1. Influence of rapid rotation on high-  NSTX plasmas 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 Ioffe Inst TRINITI KBSI KAIST ENEA, Frascati CEA, Cadarache IPP, Jülich IPP, Garching U Quebec J.E. Menard, for the NSTX Team With contributions from: R.E. Bell, A. Bondeson, M.S. Chu, J. Ferron, E.D. Fredrickson, D.A. Gates, A. Glasser, C. Greenfield, S.M. Kaye, L. Lao, B.P. LeBlanc, T. Luce, W. Park, S.A. Sabbagh, D. Stutman, K. Tritz, and M. Wade 45th Annual Meeting of the Division of Plasma Physics Monday, October 27, 2003 Albuquerque, New Mexico

2. DPP2003 - BI1.002, J.E. Menard 2 NSTX has achieved high-  and long-pulse High-  obtained with  7MW of tangential co-NBI Drives toroidal flow velocities up to 40% of v Alfven How does rapid rotation impact NSTX  MHD? f BS up to 50% Pulse-length up to 1s  T = 15-20%  N = 5-6.2 at I P /aB T0  3  T = 30-35%  N = 5-6 at I P /aB T0 = 5-6 Typical pulse-length = 0.3-0.4s  T  2  0  p  / B T0 2 All shots at peak W TOT

3. DPP2003 - BI1.002, J.E. Menard 3 Rotation impacts several MHD areas Equilibrium: Centrifugal force from rotation shifts particle density off flux surfaces –Complicates kinetic profile/transport interpretation –Rotation not typically included in equilibrium codes NSTX beginning to use EFIT with rotation, FLOW code Stability: Flow and flow-shear potentially stabilizing to a variety of MHD modes –At highest toroidal , flow and flow-shear may aid saturation of internal modes –At high poloidal  and elevated q  rotation + dissipation stabilize external modes (RWM) Comparisons with DIII-D AT discharges

4. DPP2003 - BI1.002, J.E. Menard 4 Rotation effects evident in n e (R) profiles Single-fluid MHD force balance: J  B =  p +  v  v  –Near axis, J  B small  R/p  p/  R = 2M A 2 /  where M A  v  / v A NSTX total M A = 0.15-0.4 –2  higher than typical DIII-D AT –  also 4-10  higher in NSTX –Similar p shift in DIII-D (?) 107540 at t=330ms  n e (  =0)  0 Maximum n e off-axis MAMA T e (keV) n e (m -3 ) 4x10 19 local T e = T e (  ) Most easily seen in MHD-quiescent L-mode discharges Magnetic axis

5. DPP2003 - BI1.002, J.E. Menard 5 Total force balance in multi-species plasma  J  B =  s  ( n s T s (  ) ) -  s m s n s   s (  ) 2  (R 2 /2) B  this equation = 0 has solution: n s ( ,R) = N s (  ) exp( U(  )  (R 2 /R 0 2 -1) ) U(  ) =  P  (  ) / P T (  ) P  (  ) =  s m s N s (  )   s (  ) 2 R 0 2 / 2Centrifugal pressure P T (  ) =  s N s (  )T s (  )Thermal pressure  s N s (  )Z s = 0Charge neutrality Charge neutrality  all species have same exponential form –Test consistency: can this model fit measured n e, T e, T C,   C, n C ? Use neoclassical   D from TRANSP/NCLASS (    C ) Treat fast ions as having P fast = P fast (  ),   fast =   fast (  ) Then, compare to first EFIT reconstructions with rotation MHD force balance model of density asymmetry:

6. DPP2003 - BI1.002, J.E. Menard 6 MHD model can predict density asymmetry Cannot match n e data w/o fast ion P   included For this shot, P  (fast)   1.5  P  (thermal) Ne()Ne() MHD model n e ( ,R) can match n e data nDnD 107540 at t=333ms Model n e ( ,R) without P  (fast) Solid curves: MHD model n s ( ,R) Dashed curves: N s (  density w/o rotation

7. DPP2003 - BI1.002, J.E. Menard 7 p iso-surfaces clearly shift outward from flux surfaces when rotation high black – flux surfaces white – constant pressure surfaces Recall n s ( ,R) = N s (  ) exp( U(  )  (R 2 /R 0 2 -1) )  p( ,R) = P(  ) exp( U(  )  (R 2 /R 0 2 -1) )  n s ( ,R) / N s (  ) should = EFIT p( ,R) / P(  ) For cases studied so far, this works well For more info on NSTX EFITs w/ rotation, see contributed oral KO1.004 by S. Sabbagh Density asymmetry from EFIT with rotation: 109070, 534ms Future: incorporate results into transport & MHD stability analysis

