Development of Quantitative Atomic Modeling for Tungsten Transport Study Using LHD Plasma with Tungsten Pellet Injection

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1 1 EX/P6-28 Dvlopmnt of Quantitativ Atomic Modling for Tungstn Transport Study Using LHD Plasma with Tungstn Pllt Injction I. Murakami 1, H. A. Sakau 1, C. Suzuki 1, D. Kato 1, M. Goto 1, N. Tamura 1, S. Sudo 1, S. Morita 1, and LHD Exprimnt Group 1 1 National Institut for Fusion Scinc, Oroshi-cho, Toki, Gifu , Japan contact of main author: murakami.izumi@nifs.ac.jp Abstract. Quantitativ tungstn study with rliabl atomic modling is important for succssful achivmnt of ITER and fusion ractors. W hav dvlopd tungstn atomic modling for undrstanding th tungstn bhavior in fusion plasmas. Th modling is applid to th analysis of tungstn spctra obsrvd from currntlss plasmas of th Larg Hlical Dvic (LHD) with tungstn pllt injction. W found that xtrm ultraviolt (EUV) lins of W 24+ to W 33+ ions ar vry snsitiv to lctron tmpratur (T) and usful to xamin th tungstn bhavior in dg plasmas. Basd on th first quantitativ analysis of masurd spatial profil of W 44+ ion, th tungstn concntration is dtrmind to b n(w 44+ )/n = 1.4x10-4 and th total radiation loss is stimatd as ~4 MW, of which th valu is roughly half th total NBI powr. 1. Introduction Tungstn is plannd to b usd as plasma-facing matrial of th divrtor targt for ITER and futur fusion ractors, bcaus of high mlting point, low sputtring yild by hydrogn, and low tritium invntory. Howvr, onc tungstn is sputtrd from th targt by som impuritis, it is transfrrd into th main plasma and causs radiation powr loss to cool plasma. Tungstn is not fully ionizd vn in th cor of ITER plasma with an lctron tmpratur of kv, whr tungstn is ionizd up to W 71+ (Li-lik tungstn), and radiation powr of such tungstn ions is larg. It is also important for th stabl opration of ITER to study th influx and dg transport of tungstn ions. Tungstn bhaviour in plasmas can b studid with a spctroscopic mthod, and w nd a rliabl atomic modl for tungstn to analyz spctral data. Prvious studis on tungstn atomic modlling hav not fully xplaind th tungstn xtrm ultraviolt (EUV) spctra,.g., an unrsolvd transition array (UTA) sn at nm in plasma with T < 1.5 kv [1], which corrsponds to dg plasma tmpratur for ITER. Sinc th UTA is composd of numrous insparabl mission lins, it has bn difficult to analyz th UTA quantitativly. In particular, th scond pak of UTA at ~6 nm was not rproducd by prvious work of Püttrich t al. [1]. Thy xplaind that this pak could b producd by lowr-chargd tungstn ions or via dilctronic rcombination procsss which thy did not includ in thir atomic modl, sinc thr wr no significant mission paks obsrvd in Brlin EBIT spctra [2]. Howvr, th atomic data usd in th modl of Püttrich t al. did not considr dtaild atomic structur and th numbr of nrgy lvls wr limitd up to ~2000 for on ion. Elctron impact xcitation cross sctions wr calculatd with Coulomb-Born approximation, which was rliabl only at high collision nrgy. Thrfor,

2 2 EX/P6-28 thir modl was not sufficint to analyz spctra in dtail. Th charg stat distributions in th Brlin-EBIT xprimnts wr not so wll controlld [2]. W hav dvlopd a tungstn atomic modl with dtaild atomic structur, and w validatd th modl by comparing with EUV spctra masurd from compact lctron bam ion trap (CoBIT) plasmas [3] with tungstn hxacarbonyl vapour and from th LHD plasmas with tungstn pllt injction. Th LHD discharg is ntirly stabl for substantial amount of tungstn injction xhibiting no MHD instabilitis. Th CoBIT xprimnts wll control th