EDGE PEDESTAL STRUCTURE AND TRANSPORT INTERPRETATION (In the absence of or in between ELMs)

Transcription

1 I. EDGE PEDESTAL STRUCTURE AND TRANSPORT INTERPRETATION (In th absnc of or n btwn ELMs) Abstract W. M. Stacy (Gorga Tch) and R. J. Grobnr (Gnral Atomcs) A constrant on th on prssur gradnt s mposd by momntum balanc. Th constrant nvolvs θ, φ, Er, r, tc. and momntum transfr rats, all of whch can b obtand from xprmnt. n p T Intgraton of = usng th xprmntal, n r p r T mom r xp tc., ylds dnsty profls that agr wll wth th drctly masurd dnsty profls.,, Er r θ φ, Ths prssur gradnt constrant can b rarrangd to obtan a pnch-dffuson xprsson for th on flux, whch can b usd n th contnuty quaton to obtan a gnralzd dffuson thory that consrvs momntum. A mthodology for nfrrng χ xp, and appld to DIII-D, wth comparson wth thory. from masurd T and n profls has bn dvlopd A mthodology for nfrrng radal transfr rats for torodal angular momntum from masurd φ profls has bn dvlopd and appld to DIII-D, wth comparson wth thory. A mthodology for calculatng θ has bn dvlopd and compard wth xprmntal data from DIII-D.

2 A. Momntum Balanc Constrant on Ion Prssur Gradnt Combnng th radal and torodal componnts of th momntum balanc lads to 0 dp r * pnch, mt ν Lp =, whr I ν D d 0 p dr D 2 ( ) I ZI B ν θ and A * E M r φ n Eφ + nm ( νi + ν d ) f p θ + B nmν Iφ I θ pnch, = n Bθ + () (2) Fgur Contrbuton of th varous trms on RHS of Eq. 2 to th pnch vlocty (a and b), and contrbuton of th pnch vlocts and radal partcl vlocty pakng du to onzaton of rcyclng nutrals for two DIII-D H-mod dschargs. (PoP, 3, 0253, 2006)

3 r wth drctly masurd (Thomson scattrng) lctron dnsts n thr DIII-D H-mod shots. Fgur 2 Intgraton of ( υ υ pnch, ) dn n dr = D dt T dr (sold ln) compard

4 B. GENERALIZED DIFFUSION THEORY Rwrtng th prssur gradnt constrant as a pnch-dffuson rlaton for th partcl flux and substtutng nto th contnuty quaton rsults n a gnralzd dffuson quaton basd on momntum and partcl balanc. ( nυpnch, ) n n n T n T D D D D + = S r r r r T r r T r r k k k k r k (3) whr ( ν + ν ) m T ν 2 k 2 k B B ( θ ) θ m T D, D d k k k (4) 0 dffuson coffcnts D (m 2 /s) D D I D II D I normalzd radus, rho Fgur 3 Gnralzd dffuson coffcnts n th dg of DIII-D H-mod shot (CPP, 48, 94, 2008)

5 C. INFERRENCE OF EXPERIMENTAL HEAT DIFFUSIITY (PoP, 3, 07250, 2006) FROM DEFINITION OF HEAT CONDUCTION χ xp,,,, r = LT, r LT, r,,,, 2, L T r T, whr T ( ),, /, q r Q r 5 Γ r n r T r n r T r n r SOLE FOR HEAT AND PARTICLE FLUXES, USING EXP n & T DATA Q r Q r Γ r = c c nt + q T To n no συ q, Q rsp Q t 2 nb 2 cx + = l 3 3 xp sp xp 3 = n T + q + q, 2 nb n n συ E on on n n L Q r = Q t o z z sp sp n = + nno συ + S, Γ on nb r = Γ t xp ( sp ) sp 5.0x x x0 4 Hat Flux (W/m 2 ) 3.5x x x x0 4 total Q.5x0 4 total Q 2.5T Γ.0x T Γ 5.0x Normalzd Radus, rho

6 INFERRENCE OF EXPERIMENTAL HEAT DIFFUSIITY (PoP, 3, 07250, 2006) FROM DEFINITION OF HEAT CONDUCTION χ xp,,,, r = LT, r LT, r,,,, 2, L T r T, whr T ( ),, /, q r Q r 5 Γ r n r T r n r T r n r SOLE FOR HEAT AND PARTICLE FLUXES, USING EXP n & T DATA Q r Q r Γ r = c c nt + q T To n no συ q, Q rsp Q t 2 nb 2 cx + = l 3 3 xp sp xp 3 = n T + q + q, 2 nb n n συ E on on n n L Q r = Q t o z z sp sp n = + nno συ + S, Γ on nb r = Γ t xp ( sp ) sp Hat Flux (W/m 2 ) 5.0x x x x x x x0 4 total Q.5x0 4 total Q 2.5T Γ.0x T Γ 5.0x Normalzd Radus, rho Fgur 6a Hat fluxs n DIII-D ELMng H-mod shot 9436

7 Hat Flux (W/m 2 ) 3.5x x x x0 4.5x0 4.0x x total Q total Q 2.5T Γ 2.5T Γ Normalzd Radus, rho Hat Flux (W/m 2 ) 3.0x x x x x x0 4.8x0 4.6x0 4.4x0 4.2x0 4.0x x x x x0 3 total Q total Q convct 2.5T Γ convct 2.5T Γ Normalzd Radus, rho Fgur 4 Hat fluxs n L-mod 525ms (4a) n th ELM-fr 240ms (4b) of DIII-D shot lctron χ (m 2 /s) 0 xp Eq56 xp_ff Eq60 palo Eq35 tg Eq39 tm Eq43 drb Eq48 lctron χ (m 2 /s) 0 0. xp Eq56 xp Eq60 palo Eq35 tg Eqs39&4 tm Eqs43&47 drb Eqs48&5 0. lctron hat dffusvty summary L-mod shot 8897@525ms Normalzd Radus, rho 0.0 lctron hat dffusvty summary--shot 8897@240ms Normalzd Radus, rho Fgur 5 Comparson of thory and xprmnt for lctron hat dffusvty n L-mod (4a) and ELM-fr H-mod (4b) phass of DIII-D shot 8897.(Eq. numbrs rfr to PoP, 5, July 2008).

