Predicted effects of parallel temperature gradients on the overestimation of TCV divertor target Langmuir probe T e measurements

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1 Journal of Nuclar Matrals (23) Prdctd ffcts of paralll tmpratur gradnts on th ovrstmaton of TCV dvrtor targt Langmur prob T masurmnts J. Horack a, *, R.A. Ptts a, P.C. Stangby b, O. Batshchv c, A. Loart d a CRPP-EPFL, Batmnt PPB, Lausann, CH-115, Swtzrland b Insttut for Arospac Studs, Unvrsty of Toronto, Canada M3H 5T6 c Lodstar/MIT, Cambrdg, MA 2139, USA d EFDA-CSU, Max Planck Insttut f ur Plasmaphysk, D Garchng, Grmany Abstract Durng hgh rcyclng condtons and dvrtor dtachmnt n th TCV tokamak, dvrtor targt Langmur probs nvr masur lctron tmpraturs much blow 5 V. Cod smulatons usng B2 EIRENE of ths plasmas ndcat that T 1 V. Ths nconsstncy has also bn sn n othr tokamaks. In ths papr, th nflunc on a thortcal Langmur prob VI-charactrstc of a strong T gradnt paralll to th magntc fld s xamnd by usng B2 EIRENE smulatd T and n profls and adoptng a smpl numrcal approach to comput dvrtor targt lctron nrgy dstrbuton functons. Standard fttng of ths thortcally gnratd VI-charactrstcs rsults n a tmpratur vry clos to th prdctd valu at th hghst dnsts corrspondng to dvrtor dtachmnt n TCV. At ntrmdat dnsts, th computd tmpratur at th nnr targt s found to b vry snstv to assumptons rgardng th magntud of th assumd lctron collson man-fr-path. Ó 23 Elsvr Scnc B.V. All rghts rsrvd. PACS: 52.7.)m; 52.7.Ds Kywords: Tokamak; Dvrtor; Langmur prob; Collsonalty; Tmpratur gradnt 1. Introducton It s frquntly obsrvd, but nfrquntly rportd, that tokamak dvrtor targt Langmur probs undr hgh rcyclng and dtachd condtons yld lctron tmpraturs hghr than thos masurd by altrnatv mthods,.g. spctroscopy, Thomson scattrng and thrmography, s.g. [1]. In partcular, th vry low T (1 V) assocatd wth strongly rcombnng dtachd or partally dtachd dvrtor plasmas ar oftn not rproducd by probs, wth valus n th rang T 5V bng typcal. Ths s rgularly xprncd n th TCV * Corrspondng author. Tl.: ; fax: E-mal addrss: jan.horack@pfl.ch (J. Horack). tokamak [2]. In such plasmas, strong tmpratur and dnsty gradnts paralll to th magntc fld ars whch may prturb th form of th targt lctron nrgy dstrbuton functon (EDF), partcularly at hgh nrgs, snc fastr lctrons orgnatng furthr upstram of th dvrtor may travl collsonlssly to th targts. Bcaus Langmur probs ar snstv only to th hgh nrgy tal of th dstrbuton, such dstortons can lad to ovrstmatd prob T and subsqunt undrstmaton of th local dnsty (snc n / T 1=2 ). A numbr of authors hav addrssd ths quston thortcally [3 9]. Rcntly [3], a smplfd kntc approach adoptd n [5] dscrbng such T ovrstmaton, has bn modfd by ntroducng an adjustmnt to th lctron man-frpath, k / T 2 =n, assumd n [5] and by ntroducng a smpl tchnqu for numrcal constructon of th targt EDF whch can thn b usd to drv th xpctd /3/$ - s front mattr Ó 23 Elsvr Scnc B.V. All rghts rsrvd. PII: S (2)1479-4

2 932 J. Horack t al. / Journal of Nuclar Matrals (23) Langmur prob charactrstc. Th modl rqurs th paralll T and n profls as nput. Ths ar currntly unavalabl on TCV and so ths papr uss B2 EIRENE smulatons of th paralll profls n conjuncton wth th smpl kntc modl to xamn thortcally th mpact of fast lctrons on TCV targt prob T. 2. Exprmntal charactrstcs and B2 EIRENE cod modllng Th TCV tokamak (R ¼ :89 m, a ¼ :25 m, B u ¼ 1:43 T) s a mdum-szd dvc wth an opn dvrtor and hghly unconvntonal, varabl dvrtor gomtrs [2]. In th qulbrum of Fg. 1, on of th standard TCV sngl-null lowr dvrtd confguratons, th