J. Plasma Fusion Rs. SERIES, Vol. 9 (010 A Slf-calibration thod for th Edg Thomson Scattring Diagnostic in ITER Eiichi Yatsuka, Takaki Hata, Yoshinori Kusama Japan Atomic Enrgy Agncy (Rcivd: 0 Novmbr 009 / Accptd: 5 January 010 Calibration of spctral transmissivity of th collction and transmission optics is on of th most crucial issus for th Thomson scattring diagnostic systm. Radioactivation of th vacuum vssl in ITER maks it difficult to calibrat spctral transmissivity in aras nar th vacuum vssl. By using an additional calibration lasr whos wavlngth diffrs from thos of th diagnostic lasr and quipping two lasrs with Thomson scattring lights, w can obtain th lctron tmpratur and th rlativ transmissivity of ach spctral channl of th polychromator from th Thomson scattring signal itslf. A ruby lasr is a promising candidat as a calibration lasr bcaus th wavlngth dos not divrg gratly from that of a diagnostic lasr and from th lowr limit of an obsrvabl wavlngth. Evn if th signal-nois ratio dgrads, th availabl lctron tmpratur data during calibration oprations rmain largly unaffctd. A dgrading signal-nois ratio incrass statistical rror in lctron tmpratur data and rlativ spctral transmissivity. Evn whn th spctral transmissivity is unknown, lctron tmpratur data may b obtaind within a 10% margin of rror, which fulfills th rquirmnts for dg lctron tmpratur masurmnt in ITER. Kywords: Thomson scattring, ITER, Slf-calibration, Spctral transimissivity, Statistical rror analysis 1. Introduction Incohrnt Thomson scattring diagnostics is a standard mthod to masur profils of lctron tmpratur T and lctron dnsity n in fusion plasmas. Th dg Thomson scattring diagnostics for ITER is rquird to masur th rgion in which r / a 0.85, whr r and a dnot th minor radii of a masurmnt point and th sparatrix, rspctivly. Errors in dg plasma diagnostics ar rquird to b lss than 10% for T and 5% for n in th rang of 50 V to 10 kv, and 5 10 18 to 3 10 0 m -3, rspctivly [1. To satisfy ths rquirmnts, it is ncssary to dvlop a high-powr lasr and high-prformanc spctroscopic optics. A 5-J, 100-Hz YAG lasr will b installd for th dg Thomson scattring systm [, so a polychromator systm will b mployd to analyz th spctrum for Thomson scattring. Optimization of th band pass filtrs of th polychromator for th dg Thomson scattring systm in ITER was xamind by Kaita [3,4. In this optimization, th rrors of T wr valuatd rlativ to th rror in th numbr of dtctabl photons for ach spctral channl. Howvr, th dtrioration in spctral transmissivity by browning as a rsult of nutron and gamma ray irradiation and chmical sputtring, was not considrd. Dtrioration in spctral transmissivity causs not only a drop in th total numbr of dtctabl photons but also introducs svr systmatic rror in th masurmnt of T. For instanc, if th dtrioration of transmissivity in th shortr-wavlngth rgion is largr than that in th longr-wavlngth rgion, T will b obsrvd as a lowr valu than th tru T. An in-situ slf-calibration mthod of rlativ transmissivity of th optical systms for Thomson scattring diagnostics was proposd by Smith [5. In this mthod, a calibration lasr having a diffrnt wavlngth from that of th diagnostic lasr is applid to valuat th rlativ transmissivity of ach spctral channl of th polychromator, which can b calibratd by th Thomson scattring signal. W applid Smith s mthod for th dg Thomson scattring systm in ITER. Th obctivs of this work ar to clarify what kind of lasr is promising, to valuat how hot and dns th plasma nds to b for th slf-calibration opration and to