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2 Millimtr-wav phas-imaging intrfromtr for th GAMMA Q tandm mirror K. Hattori,a) A. Mas, A. takura, M. nutak, and S. Miyoshi Plasma Rsarch Cntr, Univrsity of Tsukuba, Tsukuba 30.5, Japan K. Uhara, T. Yonkura, H. Nishimura, K. Miyashita, and K. Mizuno Rsarch nstitut of Elctrical Communication, Tohoku Univrsity, Sndai 980, Japan (Rcivd 23 April 1991; accptd for publication 10 Sptmbr 1991) A millimtr-wav phas-imaging intrfromtr has bn dvlopd for th study of dnsity profils of th GAMMA 10 tandm mirror. Th intrfromtr uss a 70-GHz klystron oscillator and a quasi-optical transmission systm. Th prob bam is xpandd so as to fill an orthogonal viw of a plasma cross sction. Th viw is imagd onto a dtctor array. Th dtctor array consists of bam-lad GaAs Schottky barrir diods bondd to antnnas fabricatd using photolithographic tchniqus on a fusd-quartz substrat. Two typs of antnnas, bow-ti and Yagi-Uda antnnas hav bn usd in ordr to provid an ffctiv matching to millimtr-wav bams, and compard for th prformanc of an imaging systm. Th intrfromtrs hav bn applid to th cntral-cll and plug-cll plasmas of GAMMA 10.. NTRODUCTON. DESCRPTON OF THE PHASE-MAGNG-SYSTEMS n rcnt yars, phas-imaging intrfromtrs hav bn usd and constructd in svral plasma xprimnts in ordr to masur multichord lin-intgratd lctron dnsitis. Th first xampl was a CO, lasr intrfromtr using a 15-lmnt PbSnT dtctor array which was applid to a high-dnsity arc plasma.* A far-infrard lasr intrfromtr with a 20-lmnt intgratd microbolomtr array has bn applid to a tokamak plasma by th UCLA group.2 A st of cylindrical lnss or off-axis parabolic mirrors producs a sht-lik bam to illuminat th ntir cross sction of a plasma. Th phas distribution producd by th plasma is imagd onto a dtctor array. Th numbr of channls is dtrmind by th numbr of dtctors in th array and a singl st of optics is usd for all channls. This ass problms in convntional multichannl intrfromtrs such as cost and spatial rsolution. W hav dvlopd a millimtr-wav phas-imaging intrfromtr using a Schottky barrir diod array for th f&t tim and applid to a tandm mirror plasma. Millimtr-wav imaging tchniqus bcom important in rmot snsing, atmosphric radiomtry, radio astronomy, and radars as wll as in plasma diagnostics. Th manuscript is organizd as follows. n Sc., w dscrib th phas-imaging systms applid to th cntralcll and plug-cll plasmas of GAMMA 10. Th rsults of th tsts on th imaging arrays using bow-ti and Yagi- Uda antnnas and th systm calibration using a dilctric objct ar prsntd in Sc.. Sction V givs xprimntal rsults of lin-dnsity profils. n Sc. V w summariz. Prsnt addrss: Nobyama Radio Obsrvatory, National Astronomical Obsrvatory, Nobyama, Nagano , Japan. A. Optical systm Th principls for dsigning an optical systm ar as follows. A prob bam should covr th majority of plasma cross sction. Cross sction of th bam at th vacuum windows must b small nough compard with th siz of th windows. Sphrical abrration of th optical systm must b as small as possibl spcifically on th dtctor array. Th optical systms hav bn dsignd and stimatd by using a ray-tracing cod as wll as a Gaussianbam propagation thory.3 W hav constructd two diffrnt phas-imaging systms for GAMMA 10 plasmas. Figur 1 (a) shows a schmatic viw of th systm dsignd for th cntral-cll plasma. A 400-mW microwav of frquncy f = 70 GHz is launchd through a transmittr horn, and dividd by a polythyln bamsplittr BSt into two bams, a prob bam and a rfrnc bam. Th prob bam is xpandd in on dimnsion using polythyln cylindrical lnss L2 to L, so that it covrs th majority of th plasma cross sction, 360 mm in diamtr, which is dtrmind by th limitr installd in th cntral cll. Th vacuum windows ar mad of fusd-quartz with 400 rnrn~ 140 mm. Th distanc btwn th vacuum windows is 1.2 m. Th prob bam and th rfrnc bam ar suprimposd coaxially by a bamsplittr BE+. A similar st of lnss L6 to Lg and an objctiv lns Ll,, dmagnify th bam again and cast th imag onto a dtctor array. A substrat lns is usd on th back sid of th dtctor array in ordr to liminat a crosstalk btwn nighboring antnnas and sphrical abrration or coma.4 Th systm applid to th plug-cll plasma is shown in Fig. 1 (b). n this systm, numbr of lnss and optical paramtrs ar diffrnt from th cntral-cll systm sinc th distanc btwn th vacuum windows, 3.0 m, and th plasma radius, 200 mm, ar diffrnt. Th rfrnc bam 2857 Rv. Sci. nstrum. 62 (12), Dcmbr Amrican nstitut of Physics 2857

