Search for a Critical Electron Temperature Gradient in DIII-D L-mode Discharges

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1 Seach fo a Citical Electon Tempeatue Gadient in DIII-D L-mode Dischages.C. Deoo, S. Ciant 1, T.C. Luce, A. Manini, C.C. Petty, F. Ryte, M.E. Austin 3, D.R. ake, K.W. Gentle 3, C.M. Geenfield,.E. Kinsey and G.M. Staeble DIII-D National Fusion Facility 1 Instituto di Fisica del Plasma - CNR IPP-Gaching 3 Univesity of Texas at Austin Lehigh Univesity th IAEA Fusion Enegy Confeence Novembe 1-, Vilamoua, Potugal DIII D NATIONAL FUSION FACILITY SAN DIEGO Deoo IAEA

2 Intoduction Pevious expeiments on DIII-D L-mode and H-mode dischages showed no evidence of nonlinea behavio in the T e esponse to modulated ECH. Othe tokamaks, notably ASDEX-U and FTU, have found that a tanspot model based on a citical tempeatue gadient scale length agees well with both steady state powe balance analysis and the esponse fom modulated ECH. Two expeiments on DIII-D have been pefomed with the pupose of seaching fo evidence of χ e dependent on a citical value of T e. ECH swing expeiment (based on FTU expeiments) systematic heat flux scan (based on AUG expeiments) DIII D NATIONAL FUSION FACILITY SAN DIEGO Deoo IAEA

3 ECH Swing Expeiment Fist caied out in FTU (Ciant, IAEA 3). Citical tempeatue gadient model χ e = χ o + f(t e )( T e HP (q/n) k cit )H k χ e T e T e = χ o + f(t e )( T e T e k cit )H k If the dive is stong enough to cause the local T e to go fom below a citical value to above it then the nonlinea change in χ e HP will poduce a nonlinea esponse in T e. Utilize 1 o out-of-phase, squae wave modulation of pais of gyotons absobed at slightly diffeent adii in ode to localize the heat flux and T e modulation at constant total input powe. DIII D NATIONAL FUSION FACILITY SAN DIEGO Deoo IAEA

4 L MODE TARGET PLASMA Inside wall limited L mode. MA,. T x 1 19 m 3 Sawtooth fee ECH esonance at ρ ECH =.-.3 and.-.5 fmod = 5 Hz and PECH1 ~ PECH ~ 1 MW Thee heat flux conditions:.,., MW NI R (m) = a (m) =. κ = ECH Resonance Laye ECH Launch DIII D NATIONAL FUSION FACILITY SAN DIEGO T e (kev) ECH1 ECH ρ Deoo IAEA

5 3 Compaison of Pofiles with P NI = MW and MW ECH deposition at ECH =.-.3 Cental T i is educed without NI Lowe density causes an incease in Zeff T e (kev) 115 MW NI 115 No NI 3 T i (kev) 3 T i W (1 ad/sec) n e (1 19 m -3 ) 5 Z eff Deoo IAEA

6 -ST e /T e in the ECH Absoption Region -ST e vaies fom.5 to 5 m -1 at =.9 whee T e is nealy constant T esponse is clealy not vey stiff as ST vaied by facto e e T aveaged ove 9 modulation peiods fom 11-1 msec on shot e ECH on ECH1 on Rho msec 1117 msec ECH1 ECH Time (msec) Deoo IAEA

7 The Relative Change in ST e Is Lagest Fo The Ohmic Case The Ohmic case is most likely case to obseve nonlinea behavio Changes in ST e ae small outside the ECH deposition since in this egion the ECH heat flux is essentially constant ST max -ST min ST min 1 Ohmic, ECH ~. MW, ECH ~. MW, ECH ~ Deoo IAEA

8 No Evidence of a Non-lineaity in c e HP is Obseved Fo Case with no NI and ECH =.-.3 o Any Othe Case The linea combination of the Fouie amplitude and phase of the Te oscillations due to ECH1 and ECH applied individually is the same as the esult with ECH1 and ECH modulated simultaneously and out of phase with espect to each othe 115 Simultaneous modulation of ECH1 and ECH 15 Calculated linea combination of ECH1 and ECH applied individually ECH1 ECH Deoo IAEA

9 Heat Flux Scan Expeiments Expeimental appoach (follow expeiments on AUG, Ryte NF 3 3) scan T e locally by vaying the electon heat flux while holding the flux at the edge (total powe) 3 constant ECH at two locations, ρ 1 and ρ vay P ECH1 and P ECH at constant 1 P ECH1 + P ECH... modulate one gyoton at ρ to ρ obtain χ HP. 1 T e (kev) Taget plasma (simila to low density ECH swing plasmas) L-mode limited on inside wall of vessel I p =. MA, T =.T, n e = 1.7x1 19 m -3, q a = 7 ealy NI to delay onset of sawteeth, then ECH only DIII D NATIONAL FUSION FACILITY SAN DIEGO Deoo IAEA

