1. NSTX MHD Mode Control Mtg. 2007 S.A. Sabbagh 1 RWM Stabilization and Control Research on NSTX S.A. Sabbagh 1, J.M. Bialek 1, R.E. Bell 2, D.A. Gates 2, B. LeBlanc 2, J.E. Menard 2, J.W. Berkery 1, A.H. Boozer 1, A.H. Glasser 3, F. Levinton 4, K. Tritz 5, H. Yu 4 1 Department of Applied Physics, 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 Nova Photonics, Inc., Princeton, NJ, USA 5 Johns Hopkins University, Baltimore, MD, USA Workshop on Active Control of MHD Instabilities November 18, 2007 Columbia University New York, NY Supported by Office of Science Culham Sci Ctr U St. Andrews York U Chubu U Fukui U Hiroshima U Hyogo U Kyoto U Kyushu U Kyushu Tokai U NIFS Niigata U U Tokyo JAEA Hebrew U Ioffe Inst RRC Kurchatov Inst TRINITI KBSI KAIST ENEA, Frascati CEA, Cadarache IPP, Jülich IPP, Garching ASCR, Czech Rep U Quebec College W&M Colorado Sch Mines Columbia U Comp-X General Atomics INEL Johns Hopkins U LANL LLNL Lodestar MIT Nova Photonics New York U Old Dominion U ORNL PPPL PSI Princeton U SNL Think Tank, Inc. UC Davis UC Irvine UCLA UCSD U Colorado U Maryland U Rochester U Washington U Wisconsin v1.0

2. NSTX MHD Mode Control Mtg. 2007 S.A. Sabbagh 2 Controlling RWMs and understanding stabilization is critical for future high performance tokamaks  Motivation  Resistive Wall Mode (RWM) growth leads to beta collapse, disruption  High reliability control needed for future burning plasma devices (at low or high plasma rotation,   )  Outline  Active RWM Control  RWM Stabilization Characteristics

3. NSTX MHD Mode Control Mtg. 2007 S.A. Sabbagh 3 RWM active control research emphasized in 2007  Increase reliability and understanding of RWM active control  Analysis of RWM control system performance  RWM control experiments using expanded magnetic sensor combinations  Variations for improved control Active n = 1 RWM control in NSTX (2006) S.A. Sabbagh, et al., PRL 97 (2006) 045004. 0.40.50.60.70.80.9 t(s)  Upper B p sensors for feedback  Non-resonant magnetic braking  n = 2 RWM amplitude rises, remains stable while n = 1 stabilized  Plasma  N > 5.5 reached

4. NSTX MHD Mode Control Mtg. 2007 S.A. Sabbagh 4 RWM active stabilization coils RWM sensors (B p ) RWM sensors (B r ) Stabilizer plates  Stabilizer plates for kink mode stabilization  External midplane control coils closely coupled to vacuum vessel  Varied sensor combinations used for feedback  24 upper/lower B p : (B pu, B pl )  24 upper/lower B r : (B ru, B rl )  Midplane n = 1 B r sensors  Outboard of control coil  Not used for feedback to date RWM control system uses expanded sensor set

5. NSTX MHD Mode Control Mtg. 2007 S.A. Sabbagh 5 VALEN code reproduces B pu sensor feedback performance  New model simulates experiment  Upper B p sensors located as on device  Compensation of control field from sensors  Experimental equilibrium reconstruction (including MSE data)  Proportional gain  Advanced feedback control may significantly improve future performance  Optimized state-space controller with B pu sensors may stabilize  N /  N wall < 95% Growth rate (1/s) NN DCON no-wall limit Experimental  N (control off) (  collapse) With-wall limit active control passive growth active feedback (present) Experimental  N (control on) O. Katsuro-Hopkins et al., this meeting state space controller reached

6. NSTX MHD Mode Control Mtg. 2007 S.A. Sabbagh 6 45 o (119761) 315 o (119755) 290 o (119764) 225 o (119770) negative feedback response  f 6 4 2 0 8 6 4 2 0 30 20 10 0 NN   /2  ( kHz )  B pu n=1 (G) 0.50.40.60.70.80.9 t (s) feedback on  Feedback control current has relative phase  f to measured  B pu  Internal plasma mode seen at  f = 225 o, damped feedback system response Varying relative phase shows positive/negative feedback  Phase scan shows superior settings for negative feedback  Agreement between theoretical and experimental feedback behavior VALEN modeled active feedback Growth rate (1/s)  f (deg) Mode locked Mode rotating Passive 45225290315 poloidal

