Thermal transport analysis of the edge region in the low and high confinement stages of a DIII-D discharge

Transcription

1 Thrmal transport analyss of th dg rgon n th low and hgh confnmnt stags of a DIII-D dscharg W. M. Stacy, Gorga Tch, Atlanta, GA 3033 and R. J. Grobnr, Gnral Atomcs, San Dgo, CA 9186 August, 006 Rvsd Octobr, 006 Abstract Th on and lctron thrmal dffusvts hav bn nfrrd from masurd dnsty and tmpratur profls n th dg of a DIII-D [J. Luxon,, Nucl. Fuson, 4, 614 (00)] dscharg wth a low confnmnt (L-mod ) stag followd by a hgh confnmnt (H-mod) stag fr of dg localzd mods (ELMs). Conductv hat flux profls usd to construct th nfrrd thrmal dffusvts wr calculatd takng nto account hat convcton, radaton, atomc physcs ffct of rcyclng nutrals, onlctron qulbraton and nutral bam hatng. Th nfrrd thrmal dffusvts wr compard wth thortcal prdctons. PACS 5.55.F

2 I. Introducton Th physcs of th stp-gradnt, dg pdstal rgon n H-mod (hgh confnmnt mod) plasmas has bn th subjct of xprmntal nvstgaton for many yars (.g. Rfs. 1-8). Th motvaton for undrstandng th dg pdstal s basd, at last n part, on calculatons 9,10 whch ndcat that bcaus of stffnss n tmpratur profls th prformanc of futur tokamaks wll b snstv to th valu of th dnsty and partcularly th tmpratur at th top of th dg pdstal. Thortcal fforts to undrstand th dg pdstal hav focusd on svral dffrnt aspcts of th undrlyng physcs. Invstgatons (.g. Rfs ) of th MHD stablty of th dg prssur pdstal aganst balloonng and plng (surfac knk) mods hav ld to an undrstandng of dg prssur/prssur gradnt lmts ladng to th onst of dg-localzd-mod (ELM) nstablts whch momntarly dstroy th dg pdstal structur. Svral othr lns of nvstgaton 15- hav bn dvlopd to th nd of xplanng (or at last modlng) th dg pdstal structur obsrvd n th absnc of or n btwn or avragd ovr ELMs. Th on and lctron thrmal dffusvts ar mportant paramtrs n any attmpt to undrstand th dg tmpratur pdstals. Knowldg of ths dffusvts to dat coms almost ntrly from thr tral and rror adjustmnt n transport smulatons to obtan agrmnt wth obsrvd dg tmpratur profls 7,8,16,17,19,0, although thr hav bn som ntal fforts to calculat dg thrmal dffusvts from dg turbulnc cods (.g. Rfs. 3 and 4). W rcntly ntroducd a procdur to tak nto account th ffcts of radaton, atomc physcs of rcyclng nutrals, on-lctron qulbraton and convctv hat fluxs n nfrrng thrmal dffusvts from masurd profls n th plasma dg and appld that procdur to nfr thrmal dffusvts n svral ELMng H-mod dschargs 5. Our purpos n ths papr s apply th sam procdur to xamn th chang n thrmal transport btwn th L-mod phas and H-mod phas of a dscharg wth a long ELM-fr H-mod. Th radal varaton of total and convctv hat fluxs ar calculatd ovr th dg rgon n both th L-mod and H-mod phass. Exprmntal thrmal dffusvts ar nfrrd and compard wth varous thortcal prdctons n ordr to nvstgat possbl undrlyng transport mchansms, wthout th complcaton of ELMs.

