1. NSTX The Resistive Wall Mode and Beta Limits in NSTX S. A. Sabbagh 1, J. Bialek 1, R. E. Bell 2, A. H. Glasser 3, B. LeBlanc 2, J.E. Menard 2, F. Paoletti 1, M. Bell 2, T. Biewer 2, R. Fitzpatrick 4, E. Fredrickson 2, A. M. Garofalo 1, D.A. Gates 2, S. M. Kaye 2, L. L. Lao 5, R. Maingi 6, D. Mueller 2, G. A. Navratil 1, M. Ono 2, Y.-K. M. Peng 6, D. Stutman 7, W. Zhu 1, and the NSTX Research Team 1 Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY, USA 2 Plasma Physics Laboratory, Princeton University, Princeton, NJ, USA 3 Los Alamos National Laboratory, Los Alamos, NM, USA 4 University of Texas at Austin, Austin, TX, USA 5 General Atomics, San Diego, CA, USA 6 Oak Ridge National Laboratory, Oak Ridge, TN, USA 7 Johns Hopkins University, Baltimore, MD, USA 44th Annual Meeting of the APS Division of Plasma Physics Orlando, Florida - November 11th, 2002

2. NSTX NSTX is operating at sufficiently high beta to study passive wall stabilization Operation in wall-stabilized, high beta regime Resistive wall mode (RWM) and rotation damping Physical mechanisms for higher  N and longer pulse

3. NSTX NSTX is equipped to study passive stabilization Machine Aspect ratio≥ 1.27 Elongation≤ 2.5 Triangularity≤ 0.8 Plasma Current≤ 1.5 MA Toroidal Field≤ 0.6 T NBI≤ 7 MW Stabilizing plates Analysis EFIT – equilibrium reconstruction DCON – ideal MHD stability (control room analysis) VALEN – RWM growth rate

4. NSTX Plasma operation now in wall-stabilized space EFIT 2001 Data  N = 6 i Wall stabilized Nominal “no-wall limit” 2002 Data EFIT 4 l i 6 l i 8 l i 10 l i Normalized beta,  N = 6.5, with  N /l i = 9.5;  N up to 35% over  N no-wall Toroidal beta has reached 35% (  t = 2  0 / B 0 2 ) Design target

5. NSTX Maximum  N strongly depends on pressure peaking F p = p(0) / P profile from EFIT using P e, diamagnetic loop, magnetics Time-dependent calculations required to evaluate stability limits and mode structure

6. NSTX Operational improvements yield higher, sustained  N n=1 error field reduced by an order of magnitude in 2002 H-mode pressure profile broadening raises  N limit q min > 1 maintained (EFIT q min without MSE) 2001 (High error field)2002 (Reduced error field) t(s) RWM H-mode q min FpFp NN  B r n=1 (G) 0.00.10.20.30.4 0.00.10.20.30.40.5 0 10 1 2 3 3 4 5 2 4 6 2 n = 1 no-wall unstable (DCON) n = 1 unstable (with-wall) (no-wall) n = 1 unstable 106165 107636 Locked mode detector 3.5  wall (VALEN)

7. NSTX Rotation damping rate larger when  N >  N no-wall Rotation damping rate is ~ 6 times larger when  N >  N no-wall Toroidal Rotation F  (kHz) NN  B r n=1 (G) 0 2.0 2 4 6 1.0 t(s) 0.00.10.20.30.4 0.00.10.20.30.40.5 2 4 6 8 10 108197107994 Locked mode detector F  (q = 2) F  (R = 1.35m) n = 1 no-wall unstable RWMNo RWM n = 1,2 rotating modes F  (q = 2) F  (R = 1.35m) 3.5  wall (VALEN) n = 1 rotating mode

8. NSTX Two stages of rotation damping during RWM Initial stage: Global, non-resonant rotation damping Final stage: Local rotation damping at resonant surfaces appears as rotation slows Analogous to rotation dynamics in induced error field experiments  E. Lazzaro, et al., Physics of Plasmas 9 (2002) 3906. (JET)

9. NSTX Rotation damping during RWM is rapid and global Field ripple damping by neoclassical toroidal viscosity ~  B r 2 T i 0.5 candidate for observed damping profile during RWM R (m)  F  (kHz) F  (kHz) 0.43 s 107994 0.27 s 0.29 s 0.31 s 0.33 s 0.35 s 0.37 s 0.39 s n = 1, 2 rotating modes  F  (kHz) F  (kHz) 108197 0.29 s 0.31 s 0.33 s 0.31 s 0.33 s RWM R (m) 0.41 s 0.45 s 0.43 s 0.27 s 0.29 s 0.31 s 0.33 s 0.35 s 0.37 s 0.39 s 0.41 s 0.45 s