charg distribution of tungstn ions by changing th lctron bam nrgy which dtrmins th highst charg stat in th plasma and by controlling th vapour gas prssur of hxacarbonyl. Th information from th CoBIT spctra is absolutly hlpful to idntify th EUV lins in th LHD. In th following sctions, our tungstn atomic modl is xplaind in sction 2, and th spctroscopic xprimnts in CoBIT and LHD ar shown in sction 3. W discuss th rsults of charg stat distributions obtaind by analyzing EUV spctra of LHD discharg in sction 4, and radial profil masurmnt of W 44+ ion in sction 5. Summary is givn in sction Tungstn atomic modl As th tungstn atomic modl, w hav constructd a collisional-radiativ (CR) modl for tungstn ions. In th CR modl, w solv rat quations for population dnsitis n(i) of xcitd lvls with quasi-stady stat assumption for givn lctron tmpratur and dnsity, bcaus th rlaxation timscal of th population dnsitis for xcitd lvls is fast nough compard to th timscals for changs in lctron dnsity and tmpratur. W includ lctron-impact ionization, xcitation and d-xcitation procsss, and radiativ dcay in th rat quations. Th rat quation for th xcitd lvl i is dscribd as dn( i) / dt = j< i { C( j, i) n n( j)} + [ S( i) n + k> i k> i C( i, k) n { F( k, i) n + j< i + A( k, i)} n( k) { F( i, j) n + A( i, j)}] n( i), whr C(j,i) and F(k,i) ar lctron-impact xcitation and d-xcitation rat cofficints, n is lctron dnsity, A(k,i) is th radiativ transition probability, and S(i) is th lctron-impact ionization rat cofficint. Th rcombination procsss ar ignord sinc ths procsss ar not important for plasmas considrd hr. Enrgy lvls, radiativ transition probabilitis, lctronimpact xcitation, and ionization cross sctions ar calculatd with th HULLAC cod [4]. In th HULLAC cod, atomic structur is calculatd with Dirac Hamiltonian using paramtric potntial mthod and configuration intraction is includd. Collision cross sctions ar calculatd with a rlativistic distortd wav mthod, which is rliabl ovr a wid rang of collision nrgy. W considr lctron configurations with principal quantum numbr n up to 6 including innr-shll (1) Fig.1 Enrgy lvls for W 33+ ion, calculatd with HULLAC cod (rd) in our modl and data in ADAS databas (blu) which Püttrich t al. usd [1]. Data in ADAS considrs only 5 configurations.

3 3 EX/P6-28 xcitd stats for atomic structur and up to 20,000 J-rsolvd fin-structur lvls for on ion ar includd in th CR modl. As an xampl, nrgy lvls of W 33+ ion ar shown in Fig. 1. W considr 19 lctron configurations, i.., 4s 2 4p 6 4d 5, 4s 2 4p 5 4d 6, 4s 2 4p 6 4d 4 nl (n = 5 6 and l = 0 4), 4s 2 4p 5 4d 5 5l (l = 0 4) stats and 14,050 fin-structur lvls in total, whras ADAS datast for fin structur J-rsolvd lvls includs only 5 configurations. Rat cofficints for lctron-impact xcitation and ionization procsss ar obtaind by avraging with lctron vlocity distribution as C( i, j ) = <σ(i,j)v>. W us th Maxwllian vlocity distribution to compar with spctra takn in LHD, and mono-nrgy distribution for CoBIT spctra. Hr w xamin W q+ ions with q = and thy ar N-shll ions, i.., th outrmost lctron is in n = 4 shll for th ground stat. Ionization potntials for ths ions ar 543 2,414V [5] and thy can b sn in LHD plasmas. Spctral lin intnsitis ar obtaind with th population dnsitis of th uppr lvl for th transition as I (i, j; T, n ) = n(i) A(i, j) E(i,j), (2) whr E(i,j) is th transition nrgy and n(i) is calculatd from th CR modl with givn lctron dnsity n and tmpratur T. Using our tungstn modl, w synthsiz EUV spctra at 2 7 nm with ion dnsity distribution calculatd with assumption of ionization quilibrium [6], as shown in Fig. 