3 II. componnts Procdur for Infrnc of Hat Transport Coffcnts from Exprmnt Th total on and lctron radal hat fluxs consst of conductv and convctv 1 5 Q, = n, T,, LT, + Γ, T, (1) Thus, f n,, T, and 1 L T, ar dtrmnd xprmntally and, Q and Γ, ar calculatd from hat and partcl balancs, th xprmntal, profl can b valuatd from ( r) L ( r), T, ( ) ( ) ( ) ( ) ( ) Q, r 5 Γ, r = n, r T, r n, r W not that ths nfrnc of, dpnds not only on th masurd tmpratur and dnsty profls and th total hat flux Q,, but also on th convctv hat flux. W us an ntgratd modlng cod systm 6 that prforms ) partcl and powr balancs on th cor plasma to dtrmn th nt partcl and hat fluxs outward across th sparatrx, whch ar usd as nput to ) an xtndd -pont dvrtor modl (wth radaton and atomc physcs) that calculats plasma dnsts and tmpraturs n th dvrtor and SOL and th on flux ncdnt on th dvrtor plat, whch ) s rcycld as nutral molculs and atoms that ar transportd (D Transmsson-Escap Probablts [TEP] mthod, a form of kntc ntgral transport thory [Rf. 6]) through th dvrtor rgon across th sparatrx nto th plasma dg rgon. Any sourcs of gas puffd nutrals ar also smlarly transportd nward. Ths ntgratd cod systm s usd to calculat th on partcl and total hat fluxs crossng th spartrx from th cor nto th SOL (scrap-off layr). Th rcyclng nutral sourc s adjustd so that th ntgratd calculaton ylds th masurd ln avrag dnsty n ordr to nsur that fulng s calculatd corrctly. Usng ths valus from th ntgratd modl calculaton as sparatrx boundary condtons, w can thn ntgrat th plasma on partcl balanc quaton n t Γ = + nn < o συ > + on Snb r xp, Γ ( r sp ) = Γ sp (3) across th dg rgon to dtrmn th dg dstrbutons of Γ ( r), whr n o s th dnsty of rcyclng and gas fulng nutrals and Snb () s th sourc rat of plasma ons du to nutral bam (and pllt) njcton. W can also ntgrat th hat balanc quatons Q 3 3 ( c ) c = n T + q T T n n < συ > + q r t 3 nb o o cx l xp, Q ( r ) Q = (4a) sp sp

4 and dq dr 3 = n T + q + q n n < συ > E n n L t nb o on on z z Q r = Q (4b), ( ) xp sp sp nward from th sparatrx to dtrmn th Q, ( r) ndd to valuat th radal dstrbuton of, from Eq. (). Th boundary condtons at th sparatrx wr dtrmnd by modlng th xprmntal condtons wth global partcl and powr balancs. Hr q nb, s th local nutral bam powr dposton dnsty, n o s th rcyclng nutral dnsty, colldd nsd th sparatrx and 1.5 c o c no s th dnsty of cold rcyclng nutrals that hav not yt q T T T T s thr avrag nrgy, ( ) 1.5 s th on-lctron qulbraton rat, Eon ( T, n ) s th onzaton nrgy, n z s th mpurty (carbon) dnsty, L ( T, n ) s th mpurty radaton mssvty, ( T ) z o < συ > cx+ l s th charg-xchang plus lastc scattrng rat coffcnt, and συ ( T, n ) < > s th on lctron mpact onzaton rat coffcnt. Th xprmntal n, z and T, and th calculatd nutral dnsty ar usd to valuat th trms n Eqs. (3) and (4), whch ar thn ntgratd radally nward from th xprmntal sparatrx boundary condtons for th partcl and hat fluxs dtrmnd as dscussd abov. W must at prsnt stmat th splt of Q sp nto Q sp and Q sp. Th atomc physcs data ar takn from Rf. [7] (wth subsqunt xtnsons to hghr tmpraturs), and th radaton mssvty s calculatd from a ft to coronal qulbrum calculatons (takng nto account th ffct of charg-xchang and rcombnaton n th prsnc of rcyclng nutrals) basd on th ADPAC data 8. III. Dscrpton of ELM-fr Phas of DIII-D Shot Th man goal of ths study was to xamn th dg transport n th absnc of MHD vnts, such as ELMs. For ths purpos, a convntonal H-mod dscharg was producd wth a long ELM-fr phas by usng modratly hgh trangularty to provd good dg MHD stablty and by opratng at low hatng powr to dlay th onst of ELMs, as llustratd n Fg. 1. Analyss tms wr chosn cntrd at 155 ms, 1640 ms and 140 ms, corrspondng to th L-mod phas, arly n th H-mod phas and lat n th ELM-fr H-mod phas. Each profl usd n th analyss s basd on a compost 4

