Confinement Understanding and the Extrapolation to ITER presented by J G CORDEY in collaboration with the ITER Confinement Database and Modelling Working Group - 1 -
Confinement Database and Modelling Working Group Data representatives Alcator C-mod Asdex/Asdex U Compass-D DIII DIII-D FT-U JET JFT-2M / JT6-U PBX-M, PDX, TFTR START TEXTOR Tore-Supra T1 TCV Statistical Modelling J A Snipes, M Greenwald F Ryter*, O Kardaun, A Kus M Valovic J C DeBoo* D P Schissel, T Carlstrom G Bracco K Thomsen, J G Cordey*, E Righi Y Miura*, T Takizuka*, T Fukuda, H Shirai S M Kaye*, D Mikkelsen M Walsh J Ongena G T Hoang A Chudnovskii*, M Osipenko* Y Martin O Kardaun 1-D Modelling S Attenberger, G Bateman, D Boucher* J Connor*, W Dorland, A Fukuyama, W Houlberg*, J Kinsey, M Kotschenreuther, V Leonov, D Mikkelsen, Y Ogawa*, A Polevoi, A Taroni, M Turner, R E Waltz J Weiland, G Vlad *ITER Expert Group members - 2 -
Contents Introduction Global Energy Confinement Approach Dimensionless Physics Parameter Similarity Approach 1-D Modelling Approach Complementary papers Analysis of H-mode threshold database by J A Snipes etal Global Confinement ITER Fusion Performance Projections by J P Christiansen by D Boucher 1-D modelling papers by G Vlad etal by J Kinsey etal Dimensionless Scaling by C Petty and T Luce - 3 -
Introduction Preferred operational regime of ITER is the steady state ELMy H-mode. This type of pulse is particularly complex because there are probably different turbulence mechanisms determining the core and edge transport, most likely gyro-bohm in the core with MHD events (ELMs) playing a role in the edge region.these two types of turbulence will scale differently with size ρ* ( ρ i /a). A fully tested 1-D model describing the transport from the separatrix to the centre is not yet available, so 3 approaches to predicting the confinement in ITER are being used. Each approach has its own strengths and weaknesses. a) Statistical analysis of the energy confinement data. Virtues: Simplicity and data contains all the key physics. Good track record in prediction of L-mode behaviour. Weaknesses: Statistical models ignore profile effects, such as those of heating, Te, ne etc which may be important. Possibility of hidden parameters. b) Dimensionless physics parameter similarity approach. Virtues: Profile effects are fully included. Weaknesses: Range ρ* in present experiments too small for accurate predictions to be made; need to form a database of similarity pulses. Some uncertainty as to which are key dimensionless parameters. c) Full 1-D modelling. Progress in modelling the core but no tested model available for edge pedestal yet. ITER predictions with some of the models are very sensitive to the edge conditions. - 4 -
Statistical Analysis of Energy Confinement Data New database DB3 has been formed which includes data from five new machines ASDEX-U, C-MOD, COMPASS-D, JT6-U, and TCV, and additional pulses from DIII-D and JET. Similar data selection rules were used to those used in DB2 from which the ITERH-93P scaling was derived. In new selection ICRH and ECRH are included as well as NBI and ohmic data from COMPASS and TCV are also included. Standard set consists of 1112 ELM-free and 119 ELMy discharges. Principal Component Analysis was completed to determine the condition of the database w.r.t. to ITER projections. The two weakest principal components have the form PC 7 ~ Bn/Rκ 2 PC 8 ~ ab/i which are similar to those of DB2. However, the number of standard deviations to ITER of the most important one PC 7 has been reduced from eight to four. The main reason for the reduction is due to the inclusion of CMOD which has a large value of B/R. - 5 -
