GLOBAL ENERGY CONFINEMENT SCALING, UNCERTAINTIES, AND PROJECTIONS TO ITER

Transcription

1 GLOL ENERGY CONFINEMENT SCLING, UNCERTINTIES, ND PROECTIONS TO ITER presented by. C. Deoo* General tomics *in collaboration with Confinement Database and Modeling Working Group

2 Confinement Database and Modeling Working Group Data representatives lcator C-mod sdex/sdex U Compass-D DIII & DIII-D FT-U ET FT-2M/T60-U PX-M, PDX, TFTR STRT TEXTOR Tore-Supra T10 TCV Statistical Modelling.. Snipes, M. Greenwald F. Ryter*, M. lexander, O. Kardaun,. Kus M. Valovic.C. Deoo*, D.P. Schissel, T. Carlstrom G. racco K. Thomsen+,.G. Cordey*, E. Righi Y. Miura*, T. Takizuka*, T. Fukuda,. Shirai S.M. Kaye*, D. Mikkelsen M. Walsh. Ongena G.T. oang. Chudnovskii*, M. Osipenko* Y. Martin O. Kardaun 1-D Modelling S. ttenberger, D. oucher*,. Connor*, W.ÊDorland,.ÊFukuyama, W.Êoulberg*,. Kinsey, M. Kotschenreuther, V. Leonov, D.ÊMikkelsen,ÊY.ÊOgawa*,Ê.ÊPolevoi,.ÊTaroni, M. Turner, R.E. Waltz,. Weiland, G. ateman * ITER Expert Group members Global databases: L-mode, -mode, Threshold Local database: Profile

3 KEY POINTS ased on empirical, power law scaling expressions, the thermal energy confinement time in ITER is projected to be ~6 sec. 95% interval estimate of sec is estimated which represents effects such as the use of other functional forms for the scaling expression and the impact of systematic measurement errors. Good progress toward physics based scaling has been achieved from nondimensional scaling studies in several tokamaks. validation experiments ρ *, β and ν * scaling

4 -MODE DTSE CRCTERIZTION Nearly 6000 time slices from SDEX, DIII-D, ET, FT-2M, PX-M and PDX containing Ohmic, L-mode and -mode times. New data from additional tokamaks is being added to update the database. Set of selection criteria established to choose data of interest to ITER including steady state (small dw/dt) - mode, NI heated, limited radiated power and fast ion energy content. ave chosen ELM-free and ELMing datasets for regression analysis Log-linear (power law) regressions with the ELM-free dataset meet the high β or Kadomstev constraint (dimensionality check) the ELMy dataset does not, perhaps due to mixing discharges with various types of ELMs working on including ELM characterization Log-linear regression on ELM-free dataset yields ITER93 τ th = I P 0.67 n e 0.17 M 0.41 R 1.79 ε 0.11 κ 0.66

5 -MODE SCLING REGRESSION with ELM-free DT Thermal Tau (sec) ELM free data SDEX D3D ET FT2M PXM PDX ITER93 Tau (sec) RMSE = 12.3 % I p 1.06 T 0.32 P L n e 0.17 M 0.41 R 1.79 e k 0.66

6 ITER93 SCLING COMPRED TO ELMy DT 10 SDEX DIII-D M ET FT2M Thermal Tau (sec) Ñ É P PXM PDX DIII-D rho* and kappa studies S ET rho* data SS T60U rho* ; data M ITER P S ; ; P UG ÑÑ ÑÑ Ñ ÑÑÑ Ñ P CMOD ÑÉ Ñ Ñ Ñ Ñ ÑÑ Ñ Ñ É ÉÉ Ñ ÉÉ ÉÉ ÉÉÉ É É É ÉÉ É É É É É ÉÉ É ÉÉ É É É X ITER93 (sec).c. Deoo 10/22/96

7 NONLINER FUNCTIONL FORMS The most recent nonlinear functional form developed by Dorland and Kotchenreuther has one fewer fitting parameter than ITER93 DK96 τ th = I P 0.69 M 0.28 R 1.57 κ 0.43 g ln q eng where g 2 = ( q 95 q eng )a nε and q eng = 5a2 κ IR RMSE = 11.4 %, somewhat smaller than ITER93 two weakest principal components less uncertain compared to ITER93 and smaller extrapolation to ITER Offset-linear functional forms have also been proposed W th = W 0 +τ 0 P where and W 0 = C 1 I x I x n x n M x M R x R κ x κ a x a τ 0 = C 2 I z I z n z n M z M R z R κ z κ a z a because there are too few tokamaks with different sizes to determine all the geometric exponents in this functional form additional assumptions must be made projections to ITER are more optimistic than ITER93

8 PYSICS-SED SCLING STUDIES Dimensionless parameter scaling, DPS Global Local Ωτ = F(ρ *,β,υ *,q,...) χ a 2 = G(ρ *,β,υ *,q,...) λ D << ρ i atomic physics is negligible in confinement and transport Validation of technique match all dimensionless parameters in two different tokamaks with different engineering variables should obtain same value of normalized confinement time, τ, and normalized thermal diffusivity Similarly, if assume ρ * scaling of F or G is separable then can study ρ * scaling τ=τ ρ * α F(β,υ *,q,...) where or χ=χ ρ * α G(β,υ *,q,...) α = 1 gyro-ohm scaling α = 0 ohm scaling

