1. NSTX S. A. Sabbagh 1, M.G. Bell 2, R.E. Bell 2, L. L. Lao 3, B.P. LeBlanc 2, F.M. Levinton 4, J.E. Menard 2, C. Zhang 5 Reconstruction of NSTX Equilibria including MSE data Supported by Columbia U Comp-X General Atomics INEL Johns Hopkins U LANL LLNL Lodestar MIT Nova Photonics NYU ORNL PPPL PSI SNL UC Davis UC Irvine UCLA UCSD U Maryland U New Mexico U Rochester U Washington U Wisconsin Culham Sci Ctr Hiroshima U HIST Kyushu Tokai U Niigata U Tsukuba U U Tokyo JAERI Ioffe Inst TRINITI KBSI KAIST ENEA, Frascati CEA, Cadarache IPP, Jülich IPP, Garching U Quebec 1 Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 2 Plasma Physics Laboratory, Princeton University, Princeton, NJ 3 General Atomics, San Diego, CA 4 Nova Photonics, Inc., Princeton, NJ 5 Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China 17 th NSTX Program Advisory Committee Meeting January 20 - 21, 2005 Princeton Plasma Physics Laboratory

2. NSTX Approach  “Best” model for a given physics model / data set, reliably fit all data within error improved physics/data set reduces artificial constraint  “Rapid” reconstruction between-shots find one constraint set for a given (data,model)  “Levels” of reconstruction based on available data seamlessly switch levels during shot if needed data physics model basic advanced magnetics kinetic profiles rotation profile B pitch angle profile Motional Stark Effect data is a natural addition to NSTX EFIT reconstructions rotating plasma 3-D effects vessel currents plasma current vacuum

3. NSTX MSE can be included in all levels of EFIT NSTX EFIT “Levels”  Level 1: external magnetics data alone  Level 2: partial kinetic profile data added  Level 3: toroidal rotation added Statistics on MSE fits so far:  Four channels span typical magnetic axis position; 0.3 degree error  MSE data for 58 shots available on data tree  All 58 shots reconstructed with NSTX EFIT and written to NSTX database More than 7,500 equilibria available to the group More than 11,000 equilibria run in MSE testing so far fitted parameters artificial constraints 4strong 103 weak 20none

4. NSTX Physics constraintsData points  Internal magnetic field pitch angle (MSE)4  Plasma rotational pressure (CHERS)51  Flux surfaces are electron temperature isotherms20 T e = T e (  (R)| z=0 ) directly from Thomson data - rapid analysis  required to insure self-consistent solution with toroidal rotation  Plasma kinetic pressure Ion pressure (CHERS)51 Electron pressure (Thomson)20  External magnetics / plasma current119  Plasma diamagnetism1  Vacuum vessel current (includes “3-D” vessel effects)25  Shaping coil / TF currents9 MSE data adds further constraint to present rotating, high  ST equilibrium reconstructions Total (per time point)300

5. NSTX B field pitch angle profile added to reconstruction P kinetic (kPa) P dynamic (kPa) 10 20 30 0 2 3 4 5 6 Poloidal flux and pressure -2 1 2 0 Z(m) 0.52.01.01.5 R(m) 2.01.5 R(m) 01.02.00.51.5 R(m)  isotherm constraint (mWb/rad*10) -6 -4 -2 2 0 magnetic axis 0.0 114444 t=0.257s 1 01.00.5 magnetic axis 0 0.96 1.08 1.00 1.04 R(m) -0.2 0.2 0.0 Pitch angle (rad) vs. R MSE data peak pressure

6. NSTX Fits with / without MSE confirm high  results Few % change in stored energy Fits without MSE give good q 0 values  “calibrated” constraint set (using sawtooth onset, rational surface position from USXR in selected shots)  can now use MSE for “calibration” Correlation with crossing q 0 = 1 and  collapse I p (MA)  t (%) R axis (m) q0q0 q min 22 MSE data available solid (red) – with MSE dashed (black) – w/o MSE Partial kinetic fits 114465 MSE data starts

7. NSTX Fitted pitch angle evolution follows MSE data Pitch angle (rad) R = 0.975 mR = 1.107 m R = 1.059 mR = 1.10 m 114465 0.00.20.40.6 t(s) 0.6 0.4 0.2 0.0 -0.2 0.8 0.6 0.4 0.2 0.0 -0.2 0.6 0.4 0.2 0.0 -0.2 0.8 0.6 0.4 0.2 0.0 -0.2 0.8 0.00.20.40.6 t(s) 0.00.20.40.6 t(s) 0.00.20.40.6 t(s) Fit

8. NSTX MSE finds q 0 ~ 1 in plasmas with sawteeth External magnetics- only fit has q 0 = 1.1 Partial kinetic fit does not give q 0 ~ 1 at low stored energy  MSE required to find reasonable q 0 I p (MA)  t (%) USXR (arb) q0q0 q min 22 solid (red) – with MSE dashed (black) – w/o MSE 113983 MSE data available Partial kinetic fits

9. NSTX MSE fits indicate shear reversal in some equilibria Shear reversal not seen in reconstruction for this shot without MSE Shear reversal not apparent in l i evolution Collapse in  when q 0 = 2, q min = 1.5 I p (MA)  t (%) lili q0q0 q min 22 q MSE data available 114140 2.0 1.5 NBI (4 MW)

10. NSTX CY05 MSE channels will provide additional q constraint 114140 t = 0.208 s span of present MSE data Pitch angle (rad) vs. R q 0.0 0.5 1.0 1.5 R(m) Present MSE measurements do not span q min position in shear reversed equilibrium 0 1 2 3 4 1.00 1.04 1.08 R(m) MSE data EFIT reconstruction 0.96 -0.6 -0.4 -0.2 0.0 0.2 0.4 planned channels