7. NSTX MHD Mode Control Mtg. 2007 S.A. Sabbagh 7 n = 2 RWM does not become unstable during n = 1 stabilization Control OFF (RWM disrupts plasma) Control ON (fast  N drop, plasma recovers) 0.560.600.640.68 20 40 0 t(s) 0.5 1.0 1.5 0.0  B pu (G) 20 40 0  B pu (G) USXR (arb) edge core 0.5 1.0 1.5 0.0 USXR (arb) edge core 0.72400.72410.72420.7239 t(s) 0.660.700.740.78 t(s)  Internal mode ~ 25 kHz  Plasma rotation ~ 12 kHz (n = 2) 5 ms 20  s 120717 negative feedback response 120705 mode strongest at edge n = 2 RWM n = 1 n = 2 n = 2 internal mode 0.60.8 20 40 0 t(s) (kHz) n = 1 n = 2

8. NSTX MHD Mode Control Mtg. 2007 S.A. Sabbagh 8 Combination of upper/lower B p sensors used to improve control  Feedback phase scan using B pu and B pl  Best phase shown 90 o, not optimal configuration Reduction in  B pu n=1 growth rate  Spatial phase offset between upper/lower B p sensor flux can improve feedback  Control using B pu and B pl also reduces  B r  Correlation of  N collapse and  B ru n=1 amplitude  Suggests that feedback on  B r may allow mode control t (s) 275 o (124034) (124032)  f (124608) NN Poloidal  B pu n=1 (G) Radial  B ru n=1 (G) Midplane B r  B r-ext n=1 (G) Feedback I A (kA) I p (MA) (124033) “B r threshold” reduced growth rate 0.30.40.50.60.7 1.0 60 0.0 40 20 0 0 10 0 4 8 0 4 2 0 4 8 1.2 feedback on 225 o 150 o 90 o

9. NSTX MHD Mode Control Mtg. 2007 S.A. Sabbagh 9 Feedback on B r sensors alone insufficient for control  Feedback on  B ru alone  Clear initial drop in  B ru  Continued drop in  B r and increase in  B rl (also  B pu )  leads to  N collapse  Feedback on  B ru and  B rl  Controlled, steady  B ru,  B rl  rapid RWM growth, rotation:  N collapse t (s) 0.30.40.50.60.7  B pu n=1 (G) (upper poloidal)  B ru n=1 (G) (upper radial)  B rl n=1 (G) Feedback I A (kA) NN 8 0 4 40 20 0 8 0 4 0.8 0.0 0.4 0 2 4 1 3 5 124616 124623 feedback on Want feedback on both  B r and  B p for most reliable control 0.600.620.640.66 t (s) unstable RWM n = 1 B pu n = 1 phase n = 2 B pu 40 20 0 10 0 (deg) (G) 360 0 (lower radial)

10. NSTX MHD Mode Control Mtg. 2007 S.A. Sabbagh 10 Multimode theory applicable at high  N  Boozer multimode criterion for n = 1 met at high  N  |  W | smallest for 2 nd n = 1 eigenfunction  Multiple n > 1 RWM also observed in NSTX NN  W (arb) t(s) n = 1 multimode periods 120038 5 -5 -10 0 0.20.80.40.60.0 mode 1 mode 2 DCON (PoP 10 (2003) 1458.) t = 0.641s  Multiple n = 1 modes may explain observations  Upper/lower sensor phases do not always match single mode  Poloidal deformation of mode during feedback (mode “non-rigidity”) 1.0 bulge mode 1 mode 2 2.01.00.0 R(m) Z(m) 1.5 0.5 0.0 -0.5 -1.5 S.A. Sabbagh, et al., PRL 97 (2006) 045004. (Sabbagh, et al., Nucl. Fusion 46 (2006) 635.) DCON  B N no-wall stability

11. NSTX MHD Mode Control Mtg. 2007 S.A. Sabbagh 11 Feedback control modifications used successfully at moderate    NSTX record pulse length at I p = 0.9 MA  Feedback used combined upper/lower B p sensors with spatial phase offset  Moderate plasma rotation keeps  B r in check  n = 3 DC field phased to best maintain    Next steps toward further control reliability  Feedback on upper and lower arrays of both B r and B p sensors  Determine optimal sensor spatial phase offsets  Test reliability at further reduced plasma rotation J.E. Menard, et al., this meeting NN  B pu n=1 (G)  B ru n=1 (G)   /2  (kHz) I p (MA) t (s) 0.00.40.60.81.01.41.20.2 I A (kA) 10 40 20 0 0 4 8 0 4 2 0 6 1.0 0 0