polodally long outr dvrtor lg rachs condtons of hgh rcyclng at mdum upstram plasma dnsts, wth partal dtachmnt occurrng frst at th strk pont as th dnsty s ncrasd furthr. For th standard opratng condton on TCV, wth th B rb drft drcton away from th X-pont, th nnr dvrtor tnds to b hottr and bgns to dtach only at th hghst dnsts. In Fg. 2(a), svral xprmntal dvrtor LP VIcharactrstcs ar compld from probs nar th nnr and outr strk ponts durng a TCV ohmc dnsty ramp dscharg wth magntc qulbrum shown n Fg. 2. (a) Exprmntal sngl Langmur prob charactrstcs obsrvd clos th nnr (#51) and outr (#4) targt strk ponts for a TCV dnsty ramp dscharg. Exampl fttd charactrstcs ar gvn at thr dffrnt tms (dnsts). (b) Full analyss for T, n, and j sat. Th vrtcal dashd lns ndcat th tms at whch th charactrstcs n (a) ar plottd. Fg. 1. TCV qulbrum (#17823, I p ¼ 34 ka, t ¼ 1: s) modlld by B2 EIRENE. Langmur prob data shown n Fg. 2 ar obtand from ths dscharg. A sngl polodal flux surfac corrspondng to a dstanc 1.8 mm from th LCFS at th outsd mdplan s hghlghtd. Paralll T and n profls gnratd by th B2 EIRENE along ths flux surfac ar usd throughout ths papr. Fg. 1. Th strong outr targt strk pont dtachmnt s clarly vsbl at hgh plasma dnsty. At th nnr targt, dtachmnt at th strk pont occurs only at th hghst dnsts. At th outr targt strk pont, T nvr drops blow 5 V and nvr blow 1 V at th nnr strk pont. On should also not n addton that at hgh dnsty, th rato of on to lctron saturaton currnts at th outr targt prob approachs unty and th charactrstcs dvrg n many cass strongly from xponntal bhavour. Th B2 EIRENE cod [1] s routnly appld to modllng of dtachmnt n TCV [2]. Paralll fld T and n profls at varous rad n th scrap-off layr ar an

3 J. Horack t al. / Journal of Nuclar Matrals (23) vdng a dscrpton of th targt EDF n th prsnc of a paralll T gradnt. A numrcal approach s adoptd n whch lctrons ar launchd from th targt back upstram wth gvn kntc nrgy, (n fact, n ths papr ÔtargtÕ s takn to mply at th shath dg). Thr collson probablty s computd for small stps along th fld (accountng for th varatons n T, n and plasma potntal, /) untl th sum of ths probablts rachs unty. Ths dfns a dstanc, x c, at th lastcollson as pðx c ; Þ¼1whr th collson probablty s Z xc dx pðx c ; Þ¼ kð þ /ðxþ; T ðxþ; nðxþþ : Mor dtald dscusson on th choc of k ¼ kð; T ; nþ can b found n [3]. Varaton n / s allowd for usng nrgy consrvaton: ðxþ ¼ þ /ðxþ. In common wth Wsson [5], a Maxwllan EDF, f M, s assumd to xst at vry pont on th paralll profl. Th targt EDF can b thn valuatd as f ð Þ¼f M ððxþþ: Fg. 3. B2 EIRENE computd paralll T, n profls for th flux surfac hghlghtd n Fg. 1. Th labls A, B, C dnot ncrasng upstram dnsty n u ¼½8; 23; m 3 ], n th cod. Broadly spakng th lowst dnsty cas corrsponds n th cod to low rcyclng (shath lmtd) condtons, whlst th ntrmdat and hgh dnsty ar hgh rcyclng solutons. automatc rsult of any convrgd soluton. In ths papr, rsults from th SOLPS4 B2 EIRENE packag ar usd wth no drfts ncludd and wth carbon as th only mpurty spcs. Fg. 3 compls profls, T ðxþ and n ðxþ, wth x th coordnat along th magntc fld, corrspondng to th flux surfac at dstanc of 1.8 mm outsd th outr mdplan sparatrx (s Fg. 1). Ths smulatd T ðxþ and n ðxþ profls ar usd as nput to th kntc analyss dscrbd blow n Scton 3. At th outr dvrtor th hgh rcyclng stat s achvd n th smulaton alrady at low upstram dnsty. Dtachmnt follows as dnsty s ncrasd furthr. On may not n th hghr dnsty cass an xtndd ÔconvctvÕ rgon blow th X-pont n whch T ðxþ s flat, and th low prdctd valu of T at both nnr and outr targts n th rang :6! 