A Model for Antenna-Plasma Wave Coupling towards Control of Uniformity in Slot-Excited Microwave Discharges

Transcription

1 J. Plasa Fusion Rs. SERIES, Vol. 9 () A Modl fo Antnna-Plasa Wav Couling towads Contol of Unifoity in Slot-Excitd Micowav Dischags Daichi SAWADA, Akihio TSUJI, Takanoi KITSUDO, Yasuyoshi YASAKA, and Hioasa TAKENO Datnt of Elctical and Elctonic Engining, Kob Univsity, - Rokkodai, Nada, Kob , Jaan (Rcivd: 3 Octob 9 / Acctd: May ) A sufac wav lasa dvic using th slot lat with a fw slots sotis xhibits a ju o hystsis bhavio of lasa ofils whn th inut ow is changd. On th oth hand, a ulti-slot xcitd lasa dvic, in which th slot lat has slot onings of o than, has oducd unifo lasas with sooth chang in dnsitis fo a wid ang of th inut ow and gas ssu. It is iotant to contol th satial ofil of th adiatd wavs fo unifo and stabl lasa oduction in slot-xcitd icowav dischag dvics. Th adiatd wav ofil can b calculatd by sval nuical thods. Howv, th calculation cost is high. Th uos of this study is to stablish a sil analysis odl. In this odl, th od sctu of th adiatd wav fild is obtaind by convolving th od scta of th incidnt wavs fod in th antnna cavity and th atu function of th slot lat. Th calculation sults a coad with xintally asud valus and full-wav calculations. Ths tnds hav a good agnt in th viwoint of th od scta. Kywods: icowav dischags, sufac wav ignod, ulti-slottd lana antnna, od sctu. Intoduction It has bn known that slot-xcitd icowav dischags can oduc lasas suitabl fo lasa-aidd anufactuing that quis lag aa, low daag and high sd ocssing. In th slot-xcitd dvic, th icowav oagats though a wavguid, a cavity sac, a slot lat and a dilctic window and is sulid to th lasa. Sufac wav lasa (SWP) dvic oftn uss th slot lat with a fw slots sulting in th ju o th hystsis bhavio of lasa ofil whn th inut ow is changd []. On th oth hand, ulti-slot xcitd lasa (MSP) dvic, in which th slot lat has slot onings of o than, has oducd unifo lasas with sooth chang in th dnsitis fo a wid ang of th inut ow and gas ssu []. W consid th ason fo th diffnc btwn th SWP and th MSP in th lasa oduction. In both lasas, th lasa is ainly oducd by th sufac wavs and/o nhancd icowav filds du to th sonant absotion aisn just und th dilctic window [3]. Whn th lasa is oducd in th chab with th cylindical stuctu, th lasa ofil is ind by th satial stuctu of th wavs chaactid by th aiuthal od nub and th adial od nub n. If th ultil ods of (, n) a xcitd by th slot antnna, th lasa slcts on od fo on valu of th dnsitis. As a sult, th ods of th wavs chang as th inut ow is changd. This is th cas of th SWP. In th cas of th MSP, it is xctd that ths obls can b autho s -ail: a.tsuji@stu.kob-u.ac.j vntd by contolling th satial stuctu of th wavs. Th wav ofil can b calculatd by sval nuical thods, fo xal, th-dinsional finit-diffnc ti-doain (FDTD) sch with o odl of th antnna cavity, th slot lat, th lasa and so on. It is, howv, ti-consuing and not suitabl fo th analytical considation. Th uos of this study is to stablish a sil analysis odl that lats th incidnt wav fod in th antnna cavity to th wav ofil adiatd to th lasa. Th calculation sults by th odl a coad th od scta obsvd in th xints. Ths tnds hav a good agnt in th viwoint of th od scta.. Exintal quints Figu shows th xintal quint schatically. A dischag chab has th adius of R = 5 and th h of 38 and a quat window with th sa diat and th thicknss of 3 is st on th to. Th ulti-slottd lana (MSP) antnna is st abov th quat window and it is usd to adiat th icowav divn at =.45 GH. Th antnna syst consists of so coonnts connctd to th icowav souc, th slot lat with th concntic aay of th slots and a back lat. W us th cylindical wavguid with a olai fo th otating TE od xcitation [4]. A quadul th stub tun is st btwn th olai and th slot antnna to vnt th ow flctd fo th antnna o th lasa fo going back 65 by Th Jaan Socity of Plasa Scinc and Nucla Fusion Rsach

