDUCTIVELY COUPLED AR-HG PLASMA

Transcription

1 Journal of Thortical and Applid Inforation Tchnology 8 th Fbruary 13. Vol. 48 No JATIT & LLS. All rights rsrvd. ISSN: E-ISSN: A HYBRID METHOD TO SIMULATE AN INDUCTIVELY COUPLED AR-HG PLASMA 1, YANG LIU, 3 GEORGES ZISSIS, 1,,, *YUMING CHEN 1 Institut for Elctric Light Sourcs, Fudan Univrsity; Handan Road, Shanghai 433, China Enginring Rsarch Cntr of Advancd Lighting Tchnology, Ministry of Education, Handan Road, Shanghai 433, China 3 LAPLACE (Laboratoir Plasa t Convrsion d'enrgi) Univrsit Paul Sabatir - Toulous III Build. 3R; 118 rt d Narbonn F-316 Toulous Cdx 9; FRANCE Eail: ly@fudan.du.cn, gorgs.zissis@laplac.univ-tls.fr, yuingchn@fudan.du.cn ABSTRACT A hybrid thod is usd in siulating an inductivly coupld Ar-Hg discharg plasa. In this hybrid odl th cobination of plasa fluid odl and th Boltzann Equation is applid. With this odl, not only th acroscopic paratrs of th discharg, such as lctron dnsity, lctron tpratur, can b siulatd, but also th lctron bhavior can b drivd, which is not accssibl in r fluid odl. Kywords: Inductivly Coupld Plasa, Ar-Hg Discharg, Elctrodlss Fluorscnt Lap, Fluid Modl, Boltzann Equation, Hybrid Mthod 1. INTRODUCTION In th past twntis, lctrodlss fluorscnt laps basd on inductivly coupld Ar-Hg discharg bco nown to th public du to its longvity and high fficacy. Scintists ad fforts fro diffrnt aspcts to clarify chaniss bhind th discharg plasa. In thortical sns, plasa odls wr stablishd to rval th physics difficult to b found in xprints [1-9]. But fforts ar still ndd for bttr and dpr undrstanding of th discharg. In plasa fluid odl, rat cofficints ar iportant input paratrs bcaus thy can significantly affct siulation rsults. To calculat rat cofficints, lctron nrgy distribution function (EEDF) ust b nown. For siplicity, prvious odls usually assud a Maxwllian EEDF [9, 1]. In high currnt and high frquncy discharg, this assuption is ostly justifid. But dtaild dscription on lctron bhavior is issing in this cas. To ovrco this fault, it would b bst to dirctly solv th Boltzann Equation of lctron. But th colossal athatical fforts bhind hindr th pathway. Now, two ajor coprising thods ar prsnt. On is to cobin particl-in-cll (PIC) odl and fluid odl; th othr is to cobin nrgy-doain Boltzann Equation and fluid odl. In this articl, w will siulat an inductivly coupld plasa by cobination of plasa fluid odl and th Boltzann Equation. With this odl, w can hav inforation on acroscopic paratrs of th discharg, such as lctron dnsity, lctron tpratur and so on; furthror, w can also hav dscription on lctron bhavior, which is not accssibl in r fluid odl. Th raining part of this articl is organizd as follow: in Sction, th subjct discharg will b introducd; in Sction 3, odl coposition will b xplaind; in Sction 4, solution thod of th odl is prsntd, in Sction 5, so of th siulation rsults will b givn and in Sction 6, suary of th papr will b ad.. DISCHARGE DESCRIPTION Fig. 1 shows th structur and dinsion of th subjct discharg bulb. Th bulb has th siilar shap as th Philips QL lap, whr th uppr part is sphrical and th lowr part is cylindrical. Th bulb has a r-ntry chabr in th cntr to allow insrtion of frrit cor and coil. Onc lctricity is on, discharg will b inducd on th aziuthal dirction (shown by th arrow in Fig. 1). Sinc th bulb is sphrically sytric, siulation will b prford only in th paintd rgion of Fig. 1. Dinsion of th discharg chabr has alrady bn annotatd on Fig

