Macroscopic Stability Research on NSTX – Results and Theory Interaction S.A. Sabbagh 1, S.P. Gerhardt 2, R.E. Bell 2, J.W. Berkery 1, R. Betti 3, J.M. Bialek 1, J. Breslau 2, R. Buttery 4, L. Delgado- Aparicio 5, D.A. Gates 2, B. Hu 3, R. LaHaye 4, J-K. Park 2, J.E. Menard 2, H. Reimerdes 1, K.C. Shaing 5, K. Tritz 6, and the NSTX Research Team 1 Department of Applied Physics, Columbia University, New York, NY 2 Plasma Physics Laboratory, Princeton University, Princeton, NJ 3 University of Rochester, Rochester, NY 4 General Atomics, San Diego, CA 5 University of Wisconsin, Madison, WI 6 Johns Hopkins University, Baltimore, MD PPPL MHD Science Focus Group Meeting January 6th, 2010 PPPL 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 v1.0

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, NSTX Macrostability Research is Addressing Topics Needed to Maintain Long-Pulse, High Performance ST  Motivation / Goals (e.g. from recent ReNeW process)  Maintenance of high  N with sufficient physics understanding allows confident extrapolation to ST applications (Hybrid, CTF, DEMO)  Sustain target  N of ST applications with margin to reduce risk  Physics studied in NSTX to best ensure steady-state ST operation  Locked mode behavior at low to moderate  N <  N no-wall  Ability of plasma rotational stabilization to maintain high  N  Possibility of multiple RWMs that can affect active control  Physics of 3D fields to control plasma rotation profile (for greater stability, confinement)  NTM onset and marginal island width for stabilization  Multiple scalable control systems to maintain pulse Successful connections being made to theory – continue/expand interaction…

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, NSTX Macrostability Research – Topics Covered in Talk  Error fields (n = 1 and n = 3)  Resistive wall modes  Non-resonant magnetic braking physics  NTM threshold physics  Improving pulse with n = 1 and  N feedback

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th,  n = 1 error field threshold for mode locking decreased as β N increased  n = 1 rotating modes sometimes observed, study limited to static modes  IPEC resonant field joins linear n e correlation from low-β to increased-β Ideal plasma amplification of applied resonant field restores linear correlation of mode locking threshold with density Lower-β locked later (w/ larger RWM currents) XP903: J.-K. Park Ideal Plasma Amplification Higher-β locked earlier (w/ smaller RWM currents) vacuum IPEC

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, Optimal n=3 Error Field Correction Determined vs. I P, B T 2009  “optimal” n = 3 error field correction attained by maximizing angular momentum, scanning I p, B t, elongation  n = 3 error field consistent with known equilibrium field coil distortion  scales with equilibrium field coil current  field phase and amplitude of correction is consistent with that expected from coil distortion  n = 3 error field correction routinely used to maximize plasma performance in conjunction with n = 1 RWM feedback control  NTV theoretical analysis performed by J-K Park for these cases XP902: S. Gerhardt

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, NSTX Macrostability Research – Topics Covered in Talk  Error fields (n = 1 and n = 3)  Resistive wall modes  Non-resonant magnetic braking physics  NTM threshold physics  Improving pulse with n = 1 and  N feedback

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th,  Resistive wall modes can terminate NSTX plasmas at intermediate plasma rotation levels without active control (no simple, scalar  crit )  Kinetic modification to ideal MHD growth rate  Trapped and circulating ions, trapped electrons  Alfven dissipation at rational surfaces  Stability depends on  Integrated   profile: resonances in  W K (e.g. ion precession drift)  Particle collisionality Trapped ion component of  W K (plasma integral) Energy integral collisionality   profile (enters through ExB frequency) Hu and Betti, Phys. Rev. Lett 93 (2004) precession driftbounce Modification of Ideal Stability by Kinetic theory (MISK code) investigated to explain experimental RWM stabilization

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, Kinetic modifications show decrease in RWM stability at relatively high V   Marginally stable experimental plasma reconstruction, rotation profile   exp  Variation of   away from marginal profile increases stability  Unstable region at low    Role of energetic particles now under investigation (Berkery, et al.) Theoretical variation of   Marginally stable experimental profile RWM stability vs. V  (contours of  w ) /a/a   /   exp   /2  (kHz) Im(  W K ) Re(  W K )   /   exp  w experiment unstable   /   exp J.W. Berkery