2. EUV spctrum masurd in th LHD is also shown in Fig. 2. Our modl can rproduc th two-pak UTA fatur in th tungstn EUV spctra at T = 1 kv. Th first pak at ~5 nm is producd with 4d n- 1 4f 4d n transition (4f 4d transition) and th scond pak at ~ 6 nm is producd with 4d 9 4f n+1 4d 10 4f n transition of W 25+ W 28+ ions (4f 4d transition) and 4p 5 4d n+1 4p 6 4d n Fig. 2 Tungstn EUV spctra from (a) masurmnt in LHD and (b) modl calculation with assumption of ionization quilibrium with T = 0.53 kv (W 23+ -W 31+ ; dot-dashd lin), 1 kv (W 26+ -W 36+ ; solid lin), and 2 kv (W W 47+ ; dottd lin). UTA is rproducd at T < 1.5 kv and disappars at T = 2 kv forming isolatd lins. transition of W 29+ W 34+ ions (4d 4p transition). Such innr-shll transitions bcom strongr whn highr innr-shll-xcitd lvls ar includd in th modl. For xampl, population dnsitis of 4p 5 4d 6 lvls of W 33+ ion (Fig. 1) bcom largr with d-xcitation or cascad procsss from highr lvls such as 4p 5 4d 5 4f lvls, which ar not includd in th ADAS datast, thn 4p 5 4d 6 4p 6 4d 5 transitions can produc strongr 6nm UTA pak. Such procsss can occur in fusion plasmas. Sinc Püttrich t al. [1] usd limitd lvls from th ADAS atomic datasts for thir modl, thy did not rproduc th 6nm UTA pak in thir modl. For th highr lctron tmpratur cas (T = 2 kv), W 37+ W 47+ ions do not produc UTA and isolatd lins appar, as shown as th grn lin in Fig. 2b. 3. Spctroscopic masurmnts in CoBIT and LHD Tungstn EUV spctra ar masurd for plasma in CoBIT [7]. Tungstn hxacarbonyl vapor is introducd into CoBIT, and tungstn is ionizd squntially by th lctron bam and

4 4 EX/P6-28 Fig. 3 EUV spctra of tungstn ions; (a, d) CoBIT with two lctron bam nrgis E, (b, ) LHD with diffrnt cntral lctron tmpratur T 0 at t= 4.64s and 4.80s of discharg #112880, and modl calculations for (c) W 23+ W 28+ and (f) W 28+ W 34+ ions. Wavlngths in calculation at (c) ar shiftd by nm to fit th position to masurmnts. trappd by lctrostatic potntial wll in th axial dirction and by lctronic spac charg potntial in th radial dirction. EUV spctra at th nm wavlngth rgion wr masurd with various lctron bam nrgy and th charg stats of obsrvd Fig.4 Tmporal volution of stord nrgy W p, NBI port-through powr, cntral lctron tmpratur T 0, lin-intgratd lctron dnsity n l, and total radiation powr for discharg # with a tungstn TESPEL injction at 3.8s. Fig. 5 Elctron tmpratur distribution at t=3.77, 4.20, 4.64, and 4.80s for discharg # masurd by a Thomson scattring systm, as a function of normalizd minor radius. mission paks ar dtrmind. Using th CR modl, w calculatd EUV spctra with th physical condition of CoBIT, i.., n = m -3 and mono-nrgy lctron distribution with th bam nrgy and idntifid mission paks as 6g 4f, 5g 4f, 5f 4d, and 5p 4d transitions of W 19+ W 33+ ions, as shown in Figs. 3a and 3d. Th pak wavlngths shift shortr for highr charg stats and thy ar usful to dtrmin charg stat distribution in LHD plasmas. For LHD plasmas, tungstn is injctd as a coaxial impurity pllt ( mm φ x 0.7 mm L tungstn in 0.7 mm φ x 0.7 mm L cylindrical carbon) [8] or a tracr-ncapsulatd solid pllt (TESPEL, mm diamtr) [9] in NBI hatd dischargs. A pllt is ablatd in th vicinity of normalizd minor radius ρ ~ 0.8, and tungstn is ionizd and transfrrd into a cor plasma rgion for dischargs with typical cntral lctron dnsity n ~ a fw m -3. A typical NBI hatd discharg with tungstn pllt injction is shown in Fig. 4. Aftr a tungstn TESPEL was injctd at t = 3.8 s, lctron tmpratur droppd du to larg radiation loss by