2 Journal of Thortical and Applid Inforation Tchnology 8 th Fbruary 13. Vol. 48 No JATIT & LLS. All rights rsrvd. ISSN: E-ISSN: Fig. 1 Structur And Dinsion Of Th Subjct Discharg Bulb 3. MODEL INTRODUCTION Th odl consists of thr parts: th lctroagntic part, th plasa fluid part, and th Boltzann Equation part. 3.1 Elctro-agntic part Th discharg is xcitd by high frquncy lctric-agntic fild (.65 MHz). Variation of lctro-agntic fild is govrnd by th Maxwll Equations. Taing into account cylindrical sytry and oitting displacnt currnt, aziuthal lctric fild E (r,z)can b writtn as: E(, rz) µ ( σeθ(, rz)) t θ = (1) whr is prissivity, and is conductivity. Conductivity undr high frquncy can b xprssd as: E υ iω f σ = n ε dε 3 υ + ω ε () whr n is lctron dnsity, is Coulob charg, is lctron ass, υ is ontu transfr frquncy, ω is angular frquncy of lctric fild, ε is lctron intic nrgy, and f is EEDF. Elctron dnsity is an iportant paratr, and it ay influnc production and loss of xcitd atos, nrgy transportation in th spac, and so on. This will b addrssd in th plasa part of th odl. Thus, lctron dnsity bridgs th lctroagntic part and th plasa fluid part. Th EEDF is govrnd by th Boltzann Equation part. Onc th EEDF changs, conductivity ay also follow suit. Thrfor, th lctro-agntic part and th Boltzann Equation part ar also lind togthr. 3. Plasa fluid odl part Th plasa fluid odl is th cntral part of th siulation. Th govrning quation of this part is th Navir-Stos quation. In th odl, w considr variation of Ar tastabl stat, Hg 6-3 P, 1,, Hg 6-1 P 1, Hg 7-3 S 1 and Hg 6-D stats. Th tastabl stat Ar and Hg 6-D stats ar actually cobination of svral clos stats by th thod introducd in [11]. Bsids, lctron dnsity, lctron tpratur, and gas tpratur ar also calculatd. Thrfor, th quation syst of th plasa fluid part has 1 variabls as follows: lctron dnsity n, lctron tpratur T, tastabl Ar ato narm, Hg 6-3 P stat atos n3p, Hg 6-3 P 1 stat atos n3p1, Hg 6-3 P stat atos n3p, Hg 6-1 P 1 stat atos n1p1, Hg 7-3 S 1 stat atos n3s1, Hg 6-D stat atos n6d, and gas tpratur T gas. Th govrning quation of lctron dnsity n is shown in Eq. 3 n t + ( D n ) = R whr D is diffusion cofficint of lctrons, R is su of lctron production and loss involvd in all inds of plasa ractions. In th odl, w considr radial transportation of lctrons is doinatd by abipolar diffusion, i.. D (4) µ T i Dtaild procsss of obtaining Eq. 4 can b rtrivd in [9] and [1]. Th govrning quation of lctron tpratur T is shown in Eq. 5. nt ( nd T) = P P Hating Loss (5) whr P Hating is oh hating by lctric fild; P Loss is nrgy loss of lctrons by collision; and D is th abipolar diffusion cofficint. According to [1], oh hating can b calculatd with PHating whr (3) 1 = σ _ re θ (6) _r is th ral part of conduc 17

3 Journal of Thortical and Applid Inforation Tchnology 8 th Fbruary 13. Vol. 48 No JATIT & LLS. All rights rsrvd. ISSN: E-ISSN: Gas tpratur of th plasa T gas can b obtaind with nartgas ( nardgas Tgas ) = P gas _ hating (7) whr n Ar is dnsity of ground stat Ar atos, D gas is diffusion cofficint of th gas, and P gas_hating is th sourc of hating. Sinc Ar ato is far or than that of Hg in th bulb, T gas can b tan as th tpratur of Ar gas. Thrfor, w us Ar diffusion cofficint as D gas. Assu that Ar ion and Ar ato diffus at th sa vlocity, and follow th Einstin rlation, w hav D T = D = µ, whr is th gas gas Ar Ar Boltzann constant, µ is ion obility of Ar, i.. Ar.134 V -1 s. Major channl of gas hating is lastic collision btwn lctrons and ground stat Ar atos. Th govrning quation of all xcitd atos can b xprssd as: n * + ( Dn * n*) = R n * (8) whr D n* is diffusion cofficint of xcitd atos, R n* is th su of production and loss of xcitd atos. In th odl, production and loss of lctrons, and xcitd atos ar incurrd in various plasa ractions. W considr iscllanous plasa ractions causd by lctron collision such as xcitation and dxcitation, dirct ionization, and stpwis ionization. Also, w considr ractions btwn atos, such as Pnning ionization and so on. Dtaild inforation on raction typs and cross sctions can b found in Sction 3. in [9]. 