5 of xprmntal data obtand ovr a tm wndow of 35 ms n th L-mod and 50 ms at ach of th two H-mod tms. Th lctron tmpratur and dnsty wr obtand from a mult-pont Thomson scattrng systm 9. Th lctron dnsty from ths systm was adjustd to match th ln-avragd dnsty from a CO ntrfromtr; th adjustmnts wr small roughly 5% or lss. Each tm wndow n th analyss ovrlaps to 4 pulss of th Thomson lasr. Th T and n profls from th Thomson systm wr algnd n flux spac n th followng way. Th data for ach lctron tmpratur profl wr mappd to normalzd ps wth a magntc qulbrum gnratd at th tm that th data wr acqurd. All tmpraturs and flux coordnats wthn a tm wndow wr thn groupd and ft wth a functon whch conssts of a tanh functon n th pdstal whch jons smoothly to a spln ft n th cor. Aftr ths ft, th T and n data ponts and th fttd profls wr shftd n ps spac by an amount rqurd to algn th foot of th tanh functon for th T profl wth th plasma sparatrx. Ths fts and th undrlyng data ponts ar shown n Fg.. Th on tmpratur and Carbon dnsty wr obtand from masurmnts of th C VI 590 ln wth a charg xchang rcombnaton spctroscopy systm 30. As wth th Thomson data, th data wr takn from multpl frams obtand durng ach tm wndow. No spatal adjustmnt was prformd on ths data. Th on tmpratur was ft wth a spln functon, and as shown n Fg. ths provdd a good ft both n th pdstal rgon and n th cor of th plasma. An absolut ntnsty calbraton was usd to convrt th ntnsty masurmnts of th C VI ons nto a carbon dnsty. Th carbon dnsts wr dvdd by th lctron dnsts to produc profls of fractonal mpurty contnt. Ths functon tnds not to vary strongly across th plasma. It was ft wth a spln functon wth a constrant to forc th ft to b constant n about th outr 10% of th plasma radus. Typcally, carbon s th domnant sourc of Zff n dschargs of ths typ. Thus, th man on dnsty was computd from th fts to th lctron dnsty and to th carbon fracton. IV. Analyss of ELM-fr Phas of DIII-D Shot Our purpos s to obtan a bttr undrstandng of th dg thrmal transport n L- mod and n th ELM-fr H-mod phas and of how thy dffr. For ths rason, th 5

6 dscusson s structurd as a comparson of varous quantts just bfor L-H, just aftr L-H, and wll aftr L-H. A. Powr balanc and hat flux profls Th valus of th varous coolng and hatng trms n Eqs. (4), valuatd usng th masurd dnsty and tmpraturs, ar shown n Fgs. 3. Th on-lctron nrgy q T T T transfr trm ( ) 3 s domnant at th outr rad at all tms bcaus of th larg dffrnc btwn on and lctron tmpraturs and th small valus of th lctron tmpratur, but ths trm bcoms much lss mportant at nnr rad whr th on and lctron tmpraturs bcom comparabl latr n th H-mod. Th chargxchang (and lastc scattrng) coolng trm s mportant just nsd th sparatrx, but ts profl bcoms mor sharply attnuatd wth dnsty buldup n H-mod. Th carbon radaton coolng trm s almost unform n th low T L-mod, but bcoms pakd towards th lowr T outr rad as th pdstal flattop tmpratur ncrass n H- mod. Th nutral bam (E b = 80 kv) hatng s prfrntally of th lctrons. Ths hatng and coolng rats wr usd n Eq. (4) to calculat th total on and lctron hat flux profls. Th transnt (tm drvatv) trms wr takn nto account sparatly n th pdstal and th cor. Th global cor powr and partcl balancs wr valuatd by takng d ln W / dt and d ln n dt from xprmnt, whr W s th total nrgy contnt, and multplyng by 1.5nT and n, rspctvly; ths trms had only a small ffct on th global calculaton. In solvng th dg partcl and powr balanc Eqs. (3) and (4), th masurd d ln p pd dt and d ln n pd dt at th top of th pdstal wr multpld by th local valus of 1.5nT and n from th fts of Fg. wr usd to valuat th transnt trms; ths trms wr sgnfcant for th arly (1640ms) tm n th H- mod whn th pdstal dnsty and prssur wr ncrasng rapdly. Th splt btwn th on and lctron hat flux at th sparatrx was stmatd to b ( ) f { Q Q + Q } = 0.6. hat n As sn n Fg. 4, th total on hat flux calculatd from Eq. (4a) dcrass wth radus bcaus of th ncras n radus of th on-lctron nrgy transfr and of charg xchang coolng, whch s not compnsatd by th rlatv small nutral bam hatng of ons. Th total lctron hat flux calculatd from Eq. (4b), on th othr hand, ncrass wth radus bcaus th on-lctron nrgy transfr plus th nutral bam hatng s vrywhr gratr than th radaton plus onzaton coolng of th lctrons. Th 6