1:5 V. Ths convctv zon has bn drctly masurd usng dvrtor Thomson scattrng on th DIII-D tokamak [11]. 3. Outln of numrcal approach to modllng th targt prob charactrstc Stangby has rcntly proposd [3] som modfcatons to th analytc approach du to Wsson [5] pro- f ð Þ¼ SðxÞdxf M ðnðxþ; T ðxþ; ðxþþ; whr S ¼ pðxþ s an ad-hoc lctron sourc dstrbuton rprsntng a mor physcally rasonabl dscrpton than th smpl pont sourc, S ¼ dðxþ usd n [5]. Ths procss s rpatd for a rang of such that th full targt EDF f ð Þ s constructd. Ths nw mthod has a numbr of advantags ovr th smpl analytc approach [5], most mportantly comprsng th possblty of ncludng full dscrptons of T ðxþ, n ðxþ and /ðxþ n th analyss, ncludng th Ônd ffctsõ du charactrsng a systm of fnt lngth and prmttng th gnraton of a full targt or shath dg EDF. Ths s usful for comparson wth altrnatv kntc approachs and prmts th constructon of thortcal Langmur prob VI-charactrstcs. A numbr of addtonal rfnmnts may also b ncludd n applyng ths mthod, notably wth rgard to th valdty of an argumnt that an lctron suffrng a sngl Ôlast thrmalsng collsonõ s approprat to th dtrmnaton of xactly whr along th paralll profl any partcular lctron mght ÔorgnatÕ (th SðxÞ-dstrbuton). Ths qustons ar addrssd n mor dtal n [3]. 4. Gnratng thortcal Langmur prob VI-charactrstcs For any appld voltag, V prb, th lctron currnt to th prob s gvn by: j prb ðv prb Þ¼n v f ðv Þdv f ðv Þdv ; w whr v s th vlocty at th shath dg launchng pont and w ¼½ð2=m Þð cutoff V prb ÞŠ 1=2 s th vlocty w

4 934 J. Horack t al. / Journal of Nuclar Matrals (23) Fg. 4. Calculatd Langmur prob charactrstcs for th outr (a) and nnr (b) targts. In ach cas, th thr sts of B2 EIRENE smulatd paralll fld profls of T and n shown n Fg. 3 hav bn usd as nput for computaton of th targt dstrbuton functon. Th prob charactrstcs ar gnratd usng Eq. (1) wth th prob currnt normalsd to th on saturaton currnt. corrspondng to a cut-off nrgy, ;cutoff, blow whch lctrons cannot ovrcom th shath potntal for a floatng prob, j prb ¼ j prb ðv prb ¼ ; cutoff Þ. Th on currnt at th shath dg s approxmatd by j prb ¼ n c s wth c s ¼ð2T =m Þ 1=2 th sound spd. Th prob VI-charactrstc can now b gnratd as j prb ðv prb Þ¼j prb j prb ðv prb Þ ð1þ whch can b fttd n th sam way as any xprmntal charactrstc s analysd. Exampls ar shown n Fg. 4 for th thr B2 EIRENE profls of Fg Rsults Usng th prdctd charactrstc n Fg. 4 and ncludng now addtonal B2 EIRENE runs at ntrmdat valus of upstram dnsty, Fg. 5 compls th prncpal rsults of ths papr. By fttng th charactrstc n th voltag rang prtnnt to a ral xprmntal stuaton 1 < V prb < whr hr floatng potntal s dfnd as V prb ¼, th prob thortcal T s drvd for comparson wth th valus of T from B2 EIRENE. Rsults ar shown for two assumptons for th ffctv magntud of k, a crtcal paramtr n ths kntc modllng. Opn crcls rprsnt fts to charactrstcs producd from thortcal EDFÕs assumng th manfr-path approprat to ÔfastÕ tst lctrons n a fld of Fg. 5. Dnsty dpndnc of T drvd from an xponntal ft to thortcal charactrstcs (Fg. 4) gnratd usng B2 EIRENE smulatd T, n paralll profls (Fg. 3). Full lns: outr targt; Dashd lns: nnr targt;.: B2 EIRENE T ; N: Max. valu of T ovr th B2 EIRENE profl; : T ft for k F ¼ 1; d: T ft for k F ¼ 6:5. Th valus of T and T max rprsnt lowr and uppr lmt for th T ft. Not T ff ¼ T ft=t. background Maxwllan lctrons at ach T ðxþ and n ðxþ. In ths cas thr s vry sharp brak n th n dpndnc of T ff for th nnr targt. For comparson, th flld crcls corrspond to th sam calculatons prformd for k! k=k F, whr k F ¼ 6:5. Th factor k F orgnats from