5 5 EX/P6-28 tungstn at th cntral rgion and rachd th minimum tmpratur at t = 4.20 s, as also shown in Fig. 5, and rcovrd with NBI hating (t=4.64 and 4.80s). Tungstn was supposd to b accumulatd within ρ < 0.8. W masurd tungstn EUV spctra using an EUV spctromtr [10] and a SOXMOS spctromtr [11]. At nm w obsrvd similar spctra to ons masurd in CoBIT and spctra chang according to th chang of cntral lctron tmpratur. Low and high tmpratur cass ar shown in Figs. 3b and 3, rspctivly. W calculatd spctra using our modl with th plasma condition of LHD, i.., n ~ m -3 and th Maxwllian lctron vlocity distribution with givn lctron tmpratur for ach ion and synthsizd spctra with ion abundancs dtrmind to match with th masurd spctra as shown in Figs. 3c and 3f. Our modl calculations wll rproduc th LHD spctra with mission paks of 6g 4f and 5g 4f transitions of W 23+ W 28+ for lctron tmpratur T = 0.7 kv cas (Fig. 3c), and mission paks of 5f 4d, 5g 4f, and 5p 4d transitions of W 28+ W 34+ for T = 1.4 kv (Fig. 3f). Spctral proprty is changd at W 28+ ion rflcting a chang in th atomic structur of tungstn ions. Th ground stat of W 28+ ion is 4d 10 and on of W 27+ ion is 4d 10 4f. Thus 4f ng transitions ar dominant for W 27+ and lowr chargd ions, but 4d nl transitions ar dominant for W 28+ and highr chargd ions. Fig. 6 Charg distribution of tungstn ions obtaind by fitting to th masurd LHD spctra ( and ), and calculatd o ns in ionization quilibrium obtaind in [6](purpl lins) and in [12] (grn lins). Fig. 7 Tungstn EUV spctra at 3.75s (black) bfor pllt injction of 3.80s, at 4.35s (rd) with T 0 ~3kV, and at 5.35s (grn) with T 0 ~1kV masurd in LHD NBI-discharg # Th dtrmind charg stat distributions of tungstn ions ar shown in Fig. 6. For th lowr tmpratur cas, W 25+ ion is th most abundant (solid circls), and W 29+ ion is th most abundant for th highr tmpratur cas (solid triangls). For comparison, w also plot charg distributions in ionization quilibrium calculatd by two modls [6, 12]. Dtails ar discussd in th nxt sction. As calculatd with our tungstn modl shown in Fig. 2b, th UTA at 5 7 nm was sn for LHD plasma with T 0 ~ 1 kv and not sn with T 0 ~ 3kV, as shown in Fig. 7. In this discharg, th dpositd tungstn amount to th plasma was small and th lctron tmpratur of th cor plasma did not drop as in Fig. 5. Th lctron tmpratur was kpt high vn aftr th tungstn pllt injction at 3.8 s and mission lins of W 40+ W 45+ ions wr obsrvd at T 0 ~ 3 kv, and such discrt lins ar usful to xamin th tungstn bhaviour.

6 6 EX/P Charg stat distributions As shown in Fig. 6, w obtaind charg stat distributions of tungstn ions using EUV spctra at nm. W can compar thm with xpctd distributions from ionization quilibrium calculations. Sasaki and Murakami [6] constructd a larg-scal collisionalradiativ modl with configuration avragd lvls to calculat tungstn ion dnsitis in ionization quilibrium condition. Many autoionizing lvls wr includd and dilctronic rcombination procss was tratd xplicitly as lctron-captur to autoionizing lvls, followd by radiativ dcay to bound lvls. Th xcitation-autoionization procss is also naturally includd in th modl. Ionization rat cofficints wr calculatd with Lotz s mpirical formula [13]. Traditionally, ADPAK [14] atomic datasts ar widly usd for ionization quilibrium calculations. This modl is basd on an avrag ion modl and dtaild atomic structurs ar not considrd. Asmussn t al. [12] proposd to modify th ionization rats of tungstn in this packag in ordr to xplain xprimnts don in ASDEX Upgrad. Thy incrasd th ionization rats by a factor of up to 3 for W q+ with q > 30. A part of this factor is xplaind as th xcitation-autoionization procss. W also us thir rats