10 T e is Systematically Vaied etween ECH1 and ECH Locations EC powe is moved fom ECH1 to ECH shot by shot T e pofile outside ECH is constant since PECH1+PECH is held fixed T e (kev) 3 ECH1 ECH 1 / % / 1 1 / 39 7 / 73 / 1 1 ECH1 ECH Deoo IAEA

11 The Electon Heat Flux is Systematically Vaied at the Half Radius The total powe in the electons is compised of P ~ 1.5 MW ECH and P ~.5 MW. OH The dominant loss is by conduction, convection is negligible. At =.5 adiation and collisional tansfe to ions is small..5 Suface Integated Electon Heat Flux (MW) Deoo IAEA

12 Modulate ECH Powe on One Gyoton at Outside Location to Obtain Heat Pulse Diffusivity Modulate at Hz with 5% duty cycle fequency chosen to avoid matching sawtooth fequency Fouie analyze ECE channels Spatial deivative of pulse amplitude and phase yields an estimate of the heat pulse diffusivity χ HP Use 3 d hamonic pulse amplitude and phase to estimate χ HP DIII D NATIONAL FUSION FACILITY SAN DIEGO Deoo IAEA

13 No Evidence of a Citical Gadient Scale Length Was Obseved ut the Existence of One Cannot e Ruled Out A citical gadient scale length, k cit, could exist below T e = 3. m -1 at =.5. This coesponds to L Te. m o ove % of the plasma adius. If k exists it would be at values typically found nea the plasma coe, cit indicating most of the tempeatue pofile would be above it. c e 3/ (m /sec/kev 3/ ) Heat Pulse Powe alance Data at = T e (m -1 ) c e nomed to T e 3/ to take out gyo- ohm dependence Deoo IAEA

14 Results Of This Expeiment Ae Consistent With ASDEX Upgade Expeiments The diffusivity levels and tends with 1/L Te ae simila ASDEX Upgade found k cit =.3 m -1 fit thei data (Ryte, NF 3 3) c e 3/ (m /sec/kev 3/ ) AUG DIII-D H Heat Pulse P Powealance H H H H H P PP P H P Data at =.5 P T e (m -1 ) Deoo IAEA

15 TEMs Dominate Dift Wave Spectum in Region of Inteest Analysis pefomed with the linea gyokinetic stability code GKS TEMs ae unstable ove most of plasma mino adius Lagest gowth ates fo most unstable modes occu at Deoo IAEA

16 Spectum of Wavenumbes Whee Gowth Rate Is Maximum Spectal width at =. is dk ~ 3 cm -1 Fequency at the lagest gowth ate is f ~ 1 khz = k (cm -1 ) Deoo IAEA

17 ETG Modes Ae Stable In The Region Of Inteest ETG modes unstable only nea plasma edge, >. Citical gadient fo ETG modes calculated fom linea gyokinetic stability code GKS - T e (m -1 ) Citical level fo ETG modes Deoo IAEA

18 Thee Possible Dependencies of c HP on T e Offset linea: c HP becomes negative fo T e < m -1, implying heat flux deceases as the gadient becomes steepe (pehaps due to a heat pinch) Nonlinea: ( T e ) a, fit shows a ~ 5/3. Exponent can not be too lage in ode to emain consistent with ealie expeiments whee no obvious nonlinea behavio was obseved. Citical gadient: If a citical gadient exists it must be at T e < 3. m -1 at =.5 (abitaily chose 3. m -1 fo illustation). AUG has epoted a citical value of k cit ~.3 m Offset Linea Nonlinea Citical Gadient T e (m -1 ) T e (m -1 ) T e (m -1 ) Deoo IAEA

19 Summay No evidence of a citical gadient scale length dependence of χ HP was obseved but the existence of one cannot be uled out by the expeimental esults. The T e pofile was not vey stiff since the gadient was vaied by a facto of at locations in the pofile that wee above k cit, if k cit exists. If a citical gadient scale length exists, all expeimental esults to date ae consistent with the obsevations being made at values above it. The esults indicate that if k cit exists then k cit < 3. m -1 at ρ=.5 and k cit <.5 m -1 at ρ=.9 coesponding to a citical gadient scale length lage than 3% and 5% of the plasma mino adius, espectively. Models othe than one based on k cit ae also consistent with the expeimental obsevations such as an offset linea o powe law dependence of χ HP on 1/L Te. DIII D NATIONAL FUSION FACILITY SAN DIEGO Deoo IAEA