7 transnt pdstal tmpratur and dnsty ncrass arly n th H-mod (1640 ms) rducs th outward hat and partcl fluxs; n fact th partcl flux (and convctv hat flux) bcoms ngatv nsd th strong rcyclng rgon just nsd th sparatrx. In L-mod, th convctv hat flux ncrass wth radus for th ons bcaus of th ncras n outward partcl flux du to onzaton of rcyclng nutrals. Th lctron hat flux dos not ncras much wth radus bcaus th ffct of onzng nutrals n ncrasng th partcl flux s offst by th dcrasng wth radus of th lctron tmpratur. In L-mod th partcl flux, hnc th convctv hat fluxs, s vrywhr outward (postv). On th othr hand, n th arly stag of th H-mod th partcl flux calculatd from Eq. (3) s nward (ngatv) xcpt n th outr hghrcyclng rgon of th dg, as t must b to provd for th ncrasng plasma dnsty ovr th H-mod phas of th dscharg. B. Infrrd thrmal dffusvts Th total and convctv hat fluxs shown n Fgs. 4 wr usd, togthr wth th xprmntal gradnt scal lngths dtrmnd from th fts gvn n Fgs., n Eq. () to nfr th thrmal dffusvts plottd n Fgs. 5 and 6. Th xprmntal gradnt scal lngths, L T and L T, both dcrasd monotoncally (th gradnts ncrasd monotoncally) wth radus for all tms (xcpt just at th sparatrx). Th most strkng fatur of ths fgurs s th gnrally xpctd drop n th on and lctron thrmal dffusvty btwn L-mod and H-mod (by an ordr of magntud). Th fact that ths dcras occurs ovr th ntr dg rgon (0.86 < ρ < 1.0), rathr than just n a localzd transport barrr algnd wth th stpst gradnt rgon, s notabl. In fact, n th rgon n whch th lctron tmpratur gradnt bcoms stpst xp s actually bcomng hghr than lswhr. Ths s qualtatvly consstnt wth th substantal rductons n xp, across th L-H transton that wr prvously nfrrd 31 n DIII-D dschargs for rgons n th plasma ntror (ρ < 0.85). Both xp and of th H-mod (1640 ms). xp ar largst at th sparatrx, xcpt for xp n th arly, transnt phas C. Snstvty studs Consdraton of th uncrtanty n th dtrmnaton of th thrmal dffusvts 15 s n ordr at ths pont. Errors may ntr th dtrmnaton through th xprmntal 7

8 dnsty and tmpratur profls or through th calculatd total and convctv hat fluxs. Th rror bars on th masurd tmpraturs ar < 10% and on th masurd dnsts < 5%. Th ncssty of spcfyng th hat flux splt f Q ( Q Q ) { + } btwn hat n ons and lctrons ntrng th dg rgon from th cor ntroducs an uncrtanty nto th analyss. As dscussd prvously 5, a physcally plausbl rang (found prvously to b cntrd about fhat 0.5 ) can b dtrmnd by th physcal rqurmnt that th convctv hat flux can not xcd th total hat flux for thr spcs (not from Fg. (4b) that fhat 0.6 s almost at ths lmt at 1640 ms). Th ntr calculaton was rpatd for f hat = 0.4, and th nfrrd thrmal dffusvts ar compard n Fg. 7. Basd on a prvous study 5 of th rang of fhat for whch physcally plausbl solutons ar found, Fg. 7 s probably rprsntatv of th uncrtanty n th dtrmnaton of xp, du to th ncssty of stmatng f hat. Nxt, w xamnd th snstvty of xp, to th spatal hat flux profl usd n valuatng Eq. (). Th prvous rsults calculatd usng Q(r) and Γ(r) n Eq. () ar dnotd xp n Fgs. 8. Th calculaton was rpatd nglctng th convctv componnt by sttng Γ = 0 n Eq. (), wth th rsult dnotd xp n Fg. 8. Thn th calculaton was rpatd onc agan sttng Γ = 0 and rplacng th spatal profl Q(r) by th constant valu of th total hat flux at th sparatrx Q(r sp ), wth th rsult bng dnotd xp3 n Fg. 8. Clarly, th rsults ar snstv to th us of th propr spatal hat and partcl flux profls to valuat Eq. (). V. Thortcal transport modls Although gyroflud or gyrokntc calculatons of turbulnt transport ar probably ndd to accuratly rprsnt th currnt thortcal undrstandng of transport, ths gnrally rqur larg-scal computr smulatons, and such calculatons for dg plasmas ar byond th currnt stat-of-th-art. Howvr, th analytcal thortcal formulas commonly usd n transport cods can provd usful nsghts. A. Ion transport 1. Noclasscal Th Chang-Hnton noclasscal xprsson for th on thrmal conductvty s 3,33 8