9 . G. Cordey,. alet T. C. Luce, C. C. Petty

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11 SCLING WIT DIMENSIONLESS PRMETERS ρ * scaling experiments in ITER-like discharges have been performed on SDEXU, DIII-D, ET and T-60U. For low q, ELMing -mode discharges, gyro-ohm-like scaling was found. Recent DIII-D and ET dimensionless parameter scaling experiments in -mode agree on the β and ν * scaling τ β 0 υ * 1/3 DPS results essentially agree with ITER93 scaling for ρ * and ν * scaling but disagree with β scaling ITER93 : τ τ ρ * 0.74 β 1.23 υ * 0.28 DPS : τ τ ρ * 1 β 0 υ * 1/3 Disagreement in β scaling is outside range of uncertainty in each expression. Reasons for disagreement are not yet understood but are under investigation. When proposed DPS experiments to determine q scaling are completed, a complete local transport scaling model will be available.

12 NONLINER COMPRED TO LOG-LINER FUNCTIONL FORMS Compare DK96 to ITER93 τ DK96 = I P 0.69 M 0.28 R 1.57 κ 0.43 g ln q eng note g 2 α then τ DK96 τ 93 βε ρ * α F αρ * ln q eng F ~ 1 over range in dataset, but drops to ~0.7 for ITER need compelling physics reason to motivate this strong curvature produced outside the range of the database Other nonlinear functional forms can be formed with values near 1 over the range in the database. One with this property but which increases for ITER is τ C τ 93 = coth(πq eng ρ * ) Functional forms τ = F ±α τ 93 with the above property of F have an unbounded range of predictions for ITER.

13 Two Nonlinear Functions which gree well with the Database and Dramatically Differ in their ITER Prediction coth (10 ρ*) 1.0 τ/τ DK ITER ET DIII D ρ* SDEX FT2M G96.494/11c G. CORDEY

14 DDITIONL COMMENTS ND CONCERNS ITER93 the two weakest principal components are relatively more uncertain, smaller variation within the database, yet require a large step size to ITER of several standard deviations. ITER operation is up to ~1.4 x n GW but the ELM-free dataset has a mean value of 0.45 x n GW recent SDEXU and DIII-D pellet injection experiments show no degradation in confinement up to 1.5 x n GW ITER will operate just above the -mode power threshold but the database discharges are generally well above the threshold. operation in C-Mod near the threshold shows no degradation in confinement

15 SUMMRY OF ITER PROECTIONS Log-linear Expressions 0.85 x ITER93 ITER projection: τ th = 6.2 ± 1.8 sec 95% confidence interval δτ τ = 2σ 1+ N eff n 2 λ ITERj 2 j=1 λ pcj 1/2 = 29% N eff ~ N/4 Other log-linear regressions on both ELMy and ELM-free datasets also result in ITER projections near or above 6 sec Nonlinear Expressions 0.85 x DK96 ITER projection: τ th = 4.3 ± 1 sec (2σ) Offset-linear scaling expressions typically give more optimistic ITER projections, τ ~ 9 sec (OL95, Kardaun), but require additional assumptions on size dependence and therefore are more uncertain.

16 ITER PROECTIONS (CONT.) Dimensionless Parameter Scaling ssuming ITER operation in ELMing -mode can be obtained along a gyro-ohm scaling path τ ρ * -α where α=3.0 for gyro-ohm and α=2.7 for ITER93 ITER demonstration discharges in ET and DIII-D Tok β N ρ * /ρ * ITER α τ ITER ET sec DIII-D Projections are optimistic compared to ITER93 Detailed error analysis is required to estimate uncertainty in projections

17 UNCERTINTY IN ITER PROECTIONS Taking into account both statistical and physics considerations, most members of the database working group believe the ITER93 scaling expression is the best choice of the various possible functional forms considered. owever, the uncertainty in the ITER projection should consider projections based on the various functional forms with similar statistical significance other effects such as systematic, tokamak to tokamak, measurement errors One can define a 95% interval estimate as one which contains all ITER projections from statistically comparable fits. y considering the distribution of ITER projections obtained by employing various functional forms and estimating systematic errors, an uncertainty interval of sec was estimated.

18 Sensitivity of ITER93 Predictions to Systematic Errors 10% Systematic errors can produce 15% to 20% variations in ITER predictions 0.4 Increased τ by 10% in an individual tokamak τ τ SD D3D ET FT PX PDX O.. KRDUN sdex

19 ITER PERFORMNCE vs. CONFINEMENT ENNCEMENT FCTOR () WIT DIVERTOR IMPURITY MODEL Fusion power (MW) β N n e / n GW uxiliary heating (MW) factor factor

20 CONCLUSIONS ND FUTURE WORK The database and modeling working group has recommended using the ITER93 scaling expression for addressing ITER issues where information on parametric scaling of global confinement time is required. Several log-linear scaling expressions project to τ th ~ 6 sec ± 30% for ITER. owever, in recognition of a wider span of projections from non-linear functional forms, the group has recently recommended ITER consider contingency scenarios based on a confinement time interval of sec. Future -mode database work new regression analysis on combined dataset with new data from SDEXU, C-Mod, DIII-D, ET and T-60U ELM characterization add results from new dimensionless parameter scaling experiments to database further study on β scaling discrepancy