8 D. Infrrnc of Exprmntal Torodal Angular Momntum Transfr Frquncs from Massurd Torodal Rotaton locts (PoP, 5, 02503, 2008) If both th dutrum and carbon rotaton vlocts could b masurd, thn thr rspctv torodal momntum balanc quatons could b solvd backwards for thr momntum transfr frquncs ν d φ θ r φ φk k φ φ n E A B M + Γ + = ν k n m ν but snc thy ar not, a prturbaton approach s ndd. ) add th tor. mom. quatons for th 2 spcs and dfn (= dut, k= carbon) ν ff d n n ν + n m ν d k k dk = n m + n m k k φ θ r φ k k φ k θ rk φk d φ φk n E A + B Γ + M + n E A + B Γ + M { n m ν } 2) obtan a zro ordr stmat 3) us ν d 0 ( n m + n m ) k k φk ν by sttng = 0 φ n dutrum tor. mom. quaton to solv for d 0 φk A φ + θγ r + φ φ φk = 0 n 0 m ν ν + k d 4) whch can b usd n carbon tor. mom. quaton to solv for n E B M n m ν 0 d xp φk n A kk E k B rk M φ θ φk nkmkν k + Γ + + φ φk ν = 0 dk xp n m k k φk 5) whch can b usd n dfnnton of ν df ν to obtan ν ν f d0 d d0

9 Infrrd Torodal Momntum Transfr Frquncs Momntum transfr rat, (s - ) Dxp[Eq2] Cxp[Eq4] Dgyro[EqA4] Cgyro[EqA4] Datom Normalzd Radus, rho stacy fg 5 Momntum Transfr Rat, (s - ) Dxp[Eq2] Cxp[Eq4] Dgyro[EqA4] Cgyro[EqA4] Datom Normalzd Radus, rho stacy fg 6 Fgur 6 Exprmntally nfrrd torodal angular momntum transfr frquncy avragd ovr ELMs n H-mod shots (6a) and n ELM-fr H-mod shot 8897 n DIII-D compard wth transfr frquncs calculatd for noclasscal gyrovscosty and atomc physcs ffct of rcyclng nutrals. (Eq. numbrs rfr to PoP, 5, 02503,2008).

10 E. POLOIDAL ROTATION POLOIDAL ROTATION ELOCITIES ARE CALCULATED FROM THE POLOIDAL MOMENTUM BALANCE EQATIONS (PoP, 5, 0250, 2008) p n m + Π + M + n m + r θ ν g g k θ θk θ θ θ r φ θ on θ n B E + n m ν = 0 Usng a noclasscal paralll vscosty modl 3 B K T L Bg gπ η A 3 P = + + A φ 2 2 NEO r th strss tnsor s θ Bθ φ T φ Bθ 0 0 θ η l θ B l θ B Aθ θ 0 2 R θ = + + / 3 3 l R l B l θ θ θ θ θ φ R φ A0 = 2 f pr / l θ η υ ν * φ 0 = n m qrf th wth f ε 3 2 ν * = + + θ ( ε 3 2 ν * * )( ν ) lads to a coupld st of qs for th dutrum and carbon vlocts ± s ± s 2 ± c 2± c * * θ qυφ ε n +Φ + q f fp +Φ + n + fpν + fpν 3 k at ] m = Φ Φ * ± s ± s θkν f k p r qε n qε mk 4 4 q f f P q P n 2 ' ± c ' ± s ± s p φ + Φ ε φ φ + Φ + φ 2 wh

11 Polodal locty, θ (m/s) 3.0x x x0 4.5x0 4.0x x x x0 4 xp Stacy-Sgmar Eqs Stacy-Sgmar Eqs. 25 Hrshman-Sgmar Eqs. 26 Km-Damond-Grobnr CARBON -.5x Normalzd Radus, rho Fg 2 Stacy Fgur 7 Comparson of calculatd and masurd carbon vlocts n DIII-D shot H-mod (Eq. numbrs rfr to PoP, 5, 0250,2008.)

12 F. CONCLUSIONS Momntum balanc consstntly rlats th masurd on prssur gradnt wth th masurd φ, θ, Er, tc. and th calculatd r, mplyng that f w could calculat th E and knw th thrmal transport coffcnts w would b abl to prdct th,, r φ θ, r dnsty and tmpratur profls n th dg pdstal. A gnralzd dffuson thory whch prsrvs ths consstncy btwn prssur gradnts E tc. has bn dvlopd and should b usd for calculatng on partcl and,, r φ θ, r profls n th dg pdstal. Th smpl analytcal xprssons for thrmal dffusvts that ar wdly usd n transport cods do not rlably prdct χ, that agr wth xprmntally nfrrd valus n th dg pdstal, although som of th tg and tg comparsons ar promsng. Th radal transfr rat of torodal angular momntum s much largr than transfr rats calculatd from noclasscal gyrovscous thory and from atomc physcs, xcpt ust nsd th sparatrx, mplyng th nd to dntfy othr momntum transfr mchansms n th dg pdstal. An xtndd noclasscal thory prdcts θ profls rasonably nar to masurd profls, and thr s a possblty that a bttr calculaton of th polodal and radal lctrc fld n th dg pdstal could rsolv th prsnt dsagrmnt.