valuat th magnitud of th statistical rror of paramtrs rlatd to th slf-calibration mthod. W valuatd th statistical rror of T C numrically, whr dsignats a spctral channl and C dnots th transmissivity dtrioration factor (< 1 from baslin, i.. at calibration. Sction dscribs how to simulat xprimnts and to apply th slf-calibration mthod to th dg Thomson scattring systm in ITER. In sction 3, th statistical rror of th slf-calibration mthod is valuatd and its availability is vrifid through similar procdurs via xprimntal data analysis. Conclusions ar dscribd in sction 4. author s -mail: yatsuka.iichi@aa.go.p 1 010 by Th Japan Socity of Plasma Scinc and Nuclar Fusion Rsarch
E. Yatsuka t al., A Slf-Calibration thod for th Edg Thomson Scattring Diagnostic in ITER. Calculation of th dg Thomson scattring diagnostics Figur 1 shows th flow chart of th numrical xprimnts. At first, w assumd T, n and C. A st of band-pass filtrs of th polychromator was prviously dtrmind to minimiz th maximum rror of T in 50 18 V < T < 10 kv whn n 510 m -3, a condition which yilds th highst dgr of statistical rror bcaus of th minimum dtctabl numbr of photons. Signal and nois wr valuatd using th configuration and paramtrs of dg Thomson scattring in ITER, as shown in Fig. and Tabl 1, rspctivly. Statistical rror in th numbr of dtctabl photons is usd to calculat th signal variabl and was computd by using a random numbr whos shap is Gaussian with a standard dviation of,, as dfind in Eqs. (1, ( and (4. Thraftr, T and n C wr fittd through th last-squars mthod, and ths paramtrs subsquntly wr compard with assumd valus. Th numbr of photons du to Thomson scattring from th lasr dtctd in th th spctral channl N S,, ( = (main, C (calibration can b writtn as Thomson scattring [6,7, th quantum fficincy of th avalanch photo diod (APD and spctral transmissivity of optics, rspctivly; and ( S i, i, ( S and i, dnots th scattrd and incidnt wavlngths of lasr, mc T (m and dnot th lctron rst mass and th Boltzmann constant, rspctivly. Th normalizd wavlngths 1, and, corrspond to th lowr and uppr wavlngth boundaris of th th spctral channl. Othr nomnclatur is shown in Tabl 1. Wavlngth dpndnc upon spctral dnsity in th cas of T = 10 kv, which corrsponds to th uppr rquirmnt N S,,, i,ei, C nr Δl S(,, ( T( d hc 1, C n g, ( T, (1 whr h, c, S (,,, ( and T ( dnot th Planck constant, light spd, th spctral dnsity of Assum, T, n and C (whr dsignats a spctral channl Fig. Configuration of dg Thomson scattring diagnostic systm. Evaluat th Signal (Thomson scattring and Nois (brmmstrahrung Add statistical rror for th numbr of dtctd photons using a random numbr with a Gaussian distribution Prform ast-squars fitting Compar assumd paramtr valus with th fittd ons Conduct aggrgat avraging and rror valuation Fig. 1 Flow chart of numrical calculations. Tabl 1 Paramtr list symbol maning valu E i, ain lasr puls nrgy 5 J i, Wavlngth of main lasr 1064 nm d i asr diamtr 5 mm Δl Scattring lngth 5 mm Solid angl 10 msr Scattring angl 140 Z ff Effctiv charg numbr 3 K Enhancmnt factor Δt Gat opning tim 30 ns D Effctiv lngth of plasma 4.5 m Fig. 3 Spctrums of Thomson scattring whn T =10 kv. Fig. 4 Assumd transmissivity and quantum fficincy of APD. 13