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, Channel of “Weak Rotation” for RWM passive stabilization observed in MISK calculations for NSTX; altered by plasma collisionality  Stabilization from precession drift resonance at low rotation and bounce resonance at high rotation  Stability dependence on collisionality key for ST fusion burn devices  w contours vs. ν and   NSTX unstable Marginal stability experiment J.W. Berkery (APS DPP 2009 invited talk; PRL accepted)

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, High  N shots exhibit low frequency mode activity in magnetic and kinetic diagnostics t(s) Multi-energy SXR data shows ~ 30 Hz mode activity edge core NN t(s) I RWM-6 (kA)    ch-18 (kHz)  B pu n=1 (G)  B N n=1 (G) I p = 0.8 MA ME-SXR low  Soft X-ray measurements show low frequency mode activity is global  Mode activity in RWM frequency range coincident in magnetics, SXR n = 1 RWM feedback on (arb) XP935: S.A. Sabbagh  When unstable, growing n = 1 RWM appears to be independent of ~30 Hz activity

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, RWM multimode response theoretically expected to be significant at high  N based on ideal MHD theory  Boozer multimode criterion for n = 1 met at high  N  |  W | smallest for 2 nd n = 1 eigenfunction  Ratio of |  W | for 3 rd vs. 1 st least stable mode sometimes also > 1 NN (PoP 10 (2003) 1458.) mode 3 mode 1 mode 2 t(s)  W (arb) no-wall stability DCON |  W| ratio mode 1/mode 3 mode 1/mode 2 n = 1 multimode period t = 0.655s mode 1 mode R(m) 1.0 Z(m) DCON  B N mode 3   (deg) 1800  B N (arb) mode 1 mode 2 mode XP935: S.A. Sabbagh

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, Multi-mode VALEN code (RWM control) testing successfully on high  N NSTX plasmas  mmVALEN to be used to examine response of 2 nd mode to n = 1 feedback, error field and compare to experiment NN Growth rate vs. # of modes – mmVALEN t = 0.655s 116 DCON modes 76 DCON modes Typical growth times (experiment) J. Bialek

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, NSTX Macrostability Research – Topics Covered in Talk  Error fields (n = 1 and n = 3)  Resistive wall modes  Non-resonant magnetic braking physics  NTM threshold physics  Improving pulse with n = 1 and  N feedback

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, Stronger braking with constant n = 3 applied field as  E reduced – accessing superbanana plateau NTV regime XP933: S.A. Sabbagh t = s  i = 1 nq  E i /  (kHz)  Torque not  1/    (non-resonant)  NTV in “1/ regime” (|nq  E | < i /  and * i < 1)  Stronger braking expected when  E ~ 0 (superbanana plateau) ( K.C. Shaing et al., PPFC 51 (2009) ) – theoretical analysis continues (Sabbagh)  E ~ 0   /2  (kHz) R(m) t(s) NN 4 I c (kA) 2    ch-5 (kHz)    ch-12 (kHz)    ch-18 (kHz) core mid outer  Faster braking with  Constant  N, applied n = 3 field  No mode activity t (s) 40 0 Broad, near zero   WITHOUT rational surface locking n = 3 braking 80

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, NSTX Macrostability Research – Topics Covered in Talk  Error fields (n = 1 and n = 3)  Resistive wall modes  Non-resonant magnetic braking physics  NTM threshold physics  Improving pulse with n = 1 and  N feedback

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, Consistent pre-2009 DIII–D/NSTX results on m/n = 2/1 NTM marginal island width for stability; good restabilization data sets in 2009  W marg /  0.5   i ratio ~ 2 in tokamaks  AUG, DIII-D, JET data for 3/2 mode  First results show W marg /  0.5   i also ~ 2 for NSTX (2/1 mode) (!) NSTX XP914: R. LaHaye Pre data  Status: DIII-D  Used gas puff to stay in H-mode  5 good 2/1 (and 2 good 3/1) cases  Status: NSTX  Achieved a reproducible onset condition using modest Li evaporation  8 good cases (2009)

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, Required (missing) bootstrap drive for NTM onset better correlated with rotation shear than rotation magnitude  Rotation variation via n = 1 or 3 applied field  Operational space fully spanned up to locked mode limits  No measureable trend vs. rotation  Weak positive correlation with normalized rotation shear  Lowest/highest thresholds at low/high rotation shear  2d fit vs rotation & rotation shear offers little improvement  Consistent with prior results (S.P. Gerhardt, et al., 2008)  0 L q  j BS,Sauter /B   (dF/dr)  A L S F 2/1 Hz XP915: R. Buttery