9 1 noch = a1g1 + a g1 g θ ε ρ ν ( ) (5) whr th a s account for mpurty, collsonal and fnt nvrs aspct rato ffcts and th g s account for th ffct of th Shafranov shft ( + α ) + ( ε ε )( + α ) a1 = µ µ a g g j 3 j 1 ( + ) 0.59µ ε 1.33α α = µ ε α ( ε + ε ') + ε ' = ε ' ε ' 1 ε 1+ = ' 1+ ( 1 ε 1) ε j j (6) whr α = n I Z I /n Z, µ * = ν I qr/ε 3/ υ th and = d /dr, whr s th Shafranov shft. Th mpurty thrmal conductvty s obtand by ntrchangng th and I subscrpts n th abov xprssons. Th Shafranov shft paramtr may b valuatd from 34 = r ' d r ' ' B β θ θa B r dr dr RB a r o θ θ (7) whr β θ = p/(b θ /µ 0 ) and B θa dnots th polodal magntc fld valuatd at r = a. Snc w nd ths quantty at r a, w can tak advantag of th dfnton of th ntrnal nductanc l a ' ' B o θ r dr a Bθ a = (8) whr β θa dnots th quantty valuatd usng th avrag prssur ovr th plasma and B θa. Usng a parabola-to-a-powr currnt profl j(r) = j 0 (1 (r /a )) ν, for whch th rato of th valus of th safty factor at th dg to th cntr s q a /q 0 = ν + 1, and a ft 3 l = ln( ν) lads to th smpl xprsson 9

10 a 1 ' = βθ a + l R a 1 q a = βθ a + ln R q o (9) In th prsnc of a strong shar n th radal lctrc fld, th partcl banana orbts ar squzd, rsultng n a rducton n th on thrmal conductvty by a factor of S -3/, whr 35 d ln Er E r S = 1 ρ θ dr υthbθ (10) Hr ρθ s th on polodal gyroradus.. Ion tmpratur gradnt mods For a suffcntly larg on tmpratur gradnt ( L ( ) crt T T dt dr < LT 0.1R 0.18) th torodal on tmpratur gradnt (ITG) mods bcom unstabl. Ths crtron for nstablty of th ITG mods was satsfd ovr th dg rgon of shot for th tms xamnd xcpt just at th sparatrx n th L-mod stag. An stmat of th on thrmal conductvty du to ITG mods s 36 whr 1 tg T m T = ρ RL m B ρ s th gyroradus n th magntc fld B, and k ρ = has bn usd. Th paramtr η = Ln LT for shot s shown n Fg. 9, from whch t may b nfrrd that ITG mods should b prsnt ovr th ntr dg rgon n ths shot, xcpt just nsd th sparatrx at 155 and 140 ms. 3. Drft Alfvn mods (11) Drft Alfvn nstablts ar drvn by collsons and hnc bcom mportant n th collsonal dg plasma. Numrcal modlng 37 ndcats that ExB shar alon can not stablz ths mods (low collsonalty and a stp prssur gradnt ar also ndd). An analytcal modl 38 xprsson ( ) whch taks ths ffcts nto account ylds th da gb = β, ν / µ (1) n whr th on gyro-bohm thrmal conductvty s = ρ c L, wth L p ( dp dr), gb s s p p 10

11 k L m T L m T µ = p p mt mt (13) for k 1 qr, and qr whr ( 1 β ) 3 n + + ν n = βn + ν n ( qrl ) 1 p qr,, n p B µ 0 β m n T m n m β L β = ν m λ (14) (15) wth λ = υ / ν bng th lctron man fr path. th 4. Thrmal nstablts In th wak on-lctron qulbraton lmt, local radal thrmal nstablts n th dg on and lctron nrgy balancs ar dcoupld, and th lnar growth rats may b wrttn n th gnral form 39 ( ) Γ 1 T r T 5 ω = 0 ν L + k + ν L α 3 n whr th frst two trms rprsnt th gnrally stablzng ffct of hat conducton and convcton, rspctvly, wth L -1 T = (-dt/dr)/t for th spcs n quston, Γ bng th on or lctron partcl flux, and ν charactrzng th tmpratur dpndnc of th undrlyng thrmal conductvty for that spcs, 0 ~ T ν. W usd ν =.5, but th rsults ar rlatvly nsnstv to ths valu. Th α-trms rprsnt th gnrally dstablzng atomc physcs and mpurty coolng trms n th rspctv growth rats for th ons 5 3 c c T ν at 1 H H α = ( ν 1 ) νon + ν at ν 1 + ν c ν at T n T T and for th lctrons ν Lz Lz 5 Eon 3 Eon T ν on α = nz + ν on ( ν 1 ) + ν + T T T T νon T 1 H H ν n T T Th trms ν on and ν at ar th nutral onzaton frquncy n th pdstal rgon and th frquncy of charg-xchang plus lastc scattrng vnts nvolvng cold nutrals that hav not prvously undrgon such an vnt n th pdstal rgon. E on s th onzaton (16) (17a) (17b) 11