2 D. Sawada t al., A Modl fo Antnna-Plasa Wav Couling towads Contol of Unifoity in Slot-Excitd Micowav Dischags into th olai. Th slots a 3-6 in lngth, in wih and 4 in slot intval in th adial diction and about slots on th MSP antnna a distibutd on th whol gion xct th cntal at. A gas ssu A is contolld in th ang of - 3 To and th flow at is st at scc. Th lasa aats a asud by a adially fast-scanning Langui ob. Th two-dinsional distibution of th light ission fo th lasa is onitod using th chag-could dvic (CCD) caa locatd bnath a substat stag. icowav.45gh Fig.. An xintal quint. 3. Th od sctu In th cylindical goty, th wav distibution on th lan fo th tansvs agntic ( TM ) wavs is givn by E quat window gas to u, Acos B sin J ( jn ), () n R wh A and B a constants, R is inn adius of th lasa chab, is th adial osition, θ is th aiuthal angl and j n is n-th o oint of th Bssl function J [3]. Th dission lation of th sufac wav ignods fo TM wavs in th cylindical lasa aoxiatd by a sil -lay odl which consists of th dilctic window and th lasa lay is givn by tanh( h) q tan( qh) tun ow onito 5 substat stub tun cicula olaiation convt ulti-slottd lana (MSP) antnna 3 38 CCD caa to dislay and (), (3) 8 Langui ob wh k,, q k, k 4., ( ), k c, j n R, h.3, is a dilctic constant of th quat window, is lasa angula fquncy, c is th vlocity of light, h is th thicknss of th quat window [3]. Equations () and (3) snt dission quations of u and hybid ods, sctivly. It is otd that th lasa oducd by a fw slots antnna dvic has vaious sufac wav ignods []. Thfo, it is xctd that th lasa oducd by th fw slot antnna will tak lac jus at scific dnsitis. On th oth hand, in cas of th lasa oducd by th MSP dvic, th ain coonnt of th adial od nub asud by th analysis of th bightnss attn is 4-6 [4]. 4. Elctoagntic fild calculations Th lctoagntic filds can b calculatd by sval nuical thods. W us two-dinsional FDTD sch fo th cylindical goty. Figu shows th dvic goty usd in th calculation. Th dvic consists of th antnna cavity, th slot lat, th quat window and th lasa chab. In Fig., d a and d ai show th distanc btwn th to sufac of th antnna cavity and th to sufac of th quat window and th distanc btwn th botto sufac of th slot lat and th to sufac of th quat window, sctivly. In this odl, th slot lat has slots with th ing stuctu and th wih of th slot and th intval of th adjacnt slots a and, sctivly. This thod solvs th Maxwll quations, th quation of th cunt dnsity fo th lctons and th quation of otion fo th lctons givn by de H J, (4) dh E μ, (5) J n v and (6) dv E v, (7) wh H, E, J, v,,, μ,, n, and snt th agntic filds, th lctic filds, th cunt dnsity, th vlocity of th lctons, th ittivity in th vacuu, th lativ ittivity of th diu, th ability in th vacuu, th lcton chag, th lcton dnsity, th ass of th lcton and th ontu tansf collision fquncy, sctivly. Th calculation is fod by assuing = bcaus is fixd to b by th wavguid in th xints. Th icowav souc fo TE od xcitation is st on th to fac of th wavguid. Th lcton dnsity in th lasa has th dnsity gadint in th -diction and th lan of ω=ω 66

3 D. Sawada t al., A Modl fo Antnna-Plasa Wav Couling towads Contol of Unifoity in Slot-Excitd Micowav Dischags is st at = 5, whω snts th lcton lasa angula fquncy. Figu 3 shows th distibution of th lctic filds E on ω = ω lan in cas of d ai = 3. O ai quat ( q = 4) lasa cylindical wavguid slot lat ( a = ) d a d ai d q antnna cavity = n adial od nub n wih of ai ga d ai () Fig. 4. Th lation btwn th d ai and n. lctic filds on sonant lan Fig.. Th dvic goty usd in th calculation x axis (c) - - y axis (c) Fig. 3. Th lctic fild distibution on th sonant lan in cas of d ai = 3. Figu 4 shows th lation btwn d ai and th adial od nub n of E on ω=ω lan, wh d ai is vaid fo to 39. Th od scta fo th n a calculatd fo E () by th Foui-Bssl tansfo in cas of =. In gnal, th sults show th ain scta and a fw sub scta. In this study, th aithtic wightd an is usd to valuat th shift of th ak osition in th n-diction. In Fig.4, th squas show th aithtic wight an calculatd fo th n and th sctu and th dashd lin is th lina aoxiation lin fo th squas. Th sult shows that th n slightly dcass whn th d ai incass. If th d ai incass, in th sac bcos sall. In gnal, th wavlngth is invsly ootional to th squa oot of. Thfo, this hnonon is xlaind that th dcas of n sults fo th incas of lativ cosonding to d ai. Howv this calculation cost is high and it is sowhat had to intt th sults bcaus of th colxity of th dvic goty. Thfo it is not suitabl fo th analytical considation. 5. Sil analysis odl Th satial stuctu of th wavs is chaactid by th od nubs (, n). W oos th sil analysis odl. This odl can idiatly calculat th od scta of th adiatd wavs. Fist of all, th incidnt wavs a(, ) fod just abov th slot lat a calculatd by using th FDTD sch. In this calculation, th analysis sac consists of th wavguid and th antnna cavity with a lativ dilctic constant which is givn as th avag valu of thos of dius foing th cavity sac, th dilctic window and th sac btwn th. Th slot goty is sntd by th atu function g(, ), wh g is qual to fo th oning at and fo th oth. In this study, th slot lat has 6 slots xct th cntal at. Th adiatd wavs in th al sac w(,θ) is dfind by ultilying a(, ) by g(, ). H w dfin th od scta fo a, g and w as A(, n), G(, n) and W(, n), sctivly. Ths od scta a calculatd by th Foui-Bssl tansfo F(, n) R J R ( j f (, )J n ) ( j n ) x( i ) dd, (8) R wh F and f snt th function in th wavnub sac and th function in th al sac, sctivly. In addition, th od scta of th adiatd wavs W a also obtaind by th convolution of A and G; W A G A( a, b) G( a, n b) dadb. (9) Th n dnds on a lativ ittivity bcaus th wavlngth is invsly ootional to th squa oot of th lativ ittivity in gnal. In this study, w dfin th lativ ittivity as 67