11. NSTX Diagnostic input / code interaction continues to expand Add new MSE channels  8 channels start of FY05 run  Up to 14 channels by end of FY05 run Include computed fast-ion profiles directly from TRANSP  Understand possible role of MHD on fast-ion diffusion/loss  Include beam pressure anisotropy and flow of fast ions Use EFIT to help benchmark other reconstruction codes  LRDFIT: time-evolved circuit model of vessel included in fit Reconstruction of 20kA PF-only start-up plasmas  ESC: reconstruction version built around fixed-boundary code Used on JET for current holes, being developed for CDX-U (LTX)

12. NSTX NSTX EFIT with MSE is ready for the 2005 run Pre-run testing / analysis  Greater basis function flexibility, constraint optimization  Radial electric field correction to MSE data (using toroidal flow)  Further consistency checks with other diagnostics  More tests of rotating equilibria – comparison to static case  Physics analysis effects of reversed shear low-order rational surfaces and  collapse Between-shots EFIT reconstructions with MSE will improve analysis including present control room MHD stability calculations

13. NSTX Supporting slides follow

14. NSTX Expanded magnetics set reproduces 3-D eddy currents as axisymmetric currents during OH ramp VALEN (J. Bialek)  plate eddy currents 1 3 2 4 1 3 2 4 10 5 0 -5 -10 8 4 0 -4 I v (kA) 10 5 0 -5 -10 10 5 0 -5 -10 0.0 t(s) 1.00.01.0 t(s) Black points: plate current approximated from V loop sensors Solid lines: EFIT reconstructed plate currents using all magnetics data  Fitted currents match 3-D eddy currents as a 2-D analog

15. NSTX External magnetics data allow basic reconstruction Over 60 attempted variations to find model Profile constraints: p’(0) = 0, (ff’)’(1) = 0  constraints reproduce q 0 = 1 appearance, rational surface position from USXR  allows finite edge current (to model current transients) 4 profile variables (1 p’, 3 ff’; 2 nd order polynomial in p’, 3 rd order in ff’) Goodness of fit  2 ~ 70 over majority of pulse for 108 measurements 0.2 t(s) 0.00.40.60.8 I p (MA)  t (%) lili   22 100 0 0.8 0.4 0.0 2 1 0 1.0 0.0 20 10 0 1.0 0.0 112783 (P NBI = 7 MW)  t = 2  0 / B 0 2

16. NSTX “Partial kinetic” prescription reduces artificial constraint Over 110 attempted model variations used to find model 10 profile variables (5 p’, 5 ff’); allows finite edge current External magnetics plus 20 Thomson scattering P e points to constrain P profile shape  P tot = P e + “P i ” + “P fast ”; errors summed in quadrature (large total error) Diamagnetic flux to constrain stored energy  Greater freedom in ff’ basis function for good fit over full discharge evolution and for various shots Weak constraints on p’(0), ff’(0) yield “reasonable” q(0) 112783 t = 0.445s 0.01.02.00.51.5 R(m) 60 40 20 0 P tot (kPa) 0.52.01.01.5 R(m) 0.0 -2 1 2 0 Z(m) 112783 t = 0.445s “partial kinetic” assigned error

17. NSTX NSTX EFIT* alterations required for low A geometry Uniform discretization of elements at low aspect ratio Vessel currents required  Lower A components have lower resistance  Total vessel currents ~ 0.3 MA; plasma current ~ 1.0 MA  Vessel / plates broken into 30 groups (poloidally)  Wall currents determined by local loop voltage data (9 loops)  Vessel element resistances matched against independent model of vacuum field shots Stabilizing plates / divertor plates included (~5 kA)  plate currents not well-diagnosed * S.A. Sabbagh, et al., Nucl. Fus. 41 (2001) 1601. flux loops / voltage monitors pickup coils 0.52.01.01.5 R(m) 0.0 -2 1 2 0 Z(m) stabilizing plates initial diagnostics

18. NSTX Expanded magnetics to yield more accurate X-point and plate currents Significant upgrade to magnetics set  57 pickup coils vs. 23  25 local loop voltage data vs. 9 for wall current distribution  Compensation for stray field from TF leads Stabilizing plates / divertor plates currents now better resolved new pickup coils (tangential and normal) 0.52.01.01.5 R(m) 0.0 -2 1 2 0 Z(m) CY 2004 diagnostics

19. NSTX Pure toroidal flow allows a tractable equilibrium solution Solve , ,  R components of equilibrium equation  MHD:  v  v = JxB –  p ;  = mass density  f(  ) = RB t  R  2P d ( ,R)/R = p’( ,R)|  ; P d   ( ,R)  2 (  )R 2 /2 (Bernoulli eq.)  *  = -  0 R 2 p’( ,R)| R -  0 2 ff’(  )/(4  2 ) (G.S. analog)  Pure toroidal rotation and T = T(  ) yields simple solution for p p( ,R) = p 0 (  ) exp (m fluid  2 (  )(R 2 – R t 2 )/2T(  )) Constraints for fit  EFIT reconstructs two new flux functions: P w (  ), P 0 (  ) P w (  )   (  ) R t 2  2 (  )/2;P 0 (  ) defined so that: p( ,R) = P 0 (  ) exp (P w (  )/P 0 (  ) (R 2 – R t 2 )/ R t 2 )  Standard input: P w (  ), P 0 (  ) from approximation or transport code  New approach: Solve for P w (  ), P 0 (  ) in terms of measured P( ,R)| z=0, P d ( ,R)| z=0