10. NSTX Core rotation damping decreases with increasing q Largest rotation damping (dF  /dt = -600 kHz/s) at B t < 0.4T, q min < 2  Factor of 8 times larger than damping from n=2 island alone When q min ~ 2 damping rate is reduced and F  is maintained longer Consistent with theory linking rotation damping to low order rational surfaces q min 1.4 1.7 1.9 2.1 1.41.71.9 2.1 q min EFIT q min without MSE I p = 0.8 MA

11. NSTX Plasma stabilized above no-wall  N limit for 18  wall 108420 I p = 0.8 MA DCON n = 1 with-wall n = 1 no-wall VALEN mode growth time = 15 ms VALEN mode growth time = 0.03 – 0.05 ms Plasma approaches with-wall  N limit  VALEN growth rate becoming Alfvénic F  (0) increases as  N >>  N no-wall Passive stabilizer loses effectiveness at maximum  N  Neutrons collapse with  N - suggests internal mode TRANSP indicates higher F p  Computed  N limits conservative 30 kHz F  (0) 5MW NBI  N > no-wall limit q min > 2

12. NSTX Research on passive stabilization and high  N rotation damping physics has begun Passive stabilization above ideal no-wall  N limit by up to 35%  Improvement in plasmas with highest  N up to 6.5;  N /l i = 9.5 The  N limit increases with decreasing pressure profile peaking Rotation damping at  N >  N no-wall has two stages  Global, non-resonant damping  Local, resonant field damping during final stage Rotation damping rate substantially decreases as q increases Passive stabilization becomes less effective at highest  N Active feedback design shows sustained  N /  N wall = 94% possible  See Bialek, et al., GP1.107 Tuesday For more RWM detail, see NSTX poster session (Tuesday)

13. NSTX Other presentations on NSTX beta limits, RWM, and mode stabilization High toroidal beta plasmas Gates, et al., BI1.001 Monday High poloidal beta plasmas Menard, et al., CO1.002 Monday Resistive wall modes Zhu, et al., GP1.106 Tuesday (Sabbagh for) Paoletti, et al., GP1.105 Tuesday RWM active feedback design Bialek, et al., GP1.107 Tuesday Presentation Subject

14. NSTX Active stabilization might sustain 94% of with-wall  limit System with ex-vessel control coils can reach 72% of  N wall System with control coils among passive plates can only reach 50% of  N wall VALEN model of NSTX (cutaway view) Growth rate (s -1 ) NN 5.5 10 -1 5.06.06.57.07.5 10 0 10 1 10 2 10 3 10 4 10 5 Passive With-wall limit (  N wall) 0.1 1.0 Modeled active feedback coils In-vessel control coils Active gain (V/G) Bialek, et al., GP1.107 Tuesday

15. NSTX T e perturbation measured during RWM No low frequency (< 80 kHz) rotating modes observed during measured  T e  T e displacement precedes n=2 rotating mode t = 0.293 s t = 0.310 s 0.2 0.4 0.6 0.81.01.21.4 0.0 0.5 1.0 1.5 T e (keV) R (m) 109030 Thomson scattering (LeBlanc) 0.260.300.34 Frequency (kHz) 20 0 40 60 80 100 t(s) 1234 mode number t = 0.293 st = 0.31 s NN 2 4 6 0.00.10.20.30.4 2 1 0 t(s)  B r n=1 (G) Locked mode detector  N > no wall limit

16. NSTX  N limit now insensitive to plasma proximity to wall At high  N ~ 5, external modes are well-coupled to passive stabilizing plates, independent of gap  Confirmed by ideal MHD stability calculations Higher error field (2001 data) may have also lowered  limit for smaller outer gap See W. Zhu, et al., GP1.106 Tuesday 2002 data (H-mode) 2001 data (L-mode)

17. NSTX Rotation damping strongest where mode amplitude largest Field ripple damping by neoclassical parallel viscosity ~  B r 2 T i 0.5 possible candidate for observed damping profile NN axisedge Mode decomposition Toroidal rotation evolution 106165 axisedge t = 0.15 s t = 0.17 s t = 0.19 s  (arb) t = 0.192 s R (cm) 100120140160 F  (kHz) 25 20 15 10 5 0

18. NSTX Mode intensifies in divertor region at highest  N  N = 5.1 VALEN / DCON computed n = 1 external mode currents  N = 7.1 Increased  p drive more significant in producing higher growth rate