E. Yatsuka t al., A Slf-Calibration thod for th Edg Thomson Scattring Diagnostic in ITER of dg T masurmnts in ITER, is shown in Fig. 3. In th cas of 140 dgr scattring, which approximatly corrsponds to th dg Thomson scattring diagnostics in ITER, th lowr rang of th spctrum of Thomson scattring lis around D β lin (486 nm. Figur 4 shows th simulatd quantum fficincy of th APD (Hamamatsu Photonics SP 5068 and transmissivity of optics (1 Rhodium mirror, Aluminum mirrors and Fluorin-dopd silica cor OH-fr optical fibr [8. For background nois, w considrd only brmmstrahlung radiation. An intns lin spctrum,.g. D α (656 nm, incrass th lvl of background radiation. Thrfor, w fixd th boundary of a band-pass filtr (a sgmnt of th polychromator at 656 nm to rduc th D α lin spctrum. In addition, to rduc th D β lin spctrum w limitd th lowr limit of th obsrvd wavlngth so that it is not shortr than 486 nm. In this way, w liminatd th two most dominant lin spctra using th band-pass filtr. Th spctrum of brmmstruhlung is writtn as N B, whr C d Δsin ΔtK 8 3 ( r 3 i i, s mc (1 ds, 1, n Z 4Ti, (1 ln hc i, T (1 ( ( ( d hc ff mc T xp T, (, (3 whr dnots th Eulr s constant, and K dnots th nhancmnt factor rprsnting th diffrnc btwn th thortical and masurd brmmstruhlung intnsitis arising du to th multi-rflction in th vacuum vssl and impurity radiation. Th Gaunt factor was valuatd using a low-frquncy Born approximation [9. In quations ( and (3, th wavlngth is normalizd so that it corrsponds to that of th main lasr as a mattr of convninc. In this papr, th spcial intgration of th brmmstruhlung was approximatd using th avragd valu on th viwing path, i.. T = 1 kv, n = 1. 10 0 m -3 and th ffctiv lngth of th plasma D = 4.5 m, rspctivly [3,10. Sinc NS,, is proportional to both n and C, w cannot obtain n and C indpndntly solly from th Thomson scattring lights. Obtainabl paramtrs through th application of Smith s slf-calibration mthod ar T C. Th numbr of unknown paramtrs is 1 plus th numbr of spctral channls. If th main and calibration lasrs ar fird at diffrnt tims, th numbr of obtainabl signals ( th numbr of spctral channls is sufficint to fit all unknown paramtrs. Thus, w nd to masur th Thomson scattring lights from th main and calibration lasrs sparatly. A concptual timing chart of th slf-calibration mthod is shown in Fig. 5. A typical valu of statistical rror for th numbr of dtctabl photons du to Thomson scattring is rprsntd as i, hc (1, (4, N S,, NB, Fig. 5 Concptual timing chart of th slfcalibration mthod. For simplicity, a 3-spctral channl systm is assumd. Th wavform will b distortd du to th charactristics of th APD circuit,.g. capacitanc. In this xampl, th fittd paramtrs ar T, n C 1, n C C 3, (1+3 paramtrs whras th obtainabl paramtrs ar N S,1,, N S,,, N S,3,, N S,1,C, N S,,C, and N S,3,C ( 3 paramtrs. whr th scond factor of th arriving photons du to brmmstruhlung indicats that th Thomson scattring signal, dtctd xprimntally, will contain background radiation. Thrfor, w nd to subtract this signal from th valus of a signal without Thomson scattring light, i.. background light. W invstigatd th ffct of brmmstrahlung on th validity and availability of th slf-calibration mthod. In this papr, th polychromator was dsignd to b optimizd for standard xprimnts; i.., only th main lasr is considrd and th transmissivity dtrioration factor C is assumd to hav a valu of 1 for all spctral channls. With th Gaussian assumption, th probability P ( T, n of obsrving X with a standard dviation, for obsrvations about th tru valu N S,, ( T, n is 1 1 X NS, P( T, n xp, so that on can obtain th most probabl minimizing th following [11,1: ( T, n, (5 T by. (6 Sinc th first trm of Eq. (5 is th normalizd paramtr, th statistical rror for T is valuatd from. Th paramtr may b paraboloid around th most probabl T. Thus, w dfind th statistical rror of T through a Taylor xpansion of around th minimum valu 0 and assignd 1 for dviations from : whr 0 T T g, and,,( T, n 1 n n 1 X NS, n g,,,, ( g 1, g, (7, (8 g dnot th first and scond,,, g, 1 14
