1. NSTX SAS – APS DPP ‘05 Supported by Office of Science S.A. Sabbagh 1, A.C. Sontag 1, W. Zhu 1, M.G. Bell 2, R. E. Bell 2, J. Bialek 1, D.A. Gates 2, A. H. Glasser 3, B.P. LeBlanc 2, F. Levinton 4, J.E. Menard 2, H. Yu 4, D. Battaglia 5, and the NSTX Research Team Resonant Field Amplification and Resistive Wall Mode Stability in NSTX 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 47 th Annual Meeting of the Division of Plasma Physics American Physical Society October 24 – 28, 2005 Denver, Colorado 1 Department of Applied Physics, Columbia University, New York, NY 2 Plasma Physics Laboratory, Princeton University, Princeton, NJ 3 Los Alamos National Laboratory, Los Alamos, NM 4 Nova Photonics, Inc., Princeton, NJ 5 University of Wisconsin, Madison, WI v1.8

2. NSTX SAS – APS DPP ‘05 Wall stabilized plasmas allow RWM studies Operation with  N /  N no-wall > 1.5 at highest  N for pulse >>  wall Past experiments showed  Unstable resistive wall mode (RWM) with toroidal mode number up to 3  Critical rotation frequency profile ~ 1/q 2  Resonant field amplification (RFA) increases with increasing  N NN DCON WW 0 10 20 0.60.70.50.40.30.20.10.0 t(s) n=1 (no-wall) n=1 (wall) 112402 wall stabilized core plasma rotation (x10 kHz) New capabilities continue the study of RFA and RWM stability

3. NSTX SAS – APS DPP ‘05 Non-axisymmetric coils for advanced RWM experiments Upper/lower RWM Sensor Arrays Six coils spanning midplane  n = 1 - 3 DC or AC standing waves  Toroidally propagating fields Experiments address  RWM dynamics at marginal stability using modulated n = 3 standing wave fields  Resonant field amplification using toroidally propagating n = 1 fields  Triggering of other MHD using co- vs. counter- rotating applied fields with changing frequency Non-axisymmetric field coils (ex-vessel)

4. NSTX SAS – APS DPP ‘05 Modulated rotation cycles stability  “anti-lock” braking of plasma rotation  n = 1 rotates in direction of flow  n = 2 not rotating with plasma flow n=3 standing wave field probes RWM marginal stability Plasma rotation I RWM2 (kA)  Bp(n=1 )  Bp(n=2 )  Bp(n=3 )   /2  (kHz) |  B pu |(n=1) (G) |  B pu |(n=2) (G) |  B pu |(n=3) (G) NN |  B pl |(n=1) (G) 1.01.21.4 R(m)   /2  (kHz) 0 10 20 30 40 t(s) 0.416 0.426 0.436 0.446 0.456 cyclic R = 1.35m  N no-wall (DCON)

5. NSTX SAS – APS DPP ‘05 growthrotation damping RWM n=1 component shows growth and rotation  Growth rate: 268 s -1  Rotation rate (avg. one cycle): 48Hz  RWM possibly triggers rapidly rotating mode n=2 growth / phase change during n=1 damping / spin-up Last cycle before  collapse shows RWM dynamics  Bp(n=1 )  Bp(n=2 )  Bp(n=3 )  Bp(n=1 ) |  B pl |(n=1) (G) |  B pu |(n=2) (G) |  B pu |(n=3) (G) NN |  B pu |(n=1) (G)  B z (G) spin-up  N no-wall (DCON)

6. NSTX SAS – APS DPP ‘05 RWM growth/rotation modeled with VALEN consistent with measurement Boozer RWM model in VALEN code  Plasma rotation Normalized plasma torque      RWM rotation Calibrate code using NSTX data  RWM rotation measured near marginal stability  RWM growth rate measured when edge   reduced Unstable Stable  N ~ 4.7  N ~ 5.47  N ~ 5.61  N ~ 6.4  RWM (1/s),  RWM (rad/s) 10 -3 10 -2 10 -1 10 1 10 2 10 3 10 4 116178 (marginal stability  N = 5.5) 116178 (unstable - reduced   )  ~ plasma rotation Solid line: RWM growth rate Dashed: RWM rotation rate measured  

7. NSTX SAS – APS DPP ‘05 RFA magnitude dependent on applied field frequency Applied field phased to create traveling wave in toroidal direction Peak in RFA shifted in the direction of plasma flow  Peak near 30 Hz  Expected by RWM theory / experiment Observed in DIII-D (H. Reimerdes, NF 45 (2005) 368.) RFA magnitude (n = 1) Applied frequency (Hz) Direction of plasma flow RFA = B applied B plasma Counter plasma flow Shifted peak Single mode model fit

8. NSTX SAS – APS DPP ‘05 Direction of applied n=1 traveling wave alters RWM stability Field propagates with flowField propagates against flow B p n=1 (G) Phase Bp n=1 I RWM (kA) 116940116941 0.25 0.35 0.45 0.55 Time (s) 0.25 0.35 0.45 0.55 Time (s) 360 240 120 0 80 60 40 20 0 1 0.5 0 -0.5 Stronger RFA with co-flow field RWM not destabilized (co-flow)(counter-flow) Weaker RFA with counter-flow field Unstable RWM Larger RFA RWM smaller RFA

9. NSTX SAS – APS DPP ‘05 Unstable RWM avoided when rotation maintained  Applied field in the direction of plasma flow:  RFA increases and rotation damps  n=1 internal mode triggered  Rigid rotor rotation profile; beta recovers  Applied field against the plasma flow:  RWM grows  Rapid, complete rotation and beta collapse 0.0 0.2 0.4 0.6 0.8 Time (s) 0.9 1.1 1.3 1.5 R (m) 40 30 20 10 0 116940 116941 F t (kHz) 0.9 1.1 1.3 1.5 R (m) (applied field co-flow)(counter-flow) co- counter co- counter co-  N no-wall (DCON) core rotation

10. NSTX SAS – APS DPP ‘05 New non-axisymmetric coils have enabled advanced RWM experiments Precise modification of the plasma rotation profile allows control of RWM near marginal stability RWM rotation near marginal stability allows comparison to theory (Boozer model) Resonant field amplification depends on applied field frequency and propagation with respect to plasma flow Direction of applied field propagation can modify RWM evolution; triggering of other MHD modes Plasma rotation profile control / rotation damping physics (Zhu GO3.00005 – next talk) Critical rotation profile for RWM stability (Sontag RP1.00021 Thurs.)  Rotation on higher order rational surfaces not required for stability