ELMy and ELM-free data points in ρ* β N space 1/ρ* 1 4 1 3 ITER H-mode database DB3 ASDEX DIII D JET JFT 2M PBX M PDX AUG C MOD COMPASS-D JT 6U TCV ITER 1 2 3 4 JG97.293/11c β N ρ* JET At β n = 1 2.2 ρ* ITER ρ* JET At ignition β n = 2.2 = 5 ρ* ITER CMOD, TCV, AUG fill gap between large and small machines - 6 -
Log Linear (Power Law) fit to ELMy data Fit engineering form τ th =.29 Ι.9 Β.2 P.66 n.4 R 2.3 ε.19 κ.92 Α.2 τ th (s) 1 1 1 1 ASDEX DIII D JET JFT 2M PBX M PDX AUG C MOD COMPASS-D JT 6U ITER ITER H-mode database Version DB3 1 2 RMSE = 15.% 1 2 1 1 1 1 1 τ scaling (s) JG97.293/12c Free fit satisfies Kadomtsev high β constraint Physics form Βτ th ρ -2.88 β -.69 ν* -.8 Close to Gyro-Bohm ρ* -3-7 -
Predictions of ITER energy confinement time ITER parameters are R = 8.14m, a = 2.8m, Κ = 1.73, B = 5.68T, I = 21MA, n = 9.7x1 19 m -3, A = 2.5 and P loss = 18MW. Types of model an reference Principal Authors Database used RMSE % ITER τ th (s) Log-linear This paper DB3 ELM-free *.85 for ELMs 16. 6. Log-linear This paper DB3 ELMy 15. 5.8 Log-linear Tokamak This paper DB3 ELMy 16.6 6.2 Equal weighting Log-linear ITERH93-P DB2 ELMy *.85 for ELMs 12.3 6. Offset-linear O. Kardaun DB2 ELM-free 8 Log-nonlinear W Dorland & M Kotchenreuther DB2 ELM-free *.85 for ELMs 11.4 4.3 Offset-nonlinear T Takizuka DB2 + JT-6U 4.7 Near Neoclassical J P Christiansen DB2 ELMy 8.8 JG97.293/2c 95% Confidence Interval for a log-linear form δτ τ = 2σ 2 n λ ITERj 1+ 2 N eff δ=1 j λ pej cj ~ 17% for DB3 (~ 29% in DB2) Non log-linear models applied to DB2 gave rise to a wider range in the predicted performance. In view of this the group recommended that ITER consider contingency scenarios in the range = ±45%. τ This analysis needs to be repeated for DB3. 1/2 δτ - 8 -
ITER Projections versus HH factor (21MA. high pedestal case, P aux <=1MW) 15 125 PFusion (MW) Beta limit uncertainty 1 75 5 nfree ngw 25 45% 17% +17% +45% ITERH 97P (y).5.75 1. HH factor (τ/τ ITER H 97Py)) 1.25 1.5 JG97.293/1c Conservative density and temperature profiles and impurity level assumed Ignited points are indicated in red At high confinement (HH>1.1) beta limit restricts amount of fusion power At low confinement fusion power can be optimised by operating above Greenwald density - 9 -
Objectives of the dimensionless physics parameter approach to predicting future performance Provided λ turb >> λ de and atomic processes are unimportant then the thermal diffusivity can be put in the form χ Ba 2 ( ) = ρ*α F νv*,β,q,κ,... (1) when there is a single dominant transport mechanism. α = 3 gyro-bohm, 2 Bohm,1 Stochastic. Dimensionless parameters in F can be fixed at their ITER values in present experiments, so in principle, once the ρ* dependence is known, one can project to ITER confinement and profiles directly from the experimental data. To confirm that the only important variables are ρ*, β, ν*, q etc. identity pulses have been developed on DIII-D and JET having the same values β, ν*, q etc; their confinement times should then scale inversely with B. - 1 -
ELMing H-mode discharges with identical dimensionless parameters have been developed on DIII-D and JET DIII-D plasma shape closely matched that of JET Parameter DII-D JET a(m).56.97 B (T) 2.1 1.7 Ip (MA) 1.14 1. n(1 19 m 3 )7.6 2.4 W th (MJ).6.84 P tot (MW) 6.1 4.25 τ th (s).1.2 Bτ th.21.21 JG97.293/2c The normalised thermal confinement times for DIII-D and JET are equal for these H-mode identity plasmas Note: Ω ELM τ th 7. 5. - 11 -
ITER Similarity Pulse in JET B = 1.7T I = 1.7MA (#3849) υ* β n = 2.3 υ* = 1 ITER JET W (MJ) 4 2 Pulse No: 3849 JG97.293/3c ITER 1 <n> (1 19 m 3 ) D α P NBI (MW) 3 2 1 6 4 2 15 1 5 16 17 18 19 Time (s) 1x1 2 15 1 1-12 -
Profiles of ITER similarity Pulse No: 3849 JET Pulse No: 3849 JG97.293/15c ITER 6 2 T e T i T T (kev) 4 1 2 JET 3. 3.2 3.4 3.6 3.8 R (m) Pulse No: 3849 ITER 3 1 x 1 2 n e ne (1 19 m 3 ) 2 1 3. 3.2 3.4 3.6 3.8 4. R (m) - 13 -