comparson of th smpl modl usd hr wth a full PIC kntc cod [4]. Ths comparsons dmonstrat that th valu of k adoptd n th smpl modl s too larg. In a subsqunt xrcs [3], Sptzr paralll conductvty s usd to stmat th paralll hat flux dnsty, q Sptzr, for mposd n, T and dt =dx. Th rsult s thn compard to that computd usng th kntc approach to stmat f ð Þ. It turns out that for k F ¼ 6:5, q Sptzr s wthn a fw prcnt of th valu prdctd by th smpl modl. Dcrasng k by ths factor practcally lmnats th rathr unphyscal brak n th nnr targt T ff of Fg. 5. Indpndntly of th choc of k F, Fg. 5 clarly shows, that a prob at th outr targt n TCV would b xpctd to corrctly yld th local T (.. T ) at all but th lowst upstram dnsts. For th nnr targt, th choc of k F s xtrmly mportant for th prdctd T ff. For short k, th nnr targt prob s prdctd to rad th corrct local tmpratur throughout th dnsty scan but would yld consdrably hghr valus at longr valus of k. Exprmntally, TCV targt probs do not appar to yld th vry low valus of T ndcatd by B2 EIRENE smulatons at hgh dnsty, vn though th kntc modllng appld hr would suggst that thy should. An altrnatv xplanaton would thrfor appar to b

5 J. Horack t al. / Journal of Nuclar Matrals (23) ncssary. An oftn ctd possblty s th prsnc of cross-fld [6] or paralll [9] rsstanc paths n th prob crcut. Evn f th smpl kntc modllng dscrbd hr dos provd an adquat dscrpton of th targt EDF n th prsnc of a strong T gradnt, th valdty of th TCV B2 EIRENE solutons has not bn confrmd xprmntally. A dvrtor Thomson scattrng dagnostc s n prparaton [12] at TCV whch wll hopfully prmt such confrmaton. 6. Conclusons Smplfd numrcal modllng of th xpctd lctron nrgy dstrbutons at th TCV dvrtor targt plats usng smulatd paralll dnsty and tmpratur profls from th B2 EIRENE cod shows (n Fg. 5) that undr condtons of hgh dnsty, whn th dvrtor plasma s n a hgh rcyclng rgm or bgnnng to dtach, targt Langmur probs should masur corrctly th local targt lctron tmpratur T. Undr such condtons, T s prdctd to b low, 1 V, whlst th probs ndcat valus n xcss of 5 V at bst. At lowr dnsts and partcularly for th TCV nnr dvrtor targt of th hghly polodally asymmtrc qulbrum usd as a standard dvrtd confguraton, th targt probs ar xpctd to rad consdrably hghr than T du to th contrbuton of wakly collsonal lctrons orgnatng n rgons of hghr tmpraturs furthr upstram. Th magntud of ths prdctd T ovrstmaton dpnds strongly on th choc of manfr-path n th smulatons. Only at th lowst dnsts would th prob b xpctd agan to rad th local tmpratur, snc th paralll T profl s approxmatly flat. At th outr targt, vn at low dnsts, th smulatd profls of T and n ar such that collsonalty s suffcntly hgh for lctrons from upstram, hottr rgons, to b thrmalsd at th targt and th prob should rad th local tmpratur. Th fact that ths s not obsrvd at TCV ndcats that othr mchansms ar rsponsbl for ths ffct. Acknowldgmnt Ths work was partly supportd by th Swss Natonal Scnc Foundaton. Rfrncs [1] R.D. Monk t al., J. Nucl. Matr (1997) 396. [2] R.A. Ptts t al., J. Nucl. Matr (21) 94. [3] P.C. Stangby, n prparaton. [4] O.V. Batshchv t al., Phys. Plasmas 4 (5) (1997) [5] J.A. Wsson, Plasma Phys. Control. Fuson 37 (1995) [6] P.C. Stangby, Plasma Phys. Control. Fuson 37 (1995) 137. [7] J.G. Watkns, J. Nucl. Matr (1998) 98. [8] R.A. Ptts, J. Horack, A. Loart, Bull. Am. Phys. Soc. 45 (7) (2) UP181. [9] N. Ohno t al., Contrb. Plasma Phys. 41 (5) (21) 473. [1] D. Rtr t al., Plasma Phys. Control. Fuson 33 (1991) [11] A.W. Lonard t al., Phys. Plasmas 5 (5) (1998). [12] R. Bhn t al., Rv. Sc. Instrum. 7 (1999) 768.