3.3 Boltzann Equation part Th Boltzann Equation is f + v r f E v f l in C ( f) C ( f) = + (9) whr f is EEDF, E is lctric fild, v is lctron vlocity, r is spac gradint, v is gradint in vlocity spac, C l is lastic collision tr, and C in is non-lastic collision tr. Using th two-tr xpansion, rplacing vlocity v with intic nrgy u, and oitting spac variation, w can finally gt th nrgy doain Boltzann Equation: E E F u + N uf 3 u N u M u = N [ F ( u) u ( u) F ( u+ V )( u+ V ) ( u+ V )] ( ) ( σ ) σ σx x x σx x [ ( ) σ ( ) ( )( ) σ ( )] F + N F u u io u F u+ Vio u+ Vio io u+ Vio + t (1) whr F is isotropic part of EEDF.5 ( F ( u) u du = 1), N is ato dnsity, is ontu transfr cross sction, M is ass of ato, x is xcitation cross sction of spcis, V x is xcitation nrgy of spcis, io is ionization cross sction of spcis, V io is ionization nrgy of spcis, and F ar trs for lctron-lctron collision. Mathatical dtails of obtaining Eq. 1 can b rtrivd in [13] and [14]. In th prsnt cas, th discharg is run by rf powr, thrfor, th first tr of Eq. 1 bcos ( Nσ ) ue F ω 1 E [ ] 3 u ( Nσ ) + ( / u) u (11) whr 1/ cos fro th ti avrag of lctric fild. 3.4 Coupling of diffrnt parts of th odl Fig. shows th intrnal lining btwn diffrnt parts of th odl. Th lctro-agntic part provid th othr two parts inforation of lctric fild. It rcivs inforation of lctron dnsity n and EEDF for nxt round of calculation. Th plasa fluid odl part obtains rat cofficints fro th Boltzann Equation part plus th lctric fild. Thn it outputs ato dnsitis of diffrnt spcis and lctron dnsity n. Whil th Boltzann Equation part rcivs lctric fld and ato dnsitis, and givs EEDF and rat cofficints. Th calculation starts fro so trial rsults. As long as th trial is in rasonalb rang, calculation will always convrg to so crtain rsults. Th thr parts for a slf-consistnt syst, and th input paratrs such as gas spcis, gas prssur, collision cross sctions tc dfin faturs of th syst, and finally dcids what rsults will b gotton. is angular frqu 171

4 Journal of Thortical and Applid Inforation Tchnology 8 th Fbruary 13. Vol. 48 No JATIT & LLS. All rights rsrvd. ISSN: E-ISSN: Fig. Innr Corrlation Btwn Diffrnt Parts Of Th Modl 4. MODEL SOLUTION Fig. 3 dpicts th solution ara of th odl. Th Maxwll quations and fluid quations ar solvd with finit lnt thod. Th sh grid is also shown in Fig. 3. Th Boltzann Equation (Eq. 1) can b solvd with finit diffrnc thod (as in [13]) or finit volu thod (as in [14]). In th prsnt odl, w us finit volu thod with unifor sh grid. EEDF is obtaind as function of lctric fild E and lctron dnsity n. Thn rat cofficints ar calculatd and ford as intrpolation tabls. Th plasa fluid odl ay find ncssary rat cofficints by inputting E and n valus into th tabl. inforation on this can b found in [15]. In th prsnt cas, th boundary E thr is. V/. For plasa fluid odl part, w considr thr is no discharg on th boundary. So xcpt that th uppr lftost boundary is axial sytry, boundary particl dnsity, lctron tpratur, and gas tpratur ar st to vry sall valus. Choic of initial valus of lctric fild, particl dnsitis, lctron tpratur, and gas tpratur is sowhat fr. As long as initial valus ar in a propr rang, siulation will always convrg to a crtain point, which is ainly dtrind by intrinsic proprtis of th odl dfind gas typ, gas filling prssur, and collision cross sctions and so on. 5. RESULTS Fig. 4 shows th calculatd lctron dnsity n and Hg 6-3 P 1 ato dnsity. Fro th figur w can s that th axiu valu of lctron dnsity locat nar th coil; whil th Hg 6-3 P 1 ato ar or widly sprad in th discharg spac. Fig. 