to calculat charg stat distributions in ionization quilibrium for a comparison. Figur 6 shows that th quilibrium ion abundanc distributions of Sasaki and Murakami modl ar shiftd toward highr charg stats than th masurmnts for th sam lctron tmpratur. To obtain th sam maximum charg stat in th distributions as to th masurmnt, lowr lctron tmpratur must b assumd, i.., T ~ 0.4 kv for th T 0 = 0.7 kv cas, and T ~ 0.9 kv for th T 0 = 1.4 kv cas. On th othr hand, th abundanc distributions calculatd with th modifid ADPAK rats of Asmussn t al. [12] show closr maximum charg sat to th masurmnts with almost th sam lctron tmpratur for both cass. Intrstingly, abundanc calculation by Püttrich t al. [15] indicats th sam tndncy. Th rason that th modls of Amussn t al. and Püttrich t al. giv th similar charg distribution is probably that thy modifid atomic data to fit to thir xprimnts. Püttrich t al. usd ionization rats calculatd by configuration avragd distortd wav mthod [16], but thy modifid th rcombination rats from ADPAK to xplain xprimnts. Th Sasaki and Murakami modl dos not modify any atomic data artificially. Thir modl calculation shows good agrmnt with xprimnts for th lin ratio of W 44+ and W 45+ lins, although thir ionization and rcombination rats ar both largr than othr modls. Th discrpancis btwn Th Sasaki and Murakami modl and masurmnts indicat that ionization of tungstn procds to highr charg stats than xpctd from masurmnts at a fixd tmpratur bcaus of larg ionization rats or larg rcombination rats. Th EUV spctra at nm of this discharg shown in Fig. 3 show vry rapid tim variation, following th chang of th cntral lctron tmpratur. It mans that th charg stat distribution follows th chang of lctron tmpratur vry wll and th tungstn ions sm to b in ionization quilibrium. W do not includ th ffcts of transport and spatial profils in this analysis yt, thus w nd to xamin such ffcts. In addition, w nd indpndnt validation for ionization and rcombination rats of tungstn ions. 5. Radial profil of tungstn ion As shown in Fig. 7, W 44+ and W 45+ ions hav discrt mission lins at ~6 nm sinc thir atomic structurs ar simplr than lowr chargd ion such as W 33+, bcaus thir ground stats

7 7 EX/P6-28 ar 3d 10 4s 2 for W 44+ ion and 3d 10 4s for W 45+ ion, rspctivly. Sinc th ionization potntial of 3d shll is larg and innr-shll ionization of a 3d lctron is not asy, thir transitions ar similar to H-lik ion and H-lik ions. Th 4s4p 4s 2 transition of W 44+ ion at 6.09nm can b usd to masur its radial intnsity profil. A radial intnsity profil of W 44+ ion at 6.09nm was masurd for th NBI hatd discharg with tungstn pllt injction. Similar to th discharg shown in Fig. 4, th lctron tmpratur droppd aftr a tungstn impurity pllt injction, and thn rcovrd latr. During th tmpratur rcovry phas, it rachd ~3kV and 6.09nm lin was Fig. 8 Radial missivity profil of W 44+ lin at 6.09 nm against normalizd minor radius ρ, fittd by calculation for NBI hatd discharg # masurd. Applying Abl invrsion tchniqu, w obtain cntrally pakd local missivity profil, shown as a solid lin in Fig. 8. W calculat radial profil of tungstn ion distribution by continuity quation in cylindrical gomtry, whr w assum diffusion cofficint and convctiv vlocity as D = 0.2m 2 /s and V = -1 m/s as typical valus. Cntrally concntratd profil is obtaind as a dottd lin in Fig. 8. Discrpancy in calculatd profil at ρ >0.5 may b causd by contamination of lowr chargd ions. Sinc th tungstn pllt is usually ablatd in th vicinity of ρ ~ 0.8, th pakd profil indicats that th tungstn is transfrrd from th dg to th cor. Quantitativ analysis basd