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, NSTX Macrostability Research – Topics Covered in Talk  Error fields (n = 1 and n = 3)  Resistive wall modes  Non-resonant magnetic braking physics  NTM threshold physics  Improving pulse with n = 1 and  N feedback

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, Successful  N feedback at varied plasma rotation levels  Prelude to   control  Reduced   by n = 3 braking does not defeat FB control  Increased P NBI needed at lower    Steady  N established over long pulse  independent of   over a large range t(s) NN I RWM-6 (kA) P NBI (MW)    ch-18 (kHz)    ch-5 (kHz) n = 3 error correcting phasing n = 3 braking phasing n = 1 feedback XP934: S.A. Sabbagh S.A. Sabbagh, S. Gerhardt, D. Mastrovito, D. Gates 0

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, NSTX Macrostability Research – Interaction with Theory  Error fields (n = 1 and n = 3)  IPEC used successful to support experiment; continue IPEC development, including interface of ideal plasma response to other analyses (Park, Boozer)  Resistive wall modes  MISK development continues (CU, U. Rochester, PPPL), present focus on energetic particle description, comparison to experiment (Berkery, et al.)  Multi-mode RWM analysis with new mmVALEN code (Bialek, Boozer), comparison to experiment (Sabbagh)  Non-resonant magnetic braking physics  Continued development of MHD models (CU, PPPL, UW), working from Shaing model (Sabbagh), Park/Boozer model (Park), etc. (e.g. Cole, et al.)  Work aimed for comparison to particle codes (GTC-Neo (Wang), FORTEC-3D (Satake)) should continue  NTM threshold physics  Mostly empirical, or simple MRE assumptions to date, largest gap in theory support here (linear – computation of  ’ (PEST 3), non-linear codes ?)  Improving pulse with n = 1 and  N feedback, general RMPs  Multi-faceted, including beta, rotation control (Gerhardt, Koleman), RWM control optimization (Hopkins, et al.), ideal, RWM, NTM, ELM stability theory

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, Backup Slides

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, NSTX Macrostability Research in 2009 is Addressing Topics Furthering Steady Operation of High Performance Plasmas  Ideal plasma amplification of applied n = 1 resonant field (IPEC) joins linear density scaling of mode locking threshold from low to moderate-β  Optimal n=3 error field correction determined vs. I P, B T  RWM instability, observed at intermediate plasma rotation, correlates with kinetic stability theory; role of energetic particles under study  Low frequency ~ O(1/  wall ) mode activity at high  N being investigated as potential driven RWM  Theory shows multi-mode RWM response may be important at high  N ; multi-mode VALEN code now passing initial tests  Strong non-resonant braking observed NTV braking observed from all i /nq  E (R) variations made; apparent transitions in NTV at low    Expanded NTM onset experiments continue to find best correlation between NTM onset drive and flow shear  Successful NBI power limitation via new  N feedback control system; initial success in regulation of  N at varied plasma rotation levels

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, When unstable, observed growing n = 1 RWM appears to be independent of the driven, ~30 Hz activity  Unstable RWM is locked; driven mode co-rotating at low frequency  Unstable RWM grows (magnetics); low frequency mode appears steady in SXR high-f mode core edge NN I RWM-6 (kA)    ch-18 (kHz)  B pu n=1 (G)  B N n=1 (G) I P (MA)    ch-5 (kHz)  B Ru n=1 (G) t(s) 0.8 t(s) NN  B N n=1 (G) 2 6 ME-SXR low unstable RWM n = 3 braking unstable RWM

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, Multi-mode VALEN code (RWM control) testing successfully on ITER Scenario 4 cases (reversed shear)  At highest  N, n =1 and 2 are unstable NN Number of modes (VALEN) Growth rate (1/s) single-mode matched to  N wall multi-mode VALEN (converged)  DCON  W shows several modes with high response  Three n = 1 modes at high  N  Two n = 2 modes at high  N n = 1 J. Bialek

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, Illustration of B n (  ) on plasma surface from mmVALEN for ITER Scenario 4,  N = 3.92  n = 1 eigenfunctions shown multi mode response (incl. wall), total B n B n from wall, plasma B n from wall alone toroidal poloidal outboard inboard outboard inboard J. Bialek

NSTX PPPL MHD SFG mtg: Macroscopic Stability Research on NSTX – Results and Theory (S.A. Sabbagh, et al.)January 6 th, Illustration of B n (  ) on plasma surface from mmVALEN for NSTX shot (t=0.655s) single mode response, total B n multi mode response, total B n B n from wall, multi mode response toroidal poloidal J. Bialek outboard inboard outboard inboard outboard inboard