1. NSTX S. A. Sabbagh 1, J. Bialek 1, A. Sontag 1, W. Zhu 1, B. LeBlanc 2, R. E. Bell 2, A. H. Glasser 3, L. L. Lao 4, J.E. Menard 2, M. Bell 2, T. Biewer 2, D.A. Gates 2, R. Fitzpatrick 5, and the NSTX Research Team Resistive Wall Mode Stabilization in NSTX 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 45 th Annual Meeting of Division of Plasma Physics American Physical Society October 27 – 31, 2003 Albuquerque, New Mexico 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 General Atomics, San Diego, CA, USA 5 University of Texas at Austin, Austin, TX, USA

2. NSTX NSTX Preparing for Active Stabilization of High  Global MHD Instabilities Motivation  Resistive wall mode (RWM) identified and associated with global rotation damping  Beta collapse can follow rotation damping when  N >  N no-wall Approach  Examine physics of passive stabilization  Enhance mode detection system (A. Sontag, talk KO1.005)  Study rotation damping mechanisms (W. Zhu, poster LP1.013)  Determine impact of rapid rotation on equilibrium  Design and implement active feedback stabilization system

3. NSTX NSTX plasmas operate in wall-stabilized space Normalized beta,  N = 6.5, with  N /l i > 9.5  N up to 35% over  N no-wall (computed using DCON)  Stability limit dependent on both l i and pressure peaking Toroidal beta has reached 35% (  t = 2  0 / B 0 2 ) Wall stabilized Design target EFIT 4 l i 6 l i 8 l i 10 l i

4. NSTX (N / m 4 ) neoclassical viscous drag profile Rapid rotation damping before  collapse at B t < 0.4T Rotation damping rate more than 5 times greater vs.  N <  N no-wall Global F  damping mechanism rather than localized, resonant effect 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 0.5 2 4 6 8 10 108197 Locked mode detector F  (q = 2) F  (R = 1.35m) n = 1 no-wall unstable (DCON) RWM 3.5  wall (VALEN) n = 1 rotating mode R (m) F  (kHz) 108197 0.29 s 0.31 s 0.33 s t = 0.31 s (quantitative experimental comparison - W. Zhu, poster LP1.013) B t0 = 0.39T 1.0 1.2 1.4 0.0 0.04 0.08 0.12 -0.04 - FF (estimated  B) 0.8

5. NSTX Critical rotation frequency depends on  N /  N-Nowall  crit /  A (core)  N /  N No-wall

6. NSTX Plasma stabilized above  N no-wall for 18  wall (B t > 0.4T) 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 Passive stabilizer loses effectiveness at maximum  N  Neutrons collapse with  N - suggests internal mode n = 1 RWM not observed  n = 2 computed to be unstable EFIT reconstructed  N includes rotation 30 kHz F  (0) 5MW NBI  N > no-wall limit B t0 = 0.44 T 0 2 4 6 8 NN n = 2 with-wall n = 2 no-wall

7. NSTX NSTX EFIT reconstructions now using T i, Z eff profiles, and fit to plasma toroidal rotation Exact rotation solution fitting total and dynamic plasma pressure at (R, Z=0)  A few thousand shot*times run  Estimate for P fast Stored energy with/without V  = +/- 3% (R pmax – R axis )/a = 8% Significant drop in  mag 2 and  p 2 even though 50% more P channels and smaller error bars P kinetic (kPa) P dynamic (kPa) 108420 t = 0.403 s 10 20 30 40 0 0.52.01.01.5 -2 1 2 0 R(m) Z(m) 01.02.00.51.5 1 2 3 4 0 5 0.81.21.61.01.4 R(m) (special thanks to L. Lao) Poloidal flux and pressure

8. NSTX Active control may sustain 68% margin above  Nno-wall External control coil design with realistic geometry Internal control coil design computed to reach   N = 94% VALEN model of NSTX (cutaway view) Growth rate (s -1 ) 10 -1 10 0 10 1 10 2 10 3 10 4 10 5 Passive With-wall limit (  N wall) 1.02.5 0.20.00.40.60.81.0 Active feedback coil Ex-vessel RWM control coils VALEN (J. Bialek)   N  (  N –  N No-wall )/(  N wall –  N No-wall ) Active gain (V/G) Sensors (see A. Sontag, KO1.005) (Equilibria used have  Nno-wall = 5.1;  Nwall = 6.9)

9. NSTX Exterior control coil can provide adequate stabilizing field Initial system plan has 6.8kA*turns (Applied B edge = 27G @ 54Hz) Exterior coil design decision based on time, budget, risk constraints balanced by performance Applied B edge (G) / control coil amp*turn Interior coil Skin depth limit 10 -2 10 -3 10 -4 (  N –  N No-wall )/(  N wall –  N No-wall ) 10 0 10 1 10 2 10 3 10 4 94% Realistic exterior coil VALEN (J. Bialek – poster FP1.040) Driving Frequency (Hz) Exterior coil feedback limit Original exterior coil design 68%

10. NSTX Active mode control modeling shows mode stabilization “Mode control” feedback algorithm simulation Ideal system response (no latency) Simulations including latency show 200  s is maximum time delay allowing stabilization at highest  N Time (ms) VALEN (J. Bialek) Control coil current (A) 020406080 Poloidal field from mode at sensor (G) 0 1 2 3 4 -2 Coil current Field at sensor Start feedback 200 150 100 50 0 -100 -150 -50 -3 (  N –  N No-wall )/(  N wall –  N No-wall ) = 65%

11. NSTX Preparation for active feedback stabilization research in high  N ST plasmas 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 Rapid rotation damping/  collapses at  N >  N no-wall and lower B t  Global, non-resonant damping mechanism associated with RWM  Unlike slower, localized, diffusive damping observed with island locking Plasmas passively stabilized for > 18  wall at increased B t  n = 1 RWM not observed; n = 2 computed unstable Toroidal rotation now included in equilibrium reconstructions  Large shift of core pressure contours from magnetic surfaces  Reconstructed stored energy essentially unchanged Ex-vessel active control coil design chosen for initial feedback system  Targeting sustained operation at  N = 68%

12. NSTX Supporting slides follow

13. NSTX Maximum circuit time delay to allow feedback stabilization evaluated at maximum  N Instability at  N = 65% Two-turn coil with realistic geometry yields 200  s maximum time delay with “mode control” feedback algorithm Time (ms) VALEN (J. Bialek) Control coil current (A) 0102030 Poloidal field from mode at sensor (G) Field at sensor Start feedback with 200  s delay 300 200 100 0 -100 -200 0 2 4 6 -2 -4 Coil current

14. 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

15. NSTX NSTX EFIT reconstructions now using T i, Z eff profiles, and fit to plasma toroidal rotation Exact rotation solution fitting total and dynamic plasma pressure at (R, Z=0)  A few thousand shot*times run  Estimate for P fast Stored energy with/without V  = +/- 3% (R pmax – R axis )/a = 8% Significant drop in  mag 2 and  p 2 even though 50% more P channels and smaller error bars P kinetic (kPa) P dynamic (kPa) 108420 t = 0.403 s 10 20 30 40 0 0.52.01.01.5 -2 1 2 0 R(m) Z(m) 01.02.00.51.5 1 2 3 4 0 5 0.81.21.61.01.4 R(m) (special thanks to L. Lao) Poloidal flux and pressure