on our modl can dtrmin th tungstn concntration at plasma cntr as n( W 44+ ) / n = 1.4 x In addition, th total radiation powr from tungstn is stimatd as ~ 4 MW, which is th dominant componnt in th total radiation loss and approximatly half th total NBI input powr of 8.2 MW. 6. Summary W hav constructd th tungstn atomic modl including many fin structur lvls and can us th modl for dtaild analysis of spctra to xamin tungstn bhavior in fusion plasmas. Th atomic modl is validatd by comparing calculatd spctra with masurd ons with CoBIT and LHD. W obtaind good agrmnt for EUV spctra of W 20+ W 33+ ions at nm wavlngth rgion for th CoBIT masurmnts and th modl calculation and w idntifid mission paks as n=6 4 and 5 4 transitions. W injctd a tungstn pllt into NBI hatd discharg of LHD and obtaind tungstn EUV spctra similar to ons masurd in CoBIT. Using mission paks at nm of n = 5 4 transitions w can dtrmin charg stat distribution for W 20+ W 33+ ions for th LHD plasma. Ths ions ar producd in plasma with lctron tmpratur from ~ 0.3 kv to ~ 1.5 kv and ths paks ar vry snsitiv to lctron tmpratur. This tmpratur rgion corrsponds to priphral plasma in ITER. Th obtaind charg stat distributions from EUV spctra ar compard with calculations by th atomic modl of Sasaki and Murakami [6] and modifid ADPAK of Asmussn t al. [12] in ionization quilibrium. Th thortical modl of Sasaki and Murakami shows discrpancy from th masurmnts, and w nd to find a mthod of validation on ionization and rcombination rats.

8 8 EX/P6-28 Our modl can rproduc th two-pak charactristics of th UTA at 4 7 nm. Th scond pak at ~ 6 nm is producd with 4d 9 4f n+1 4d 10 4f n transition of W 25+ W 28+ ion and 4p 5 4d n+1 4p 6 4d n transition of W 29+ W 34+ ions. Highr innr-shll xcitd stats and th transitions btwn th innr-shll xcitd stats ar important to rproduc th ~ 6 nm pak. A radial missivity profil of W 44+ ion is masurd using 6.09nm mission lin. This is th first masurmnt of th radial profil of tungstn ion in th LHD. Prforming ondimnsional transport calculation, w stimat th tungstn ion dnsity at th plasma cntr rlativ to th lctron dnsity as n( W 44+ ) / n = 1.4 x Th total radiation powr from tungstn is stimatd as ~ 4 MW and this is a dominant componnt of radiation powr for NBI hatd discharg. Acknowldgmnts Th authors acknowldg all mmbrs of th LHD Exprimnt Group for thir tchnical support and fruitful discussions. This work is supportd partly by JSPS Grant-in-Aid for Scintific Rsarch (A) and (B) , JSPS Grant-in-Aid for Young Scintists (B) , and th JSPS-NRF-NSFC A3 Forsight Program in th fild of Plasma Physics (NSFC: No ). Rfrncs [1] T. Püttrich t al., AIP Conf. Proc (2013) 132. [2] R. Radtk t al., Phys. Rv. A 64 (2001) [3] N. Nakamura t al., Rv. Sci. Instrum. 79 (2008) [4] A. Bar-Shalom t al., J. Quant. Spctr. Rad. Transfr 71 (2001) [5] A. Kramida, Yu. Ralchnko, J. Radr, and NIST ASD Tam (2013). NIST Atomic Spctra Databas (vr. 5.1), [Onlin]. Availabl: [2014, July 7]. [6] A. Sasaki and I. Murakami, J. Phys. B: At. Mol. Opt. Phys. 46 (2013) [7] H. A. Sakau t al., AIP Conf. Proc (2012) 91. [8] R. Katai, S. Morita, M. Goto t al., Jpn. J. Appl. Phys. 46 (2007) [9] S. Sudo, J. Plasma Fusion Rs. 69 (1993) [10] M.B.Chowdhuri, S.Morita, M.Goto, t al., Rv. Sci. Instrum. 78 (2007) (7p). [11] J. L. Schwob t al., Rv. Sci. Instrum. 58 (1987) [12] K. Asmussn t al., Nucl. Fusion 38 (1998) 967. [13] W. Lotz, Z. Phys. 216 (1968) 241. [14] D. Post t al., At. Data Nucl. Data Tabls 20 (1977) 397. [15] T. Püttrich t al., Plasma Phys. Control. Fusion 50 (2008) (27pp). [16] S. D. Loch t al., Phys. Rv. A, 72 (2005)