E. Yatsuka t al., A Slf-Calibration thod for th Edg Thomson Scattring Diagnostic in ITER drivativs of g, with rspct to T, rspctivly. Th polychromator was optimizd in ordr to minimiz th maximum statistical rror of T in 50 V < T < 10 kv 18 whn n 510 m -3. Figur 6 shows th dpndnc of T upon th statistical rror of th optimizd polychromator. A band-pass filtr of optimizd sgmnts is summarizd in Tabl. W usd this polychromator for valuating th slf-calibration mthod. Fig. 7 Rlationship btwn calibration lasr and statistical rror of T. An additional sgmnt was st at 53 nm, which coincids with th wavlngth of th scond harmonic YAG lasr. Th blu (rd arrow shows th availabl T with an alxandrit (ruby lasr. (a Fig. 6 Rlativ statistical rrors of optimizd polychromator. Tabl Optimizd polychromator sgmnts. Channl No. Cntr [nm Width [nm 1 571 170 759 06 3 897.8 71.6 4 995.1 13 5 1060.3 7.4 6 1070 1 3. Availability of th slf-calibration mthod In this sction, w invstigatd th availability of th slf-calibration mthod in a mannr similar to th arlir data analysis xprimnts. Th slf-calibration mthod dos not nd to b availabl ovr th ntir rang of valus for th paramtrs T. orovr, in principl, w should not rquir knowing th valus of T for a plasma during slf-calibration oprations. Th ovrlap of spctra of th main and calibration lasrs nabls us to calibrat th spctral transmissivity in th slf-calibration mthod. W invstigatd thr lasrs as candidats for a calibration lasr: a scond harmonic YAG lasr ( J, 53 nm, a ruby lasr (5 J, 694.3 nm and an alxandrit lasr (1.5 J, 800 nm. Thir puls nrgis wr assumd from past prformanc of commrcial lasrs of ach typ. Sinc th optimizd polychromator (s Tabl dos not hav a sgmnt around th wavlngth of th scond harmonic of th YAG lasr, w invstigatd th ffct of an additional sgmnt insrtd at 53 nm. As shown in Fig. 7, T at calibration was wll fittd using an Alxandrit lasr (> 0.5 kv and a Ruby (> 1.5 kv lasr as calibration lasrs. On th othr hand, if th scond harmonic YAG lasr wr usd as a calibration lasr, w Fig. 8 R-construction of rlativ transmissivity whn (a T = kv T =10 kv. could obtain a simulatd valu for T vn whn T xcds 10 kv, which corrsponds to th uppr rquirmnt of dg T masurmnts. Sinc th additional sgmnt did not ssntially improv th rsults of th fitting, it is suggstd that this is not causd by th problm of optimization of th polychromator. If th scond harmonic YAG lasr wr usd as a calibration lasr, thn whthr w can calibrat T or not dpnds on th unavoidabl rror of th dtctd, arriving photons in th dg Thomson scattring diagnostics in ITER. In this simulation, n was assumd to b 5 10 19 m -3. On th othr hand, Pachr prdictd n and T to b approximatly qual to 5.5 10 19 m -3 and 3.5 kv, rspctivly, at th sparatrix of an H-mod plasma [10. If a calibration is carrid out using an H-mod plasma, an alxandrit lasr 15