8. DPP2003 - BI1.002, J.E. Menard 8 Rotation impacts several MHD areas Equilibrium: Centrifugal force from rotation shifts particle density off flux surfaces –Complicates kinetic profile/transport interpretation –Rotation not typically included in equilibrium codes NSTX beginning to use EFIT with rotation, FLOW code Stability: Flow and flow-shear potentially stabilizing to a variety of MHD modes –At highest toroidal , flow and flow-shear may aid saturation of internal modes –At high poloidal b and elevated q, rotation + dissipation stabilize external modes (RWM) Comparisons with DIII-D AT discharges

9. DPP2003 - BI1.002, J.E. Menard 9 Sawtooth activity rare at high  –Rotating 1/1, usually   roll-over In highest  shots,  saturates or actually rises during 1/1 activity 1/1 saturates or decays at high    1.2-1.4  onset  –Onset  N = 4.2 - 4.5  n=1 ideal limit –These shots reach  N = 5.5 – 6 Synergistic effects may aid high  –1/1 mode flattens core p and J Large fast ion diffusion or loss –H-mode onset broadens p and J –Broad p, J + rotation stabilizing What is the role of rotation? 1.2MA,  7MW 1.0MA  5MW Neutron Rate (10 14 /s)  T (%) 31% 35% Mode B  (Gauss) Highest  shots obtained despite large 1/1 modes  =35% mode saturates  =31% mode decays

10. DPP2003 - BI1.002, J.E. Menard 10 Use nonlinear MHD code M3D to study 1/1 mode Initial stateIsland forms Island grows Core displaced Reconnection continues Reconnection complete Hot core (a-c) is replaced by cold island (d-f) B-field lines T iso-surface Density contours Nonlinear mode evolution: no rotation  sawtooth-like crash W. Park PPPL

11. DPP2003 - BI1.002, J.E. Menard 11 Nonlinear evolution with peak rotation of M A =0.3 P vv In experiment, the NBI power is held roughly fixed In M3D, with a fixed momentum source rate, the v  and p profiles flatten inside the island, and reconnection still occurs… Sheared-flow reduces growth rate by factor of 2-3 M A = 0 Simulated SXR signals 0 1 Time M A = 0.3 0 1 2 Time M3D simulations

12. DPP2003 - BI1.002, J.E. Menard 12 Possible saturation mechanisms identified with M3D Simulations  at least partial reconnection should occur  saturation process will be acting on subsequent non-linear state B-field lines T iso-surface Density contours (1) Following reconnection, and with initial shear-flow, perturbed  and T can spontaneously become anti-phase. This state can saturate if p highest inside island Mechanism is robust, not easily obtained (2) Sufficient source rate and viscosity to maintain sheared flow with island Robust, experimentally possible Requires slow reconnection rate (3) Fast particles, 2-fluid, being studied Are any of these mechanisms consistent with experiment? Possible mechanisms: Saturated state with higher p in island

13. DPP2003 - BI1.002, J.E. Menard 13 T e flat spots 108103 t=243ms (saturated phase) t=260ms (saturated phase)  Consider 2 nd Mechanism: Favorable profiles and rotation itself slow mode growth & reconnection - enough rotation sustained to saturate mode Electron pressure lower in island Bulk ion pressure lower in island Only carbon pressure possibly higher Island Saturated phase Mode growth phase 108103 T i has minimum at island radius T e flat-spots observed n e not higher in island Kinetic data shows higher island p unlikely Carbon p starts peaked, becomes hollow Impurity accumulation? Before mode Mode saturated 108103 Island

14. DPP2003 - BI1.002, J.E. Menard 14 SXR Data Island Model Fit error < 6% r s = 0.43 w = 0.3 f = 15.4 kHz Perturb EFIT equilibrium helical flux with m/n = 1/1   h –Reconstruct total emission as function of total helical flux Z  T = 21% rsrs Island model fits data well SXR inversion aids analysis of mode evolution

15. DPP2003 - BI1.002, J.E. Menard 15 Early growth: best-fit emission highest in displaced core Later, during saturated phase, best-fit  higher emission from island –This may indicate impurity accumulation in island and/or cooling rsrs t=227ms t=229ms t=230ms t=245ms  T  31% island grows slowly (  1ms), saturates with r s  0.5

16. DPP2003 - BI1.002, J.E. Menard 16 Rotation data  shear-flow mode saturation plausible  T  23%  T  31%  T (%) NOTE: Carbon f  data is 20ms average   growth, 1/f  Mode B  (Gauss) q 0 (w/o MSE) I P (MA) P NBI /10 (MW) f  (0) (kHz)  T =23% - Rotation flattens, broadens, collapses f rot (R,t) (kHz)  T = 31% - Rotation flattens, then core recovers f rot (R,t) (kHz) 230ms 250ms Island Favorable q or   profile slows mode growth? Enough rotation retained for later saturation? 230ms 10kHz 14kHz

