Office of Supported by Science Advances in Global MHD Mode Stabilization Research on NSTX

College W&M Colorado Sch Mines Columbia U Culham Sci Ctr Comp-X U St. Andrews General Atomics S.A. Sabbagh1, J.W. Berkery1, R.E. Bell2, J.M. York U INEL Chubu U Johns Hopkins U Bialek1, S. Gerhardt2, R. Betti3, D.A. Gates2, B. Hu3, Fukui U LANL Hiroshima U LLNL O.N. Katsuro-Hopkins1, B. LeBlanc2, J. Levesque1, Hyogo U Lodestar Kyoto U MIT J.E. Menard2, J. Manickam2, K. Tritz4 Kyushu U Nova Photonics Kyushu Tokai U New York U NIFS Old Dominion U Niigata U ORNL 1Department of Applied Physics, Columbia University, New York, NY, USA U Tokyo PPPL JAEA PSI 2Plasma Physics Laboratory, Princeton University, Princeton, NJ, USA Hebrew U Princeton U 3University of Rochester, Rochester, NY, USA Ioffe Inst SNL RRC Kurchatov Inst Think Tank, Inc. 4Johns Hopkins University, Baltimore, MD, USA TRINITI UC Davis KBSI UC Irvine KAIST UCLA ENEA, Frascati UCSD 22nd IAEA Fusion Energy Conference CEA, Cadarache U Colorado IPP, Jülich U Maryland October 13 - 18, 2008 IPP, Garching U Rochester ASCR, Czech Rep U Washington Geneva, Switzerland U Quebec U Wisconsin

v1.5 NSTX IAEA FEC 2008 – EX/5-1 – S.A. Sabbagh 1 Research advances to understanding mode stabilization physics and reliably maintaining high beta plasmas  Motivation β  Maintenance of high N with sufficient physics understanding allows confident extrapolation to ITER and CTF N L 2 N

 Outline  Active control of beta amplified n = 1 fields / global instabilities  Mode dynamics and evolution during active control  Control performance compared to theory, connection to ITER  Kinetic effects on resistive wall mode (RWM) stabilization

 Ti influence on non-resonant magnetic braking

NSTX IAEA FEC 2008 – EX/5-1 – S.A. Sabbagh 2

CTF: β = 3.8 – 5.9 (W = 1-2 MW/m ) ST-DEMO: β ~ 7.5 Nno-wall - Both at, or above ideal no-wall β-limit; deleterious effects at ~ ½ β N L 2 - high β accelerates neutron fluence goal - takes 20 years at W = 1 MW/m ) NSTX equipped for passive and active RWM control RWM sensors (Br)

Stabilizer  Stabilizer plates for kink plates mode stabilization  External midplane control coils closely coupled to vacuum vessel  Varied sensor combinations used for feedback

 24 upper/lower Bp: (Bpu, Bpl)

 24 upper/lower Br: (Bru, Brl)

RWM sensors (Bp) RWM active stabilization coils

NSTX IAEA FEC 2008 – EX/5-1 – S.A. Sabbagh 3 Active RWM control and error field correction maintain β high N plasma Shots: 129283  n = 1 active, n = 3 DC control 129067 Without control With control 6 65  n = 1 response ~ 1 ms < 44 βN 1/γRWM 3 β > β no-wall 22 β N N  βN/βNno-wall = 1.5 reached 1 Nno-wall = 4 (DCON) 0 020  ωφ 20 best maintains 15 ωφ π 129283 /2 (kHz)  1010 NSTX record pulse lengths 5  limited by magnet systems 129067 ω maintained 00 φ 14  n > 0 control first used as 12 ∆ 1210 Bpu,ln=1(G) 8 standard tool in 2008 86 4  42 Without control, plasma more 00 susceptible to RWM growth, 500500 IA (A) even at high ωφ 0  Disruption at ωφ/2π ~ 8kHz -500-500 n = 3 correction n = 1 feedback near q = 2 10 5  More than a factor of 2 higher 0.0 0.2 0.4 0.6 0.8 1.0 1.2 ωφ 0 t (s) than marginal with n = 3 -5 magnetic braking -10 0 0.2 0.4 0.6 0.8 1.0 1.2 Sabbagh, et al., PRL 97 (2006) 045004. Seconds

NSTX IAEA FEC 2008 – EX/5-1 – S.A. Sabbagh 4 β Probability of long pulse and < N>pulse increases significantly with active RWM control and error field correction

Control off (908 shots) Control on Control on (114 shots)

Control off Frequency distribution Frequency

Ip flat-top duration (s)  Standard H-mode operation shown  Control allows <βN>pulse > 4  Ip flat-top duration > 0.2s (> 60 RWM growth times)  βN averaged over Ip flat-top

NSTX IAEA FEC 2008 – EX/5-1 – S.A. Sabbagh 5 During n=1 feedback control, unstable RWM evolves into rotating global kink