4 D. Sawada t al., A Modl fo Antnna-Plasa Wav Couling towads Contol of Unifoity in Slot-Excitd Micowav Dischags d d a a q q d a d () q wh d a, d q, a and q snt th distanc btwn th to sufac of th antnna cavity and th to sufac of th quat window, th thicknss of th quat window, th lativ ittivity of th ai and th lativ ittivity of th quat window, sctivly, as shown in Fig.. In th lctoagntic fild calculation, th cavity sac is filld with th dilctic atial of to add th ffct of d ai. It is undstood that dnds on d a in Eq. (). 6. Coaison btwn xints and calculations Figu 5 shows th bightnss attn obsvd by th CCD caa and th lasa oduction condition is th otating od xcitation, P in =.5 kw and A = To, wh P in snts th inut ow of th icowav. W asud th n by th sctu analysis. It is calculatd by jn ( ) An J ( ) A and () R P n P E Q j j, () j wh A n is th od scta and E() is th xintal valu. Th od scta A n is dfind by th last-squa tchniqu as Q bcos iniu Th n is obtaind th aithtic wightd an of th th ajo coonnts of th sctu. Figu 6 shows th lation btwn th avag lativ ittivity and th adial od nub. In Fig. 6, th squas a th aithtic wightd an, th continuous lin is th lina aoxiation lin of th, th dashd lin is that of th sil calculation and th dottd lin is that of D-FDTD as shown in Fig.4. Figu 6 shows that all sults hav sa tnds that th n incass whn th avag lativ ittivity incass. In Fig. 6, th diffnc btwn th lins fo th xintal sults and th sil analysis odl is sall than. Thfo, th both sults hav a good agnt in th viwoint of th n. On th oth hand, th sults of D-FDTD calculation including th lasa gion a sall than th xintal sults. In gnal, it is known that th wavlngth bcos shot by th tubativ ffct whn th slots xist. In this calculation, any slots on th MSP antnna usd in fact a aoxiatly givn by so slots with th ing stuctu. As a sult, th lativ ittivity of th sac in th D-FDTD calculation including th lasa gion ay b sall than th oth. In Fig. 6, th diffnc btwn th sult fo th xints and th D-FDTD calculation including th lasa gion naly quals to. Thfo, th sil odl is ffctiv to valuat th antnna syst although th calculation cost is low than that of th gnal thods. Fig. 5. Th bightnss attn obsvd by th CCD caa. adial od nub n n th dg of th chab xintal valu ( th lina aoxiation lin) sil odl calculation D-FDTD lativ ittivity < > Fig. 6. Th lation btwn th avag lativ ittivity and th adial od nub. 7. Suay Th satial stuctu of th wavs in th icowav dischags using th MSP antnna is invstigatd by th xintal asunts and th calculations. In th calculation, w hav stablishd th sil analysis odl to coa with th full-wav odl. On th oth hand, th xints show that th n is contolld by th lativ ittivity which is th avag valu of th lativ ittivity of th dius foing th cavity sac, th dilctic window and th sac btwn th. Th sil analysis odl is alid to th analysis of th antnna syst and th sult is coad with th od scta obsvd in th xints. Ths tnds hav a good agnt in th viwoint of th n. Th sults of th xints and th calculations hav th sa tnd that th n incass whn th incass. Thfo, th nwly-oosd odl is ffctiv to valuat th antnna syst although th calculation cost is low than that of th gnal thods. [] H. Sugai, I. Ghanashv, and M. Nagatsu: Plasa Sci. Tchnol. 7 (998) 9. [] Y. Yasaka, N. Ishii, T. Yaaoto, M. Ando, and M. 68

5 D. Sawada t al., A Modl fo Antnna-Plasa Wav Couling towads Contol of Unifoity in Slot-Excitd Micowav Dischags Takahashi: IEEE Tans. Plasa Sci. 3 (4). [3] H. Hojo, A. Shiaua, N. Uchida, Y. Yasaka, and A. Mas: J. Plasa Fusion Rs. 8 (4) 79. [4] H. Shono, Y. Yasaka, A Tsuji, and H. Takno: snt at ICPP8, Int. Congss on Plasa Phys. 8, 8. 69