E. Yatsuka t al., A Slf-Calibration thod for th Edg Thomson Scattring Diagnostic in ITER and a ruby lasr will b usful for calibrating T. Sinc th wavlngth of th scond harmonic YAG lasr is so far from th main (fundamntal YAG lasr s wavlngth, th spctra of th main and calibration lasrs hardly ovrlap. Thrfor, w concludd that th scond harmonic YAG lasr is not promising as a calibration lasr in dg Thomson scattring in ITER. Not that for valuating th availability of th slf-calibration mthod, it is important to r-construct not only T but also all n C. Figur 8 shows th rlationship btwn th fittd and simulatd rlativ spctral transmissivity. W compard a ruby and an alxandrit lasr bcaus thy ar promising candidats as calibration lasrs from th viw point of T fitting. A ruby lasr givs significantly lss rror for th shortst spctral channl of th polychromator compard to an alxandrit lasr whn T at calibration is rlativly low (lss than svral kv. This tndncy rmaind tru vn whn th powr of th ruby and an alxandrit lasrs was th sam. Thus, w concludd that th wavlngth is th most important paramtr for dtrmining th calibration lasr. In addition, a ruby lasr is on of th most promising lasrs bcaus its wavlngth dos not diffr much from that of th main lasr and from th lowr limit of masurd wavlngths. In addition, th fixd sgmnt (656 nm to rct th intns lin spctrum of D α is nar th wavlngth of th ruby lasr (694.3 nm. As such, on may not hav to add an xtra sgmnt to th polychromator for th slf-calibration mthod. W invstigatd th statistical rror of th paramtrs obtaind through th slf-calibration mthod. W carrid out numrous trials (100 tims to valuat th validity and availability of th slf-calibration mthod whil changing th initial condition of th random numbr cration. Rsults indicat that T may b obtaind within an adquat margin of statistical rror (< 10% from a singl calibration opration using a 5-J ruby lasr. If th absolut transmissivity of a spctral channl is obtaind, thn it is possibl to obtain valus for all othr spctral channls. Tabl 3 shows th rsults whn T quals kv. Rsults do not chang significantly whn T quals 10 kv, th uppr limit rquirmnt for dg T masurmnts. Thrfor, if it is ncssary to obtain rlativ spctral transmissivity with a smallr margin of rror than that of th normal dviation, w should collct data from all calibration oprations and avrag th rsults. Sinc th transmission rgions of band-pass filtrs for long-wavlngth spctral channls of th polychromator ar much narrowr than thos of short-wavlngth channls, th statistical rror of rlativ spctral transmissivity in th long-wavlngth rgion may b rducd by incorporating ths channls. Figur 9 shows th ffct of incorporating th long-wavlngth channls with a simulatd T of kv. Th statistical rror of rlativ spctral transmissivity can b rducd by Tabl 3 Statistical rrors of fittd paramtrs. Th numbr of trials is 100. Valu Simu- Fittd Normal latd an Dviation T [kv 65 V.00.01 (3.80 % n C 1 (486-656 nm 0.0087 [10 0 m -3 0.369 0.369 (.37 % n C (656-86 nm 0.0059 [10 0 m -3 0.413 0.413 (1.4 % n C 3 (86-933.6 nm 0.0101 [10 0 m -3 0.446 0.446 (.6 % n C 4 (933.6-1056.6 0.0058 nm [10 0 m -3 0.469 0.469 (1.4 % n C 5 (1056.6-1064 nm 0.07 [10 0 m -3 0.484 0.48 (4.68 % n C 6 (1064-1076 nm 0.0185 [10 0 m -3 0.486 0.488 (3.80 % Fig. 9 By incorporating 3 longst-wavlngth channls of th polychromator, th statistical rror of rlativ spctral transmissivity was rducd. incorporating th narrow spctral channls. Howvr, ths narrow spctral channls play a crucial rol in dtrmining a rlativly low T. As such, it rmains unclar whthr obtaining avragd rlativ spctral transmissivity using multi-channl data is th bst mthod. Sinc th signal-nois ratio dcrass by a dcrmnt of n, w invstigatd th availability of th slf-calibration mthod for low n oprations. As shown in Fig. 10 (a, th lowr limit of T during calibration oprations dos not chang vn whn n dcrass by 80%. On th othr hand, th statistical rror at high (> 5 kv T bcam wors bcaus of a dcras in th dtctabl numbr of photons at longr-wavlngth spctral channls of th polychromator; i.., th dtctabl numbr of photons du to brmmstrahlung is rlativly low bcaus of th narrow transmission rgion. Th dtctabl numbr of photons du to Thomson scattring of th main (YAG lasr bcoms larg whn T is low. Thrfor, vn if n bcoms small, th lowr limit of availabl T for slf-calibration dos not chang. As xpctd, th ratio of th rlativ rror for rlativ spctral transmissivity bcam small as n incrasd (s Fig. 10. 16