1 28496  RWM grows and begins to 0.50.5 1 00 rotate -0.5 (kA) -0.5 A amperes

I  -1.0-1.0 With control off, plasma -1.5-1.5 disrupts at this point 25  (G) 2020 With control on, mode 15 n=1 RFA 1 converts to global kink, p Tesla 10 RFA reduced

B 10 5 RWM amplitude dies away

∆ RWM 0  Resonant field amplification 300300 Mode rotation

s (RFA) reduced 200 Co-NBI direction (deg) 200 Degree n=1 100100  Bp Conversion from RWM to φ 020 τ rotating kink occurs on w 1010 s timescale (G) 00 Gaus -10 n=odd -10 128496  Kink either damps away, or B

∆ 0.606 0.608 0.610 0.612 0.614 0.616 0.618 0.620 saturates 0.606 0.610 Seconds0.614 0.618 t (s)  Tearing mode can appear during saturated kink

NSTX IAEA FEC 2008 – EX/5-1 – S.A. Sabbagh 6 Soft X-ray emission shows transition from RWM to global kink USXR, no time filter, 128496 Transition14 USXR, from no time RWM filter, 128496 to kink Tearing mode appears during kink 1 14 2 12 12 10 RWM onset time + 35 ms 10 edge USXR, 2 kHz

4 edge 10 ChordNumber 4 2 8 2 0 0.608 0.610 0.612 0.614 6 core 0 time 0.608 0.610 0.612 0.614 USXR,RWM 1 kHz

ChordNumber 4 2 1 < f(kHz) < saturated kink 2 15 0 128496 core  Tearing mode appears after 10 0.6080 0.610 0.612 0.614 time 0.6080.608 0.6100.610 0.6120.612 0.6140.614 0.616 RWM growth times and stabilizes timet (s)

NSTX IAEA FEC 2008 – EX/5-1 – S.A. Sabbagh 7

g p a s s i v e g ideal (C u,C u) Experimental RWM controlg ph=230 performance G p=27.05e3 consistent with theory g r - o n k g s=0.05 G p=27.05e3 Experimental βN reached Experimentg s=0.05 G p=27.05e3 4 g s,a=0.05,0 G p=27.05e3 1 0 g s,a=0.05,0 G p=27.05e3 g s,a=0.05,0 G p=27.05e3 (control off) (control on) unstable stable unstable 1 0 0 45 225 290 315 1 0 3 DCON mode no-wall rotatin passive with- 8 0 limit wall g

2 limit [ 1 / s ] 1 0 γ active control [ 1 / s ] 6 0 γ (1/s)

γ (1/s)

mode γ locked 1 0 1 4 0 passive

active grow th rate grow th rate feedback 2 0 1 0 0 (reached) 0 0 6 0 1 2 0 1 8 0 2 4 0 3 0 0 3 6 0 1 0 - 1 4 4 . 5 5 5 . 5 6 6 . 5 7 7 . 5 phase∆φ in f[F (deg) ] [deg] NSTX.10.2007 β adv. controller Nβ NSTX.10.2007 n  Feedback phase scan shows  VALEN code with realistic sensor superior settings geometry, plasmas with reduced Vφ  Agreement between theoretical and experimental feedback behavior

NSTX IAEA FEC 2008 – EX/5-1 – S.A. Sabbagh 8 β Significant N increase expected for proposed ITER internal coil

ITER VAC02 stabilization performance ITER VAC02 design (40° sector)

passive ) -1

all midplane coils

Growth rate (s rate Growth coils upper+ lower VALEN-3D coils β N β  50% increase in N for RWM stability 3 toroidal arrays, 9 coils each

NSTX IAEA FEC 2008 – EX/5-1 – S.A. Sabbagh 9 Modification of Ideal Stability by Kinetic theory (MISK code) investigated to explain experimental stability

 Simple critical ωφ threshold stability models or loss of torque balance do not describe experimental marginal stabilitySontag, et al., Nucl. Fusion 47 (2007) 1005.  Kinetic modification to ideal MHD growth rate δ W∞ + δ W  Trapped and circulating ions, trapped electrons γ τ = − K w δ W + δ W  Alfven dissipation at rational surfaces b K Hu and Betti, Phys. Rev. Lett 93 (2004)  Stability depends on 105002. φ  ω δ Integrated profile: resonances in WK (e.g.φ ion precession drift)