3 SDE VEW BOW-TE ARRAY KLYST TOP & LOW FREOUENCY CONNECTON lb) TOP [O.lm & VEW WNDOW SPLTTER PG. 1. Schmatic viw of th millimtr-wav phas-imaging systms at (a) th cntral cll and (b) th plug cll. is obtaind from a wavguid-typ dirctional couplr and transportd by using ovrsizd wavguid. B. Dtctor array antnnas Dtctor-array antnnas of two typs ar usd for th prsnt phas-imaging intrfromtrs. On is bow-ti antnna array214 with 11 lmnts, and th othr is Yagi-Uda antnna array5 with 10 lmnts. Th dtctor array consists of bam-lad GaAs Schottky barrir diods bondd to ach antnna which is monolithically fabricatd on a fusdquartz substrat of 25 mm X 25 mm. Th spacing btwn th antnnas 2.14 mm is dtrmind from th Nyquist sampling thorm givn by T=Af /n, (1) whr il is th wavlngth in fr spac, f# is th ffctiv f numbr bf th objctiv lns, and n is th rfractiv indx of th quartz substrat. Th layout of th bow-ti antnna array is shown in Fig. 2. Th rsistiv antnna impdanc of 150 CE, which is obtaind for a 60 bow angl on a fusd-quartz (E = 4) substrat, is adoptd in ordr to provid th bst matching to th diod dtctors. Th layout of th Yagi-Uda antnna array is shown in Fig. 3. t consists of a radiator lmnt on th on sid of th substrat and a dirctor on th othr sid, btwn th substrat and th substrat lns. Th dimnsions of th antnna lmnts shown in Fig. 3 ar also dtrmind in BEAM-LEAD TYPE GaAs.- XHOTTKY BARRER DODE UNT mm FG. 2. Layout of th dtctor array using bow-ti antnnas (top) and magnification viw of th lmnt (bottom). ordr to provid impdanc matching to th diods and bam pattrn matching to th optics. ll. TEST OF PHASE-MAGNG A. Optical systm NTERFEROMETER Th bamwidth of th powr pattrn is masurd with a wavguid antnna at svral positions along th bam 2Gz=J YAG~-uDA ANGNA ARRAY 3oaomm DRECTOR N,T:mm FG. 3. Layout of th dtctor array using Yagi-Uda antnnas (top) and magnification viw of th lmnt (bottom). t consists of a radiator lmnt on th dilctric-air intrfac and a dirctor on th othr sid Rv. Sci. nstrum., Vol. 62, No. 12, Dcmbr 1991 Phas-imaging intrfromtr 2858

4 -i i Y (mm) FG. 4. Ray tracing using a gomtric optics thory applid for th cntral-cll systm.. propagation. Th valus at th plasma cntr ar 350 mm X90 mm for th cntral-cll systm and 320 mmx 120 mm for th plug-cll systm, rspctivly. Th bamwidth in th vrtical dirction covrs most of th plasma radius. Th rsults of ray-tracing using a gomtrical optics thory ar shown in Fig. 4 for th cntral-cll systm. Thick lins ar th rays without rfraction ffct of a plasma, and thin lins ar with it. Th plasma is assumd to hav a uniform and axisymmtric dnsity of 3 X 10 s m- 3. An imag has a on-to-on corrspondnc with an objct, that is, a position across th plasma corrsponds to a point on th imag plan, and th displacmnt of th rays du to th diffraction is ngligibly small at th fiv channls nar th optical axis. Th ray tracing at th plug cll is also stimatd similarly. Th optimization of th systm is don so as to obtain a good final imag at both clls. Magnifications of th cntral-cll and plug-cll optical systms ar dsignd to b 20 and 17.2, rspctivly. Th valus agr with th xprimntal valus within 4% rror, which ar dtrmind by th ratio of th movmnt of a point sourc across th objct plan and that of an imag across th imag plan. B. Charactristics of dtctor array antnnas Th vido rsponsivity of th dtctors is shown in Fig. 5 as a function of frquncy. t is confirmd that th dtctor using bow-ti antnnas hav widr rsponsivity than th on using Yagi-Uda antnnas as xpctd. Similar rsponsivity is obtaind at a frquncy band of 40 GHz for th bow-ti antnnas. Th pak vido rsponsivity of -60 V/W is valuatd from th input powr to th objctiv lns. This valu should incras whn th bst matching btwn th incidnt bam and th antnna pattrn is obtaind. Th charactristics of th htrodyn dtction ar not masurd in th prsnt xprimnt. t has bn shown that th diod has 4.0-dB convrsion loss at 20 GHz with l-2 GHz F and an LO powr of 5 mw. Th maximum cut-off frquncy of th diod is stimatd to b 2300 GHz.