Experimental Scaling results for ITER similarity discharges Scaling with the dimensionless larmor radius ρ* DIII-D Gyro-Bohm Bτ th ρ* -3.1 JET Close to Gyro-Bohm Bτ th ρ* -2.7 ASDEXU Gyro-Bohm locally Scaling with the collisionality parameter υ* DIII-D Βτ th υ* -.37 JET Βτ th υ* -.27 Scaling with β DIII-D Βτ th β.1 JET Βτ th β -.5 These contradict ITER H-93P β -1.2 DB3 ELMy β -.69 Reason for discrepancy discussed in the paper by J P Christiansen etal. - 14 -
ITER Predictions using this technique For Βτ th ρ* -α and υ* and β fixed at their ITER values Βτ th (B 2/3 a 5/6 ) α Predictions Tokamak βn ρ*/ρ*iter α δα τ th ITER (s) δτ(s) DIII D 2.1 7.7 3.1 ±.3 28 ±18 JET 2.2 5.5 2.7 ±.22 6.4 ±3 In calculating the errors δτ it is assumed that these come entirely from errors in the measurement of the stored energy of ± 15%. (2σ) - 15 -
ITER similarity data versus ITER H-93P scaling expression Bτ th 1 1 (I) DIII D (I) JET (II) DIII D (II) JET ρ* scans DIII D β n = 2. JET β n = 1.5 JET β n = 1.6 JET β n = 2. τ ITER.1.1 1 1 B τ ITERH93 P JG97.293/5c *Range in ρ* too small in a given machine to give an accurate prediction of τ th in ITER, need to form a database over at least two machines of differing sizes. - 16 -
1-D Modelling approach Systematic testing of 11 1-D models against the profile database is continuing results presented here should be regarded as preliminary. Profile database consists of 9 discharges from 9 different Tokamaks DIII-D, JET, TFTR, JT-6U, ASDEX-U, T-1, TEXTOR, TORE SUPRA and RTP. Includes both L and H-modes. Models MODEL MODELLER PHYSICS JG97.293/18c Turner Turner-IFS/PPL IIF T11/SET RLW B GLF23 Mixed Bohm Gyro-Bohm Mixed-shear IFFS/PPPL Weiland Multi-mode M Turner (EU), S Attenberger (US) M Turner (EU), S Attenberger (US) A Fukuyama (JAP), S Attenberger (US) D Mikkelsen, R Waltz (US) A Polevoi (RF) D Mikkelsen (US) D Boucher (JCT) R Waltz (US) A Taroni (EU) G Vlad, M Marinucci (EU) M Turner, S Attenberger (US), B Dorland (US), D Mikkelsen (US) R Waltz (US) J Weiland (EU) D Mikkelsen (US) R Waltz J Kinsey et al (US) Semi-empirical Semi-empirical Current Diffusive Ballooning Modes Semi-empirical Semi-empirical ITG Semi-empirical Semi-empirical ITG ITG Weiland & Resistive Ballooning - 17 -
Models are evolving as further physical effects are included Example GLF23 model of R Waltz with and without EXB shear flow stabilisation 12 1 8 Data GLF23.v4 w/o ExB GLF23.v4 w/ ExB T e (kev) 6 4 2.2.4.6.8 1. ρ/a 12 Data 1 GLF23.v4 w/o ExB GLF23.v4 w/ ExB 8 JG97.293/8c T i (kev) 6 4 2.2.4.6.8 1. ρ/a - 18 - JG97.293/9c
Bench marking of codes JET pulse 19649 8 6 4 IFS/PPPL model with EXB shear JET Pulse No: 19649, T e, t = 8.7s Boucher SMC Dorland NT Kinsey MLT Experiment 2 6 JET Pulse No: 19649, T i, t = 8.7s 4 2.2.4.6.8 JG97.293/16c Flux label - 19 -
ITER Profile Database L+H modes Ws/Wx-1 1..5. -.5-1. D R =18.8% w <R >=.97 w mixed-shear L-mode H-mode JET_19649_L JET_19691_L DIII-D_69627_L DIII-D_69648_L DIII-D_71378a_L DIII-D_71378b_L DIII-D_71384_L TFTR_4595_L TFTR_5862_L TFTR_593_L TFTR_594_L TFTR_5911_L TFTR_5921_L TFTR_52527_L DIII-D_77557_H DIII-D_77559_H DIII-D_8225_H DIII-D_82788_H JET_33131_H JET_3314_H - 2 -
Stored energy offset for 46 pulse subset L-mode (21) H-mode (25) 1. R w = 26.9% <R w > = 1.5.5 1..5 R w = 21.8% <R w > =.94.5 1. 1..5 GLF23.v4 w/ ExB Shear DII-D JET TFTR DII-D JET R w = 14.7% <R w > =.98.5 1. 1..5 IFS/PPL w/o ExB Shear DII-D JET TFTR DII-D JET R w = 24.1% <R w > =.97.5 1. Multi-mode DII-D JET TFTR DII-D JET.5 1. Offset = W s /W x 1 RMS = R w = (S i (W si /W xi 1) 2 /N) 1/2 Recalibrated Itoh-Itoh -Fukuyama DII-D JET TFTR DII-D JET Avg = <R w > = S i (W si /W xi 1)/N) JG97.293/17c