12 nrgy, and n z and L z ar th dnsty and radatv mssvty of mpurts n th dg pdstal rgon. H rprsnts any addtonal hatng or coolng n th pdstal. An stmat of th transport assocatd wth such thrmal nstablts s k (18) t, ω r In valuatng ths xprsson w usd k r = 5 m -1, corrspondng to radal nstablts wth wavlngths of 0 cm, whch s about th dpth nto th plasma that dstablzng nutral and/or mpurty radaton ffcts mght pntrat n th L-mod plasma (smlar rsults ar obtand for k r = 10 m -1 corrspondng to 10 cm nutral pntraton and radaton zon). W usd th noclasscal and paloclasscal valus of th on and lctron thrmal dffusvts to valuat 0. B. Elctron transport 1. Paloclasscal A modl basd on classcal lctron hat conducton along fld lns and magntc fld dffuson n whch th lctron tmpratur qulbrats wthn a dstanc L along th fld lns and n whch radally dffusng fld lns carry ths qulbratd tmpratur wth thm and thus nduc a radal lctron hat transport M L π qr 10 tms largr than th rsstv magntc fld dffuson rat lads to th followng xprsson for th lctron hat dffusvty 40 nc palo = 1.5(1 + ) ν δ η0 M η whr takng L as th mnmum of th lctron collson man fr path and th maxmum half lngth of th hlcal fld rsults n whr max (19) M = mn{ l, λ }/ π Rq (0) 3 1.4x10 Z ff ln Λ = 3 = c p δ ν, δ / ω,, T 17 l ( V ) π Rq π Rq n = = * max * max 1 1 dq δ 1 dq R π q πδ dρ a q dρ, 1

13 η + Z + Z ln(1 + ) 1 f 1 ( * * ) ( ) nc ff ff c = + η0 13 Zff / 4 + Z 1 fc ff + ν + ν, ( 1 ε ) ε x 16 T ( V ) 3 1 (1 ) ν* = Rq / ε λ, fc =, λ 1 = ε ε nzff ln Λ (1). Elctron tmpratur gradnt mods Th lctron tmpratur gradnt (ETG) mods (lctrostatc drft wavs wth L k cs ω p ) ar unstabl whn η n 1, whch s th cas n th dg rgon for L T shot , as shown n Fg. 9. An xprsson for th thrmal conductvty du to th ETG mods s gvn by 34 whr S ( r q)( dq dr) m tg c s υthsm = 0.13 η 1+ η ω p qr ( ) s th magntc shar and ω p s th lctron plasma frquncy. () 3. Trappd Elctron Mods Th prncpal lctron drft nstablts wth k cs Ω ars from trappd partcl 3 * th qr ffcts whn ( ) ν ν / υ ε < 1. In mor collsonal plasmas th mod bcoms a collsonal drft wav dstablzd by passng partcls. An xprsson for th lctron thrmal dffusvty that ncompasss th dsspatv trappd lctron mod (TEM) and * th transton to th collsonlss mod as ν 0 s gvn by 34 r dq υth tm c q dr s = 0.13 η 1+ η ω p qr ( ) (3) 4. Drft Rsstv Balloonng Mod Th drft-rsstv balloonng mod s dstablzd by unfavorabl curvatur on th outboard sd of th torus n a collsonal dg plasma. Lnar stablty analyss 41 13