~ p - z i+i FREQUENCY (GHz) FG. 5. Vido rsponsivity of th dtctors as a function of frquncy. Circls rprsnt th data obtaind from th bow-ti antnna array, and dots rprsnt th data obtaind from th Yagi-Uda antnna array. Th spatial rsolutions of th dtctors ar stimatd from a masurmnt of th Airy pattrn by using th plugcll systm. A Gunn oscillator is locatd at th position corrsponding to th plasma cntr. Th sourc is imagd onto ach array antnna. Th xampls of th Airy pattrn ar plottd in Figs. 6(a) and 6(b). Th thortical curvs corrspond to th Airy function which givs an intnsity distribution of a point imag by an idal lns having circular aprtur of diamtr G?, that is, h(x) = THEORY 5 (a) - EXPERMENT L T F, ;, Fi -./ i\. ~d_l~...-._cc \ i NUMBER NUMBER FG. 6. Masurmnt of Airy pattrn: (a) bow-ti antnna array, (b) Yagi-Uda antnna array. Dots rprsnt th masurd points. Th solid lins rprsnt th fitting curvs drawn by using Rq. (3). Th dottd lins ar calculatd from Eq. (2). l (2) 2859 Rv. Sci. nstrum., Vol. 62, No. 12, Dcmbr 1991 Phas-imaging intrfromtr 2859

5 whr Ji is th Bssl function of th first ordr, k- i is th wavlngth at th imag plan, and x and z ar th distanc from th optical axis to th imag plan and from th lns to th imag plan, rspctivly. Th fitting curv is drawn by using th Whittakrahannon sampling thorm givn by7 E(x)= i E J- if= - m (2fJsinc[ 2/,(x - )], (3) whr E(n/2f,) is th sampld data valu, and sin(x) = sin n-x/s-x. Th discrpancy of th imag btwn th xprimntal points and th thortical curvs may b du to th following rasons: (i) th imag is disturbd by an rror of th rsponsivity of ach diod dtctors, (ii)th imag is dtctd by antnnas with a finit siz of th aprtur, and (iii) th displacmnt of an optical axis. Th sid-lob of th pattrn is biggr for th bow-ti antnna than for th Yagi-Uda antnna probably du to th rason that th imag obtaind by th bow-ti antnnas is disturbd by a crosstalk btwn nighboring antnnas. From th dfinition of Rayligh limits,* th spatial rsolution of th antnna array is stimatd to b r, = 5.7 mm for th bow-ti antnna and 4..6 mm for th Yagi-Uda antnna, rspctivly, whr r, indicats th distanc which w can distinguish two point sourcs on th dtctor array. Spatial rsolution of th dtctor using th Yagi-Uda antnna is bttr than that using th bow-ti antnna. C. maging of a tst objct W masur phas distribution of a Tflon bar of 103 mm in width and 1.0 mm in thicknss, and th rfractiv indx of n= 1.43 in ordr to show th prformanc of th prsnt phas-imaging systm. Hr, th plug-cll systm with th Yagi-Uda antnna array is utilizd for th masurmnt. Figur 7 shows th imag of th bar targt as it is movd across th objct plan which corrsponds to th plasma cntr. Th bar targt is movd 73.6 mm ach tim at th objct plan, On th imag plan, this shift corrsponds to two channls on th array antnna. Thortical phas distribution is givn byzf9 (4) whr x is th location on th imag plan, 2a is th width of th bar, Si(x) is th sin intgral, and &, = (27r) 1 2 (n - 1) t/& is th puls hight. A good agrmnt is obtaind btwn th thory and th xprimnt, and th imag of th bar targt movs corrsponding to th movmnt of th targt across th objct plan. V. DENSTY PROFLES N GAMMA 10 PLASMAS Th phas-imaging intrfromtrs dscribd abov hav bn installd at th midplan of th cntral cll (z= 0 m) and at th wst-plug cll (z = 9.7 m) in th GAMMA 10 tandm mirror, whr th z axis coincids with th machin axis. A millimtr-wav intrfromtr with scanning horn antnnas is usd for th cross calibration at th cntral cll Rv. Sci. nstrum., Vol. 62, No. 12, Dcmbr ; (,, 0 / 1 oi- --., -&,,?i t F--%-J> 2 LK c i l ----Y,/ : T k / / 1 x [ =-, cl. * /.ff i,, 0.05;. : 0 / J )..