5 prsnts th calculatd EEDF on point A and B shown in Fig. 3. It can b sn that whn intic nrgy is blow 7V, th two EEDFs alost coincid. That ans lctron bhavior in both cass is siilar. Diffrncs start to bco significant whn intic nrgy is byond 7V. Du to sallr distanc fro th coil, th EEDF of point A rvals highr prcntag of fast lctrons. Thrfor, w can xpct that xcitation and ionization ar uch strongr hr than at point B, which xplains why lctron dnsity is highr in rgion clos to th coil. Fig. 3 Solution Ara And Boundaris For lctro-agntic part, boundary conditions ar such that nar th coil, lctric fild quals local potntial dividd by coil pritr; at th uppr lftost boundary, axial sytry is assud; and at all othr boundaris, lctric fild quals zro. Th local potntial nar th coil can b obtaind fro xprint with singl coil thod. Dtail Fig. 4 Calculatd Elctron Dnsity N And Hg 6-3 P 1 Ato Dnsity Th hybrid thod usd in this articl is suprior ovr r plasa fluid odl in th sns that th hybrid odl can provid xtra inforation. For plasa fluid odl, it is oftn assud that th EEDF is Maxwllian. In ost cass, this 17

5 Journal of Thortical and Applid Inforation Tchnology 8 th Fbruary 13. Vol. 48 No JATIT & LLS. All rights rsrvd. ISSN: E-ISSN: assuption can b justifid, and siulation rsults can b crdibl. Nvrthlss, this assuption ay not rflct variation in lctron bhavior proprly, bcaus variation in EEDF is alrady dfind by th Maxwll distribution function for a Maxwllian EEDF. It ans that bhavior of lctrons with diffrnt vlocity has alrady bn prscribd. This is obviously not ncssarily th cas sinc w cannot now xactly how lctrons will bhav bforhand. In this hybrid odl, no prscription on lctron bhavior is ad. Th EEDFs ar obtaind by dirctly solving th Boltzann Equation. Thrfor, w can hav or dtaild analyss on th discharg. For a Maxwllian EEDF, on st of rat cofficints corrsponds to only on fixd distribution of EEDF. In a hybrid odl, on st of rat cofficints ay corrspond to svral diffrnt EEDFs sinc distribution of EEDF ay vary. This allows us to now or dtails of th discharg. Fig. 5 EEDF At Two Diffrnt Points Of Th Discharg 6. SUMMARY In this articl, siulation of an inductivly coupld Ar-Hg plasa is prford with a hybrid thod. Th odl consists of thr parts: lctroagntic part, plasa fluid part, and Boltzann Equation part. Ths thr parts for a slfconsistnt syst. Not only can th odl provids inforation on plasa paratrs such as lctron dnsity, xcitd ato dnsitis, and so on; it can also rflct lctron bhavior sinc EEDF can b obtaind in th Boltzann Equation part. That as th thod strongr than r plasa fluid odl. Such siulation ay bco a powrful tool for discharg dsign. REFERENCES [1] J. W. Dnnan, J. Phys. D: Appl. Phys (199) [] G. G. Listr and M Cox, Plasa Sourcs Sci. Tchnol (199) [3] Eugn Statnic and Valntin Tanach, Plasa Sourcs Sci. Tchnol (4) [4] Eugn Statnic and Valntin Tanach, Plasa Sourcs Sci. Tchnol (6) [5] Kapil Rajaraan and Mar J Kushnr, J. Phys. D: Appl. Phys. 37 (4) [6] J. J. Curry G. G. Listr and J. E. Lawlr, J. Phys. D: Appl. Phys () [7] N. Dnisova, G. Rvald and A. Sudra, J. Phys. D: Appl. Phys (5) [8] N. Dnisova, G. Rvald, A. Sudra, G. Zissis and N. Zorina, J. Phys. D: Appl. Phys (5) [9] Yang Liu, Gorgs Zissis and Yuing Chn, Journal of Physics D: Applid Physics 44 (11) 351 [1] Ka Hong Loo t al, IEEE Transactions On Powr Elctronics 19 (4) 1117 (4) [11] Bogarts A. and Gijbls R. t al. J. Appl. Phys (1998) [1] P. Schubrt, P. Awaowicz, R. Schwfl, G. Wachuta, Surfac and Coatings Tchnology (1) [13] G. J. M. Haglaar t al. Plasa Sourcs Sci. Tchnol (5) [14] Dyato N A, Kochtov I V, Napartovich A P, Sov. J. Plasa Phys. 18 (7), 46 (199) [15] W. P. Li, Y. Liu t al. Journal of Applid Physics (8) 173