 Particle collisionality D = D − D − vθ Bφ δ ω profile (enters throughω ω φExBω frequency) Trapped ion component of WK (plasma integral) E *i 2π R Bθ  ω + (ε − 3 )ω + ω − ω − γ  5 *N ˆ *T E i  2  2 − εˆ δ W ∝ ∫ εˆ e dεˆ Energy integral K  ω + lω − iν + ω − ω − iγ   D b eff E 

precession drift bounce collisionality

NSTX IAEA FEC 2008 – EX/5-1 – S.A. Sabbagh 10 Kinetic modifications show decrease in RWM stability

at relatively high Vφ – consistent with experiment

ωφ γ τw / exp Theoretical variation of RWM stability vs. Vφ (contours of γτwω )φ ω φ 80 exp exp 0.03 ω /ω ω / ω = 0.2 exp φ φ Marginallyφ φ -0.6 ωφ/ωφ ω exp γτ φ w 0.2 60 stable ω / ω exp 0.4 φ φ = 2.0 ω ω exp 2.0 experimental φ/ φ 0.6 profile -0.4 0.8

[kHz] 40 φ (kHz) 1 .0

ω 0.02 π 1.0 1 .2

) 2.0

/2 -0.2 K φ ) K

ω 20 W W 0.0 δ 121083 δ

0.2 (

0 Im Im( 0.01 1.0 0.0 0.2 0.4ψ ψ 0.6 0.8 1.0 Ψ/Ψ/ a a 0.2  experiment Marginal stable experimental plasma unstable reconstruction, rotation profile ωφexp 0.00  Variation of ωφ away from marginal 0.00 0.01 0.02 0.03 0.04 Re(W ) profile increases stability δ K Re(δW )  Unstable region at low ωφ K

NSTX IAEA FEC 2008 – EX/5-1 – S.A. Sabbagh 11 Kinetic model shows overall increase in stability as collisionality decreases exp γ τw / exp ω φ ω φ / Increased collisionality (x6) Reduced collisionality (x1/6)ω φ ω φ 0.03 0.03 -0.6 ω ω exp γτ φ/ φ γτ w 0.2 w 0.2 0.4 0.4 -0.4 0.6 0.6 0.8 0.8 0.02 1 .0 0.02 1 .0

) 2.0 1 .2

K -0.2 ) ) 1 .4 K K

W 1 .6 W W

δ 2.0 δ δ 1.0 1 .8 ( ( Im Im Im( 0.01 0.01 0.2 0.2 exp ωφ/ωφ unstable unstable 1.0 0.00 0.00 0.00 0.01 0.02 0.03 0.000.04 0.01 0.02 0.03 0.04 Re(W ) Re(W ) δ δ K δ K δ Re( WK) Re( WK)

 Vary ν by varying T, n at constant β  Increased stability at ωφ/ωφexp ~ 1  Simpler stability dependence on ωφ  Unstable band in ωφ at increased at increased ν ωφ

NSTX IAEA FEC 2008 – EX/5-1 – S.A. Sabbagh 12 Stronger non-resonant braking at increased Ti 0.0 130720  Observed non-

(kA) 130722 n = 2 braking resonant braking -0.4 using n = 2 field coil I -0.8  Examine Ti 4 dependence of neoclassical toroidal (kHz)

φ no Li 2 Li wall viscosity (NTV) ω R = 1.37m  Li wall conditioning 0.4 produces higher Ti in 0.3 region of high (keV) i i 0.2 no lithium Li wall rotation damping T 0.1 (Ti/Ti)^2.5  0.4 1/Omega*dOmega/dt 0.5 t (s) 0.6 0.7 Expect stronger NTV torque at higher Ti 00 33 5/2 Series1 Series2(-dωφ/dt ~ T ωφ) Damping profiles Series2 (Ti ratio)5/2 i  At braking onset,

/dt) No Li 5/2 φ -5 2 Ti ratio = -5 2 5/2 ω (0.45/0.34) ~ 2

)(d Li wall  φ Consistent with ω ω measured d /dt in -10-10 11 φ 2x region of strongest (1/ damping NTV this meeting: -15-15 00 J-K. Park: EX/5-3Rb 0.90.9 1.11.1 1.31.3 1.51.5 0.90.9 1.11.1 1.31.3 1.51.5 R(m) R(m) R(m) R(m) J. Callen: TH/P8-36

NSTX IAEA FEC 2008 – EX/5-1 – S.A. Sabbagh 13 Advances in global mode feedback control, kinetic stabilization physics and magnetic braking research  Active n = 1 control, DC n = 3 error field correction maintain β β no-wall high N plasma over ideal N limit for long pulse  Growing RWM converts to kink that stabilizes; can yield tearing mode  Active control performance compares well to theory β  Significant N increase expected for ITER with proposed internal coil  Kinetic modifications to ideal stability can reproduce behavior

of observed RWM marginal stability vs. Vφ  Simple critical rotation threshold models for RWM stability inadequate

 Non-resonant Vφ braking observed due to n = 2 applied field

 Braking magnitude increases with increased Ti consistent with NTV SEE POSTER EX/5-1 on Friday afternoon for further details

NSTX IAEA FEC 2008 – EX/5-1 – S.A. Sabbagh 14