Ranking According to Goodness of Fit <R W > R W <R Winc > R Winc Multi-mode.96.15.94.23 IFS-PPPL.94.22.9.35 IIF (recalibrated).97.24.92.38 GLF23.v4 (w/exb) 1.5.27 1.1.43 IFS-PPPL (w/exb) 1.2.37 1.35.64 σt e σt i <f Te > <f Ti > Multi-mode.17.22 -.5.1 IFS-PPPL.28.26 -.4 -.7 IIF (recalibrated).25.39 -.5 -.2 GLF23.v4 (w/exb).32.34.2.3 IFS-PPPL (w/exb).53.34.17.8 R W = ( W xi /W xi )/N average R W = i W si /W xi 1 S f T = i ( T s T x )/ i T 2 x offset σ T = i ( ) 2 /N ( T s T x ) 2 / i T 2 x i Note the ranking of the models is independent of the test. averageerror rmserror On the basis of this dataset the Multi-mode performs the best, however the results are not thought to be decisive since most models can match the data to within 2-3% and it is possible that uncertainties in the experimental inputs could lead to discrepancies of this magnitude. More stringent model testing is required such as the response to localised perturbations. - 22 -
LOCAL Transport model ITER projections versus HH factor (21MA. P aux <=1MW) 15 125 Mixed shear Multi mode Canonical profiles RLW IIF PFusion (MW) 1 75 5 25 RLWB GLF 23 IFSPPPL Culham Ignited range T(.9) 4keV T ped 1.5 kev estimate (*) T(.9) 1keV.5.75 1. 1.25 1.5 HH Factor (τ/(.85τ ITERH 93P)) * Mixed shear: Strongly peaked T profile inside q = 1 HH factor IIF 1.1 1.3 RLW.9 1.2 CPM.7.9 Multimode.7.8 Culham.6.85 Mixed shear.5.7 RLWB.5 1. GLF23.35.7 IFS PPPL.3.7 JG97.293/1c - 23 -
Summary and future programme needs The three techniques being used to predict the performance of ITER have overlapping prediction intervals but the range of predicted performance using each technique is large. Further work is required to narrow these ranges. Global Energy Confinement. The condition of the database wrt to ITER predictions has been improved with the addition of the data from the new machines. A new log-linear scaling expression for the ELMy data has been derived, which satisfies the Kadomtsev high b constraint, and has a narrow 95% confidence interval (± 17%) for its ITER prediction. Other types of non log-linear models need to be tested using this new database before the overall confidence interval of±45% can be reduced. Further data is required from some of the new devices, and variables such as the divertor neutral pressure and rotation need to be added to the database so the effect of these on τ e can be assessed. We also need to examine confinement near boundaries such as the L- H threshold - 24 -
Summary and future programme needs (contd.) Dimensionless Physics Parameter Scaling Studies: Identity experiments on different size devices have validated the technique and useful results on the scaling of χ with ρ*, ν* and β have been given. To make accurate predictions using this technique a Multi machine database of ITER similarity discharges will be required with a large range of ρ*. Future programme: further pairs of identity discharges are required and experiments to determine whether there are any other dimensionless parameters that influence confinement e.g. the Mach number. 1-D modelling Approach. The systematic and open method of testing models against the ITER Profile database is now working well. The best models are now able to compete with the global confinement approach in the core region. The predictions of some of the models are very sensitive to the edge pedestal temperature. Future programme: A validated edge model is required and sensitive experimental tests of profile stiffness are also needed. - 25 -
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Log Linear fit to ELMy data with each tokamak equally weighted Fit in engineering form τ th =.3 Ι.99 Β.6 P.69 n.61 R 1.89 ε.22 κ.7 Α.11 τ th (s) 1 1 1 1 ASDEX DIII D JET JFT 2M PBX M PDX AUG C MOD COMPASS-D JT 6U ITER ITER H-mode database Version DB3 1 2 RMSE = 16.6% 1 2 1 1 1 1 1 τ scaling (s) JG97.293/13c Physics form Bτ th = ρ* 3.21 β.41 ν*.13 - x1 -