12. NSTX MHD Mode Control Mtg. 2007 S.A. Sabbagh 12 RWM passive stabilization characteristics more clear  Scalar plasma rotation at q = 2 not adequate to describe RWM marginal stability  Concluded a few years ago on NSTX, further evidence in 2007  RWM can go unstable at various levels of plasma rotation, various profile shapes  RWM stability at low rotation profile not yet found unless  internal rotating mode with frequency ~   present  active RWM control applied  Some integral of plasma rotation, convolved with other plasma profile(s), apparently required to describe stabilization  Role of Alfven frequency in description of stability criteria not yet well established in NSTX  Experiments showing stability at very low  crit /  A may suggest that  A is simply not a useful scaling variable  Ion collisionality profile appears to alter  crit

13. NSTX MHD Mode Control Mtg. 2007 S.A. Sabbagh 13 Significant variation of rotation profile shape at  crit  Benchmark profile for stabilization is  c =  A /4q 2 *  predicted by Bondeson-Chu semi- kinetic theory**  n = 3 braking field reduces  crit profile  Contrary to simple loss of torque balance hypothesis  High rotation outside q = 2.5 q = 2.0 not required for stability  Zero rotation at single q can be stable  Scalar  crit /  A at q = 2, > 2 not a reliable criterion for stability  consistent with distributed dissipation mechanism *A.C. Sontag, et al., Phys. Plasmas 12 (2005) 056112. **A. Bondeson, M.S. Chu, Phys. Plasmas 3 (1996) 3013.

14. NSTX MHD Mode Control Mtg. 2007 S.A. Sabbagh 14 Plasma with zero rotation at q = 2 stable without feedback  Equilibrium reconstruction with MSE and flux-isotherm constraint  Rotation braking physics evolves  Non-resonant n = 3 (NTV), then additional braking seen at resonant surfaces   /2  (kHz) q q = 2 t (s) 0.00.40.60.80.2 n = 3 braking NN poloidal  B pu n=1 (G)   /2  (kHz) I p (MA)   /2  (kHz) core (q ~ 2) -10 10 8 20 0 0 4 10 0 4 2 0 0.8 0 0 0.4 20 10 NTV resonant 0.2 1.01.21.41.6 R (m) 30 20 10 0 -10 1 2 3 4  B odd (G) 124010

15. NSTX MHD Mode Control Mtg. 2007 S.A. Sabbagh 15 /A/A passively stabilized (120038) experimental  crit profile (120712) (120047) R (m) Plasma rotation speed, profile altered to examine stability  High rotation typically stable, but not always  Apparent RWM observed at high core rotation  Need to understand instability mechanism  Stability at intermediate rotation depends on profile  Passively stable plasma with   = 0 at q = 2 has slower edge and faster core rotation  No reliable stable state at low rotation with feedback off  Increase number of low rotation plasmas in future research (120717) (125264) (124708) Passively stable   = 0 @ q = 2 Feedback controlled (124010)

16. NSTX MHD Mode Control Mtg. 2007 S.A. Sabbagh 16  crit not correlated with simple torque balance model  Rapid drop in   when RWM unstable may seem similar to ‘forbidden bands’ model  theory: drag from electromagnetic torque on tearing mode*  Rotation bifurcation at  0 /2 predicted  No bifurcation at  0 /2 observed  no correlation at q = 2  Similar result for n = 1 and 3 applied field configuration *R. Fitzpatrick, Nucl. Fusion 33 (1993) 1061. NSTX  crit Database (  0  steady-state plasma rotation)  crit =  0 /2

17. NSTX MHD Mode Control Mtg. 2007 S.A. Sabbagh 17 Increased Ion Collisionality Leads to Decreased  crit  Plasmas with similar v A  Consistent with neoclassical viscous dissipation model  at low , increased i leads to lower  crit  dissipation  ~ i in high dissipation limit (K. C. Shaing, Phys. Plasmas 11 (2004) 5525.) 121083 t = 0.466s 121071 t = 0.686s i (kHz)  crit /2  (kHz) |  crit | > ((1 – d/d c )/4 + (1 – d/d c ) 2 /  2 ) 1/2 wall parameters (A. C. Sontag, et al., Nucl. Fusion 47 (2007) 1005.) dissipation Critical rotation profiles

18. NSTX MHD Mode Control Mtg. 2007 S.A. Sabbagh 18 NSTX research moves toward reliable active RWM control and stabilization physics understanding  Active feedback on upper and lower arrays of both B r and B p RWM sensors as key next step for reliability  Determine optimal feedback/sensor configuration at reduced plasma rotation  Examine potential role of multiple modes  Passive stabilization physics not yet determined, however  Scalar  crit is insufficient; full   profile may play a role  Simple torque balance model  crit =   /2 insufficient  Destabilization / loss of control possible in all rotation ranges  Role of  A not yet well established  Ion collisionality profile appears to alter  crit