14 ndcats that th transport assocatd wth ths mods can b charactrzd by a partcl dffuson coffcnt scalng D ( π q) ρ ν ( R L ) and a proportonalty constant n qual to th flux surfac avrag of th normalzd fluctuatng radal partcl flux <nv r >. Subsqunt calculaton 4 of th normalzd fluctuatng radal partcl fluxs for modl rprsntatv of DIII-D cor paramtrs found <nv r > W adopt th form rb R 4 ( ) = q ρ ν (4) L n to charactrz th transport of lctron nrgy du to drft-rsstv balloonng mods, wth th cavat that thr could wll b an addtonal normalzaton constant ndd. W not that on group of transport modlrs 43 calbratd ths formula to L-mod data and found a factor of 94κ -4 should multply ths xprsson (κ s th longaton), whl anothr group 44 usd ths xprsson multpld by a factor of 4. VI. Comparson of thortcal prdctons wth nfrrd thrmal dffusvts Th thortcal xprssons of th prvous scton wr valuatd usng th masurd dnsty and tmpraturs and ar compard wth th valus nfrrd from xprmnt usng Eq. () n Fgs. 10 and 11. Th agrmnt of th thrmal nstablty prdcton for on thrmal dffusvty (Fg. 10a) and of th paloclasscal prdcton for lctron thrmal dffusvty (Fg. 11a) wth th xprmntally nfrrd profls for th L-mod (155 ms) s notabl. Th tg prdcton s of th sam magntud as th xprmntally nfrrd dffr sgnfcantly. For th H-mod th tg prdcton agrs rasonably wll wth 14 xp, but th profls xp n th arly, transnt phas (Fg. 10b), but at latr tms th noclasscal prdcton agrs bttr at th nnr rad, but both noclasscal and tg prdct a sharp dcras n at th outr xp rad that s not sn n. Th prsnc of drft Alfvn nstablty could account for addton xp ndd to match at th outr rad. It s notabl that th on thrmal nstablty was stablzd xcpt at th nnr rad by th stpr tmpratur gradnt n th H-mod than n th L-mod. Th xprmntally nfrrd xp profls for th H-mod ar wll undr all th thortcal prdctons (Fgs. 11b and 11c). As notd prvously, thr s uncrtanty n

15 th magntud to b usd for th rsstv balloonng mod xprsson, but a rducton n magntud would not chang th dsagrmnt n shap. It sms unlkly that any of th xp thortcal mchansms consdrd ar rsponsbl for th nfrrd. VI. Summary and Dscusson Th on and lctron thrmal dffusvts n th dg rgon hav bn nfrrd from dnsty and tmpratur profl masurmnts durng th fully dvlopd L-mod stag, durng an arly transnt H-mod stag and durng a fully dvlopd H-mod stag of a DIII-D dscharg wth a long ELM-fr H-mod phas. Th on and lctron conductv hat flux dg profls usd to valuat th thrmal dffusvts wr calculatd takng nto account radaton, atomc physcs ffcts assocatd wth rcyclng nutrals, on-lctron collsonal qulbraton and nutral bam hatng n th dg. Th nfrrd thrmal dffusvts for both ons and lctrons dcrasd by about an ordr of magntud btwn th L-mod and ELM-fr H-mod stags of th dscharg, as antcpatd. Ths dcras occurrd across th ntr outr 15% of th plasma mnor radus, not just n th localzd rgons n th outr 5% whr th stpgradnt pdstals n dnsty and tmpratur formd n th H-mod. Thr was a broad (wdth about 5% of mnor radus) mnmum n xp cntrd at about 95% of th mnor radus n th H-mod stags, vn though th stpnss of th masurd T gradnt ncrasd wth radus up to wthn lss than 1% of th mnor radus. Comparson of wth thortcal prdctons found rasonably good xp, agrmnt n th L-mod stag for th paloclasscal prdcton of and th thrmalnstablty prdcton of. In th H-mod stags, th broad mnmum n th nfrrd xp was wll undr any of th thortcal prdctons (paloclasscal, tg, tm, rsstv balloonng). Th nfrrd xp agrd rasonably wll wth th tg prdcton (and not qut so wll wth th noclasscal prdcton) of arly n th H-mod stag, but xp was sgnfcantly largr than thr of ths prdctons n th outr 4% of th mnor 15

16 radus latr n th H-mod stag. Th rsstv balloonng mod prdcton of agrd xp wth n magntud but not n profl ovr ths outr 4% of th mnor radus. ACKNOWLEDGEMENTS: Th authors ar gratful to mmbrs of th DIII-D tam who prformd th xprmnts and masurd and rducd th data dscussd n ths papr. Th frst author (WMS) s gratful to Gln Batman, Jm Calln, Parvz Gudzar, and Alx Pankn for dscusson and clarfcaton of crtan aspcts of th thortcal modls and to Gnral Atomcs for thr hosptalty durng th cours of ths work. Th work was supportd by th US Dpt. of Enrgy through grant DE-FG0-99ER54538 wth th Gorga Tch Rsarch Corporaton and contract DE-AC03-99ER54463 wth Gnral Atomcs. 16

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19 Fgur 1. Evoluton of masurd paramtrs n DIII-D shot (Th prssur gradnt s masurd [n kpa/m] along th vrtcal chord of th Thomson lasrs and would b approxmatly a factor of two hghr whn projctd to th outboard mdplan.) 19

