1. Progress Toward Stabilization of Low Internal Inductance Spherical Torus Plasmas in NSTX S.A. Sabbagh 1, J.W. Berkery 1, J.M. Bialek 1, S.P. Gerhardt 2, R.E. Bell 2, O.N. Katsuro-Hopkins 1, J.E. Menard 2, R. Betti 2,3, L. Delgado-Aparicio 2, D.A. Gates 2, B. Hu 3, B.P. LeBlanc 2, J. Manickam 2, D. Mastrovito 2, J.K. Park 2, Y.S. Park 1, K. Tritz 4 1 Department of Applied Physics, Columbia University, NY, NY 2 Plasma Physics Laboratory, Princeton University, Princeton, NJ 3 University of Rochester, Rochester, NY 4 Johns Hopkins University, Baltimore, MD 52 nd APS DPP Meeting November 9 th, 2010 Chicago, Illinois 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 Purdue U Sandia NL Think Tank, Inc. UC Davis UC Irvine UCLA UCSD U Colorado U Maryland U Rochester U Washington U Wisconsin 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 POSTECH ASIPP ENEA, Frascati CEA, Cadarache IPP, Jülich IPP, Garching ASCR, Czech Rep U Quebec NSTX Supported by V1.6

2. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 2 Future ST fusion applications will have high elongation, broad current profiles, high normalized beta  Broad current profiles (low l i ) consistent with high bootstrap current fraction; important to maintain high elongation  Demonstrating / understanding kink / RWM stability at low l i is important ST-Pilot (Q eng = 1)FSNF / ST-CTF  R = 2.23 m, A = 1.7  I p = 16 MA, B t = 2.4T  l i = 0.47,  = 3.2   N = 5.2,  t = 30% (Q eng = 1) J. Menard, et al., IAEA FEC 2010 Paper FTP/2-2 Y.K.M. Peng, et al., PPCF 47 (2005) B263

3. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 3 NSTX is Addressing Global Stability Needs for Maintaining Low l i, High Beta Plasmas for Fusion Applications  Motivation  Achieve high  N with sufficient physics understanding to allow confident extrapolation to spherical torus applications (e.g. ST Component Test Facility, ST-Pilot plant, ST-DEMO)  Sustain target  N of ST applications with margin to reduce risk  Leverage unique ST operating regime to test physics models, apply to ITER  Physics Research Addressed  Plasma operation at low plasma internal inductance (l i )  Resistive wall mode (RWM) destabilization at high plasma rotation  RWM active control enhancements / advances at low l i  Combined control systems to maintain pulse at varied    Multi-mode RWM spectrum in high  N plasmas NP9.00011 Peng UP9.00006 Hawryluk

4. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 4 RWM active stabilization coils RWM poloidal sensors (B p ) RWM radial sensors (B r ) Stabilizer plates  High beta, low aspect ratio  R = 0.86 m, A > 1.27  I p < 1.5 MA, B t = 5.5 kG   t < 40%,  N < 7.4  Copper stabilizer plates for kink mode stabilization  Midplane control coils  n = 1 – 3 field correction, magnetic braking of   by NTV  n = 1 RWM control  Varied sensor combinations used for RWM feedback  48 upper/lower B p, B r NSTX is a spherical torus equipped for passive and active global MHD control, application of 3D fields

5. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 5 Operation aims to produce sustained low l i and high pulse-averaged  N  Next-step ST fusion devices aim to operate at low l i (high bootstrap current fraction > 50%) and high  N  Focus on sustained low l i and high pulse  N vs. l i (maximum values)  N vs. l i (pulse-averaged values)  N (maximum) ST-CTF ST-DEMO (ARIES-ST) ST-CTF pulse ST-Pilot ST-DEMO (ARIES-ST) Recent years with “routine” n = 1 RWM feedback (red)

6. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 6 Operation aims to produce sustained low l i and high pulse-averaged  N  N vs. l i (maximum values) NN   N /l i is a common parameter to evaluate global stability  Kink/ballooning and RWM stability  Significant increase in maximum  N /l i  Upper limit now between 13 - 14 lili  N /l i 13121110 14

7. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 7 Operation aims to produce sustained low l i and high pulse-averaged  N  N vs. l i (maximum values) NN   N /l i is a common parameter to evaluate global stability  Kink/ballooning and RWM stability  Significant increase in maximum  N /l i  Upper limit now between 13 - 14  At sufficiently low l i, “current driven kink” limit exists  Plasma unstable without conducting wall, or FB control, at any  N value lili  N /l i 13121110 14 “current-driven kink limit” (schematic)

8. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 8 Ideal no-wall stability limit decreases for low l i plasmas  N vs. l i (maximum values) NN  Examine high plasma current, I p >= 1.0MA, high non-inductive fraction ~ 50%  Ideal n = 1 no-wall stability computed for discharge trajectory  Plasma exceeds no-wall limit at  N = 3.4, l i = 0.51 lili  N /l i 13121110 14

9. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 9 Operation aims to produce sustained low l i and high pulse-averaged  N  N vs. l i (maximum values) NN  Examine high plasma current, I p >= 1.0MA, high non-inductive fraction ~ 50%  Ideal n = 1 no-wall stability computed for discharge trajectory  Plasma exceeds no-wall limit at  N = 3.4, l i = 0.51  Adding trajectories yields  N /l i = 6.7 for l i = 0.38 – 0.5  Significantly lower than usual no-wall limit at higher l i (  N = 4.3) lili  N /l i 13121110 14  N /l i = 6.7 ST-CTF ST-Pilot

10. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 10 Experiments aimed to produce sustained low l i and high  N  N vs. l i (maximum values) NN  High I p >= 1.0MA, high non-inductive fraction ~ 50%  Initial experiments  Yielded low l i  Access high  N /l i  High disruption probability  Instabilities leading to disruption  Unstable RWM Half of cases run  Locked tearing modes lili  N /l i 13121110 14  N /l i = 6.7 Uncontrolled RWM Stable / controlled RWM

11. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 11 (NEW SLIDE HERE – show improved long-pulse shots – segway to rest of talk) sustained low l i and high  N  N vs. l i (maximum values) NN  High I p >= 1.0MA, high non-inductive fraction ~ 50%  Latest experiments  Yielded low l i  Access high  N /l i  Reduced disruption probability (EXPLAIN THIS) lili  N /l i 13121110 14  N /l i = 6.7 Uncontrolled RWM Stable / controlled RWM

12. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 12 Characterization of Disruption Stats and Wtot variation here  Show improved disruption statistics and Wtot variation  Disruption Statistics  Wtot variation

13. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 13 Low plasma rotation level (~ 1%  Alfven ) is insufficient to ensure RWM stability, which depends on   profile  RWM unstable plasma  Instability occurs at relatively high rotation level, and not at highest  N (4.7)  RWM stable plasma  MHD spectroscopy: increased resonant field amplification (RFA) indicates reduced stability  Plasma moves to more stable regime (lower RFA) at lower rotation (  N up to 6.5) unstable RWM RWM rotation t(s) 0.570.580.590.60 6 4 2 80 40 0 300 200 NN  B pu n=1 (G) 0  Bpu n=1 (deg) 137722 RWM unstable plasma MHD spectroscopy (stable plasma) stable 140102 (140102) Plasma rotation 100 Stable up to  N = 6.5 0 1 1 (137722) unstable t(s) n=1 tracer field n=3 braking

14. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 14  Reason: simple critical   threshold stability models do not fully describe RWM marginal stability in NSTX  Kinetic modification to ideal MHD growth rate  Trapped / circulating ions, trapped electrons, etc.  Energetic particle (EP) stabilization  Stability depends on  Integrated   profile: resonances in  W K (e.g. ion precession drift)  Particle collisionality, EP fraction Trapped ion component of  W K (plasma integral) Energy integral collisionality   profile (enters through ExB frequency) Hu and Betti, Phys. Rev. Lett 93 (2004) 105002. Sontag, et al., Nucl. Fusion 47 (2007) 1005. precession driftbounce Modification of Ideal Stability by Kinetic theory (MISK code) investigated to explain experimental RWM stabilization BP9.00057 J. Berkery, et al.

15. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 15 NSTX 121083 unstable (marginal stability) unstable Precession drift resonance stabilization Bounce/transit resonance stabilization Marginal stability eff / exp (marginal stability) 15 MISK calculations consistent with RWM destabilization at intermediate plasma rotation; stability altered by collisionality  Destabilization appears between precession drift resonance at low  , bounce/transit resonance at high    w contours vs. ν and     /   exp (marginal stability) J.W. Berkery, et al., PRL 104 (2010) 035003 S.A. Sabbagh, et al., NF 50 (2010) 025020

16. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 16 NSTX 121083 unstable (marginal stability) unstable Precession drift resonance stabilization Bounce/transit resonance stabilization Plasma evolution eff / exp (marginal stability) 16 MISK calculations consistent with RWM destabilization at intermediate plasma rotation; stability altered by collisionality  Destabilization appears between precession drift resonance at low  , bounce/transit resonance at high    w contours vs. ν and     /   exp (marginal stability) J.W. Berkery, et al., PRL 104 (2010) 035003 S.A. Sabbagh, et al., NF 50 (2010) 025020

17. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 17 NSTX 121083 unstable (marginal stability) unstable Precession drift resonance stabilization Bounce/transit resonance stabilization Plasma evolution Marginal stability eff / exp (marginal stability) 17 MISK calculations consistent with RWM destabilization at intermediate plasma rotation; stability altered by collisionality  Destabilization appears between precession drift resonance at low  , bounce/transit resonance at high    Destabilization moves to increased   as decreases  w contours vs. ν and   instability (experiment)   /   exp (marginal stability) J.W. Berkery, et al., PRL 104 (2010) 035003 S.A. Sabbagh, et al., NF 50 (2010) 025020

18. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 18 MISK calculations show reduced stability in low l i target plasma as   is reduced, RWM instability is approached  Stability evolves  l i increases in time as RWM instability is approached, but remains low (l i = 0.42)  MISK computation shows plasma to be stable at time of minimum l i  Region of reduced stability vs.   found before RWM becomes unstable (l i = 0.49) Co-incident with a drop in edge density gradient – reduces kinetic stabilization  MISK application to ITER (advanced scenario IV)  RWM unstable at expected rotation  Only marginally stabilized by alphas at  N = 3 140132, t = 0.704s stable unstable - BP9.00057 J. Berkery, et al. - Also, see poster for detail experiment RWM stability vs.   (contours of  w ) 2.0 1.0   /   exp thermal w/fast particles

19. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 19 (Bp Feedback Phase Slide): Adjusting B p sensor feedback phase around 180 degrees led to long-pulse, low l i, high  N /l i 139347 139515 139516 139517  Steady, high  N /l i  Between 12 – 13  Low l i state retained 180 deg 202.5 deg 157.5 B p n = 1 (G) I p (MA) NN lili  N /l i

20. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 20 (Br sensor slide – combine gain and phase scan?): RWM B R sensor feedback reduces n= 1 radial error field significantly  New B r sensor feedback gain scan taken on low l i target plasmas  Highest gain attempted (1.5) most favorable  B r feedback constraints slow (~ 10 ms) n = 1 radial field growth  B r n=1 = 9G consistently disrupts plasma B r Gain = 1.25 B r Gain = 1.50 B r Gain = 1.0 B R + B p feedback (B p Gain = 1) 140117 140122 140123 140124 B r n = 1 (G) NN lili No B r feedback t (s)

21. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 21 RWM B r sensor n= 1 feedback phase variation shows clear settings for positive/negative feedback  B r sensor feedback phase scan shows superior settings  Result clarified significantly by new MIU algorithm OHxTF compensation  Positive/negative feedback produced at expected phase values  180 o negative FB  90 o positive FB  n=1 growth/decay of other settings bracketed by these settings B R + B p feedback (B p Gain = 1, B R Gain = 1.5) B r n = 1 (G) NN lili V  ~q=2 (kHz) B r FB phase = 0 o B r FB phase = 225 o B r FB phase = 90 o 140124 140125 140126 140127 B r FB phase = 180 o t (s)

22. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 22 (ADD Mode dynamics / physics here): Use of combined RWM sensor n= 1 feedback yields best reduction of n = 1 fields / improved stability  Varied levels of n > 1 field correction  n = 3 DC error field correction alone more subject to RWM instability  n = 1 B p sensor fast feedback sustains plasma  Addition of n = 1 B R sensor FB prevents disruptions when amplitude reaches ~ 9G, better sustains rotation (B p + B r ) n = 1 (G) NN I FB + n = 1 B p feedback 128693 139347 140137 n = 3 correction alone (RWM-induced disruption) t (s) + n = 1 Bp + B R feedback B r n = 1 (G) + n = 1 B p feedback + n = 1 Bp + B R feedback

23. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 23 B R sensors added: longest pulse plasmas, high performance 139347 139517 139518 139519 B p n = 1 (G) I p (MA)  Combined use of Bp and Br sensor feedback is best  Cases ran with MIU compens. on, or off  Continued use of feedback has MIU compens. on with good result B p + B R feedback on Bp sensors 180 deg FB phase (last run) NN lili  N /l i

24. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 24  N feedback combined with n = 1 RWM control to reduce  N fluctuations at varied plasma rotation levels  Prelude to   control  Reduced   by n = 3 braking is compatible with  N FB control  Steady  N established over long pulse  independent of   over a large range  Radial field sensors added to n = 1 feedback (2010)  Full sensor set further reduces n = 1 amplitude, improves control 135468 135513 0.80.40.61.01.2 t(s) 0.20.0 NN 2 4 6 I RWM-6 (kA) 0.6 0 2 4 6 -0.6 P NBI (MW)    ~q=2 (kHz)    core (kHz) 4 8 12 30 10 n = 3 braking n = 1 feedback 0 20 0 q ~ 2 rotation Core rotation n = 3 error correction

25. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 25 New RWM state space controller (RWMSC) implemented to sustain high  N Balancing transformation ~ 3000+ states Full 3-D model … RWM eigenfunction (2 phases, 2 states) truncate State reduction (< 20 states) Theoretical feedback performance (   = 0, 12 states)  Controller can compensate for wall currents  Including mode-induced current  Potential to allow more flexible control coil positioning  May allow coils to be moved further from plasma, shielded  Examined for ITER - device R, L, mutual inductances - instability B field / plasma response - modeled sensor response Katsuro-Hopkins, et al., NF 47 (2007) 1157

26. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 26 RWM state space controller with 2 states reproduces initial sensor response to mode  Reasonable match to all B p sensors during RWM onset, large differences later in evolution Bp UPPER Sensor differencesBp LOWER Sensor differences Sensor not functioning 137722 180 degree differences 180 degree differences 90 degree differences 90 degree differences 90 degree differences RWM Black: experiment Red: offline RWMSC

27. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 27 RWM state space controller with 7 states improves match to sensors over entire evolution Black: experiment Red: offline RWMSC Sensor not functioning 137722 180 degree differences 180 degree differences 90 degree differences 90 degree differences 90 degree differences RWM  Some 90 degree sensor differences not as well matched  May indicate need for n = 2 eigenfunction state Bp UPPER Sensor differencesBp LOWER Sensor differences

28. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 28 New RWM state space controller sustains high  N plasma RWM state space feedback (12 states)  n = 1 applied field suppression  Suppressed disruption due to n = 1 field  Feedback phase scan  Best feedback phase produced long pulse,  N = 6.4,  N /l i = 13 Successful First Experiments (See poster for detail)

29. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 29 Multi-mode RWM computation shows 2 nd eigenmode component has dominant amplitude at high  N in NSTX stabilizing structure  NSTX RWM not stabilized by    Computed growth time consistent with experiment  2 nd eigenmode (“divertor”) has larger amplitude than ballooning eigenmode  NSTX RWM stabilized by    Ballooning eigenmode amplitude decreases relative to “divertor” mode  Computed RWM rotation ~ 41 Hz, close to experimental value ~ 30 kHz  ITER scenario IV multi-mode spectrum  Significant spectrum for n = 1 and 2  B n from wall, multi-mode response  B n RWM multi-mode composition ideal eigenmode number  B n amplitude (arb) t = 0.655s mode 1 mode 2 2.01.00.0 R(m) 1.0 Z(m) 2.0 0.0 -2.0 mode 3  133775 mode 1 mode 3 mode 2 Unstable Stabilized by rotation BP9.00059 J. Bialek, et al. mmVALEN code  N = 6.1

30. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 30 ITER Advanced Scenario IV: multi-mode RWM spectra computation shows significant ideal eigenfunction amplitude for several components Z(m)  N = 3.92 n = 1  N = 2.65 n = 1  N = 3.92 n = 2 mode 1 4 -2 6 0 -4 2 R(m) 46810 Z(m) 4 -2 6 0 -4 2 R(m) 46810 Z(m) 4 -2 6 0 -4 2 R(m) 46810 03912615 1.0 0.8 0.6 0.4 0.2 0.0 mode 2 mode 3 mode 1 mode 2 mode 3 mode 1 mode 2 mode 3 ideal eigenmode number  B n amplitude (arb) Multi-mode spectrum  N = 2.65 n = 1 03912615 1.0 0.8 0.6 0.4 0.2 0.0 ideal eigenmode number mmVALEN 03912615 1.0 0.8 0.6 0.4 0.2 0.0 ideal eigenmode number Multi-mode spectrum Multi-mode spectrum  N = 3.92 n = 1  N = 3.92 n = 2  N no-wall = 2.5

31. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 31 NSTX is Addressing Global Stability Needs Furthering Steady Operation of High Performance Plasmas  RWM instability observed at intermediate   correlates with kinetic stability theory  n = 1 RWM,  N feedback control maintains high  N at varied   using n = 3 NTV   profile modification  (text)  Initial success of RWM state space controller at high  N  Multi-mode RWM physics spectrum    profile control  Sufficient EP stabilization  Potential control compatibility  (text)  More flexibility of control coil placement  Determine RWM control impact  Sufficient EP stabilization needed at low    Potential control at low   if EP stabilization insufficient  (text)  More flexibility of control coil placement  Determine RWM control impact Physics addressed Future STs (NBI-driven, high   ) ITER advanced scenarios (low   ) Implications for

32. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 32 Work slides

33. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 33 Slide ToDos  To Do  Update words on database slides  Add n = 1 no-wall limit “extension” on n = 1 line in database plot  Add database slide showing the results of IMPROVEMENTS to control systems, etc. – can be an intro to the next sections of talk. Illustrate reduced disruptivity here best you can! Think about how best to do this in the short-term Use XP1023 runs from (some 7/29), 8/3, 8/19, 9/24, other runs, fiducials NOTE: Runs on 4/13 and 4/15 mostly were lower betaN  Add database slide(s) as time allows (, vs. pulse)  Update Bp feedback phase slide  Update (combine?) Br gain / phase variation slide  Include key PHYSICS of the change in RWM mode dynamics in the waveform slides (see EXCEL spreadsheet for this)  Update VALEN model of 3d conducting structure

34. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 34 ABSTRACT (update to include new control/stability, RWMSC) Steady-state spherical torus plasmas for fusion applications, such as a component test facility or demonstration power plant, target operation with high non-inductive current fraction. These broad current profile targets have low values of plasma internal inductance, l i, less than 0.4, near to the lower end of present NSTX operation. A key significance of this operation is that it approaches the purely current-driven ideal kink limit, which by definition exceeds the no-wall stability limit for all values of plasma normalized pressure (beta). In this regime, passive or active kink and resistive wall mode (RWM) stabilization is critical. Experiments on NSTX have recently approached this condition, evidenced by a significant reduction of the n = 1 no-wall stability limit computed by DCON. This limit drops from normalized beta of 4.2 – 4.6 at l i ~ 0.6, to 3.4 at l i ~ 0.5, to below 2.8 for l i ~ 0.4. Nevertheless, passive and active RWM control has produced high toroidal beta up to 28 percent, and normalized beta up to 6.5 (nearly double the no-wall limit), closely following a record normalized beta to l i ratio of 13 between l i = 0.4 - 0.5. Non-inductive current fraction reaches 0.5 in these high normalized current plasmas. However, the disruption probability of these plasmas increases significantly, with about half of the discharges suffering terminating instabilities. Alteration of n = 1 RWM control system parameters, plasma rotation profile, and the role of beta feedback is examined to potentially improve mode stability. Ion precession drift and bounce frequency resonance stabilization is examined for these plasmas and compared to the identified stabilization reduction at intermediate plasma rotation and higher l i [1,2]. [1] J.W. Berkery, et al., Phys. Rev. Lett. 104, 035003 (2010) [2] S.A. Sabbagh, et al., Nucl. Fusion 50, 025020 (2010) *Work supported by U.S. DOE Contracts DE-FG02-99ER54524 and DE-AC02-09CH11466.

35. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 35 NSTX is Addressing Global Stability Needs for Maintaining Long-Pulse, High Performance Plasmas  Motivation  Achieve high  N with sufficient physics understanding to allow confident extrapolation to spherical torus applications (e.g. ST Component Test Facility, ST-Pilot plant, ST-DEMO)  Sustain target  N of ST applications with margin to reduce risk  Leverage unique ST operating regime to test physics models, apply to ITER  Physics Research Addressed  Plasma operation at low plasma internal inductance, l i  Resistive wall mode (RWM) destabilization at high plasma rotation  RWM active control enhancements / advances at low l i  Combined control systems to maintain pulse at varied    Multi-mode RWM spectrum in high  N plasmas Papers: ppp ppp

36. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 36 Steady-State STs Targeted to Operate High B N /l i [1]: Peng, et al, PPCF 2005, Phase #3, 2 MW/m 2 NWL [2]: ARIES-ST Common Features of Present & Future STs High-  and strong shaping.   N values at or above the no-wall limit. Bootstrap fractions ≥50%. Confinement ≥ H-mode scaling. Comprehensive shape, profile and stability control. Configuration Specific Features Range of normalized currents. Wide range of NBCD fractions. Wide range of normalized densities.   N l i (1) I N f GW f BS f NBCD H 98 NSTX 2.6 5.7 0.55 2.5 0.8 0.54 15 1. NSTX-U 2.7 5.7 0.65 2.1 0.7 30 1.2 NHTX 3 5 0.6 3 0.45 0.7 0.3 1.3 ST-CTF 1 3.1 4-6 0.35 4.5 0.28 0.5 1.5 ST-Demo 2 3.5 7.5 0.25 6.7 0.8 0.96 0 1.3 S.P. Gerhardt (NSTX PAC-27)

37. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 37 NSTX is Addressing Global Stability Needs Furthering Steady Operation of High Performance Plasmas  RWM instability observed at intermediate   correlates with kinetic stability theory  n = 1 RWM,  N feedback control maintains high  N at varied   using n = 3 NTV   profile modification  Stronger NTV braking at reduced  E  Initial success of RWM state space controller at high  N  Multi-mode RWM physics spectrum    profile control  Sufficient EP stabilization  Potential control compatibility    profile control impact  More flexibility of control coil placement  Determine RWM control impact  Sufficient EP stabilization needed at low    Potential control at low   if EP stabilization insufficient  Further examine NTV at low    More flexibility of control coil placement  Determine RWM control impact Physics addressed Future STs (NBI-driven, high   ) ITER advanced scenarios (low   ) Implications for

38. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 38 NSTX Database Plots BetaN vs. li (maximum values) b

39. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 39 NSTX Database Plots BetaN vs. li (maximum values)

40. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 40 NSTX Database Plots BetaN vs. li (pulse-averaged values)

41. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 41 Pressure peaking factor remains an essential component of high  N operation  Broad pressure profile needed to maintain high  N stability limit BetaN vs. Pressure peaking plot here

42. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 42 Update this slide (use,,

43. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 43 MISK calculations show reduced stability in low l i target plasma as   is reduced, RWM instability is approached  Stability evolves  l i increases in time as RWM instability is approached, but remains low (l i = 0.42)  MISK computation shows plasma to be stable at time of minimum l i  Region of reduced stability vs.   found before RWM becomes unstable (l i = 0.49) Co-incident with a drop in edge density gradient – reduces kinetic stabilization  MISK application to ITER (advanced scenario IV)  RWM unstable at expected rotation  Only marginally stabilized by alphas at  N = 3 140132 t = 0.704s stable unstable - BP9.00057 J. Berkery, et al. - Also, see poster for detail experiment RWM stability vs.   (contours of  w ) 2.0 1.0   /   exp

44. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 44 VALEN comparisons to NSTX PID feedback  (Probably won’t be enough time for this – perhaps a bullet at most, if the results are in)  Show that new PID feedback settings are consistent with theory  B p sensor feedback is consistent with (old) VALEN model  Consistent with new VALEN model?  B R sensor feedback is consistent with VALEN model  VALEN comparisons

45. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 45 Include more RWM State-space controller results  New results / analysis / slides (possible ToDos)  Improved diagram for feedback phase (show more phases?)  Illustration of changing gains in experiment  Completed ideas included in talk  Theoretical stability predictions  Illustration of changing number of states in experiment Done for observer

46. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 46 New RWM state space controller sustains high  N plasma Balancing transformation ~ 3000+ states Full 3-D model … RWM eigenfunction (2 phases, 2 states) truncate State reduction (< 20 states) State space feedback with 12 states  Controller can compensate for wall currents  Including mode-induced current  Examined for ITER  Successful initial experiments  Suppressed disruption due to n = 1 applied error field  Best feedback phase produced long pulse,  N = 6.4,  N /l i = 13 - device R, L, mutual inductances - instability B field / plasma response - modeled sensor response Katsuro-Hopkins, et al., NF (2007) 1157

47. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 47 RWM State Space Control – Theoretical Performance  text Low  N input 2, 12 states High  N input Control at low plasma rotation 4.0 NN 4.55.05.56.06.57.07.5 10 0 10 1 10 2 10 3 10 4  (1/s) Proportional gain control limit Passive growth Ideal Wall Limit State space controller (low  input) (high  input)

48. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 48 RWM State Space Control – Theoretical Performance  text Low  N input 2, 12 states High  N input Control at low plasma rotation ideal wall limit passive growth input 1: 12 states input 2: 12 states 4.0 NN 4.55.05.56.06.57.07.5 10 0 10 1 10 2 10 3 10 4  (1/s) Proportional gain control limit Passive growth

49. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 49 Organization / Outline slides

50. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 50 Specifics  Talk constraints  25 minutes talk + 5 minutes discussion (8 more mins. than IAEA)  2010 IAEA had 14 slides (was tight): 1.214 min/slide  Estimate 20 - 21 slides, plus backup  2001: 20 slides (simple slides – ok length)  2006: 16 slides (good length)

51. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 51 Outline - Topics  Outline - Topics  Motivation – ST-CTF, ST Pilot Plant, ITER Maintenance of high beta state, with miminal fluctuation Active control needs to meet needs of high neutron flux devices (coils further back from device, or shielded) Outline: include both passive and active stabilization physics – and keys for how they extrapolate to future devices  Example of broad current profile target plasma (ST-CTF or ST-Pilot; NSTX-U)  Illustration of stability space (li, BetaN) showing schematic limits Show NSTX database, with schematic limits superposed Show position of ST-CTF, ST-Pilot, NSTX-U, etc. on this plot  Illustration of stability space (li, BetaN) – ZOOMED in to low li Show recent low li plasmas as a different color on this plot  Might be effective as an overlay plot, depending on where recent data / stable data lies on diagram Separate out stable plasmas vs. disruptions if possible  Ideal no-wall stability limit computation for trajectories on (li, BetaN) diagram Give margin over the n = 1 no-wall limit  Progress towards maintaining steady plasma stored energy at high beta Initial runs (2009) – high disruption probability – show statistics in bullets / stacked bar chart / plots on diagram Long-pulse shots at high betaN  ELM-free, and no large Li buildup, no n = 1 rotating mode (with lithium) Improved PID feedback control (Bp and Br sensor results) state-space control beta feedback – at varied rotation Figures of merit: pulse avg betaN, std deviation  Passive stabilization physics Rotation and EP effects - (need equilibria for most recent results) Comparison of higher li to low li plasmas – difference in physical interpretation?  RWM control at high beta; considerations for burning plasma devices Multi-mode RWM physics, observations in NSTX

52. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 52 Outline – Slides I (WORKING VERSION)  Outline – Slides (16 slides minimum, 20 slides maximum)  Title page  Motivation – ST-CTF, ST Pilot Plant, ITER Maintenance of high beta state, with minimal fluctuation Active control needs to meet needs of high neutron flux devices (coils further back from device, or shielded) Outline: include both passive and active stabilization physics – and keys for how they extrapolate to future devices  Example of broad current profile target plasma (ST-CTF or ST-Pilot; NSTX-U)  Low li plasma with RWM instability – 137722, or other (use IAEA slide directly? Good segway to MISK results)  Illustration of stability space (li, BetaN) showing schematic limits Show NSTX database, with schematic limits superposed Show position of ST-CTF, ST-Pilot, NSTX-U, etc. on this plot  Illustration of stability space (li, BetaN) – ZOOMED in to low li Show recent low li plasmas as a different color on this plot  Might be effective as an overlay plot, depending on where recent data / stable data lies on diagram Separate out stable plasmas vs. disruptions if possible  Ideal no-wall stability limit computation for (li, betaN) trajectories on (li, betaN) diagram Give margin over the n = 1 no-wall limit  Progress towards maintaining steady plasma stored energy at high beta Initial runs (2009) – high disruption probability – show statistics in bullets / stacked bar chart / plots on diagram Long-pulse shots at high betaN  ELM-free, and no large Li buildup, no n = 1 rotating mode (with lithium)  Improved PID feedback control (Bp and Br sensor results)  state-space control  beta feedback – at varied rotation  Figures of merit: pulse avg betaN, std deviation  (Continued on next page)

53. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 53 Outline – Slides II (WORKING VERSION)  Outline – Slides (16 slides minimum, 20 slides maximum)  (Continued from prior page)  Passive stabilization physics Rotation and EP effects - (need equilibria for most recent results) Comparison of higher li to low li plasmas – difference in physical interpretation?  Multi-mode RWM physics, observations in NSTX  Multi-mode RWM physics, implications for ITER  Summary (use format showing implications for future STs, ITER - worked well at IAEA)

54. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 54

55. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 55 Outline – Slides – Version 2 (IAEA)  Outline – Slides (11 slides minimum, 13 slides maximum)  Title page  Motivation – ST-CTF, ST Pilot Plant, ITER Have outline on this slide, or as a separate (very simple) slide??  NSTX device / geometry slide  RWM instability / RFA at high plasma rotation Instability at intermediate and high rotation – low rotation “threshold” not adequate for stability  Consequences for an ST-CTF / Pilot Plant, and ITER Show RFA results here from recent XP1020 as well  Passive stabilization physics – NSTX and MISK code MISK physics – intro slide  Passive stabilization physics – NSTX rotation / collisionality (thermal particles) Rotation and collisionality effects – contour plot Clearly state physics implications for ITER and ST-CTF – importance of new results vs. old (low) crit.rotation  Unification of devices using new model (MISK) DIIII-D: comparison of energetic particle fraction / stability margin due to EPs vs. NSTX JT-60U: (mention in a bullet on this slide) ITER: BULLET HERE – advetrize full slide that will appear on poster  Progress towards maintaining steady plasma stored energy at high beta As default, use slide with n = 3 EFC, n = 1 FB, betaN control Improved PID feedback control; state-space control; beta feedback – at varied rotation Figures of merit: pulse avg. betaN, std. deviation  The role of NTV physics at low nu_i/OmegaE, and low OmegaE - Superbanana plateau regime in NSTX Low OmegaE results – superbanana plateau in NSTX Optional: results for NTV offset rotation, change in rotation damping vs. collisionality, etc.  RWM state space control RESERVE the theoretical growth rate plot for the POSTER and PAPER Need to DEFINE state space control / NSTX especially well suited to test / connect to ITER First experimental results  RWM control at high beta; considerations for burning plasma devices (I) Multi-mode RWM physics, expectations in NSTX – NSTX mmVALEN mode spectrum  RWM control at high beta; considerations for burning plasma devices (II) Addition of differential rotation – change in VALEN multi-mode spectrum, rot. speed; observations in NSTX  Summary

56. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 56 Backup and Poster Slides

57. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 57 ABSTRACT (update to include improved stability, RWMSC) Steady-state spherical torus plasmas for fusion applications, such as a component test facility or demonstration power plant, target operation with high non-inductive current fraction. These broad current profile targets have low values of plasma internal inductance, l i, less than 0.4, near to the lower end of present NSTX operation. A key significance of this operation is that it approaches the purely current-driven ideal kink limit, which by definition exceeds the no-wall stability limit for all values of plasma normalized pressure (beta). In this regime, passive or active kink and resistive wall mode (RWM) stabilization is critical. Experiments on NSTX have recently approached this condition, evidenced by a significant reduction of the n = 1 no-wall stability limit computed by DCON. This limit drops from normalized beta of 4.2 – 4.6 at l i ~ 0.6, to 3.4 at l i ~ 0.5, to below 2.8 for l i ~ 0.4. Nevertheless, passive and active RWM control has produced high toroidal beta up to 28 percent, and normalized beta up to 6.5 (nearly double the no-wall limit), closely following a record normalized beta to l i ratio of 13 between l i = 0.4 - 0.5. Non-inductive current fraction reaches 0.5 in these high normalized current plasmas. However, the disruption probability of these plasmas increases significantly, with about half of the discharges suffering terminating instabilities. Alteration of n = 1 RWM control system parameters, plasma rotation profile, and the role of beta feedback is examined to potentially improve mode stability. Ion precession drift and bounce frequency resonance stabilization is examined for these plasmas and compared to the identified stabilization reduction at intermediate plasma rotation and higher l i [1,2]. [1] J.W. Berkery, et al., Phys. Rev. Lett. 104, 035003 (2010) [2] S.A. Sabbagh, et al., Nucl. Fusion 50, 025020 (2010) *Work supported by U.S. DOE Contracts DE-FG02-99ER54524 and DE-AC02-09CH11466.

58. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 58 RWM state space controller sustains otherwise disrupted plasma caused by DC n = 1 applied field  n = 1 DC applied field  Simple method to generate resonant field amplication  Can lead to mode onset, disruption  RWM state space controller sustains discharge  With control, plasma survives n = 1 pulse  n = 1 DC field reduced  Transients controlled and do not lead to disruption  NOTE: initial run – gains NOT optimized 140025 140026 Control applied Control not applied NN I RWM-4 (kA)    ~q=2 (kHz) t(s) B p n=1 (G) I p (kA)

59. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 59 Some IAEA FEC 2010 slides follow

60. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 60 NSTX is Addressing Global Stability Needs for Maintaining Long-Pulse, High Performance Plasmas  Motivation  Achieve high  N with sufficient physics understanding to allow confident extrapolation to spherical torus applications (e.g. ST Component Test Facility, ST-Pilot plant, ST-DEMO)  Sustain target  N of ST applications with margin to reduce risk  Leverage unique ST operating regime to test physics models, apply to ITER  Physics Research Addressed  Resistive wall mode (RWM) destabilization at high plasma rotation  RWM active control advancements  Combined control systems to maintain pulse at varied    Physics of 3D fields to control plasma rotation  Multi-mode RWM spectrum in high  N plasmas Papers: ppp ppp

61. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 61 NSTX is Addressing Global Stability Needs Furthering Steady Operation of High Performance Plasmas  RWM instability observed at intermediate   correlates with kinetic stability theory  n = 1 RWM,  N feedback control maintains high  N at varied   using n = 3 NTV   profile modification  Stronger NTV braking at reduced  E  Initial success of RWM state space controller at high  N  Multi-mode RWM physics spectrum    profile control  Sufficient EP stabilization  Potential control compatibility    profile control impact  More flexibility of control coil placement  Determine RWM control impact  Sufficient EP stabilization needed at low    Potential control at low   if EP stabilization insufficient  Further examine NTV at low    More flexibility of control coil placement  Determine RWM control impact Physics addressed Future STs (NBI-driven, high   ) ITER advanced scenarios (low   ) Implications for

62. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 62 Rotation profile at RWM marginal stability altered by varying energetic particle content  I p, B t altered keeping q fixed in experiment  Fast ion density increases with increased I p  Indicated by fast ion D  diagnostic  Range of TRANSP  fast /  tot 17% - 31%  General reduction of RWM marginal   profile as I p increased Rotation profiles at marginal stability Relative fast ion density profiles J.W. Berkery, et al., Phys. Plasmas 17 (2010) 082504

63. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 63 Model of kinetic modifications to ideal stability can unify RWM stability results between devices  NSTX  Less EP stability: RWM can cross marginal point as   is varied  DIII-D  More EP stability (~ 2x NSTX): RWM stable at all    RWM destabilized by events that reduce EP population  ITER (advanced scenario IV)  RWM unstable at expected rotation  Only marginally stabilized by alphas at  N = 3  Stability overpredicted with EPs – model development continues  Improve NBI anisotropic distribution  Examine effects originally thought small H. Reimerdes, et al., paper EXS/5-4 NSTX DIII-D calculation with EPs unstable thermal ions energetic particles (EPs) NSTXDIII-D (rescaled) See poster (EXS/5-5)  γτ w ~ 0.1 NSTX experiment See poster (EXS/5-5)

64. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 64 Stronger braking with constant n = 3 applied field and  N as  E reduced – accessing superbanana plateau NTV regime NN 4 I c (kA) 2    ch-18 (kHz)    ch-12 (kHz)    ch-5 (kHz) core mid outer 6 0 0.4 0.0 20 10 0 20 10 0 8 4 0 0.50.60.70.8 t (s) n = 3 braking  Torque not  1/    (non-resonant)  NTV satisfies low collisionality “1/ regime” criterion (|nq  E | < i /  and * i < 1)  Stronger braking expected at low  E (superbanana plateau regime) ( K.C. Shaing et al., PPFC 51 (2009) 035009 )  Faster braking with  Constant applied n = 3 field,  N ; No mode activity 133367 t = 0.815 s  i = 1 nq  E i /  (kHz)  E ~ 0 20 15 10 5 0 1.01.11.21.31.41.5 R(m) t(s) 0.795 0.805 0.815 40 0 Broad, near zero   WITHOUT rational surface locking 80   /2  (kHz) Callen OV/4-3

65. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 65 Additional Slides

66. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 66 NSTX is Addressing Global Stability Needs Furthering Steady Operation of High Performance Plasmas  RWM instability observed at intermediate plasma rotation correlates with kinetic stability theory  Theory of kinetic modifications to ideal stability may unify RWM stability results between devices  ITER advanced scenario 4 requires EP stabilization at expected    n = 1 RWM feedback control combined with new  N feedback control shows regulation of high  N at varied plasma rotation levels  Compatible with plasma rotation control by non-resonant 3D fields  Stronger non-resonant NTV braking observed at reduced  E  Theoretically expected (superbanana plateau regime)  New RWM state space controller sustains high  N plasma  Potential for greater flexibility of RWM control coil placement for burning plasma devices  Computed multi-mode RWM spectrum at high  N shows significant amplitude in higher order modes

67. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 67 ITER Advanced Scenario IV: RWM just reaches marginal stability by energetic particles with  N = 3  Equilibrium  With  N = 3 (20% above n = 1 no-wall limit)  Plasma rotation profile linear in normalized poloidal flux  Plasma rotation effect  Stabilizing precession drift resonance weakly enhances stability near   = 0.8   Polevoi  Energetic particle (EP) effect  Alpha particles are required for RWM stabilization at all    Near RWM marginal stability at ITER expected   /  total = 0.19 at   =   Polevoi MISK stability code

68. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 68 Energetic particles are stabilizing to RWM; computed effect is smaller in NSTX when compared to DIII-D  Smaller energetic particle (EP) fraction in NSTX  Less stability due to EPs  Scaled  W k from MISK shows larger stabilization effect due to EPs in DIII-D H. Reimerdes, et al., paper EXS/5-4

69. NSTX 52nd APS DPP Meeting: Progress Toward Stabilization of Low l i Spherical Torus Plasmas in NSTX (S.A. Sabbagh, et al.)November 9 th, 2010 69 Advancements in MISK stability model continue Electrostatic effectAdditional anisotropic term Centrifugal destabilizationOther possibilities: [B. Hu et al., Phys. Plasmas 12, 057301 (2005)] In addition to present anisotropy effects on δW K, when f is anisotropic an additional term arises that is proportional to : –Inclusion of plasma inertia term in the dispersion relation –Effect of poloidal rotation on ω E (small) –Use of a Lorentz collisionality model instead of current ad-hoc inclusion of collisionality The electrostatic component of the perturbed distribution function contributes to δW. (expected to be small). This fluid force term is usually neglected, but it is always destabilizing, and could be important if the plasma rotation Mach number is significant, or for alpha particles rotating at higher frequency ~ ω *α. (significant for NSTX in core, not edge)