17. DPP2003 - BI1.002, J.E. Menard 17 Rotation impacts several MHD areas Equilibrium: Centrifugal force from rotation shifts particle density off flux surfaces –Complicates kinetic profile/transport interpretation –Rotation not typically included in equilibrium codes NSTX beginning to use EFIT with rotation, FLOW code Stability: Flow and flow-shear potentially stabilizing to a variety of MHD modes –At highest toroidal b, flow and flow-shear may aid saturation of internal modes –At high poloidal  and elevated q  rotation + dissipation stabilize external modes (RWM) Comparisons with DIII-D AT discharges

18. DPP2003 - BI1.002, J.E. Menard 18 Elevated q sustains operation above no-wall limit 109070 computed Expt. value of  N conducting plates 109070 t=530ms Plasma Stabilization of RWM with rotation+dissipation demonstrated on DIII-D MARS Compare NSTX RWM predictions to DIII-D using MARS code Increase q the old-fashioned way: –Raise field from 0.3T to 0.5T + early H-mode –Decrease current to 0.8MA  f BS  50% Operate with  N > 5 for  t >  CR =0.25s –No rotation slow-down or evidence of RWM

19. DPP2003 - BI1.002, J.E. Menard 19 Similar RWM parameter regimes exist for NSTX & DIII-D NSTX 109070: LSN, 0.8MA, 0.5T n=1 internal disruptions at  N  6 DIII-D 113850: DND, 1.2MA, 1.8T n  3 ELM-like bursts limit  N  4 NSTXDIII-D 109070, 429ms 113850, 2802ms q 95 7 5 q 0 1.32.3 q min 1.31.6 r/a(q=2) 0.770.68    A (r=0) 15%7%    A (q=2) 4.1%3.2% l i 0.830.79 p(0)/  p  2.2-2.72.8-2.9 NSTXDIII-D    A (%) NOTE: NSTX w/o MSE Neither discharge exhibits n=1 RWM

20. DPP2003 - BI1.002, J.E. Menard 20 RWM stabilized for    A (q=2) > 2% for both cases Uncertainty in form & magnitude of dissipation remains (theory & expt.) Use  || =0.2 for sound wave damping coefficient (  =0,  wall = 10 4  A ) (  ||  0.2 used to match DIII-D, JET critical rotation data) MARS n=1 growth rate vs.  N and   NSTXDIII-D Predict RWM critical    A (q=2) = 2.1% for  || = 0.2, 1.3% for  || =1 FUTURE: Compare predictions to experiments by varying   or q no-wall limit  Wall unstable stable Both cases computed stable at experimental rotation value (i.e. at   =0)

21. DPP2003 - BI1.002, J.E. Menard 21 Plasma mode stabilized at 20-30% of experimental   As      (expt), marginal stability can vary with     –Example:  || =0.2 and   =   (expt)  NSTX  N limit = 6.1  5.3, DIII-D 4.1  4.3 Inconsistent with NSTX reaching  N = 6 May need to consider both RWM and plasma mode in AT optimization MARS n=1 growth rate vs.  N and   NSTX  || =1 no-wall limit DIII-D  || =1 no-wall limit

22. DPP2003 - BI1.002, J.E. Menard 22 Summary Density asymmetry result of high p Centrifugal / p Thermal –Data consistent with MHD force balance model –Developing analysis tools to handle high flow velocities 1/1 modes saturate or even decay in highest  shots –Rotation flattening observed in experiment and simulations Consistent with at least partial reconnection during growth –Several non-linear saturation mechanisms being studied Higher pressure in island robustly stable, but unlikely Sustainment of shear-flow with slowed reconnection plausible Higher q discharges operate above no-wall limit –MARS predicts rotational stabilization of RWM in NSTX Predictions quantitatively similar to high-  N DIII-D AT –Good position to test RWM physics across devices Please visit NSTX oral (KO1) and poster (LP1) sessions on Wednesday

23. DPP2003 - BI1.002, J.E. Menard 23 EFIT w/ rotation important tool for high  P plasmas N e (  )  p( ,R) / P(  ) from EFIT EFIT p with rotation consistent with n e profile asymmetry: For this shot, P  (fast)    P  (thermal) Now working on including P  (fast) in reconstructions 109070 at t=470ms For diamagnetic H-mode plasmas, need EFIT w/ rotation for accurate R axis  R axis = 5cm

24. DPP2003 - BI1.002, J.E. Menard 24 Plasma mode stability sensitive to   and  ||  || >>1 unphysically destabilizes plasma mode for expt.   (  )  || >>1 lowers growth rate when   =0  becomes independent of    for flat   Future: compare to “kinetic damping” model in MARS, and across devices –aid understanding of dissipation  || =5 DIII-D  || =1    ) =   (q=2) DIII-D no-wall limit