20 Fgur. Masurd and fttd dnsts and tmpraturs n th dg of DIII-D shot

21 hatng & coolng rats (W/m 3 ) @155 ms a) Normalzd radus, rho cx rad on qnb qnb q hatng & coolng rats (W/m 3 ) @1640 cx rad on qnb qnb q Normalzd radus, rho b) @140 c) hatng & coolng rats (W/m 3 ) cx rad on qnb qnb q Normalzd radus, rho Fgur 3. Hatng and coolng rats a) just bfor L-H wth P nb =4.45 MW, b) just aftr L-H wth P nb =.33 MW, and c) wll aftr L-H wth P nb =.33 MW. (cx=chargxchang+lastc scattrng coolng, rad=radaton coolng, on=onzaton coolng, qnb=nutral bam hatng of lctrons, qnb = nutral bam hatng of ons, q=collsonal nrgy xchang from ons to lctrons) 1

22 4x @155 a) hat fluxs (W/m ) 3x10 4 x10 4 1x10 4 Q Q.5T Γ.5T Γ Normalzd radus, rho 4x10 4 3x @1640 Q Q.5T Γ b) hat fluxs (W/m ) x10 4 1x T Γ -1x Normalzd radus, rho 4x @140ms c) hat fluxs (W/m ) 3x10 4 x10 4 1x10 4 Q Q.5T Γ.5T Γ Normalzd radus, rho Fgur 4. Total and convctv hat fluxs a) just bfor L-H wth P nb = 4.45 MW, b) just aftr L-H wth P nb =.33 MW, and c) wll aftr L-H wth P nb =.33 MW. (hat,=total hat flux, hatconv,=convctv hat flux)

23 ch_ (m /s) 1 155ms 1640ms 140ms Normalzd radus, rho Fgur 5. Exprmntally nfrrd on thrmal dffusvty just bfor L-H (155ms), just aftr L-H (1640ms) and wll aftr L-H (140ms) ch_ (m /s) 1 155ms 1640ms 140ms Normalzd radus, rho Fgur 6. Exprmntally nfrrd lctron thrmal dffusvty just bfor L-H (155ms), just aftr L-H (1640ms) and wll aftr L-H (140ms). 3

24 ch (m /s) ms xp, Q sp /Q+ =0.4 sp xp, Q sp /Q+ =0.4 sp xp, Q sp /Q+ =0.6 sp xp, Q sp /Q+ =0.6 sp Normalzd radus, rho Fgur 7. Snstvty of nfrrd thrmal dffusvty to assumd fhat=q /(Q +Q ) lavng th cor (@ ρ = 0.864). ch-xp (m /s) @1640 xp xp xp Normalzd radus, rho ch-xp (m /s) ms xp xp xp Normalzd radus, rho Fgur 8. Snstvty of nfrrd thrmal dffusvty to hat flux. ( xp usd conductv hat flux q(r)=q(r)-.5γ(r)t(r); xp usd total hat flux Q(r); and xp3 usd constant valu of total hat flux at sparatrx Q(r sp ). 4

25 η and η ta155 ta1640 ta140 ta155 ta1640 ta Normalzd radus, rho Fgur 9. η, Ln, LT, for DIII-D shot

26 ms a) 10 ch_ (m /s) xp noch da tg t Normalzd radus, rho @1640 b) ch_ (m /s) xp noch da tg t Normalzd radus, rho @140ms xp noch da tg t c) ch_ (m /s) Normalzd radus, rho Fgur 10. Comparson of xprmntally nfrrd on thrmal dffusvts wth thortcal prdctons a) just pror to L-H, b) just aftr L-H, and c) wll aftr L-H. (xp=nfrrd from xp., noch=noclasscal Chang-Hnton, da= drft Alfvn mod, tg=on tmpratur gradnt mod, t= thrmal nstablty) 6

27 ms a) 10 ch_ (m /s) xp palo rb tm tg Normalzd radus, rho ch_ (m /s) @1640 b) xp palo tm tg rb Normalzd radus, rho ch_ (m /s) 10 1 xp palo rb tm tg @140ms c) Normalzd radus, rho Fgur 11. Comparson of xprmntally nfrrd lctron thrmal dffusvts wth thortcal prdctons a) just pror to L-H, b) just aftr L-H, and c) wll aftr L- H. (xp=nfrrd from xp., palo=paloclasscal, rb= rsstv balloonng mod, tm=trappd lctron mod, tg=lctron tmpratur gradnt mod) 7