E. Yatsuka t al., A Slf-Calibration thod for th Edg Thomson Scattring Diagnostic in ITER (a th collction optics of th Thomson scattring systm in th JT-60U. Th statistical rror of rlativ spctral transmissivity riss as th gat opning tim incrass (s Fig. 11. Howvr, rsults indicat that th rror did not significantly worsn. Th gat opning tim will not limit th availabl conditions for calibration oprations of th dg Thomson scattring diagnostics in ITER. Fig. 10 (a Rlationship btwn statistical rror of (a T rlariv spctral transmissivity. 4. Conclusions Calibration of spctral transmissivity of collction and transmission optics is on of th most crucial issus for th Thompson scattring diagnostic systm. By using an additional lasr with a diffrnt wavlngth from that of th main diagnostic lasr and fitting two Thomson scattring signals from both lasrs sparatly, w can calibrat rlativ spctral transmissivity. Sinc an ovrlap in th spctra of th main and calibration lasrs nabls th rflction of both lctron tmpratur and spctral transmissivity in th shap of a spctrum, th availability of this mthod dpnds on th wavlngth of th additional lasr. A Ruby lasr is promising bcaus its wavlngth dos not diffr significantly from that of both th main (YAG lasr and from th lowr obsrvabl limit. Th lctron tmpratur and lctron dnsity suitabl for calibration xcd 1.5 kv and svral 10 19 m - 3, rspctivly. Evn whn th spctral transmissivity is unknown, w can obtain an lctron tmpratur within a 10% margin of rror, which corrsponds to th rquirmnts of dg tmpratur masurmnts in ITER. Acknowldgmnts On of th authors (E. Y. thank th mmbrs of ITER Diagnostic Group in Japan Atomic Enrgy Agncy for usful discussion and informativ commnts. Fig. 11 Rlationship btwn statistical rror of (a T rlariv spctral transmissivity and gat opning tim of collction optics. Sinc th dtctabl numbr of photons du to brmmstruhlung will b much gratr (10 tims or mor than that du to Thomson scattring in ITER dg Thomson scattring diagnostics, th ffct of brmmstruhlung on statistical rror should b valuatd. As shown in Fig. 11 (a, if w nglct th ffct of brmmstruhlung, th availabl T for calibration droppd to lss than 1 kv. On th othr hand, thr is a slight incras in th lowr limit of T for calibration whn th gat opning tim bcoms 100 ns, which corrsponds to [1 A. J. Donn t al., Nucl. Fusion 47, S337 (007; rcntly, rquird obsrvation rgion was changd to r/a > 0.85. [ T. Hata t al., Trans. Fusion Sci. Tchnol. 51, 58 (007. [3 S. Kaita t al., Rv. Sci. Instrum. 79, 10E76 (008. [4 S. Kaita t al., Fusion Eng. Ds. 84, 14 (009. [5 O. R. P. Smith t al., Rv. Sci. Instrum. 68, 75 (1997. [6 T. atoba t al., Japan. J. Appl. Phys. 18, 117 (1979. [7 O. Naito t al., Phys. Fluids B 5, 456 (1993. [8 T. Kakuta t al., J. Nucl. atr. 307-311, 177 (00. [9 I. H. Hutchinson, Principls of Plasma Diagnostics (Cambridg Univrsity Prss, Cambridg, 00 p. 197. [10 G. W. Pachr t al., Plasma Phys. Controlld Fusion 46, A57 (004. [11 P. R. Bvington, D. K. Robinson Data Rduction and Error Analysis for th Physical Scincs (c-graw-hill, Nw York, 003 p. 104. [1 A. P. illar t al., Plasma Phys. Controlld Fusion 4, 337 (000. 17