-.? --. ~ k. bu i ,o NUMBER FG. 7. Phas distribution of a Tflon bar with 104 mm in width and 1.0 mm in thicknss. Dots rprsnt th masurd points. Th dottd lins rprsnt th thortical curvs calculatd from Eq. (4). Th location of th bar is 73.6 mm abov th objct plan (top) and 73.6 mm blow th objct plan (bottom). Figur 8 shows th tim volutions of th lin-dnsity masurd with th phas-imaging intrfromtr and th scanning intrfromtr at th cntral cll. Th agrmnt btwn th two is satisfactory whn it is takn into account that th two intrfromtrs viw diffrnt chords, that is, th horizontal and vrtical chords. Th tim dvlopmnt of th lin-dnsity profil is shown in Fig. 9. A good agrmnt btwn th profil data from th two intrfromtrs is obtaind. Th hating systms of GAMMA 10 ar opratd as follows: nitially, a plasma is injctd by magntoplasma dynamic guns (PC?) from both 21J&c; ~ CH.4 jh-,,- PG - NB CRF EC H.B ECH,P TME (ms) FG. 8. Tim volution of th lin-dnsity masurd with th scanning intrfromtr (top) and th phas-imaging intrfromtr (bottom). Phas-imaging intrfromtr 2860 i \ t 1

6 L Txid3 t= 60ms 70h-d ki.r X (cm) FG. 9. Tim volution of th lin-dnsity profil at th cntral cll. nds of th machin. Nutral bams (NB) produc sloshing ions in th plug/barrir clls. Four gyrotrons providing lctron cyclotron rsonanc hating with a frquncy of 28 GHz ar usd to gnrat magntically trappd hot lctrons that produc thrmal barrir potntial dprssion (w = 26.&, ECH-B) and warm lctrons for positiv potntial paks that confin cntral cll ions (w = w,,, ECH- P in th plug/barrir clls. on cyclotron rang of frquncy (CRF) is mployd to hat ions in th cntral cll. Th narrow profil of th gun-producd plasma xpands to a half-maximum diamtr of about 30 cm aftr additional hating. Figur 10 shows th similar data obtaind at th plug cll. n this cas, th half-maximum diamtr of th stadystat plasma is about 10 cm. Th diamtr corrsponds to an incidnt bam-width of th ECH-P gyrotrons. Th spatial rsolutions of th systms ar stimatd to b -2.0 cm at th cntral cll and cm at th plug cll, rspctivly. Ths valus ar,difficult to obtain by using convntional multichannl intrfromtrs. V. DSCUSSON n summary, millimtr-wav phas-imaging intrfromtrs hav bn constructd and applid to th GAMMA 10 tandm mirror. Two typs of intgratd dtctor arrays using bow-ti and Yagi-Uda antnnas hav bn tstd in ordr to dmonstrat th ability of th phas- FG. 10. Tim volution of (a) th lin dnsity and (b) th lin-dnsity profil at th plug cll. imaging systm. Th spatial rsolution of Yagi-Uda antnna was found to b bttr than that of bow-ti antnna. Th tim volution and radial profils of th lin dnsity hav bn succssfully masurd at th cntral cll and plug cll of GAMMA 10. ACKNOWLEDGMENTS Th authors dply acknowldg th mmbrs of th GAMMA 10 group of Univrsity of Tsukuba for thir collaboration. Spcial thanks ar du to Profssor T. shihara of Univrsity of Tsukuba for his discussion and ncouragmnt. Thy would also lik to thank Dr. Y. Harada and his group of SANYO Elctric Co., Ltd., Smiconductor Rsarch Cntr for supplying th dtctors. C. A. J. Hugnholtz and B. J. H. Mddns, Rv. Sci. nstrum. 53, 171 (1982). P. E. Young, D. P. Nikirk, P. P. Tong, D. B. Rutldg, and N. C. Luhmann, Jr., Rv. Sci. nstrum. 56, 81 (1985). H. Koglnik and T. Li, Appl. Opt. 10, 1550 (1966). 4D. B. Rutldg and M. S. Muha, EEE Trans. Antnnas Propag. AP- 30, 535 (1982). K. Uhara, T. Yonkura, H. Nishimura, K. Miyashita, and K. Mizuno, in Procdings of th 3rd Asia-Pacific Microwav Confrnc (Tokyo, Japan, 1990), p Y. Harada, Ph. D. thsis, Tohoku Univrsity, 1989 (in Japans). 7J. W. Goodman, ntroduction to Fourir Optics (McGraw-Hill, Nw York, 1968). *M. Born and E. Wolf, Principls of Optics, 6th d. (Prgamon, Oxford, 1980). 9P. E. Yang, Ph.D. thsis, Univrsity of California at Los Angls, Rv. Sci. nstrum., Vol. 62, No. 12, Dcmbr 1991 Phas-imaging intrfromtr 2861