1. NSTX S. A. Sabbagh XP407: Passive Stabilization Physics of the RWM in High  N ST Plasmas – 4/13/04  Goals  Define RWM stability boundary in (V ,  N ) space Use past XP experience and new theories to determine boundary  Present theory and NSTX data suggests:  crit /  A ~ 1/4q 2 Define the operating space and criteria for active stabilization  Measure n > 1 resistive wall modes Present high  N plasmas are computed to be n = 2 unstable Compare to theoretical computation of n > 1 stability (structure?) Look for finite mode frequency  Set up conditions to examine physics of RWM passive stabilization in high  N ST plasmas to compare to theory Critical rotation frequency: XP by A. Sontag Rotation damping physics: XP408 by W. Zhu

2. NSTX S. A. Sabbagh Stability boundary probed and modes observed  q and pressure peaking variation were main techniques  q variation through slow B t reduction  B t reduction placed discharge in stabilized high   /  A region  B t reduction yielded variation of pressure peaking  Low frequency 370Hz mode observed before mode lock  Global collapse in rotation profile observed as in past RWM XPs  High  targets reached at high toroidal rotation speed    /  A = 0.48;  N = 6.7 (highest value at constant I p );  t = 38%  New diagnostic capabilities used to measure RWM  Internal locked mode sensor array shows n=1 ~ 10-20G; n=2 ~ 5G  51 channel, 10 ms resolution CHERS yields unprecedented detail detail of global rotation collapse  USXR data taken at two toroidal positions (not yet examined)

3. NSTX S. A. Sabbagh Past experiments show  crit depends on q  Chu/Bondeson critical rotation  crit /  A = 1/(4q 2 ) applies across the profile in CY02 plasmas

4. NSTX S. A. Sabbagh Approaches to probing (V ,  N ) stability boundary  Rapidly drive across increasing growth rate contours  This is the standard approach  Destabilize RWM by increasing  crit  Decrease B t slowly in stable discharge  Stabilize RWM once triggered  Decrease  crit by increasing B t slowly in unstable discharge  NBI step-down after destabilization  Drop out of H mode with  N >>  NNo-wall  Vary timing of NBI and B t variation to change position in (V ,  N ) space

5. NSTX S. A. Sabbagh Schematic approach to probing stability boundary  Technique 3 was most extensively used  Technique 4 occurred as pressure peaking increased at lower B t NN /A/A Unstable  N wall  N no-wall decreased q increased q 1 2 3 4 drop  N no-wall

6. NSTX S. A. Sabbagh XP407 Passive RWM - Waveforms: 4/13/04  Aspect ratio in 110184 increased in time – vary A in similar way 6 00.10.20.30.40.5 0 1.0 X10 Amps 2 4 6 (arb) Time (Seconds) Source B Source C (start with this source delayed) Default NBI timing Plasma current 00.10.20.30.40.5 0 Source A 4.5 Run NBI at max power 0.60.7 0.60.7 Use setup shot 111957 LSN 4.0 3.5 Toroidal field Optional delayed I p ramp

7. NSTX S. A. Sabbagh XP407 Passive RWM - Run plan: 4/13/04  Scan boundary of passive stabilization space (F ,  N ) TaskNumber of Shots A) Restore shot 111957,  ~ 2.1 LSN (or newer similar target) (I p ramped to 0.9 MA B t = 4.4 kG (or above),  =2.1, l i ~ 0.65) (i) 3 NBI sources (rerun 111957 with 3 rd source at t = 0.4s)1 (ii) 2 NBI + delayed 1 NBI if collapse occurs before 0.5 s2 B) Use toroidal field ramp to influence rotation evolution (i) B t = 4.4 kG, reduced to B t = 3.5 kG, vary start time of ramp 3 (ii) B t = 4.4 kG, reduced to B t ~ 4.0 kG, vary start time of ramp 3 (iii) choose best B t ramp, vary start time (2 or 3 unique times)4 (iv) B t ~ 4.0 kG, reproduce collapse time, ramp B t up to delay crash4 C) Vary NBI timing to best cover (F ,  N ) space (i) 3 NBI sources with source step-down/ vary TS laser timing5 D) Take plasma out of H-mode (ramp PF2) for high  N /  NNo-wall 4 Total shots: 26

8. NSTX S. A. Sabbagh RWM mode locking and slow phase rotation observed  Low frequency ~ 440Hz precursor to mode lock  Mode locks at t=0.49s  Rotating modes (typically islands) are clearly rotating at this time  Very slow rotation of n=1 phase observed after lock  Apparent f ~ 50 Hz

9. NSTX S. A. Sabbagh Global rotation collapse when core n=1 is triggered  Global rotation collapse when core n=1 is triggered  n=1 RWM appears to trigger core n=1 mode  RWM locks at least 30 ms before islands eventually lock  No apparent momentum transfer, which would be observed if braking were due to electromagnetic torque at island rotation profile evolution Radius (cm) rapid global collapse 440 Hz odd-n observed core n=1 triggered, RWM locked V  = 1kHz (> 440 Hz) PRELIMINARY

10. NSTX S. A. Sabbagh Slower collapse – RWM near marginal stability?  RWM rotation frequency ~ 370 Hz in this case  Mode locks/unlocks before plasma rotation terminates  Momentum transfer across rational surface observed before insland lock at 0.51s  RWM “marginally stable” near 0.5s, collapses plasma again and locks at 0.52s rotation profile evolution Radius (cm) PRELIMINARY 370 Hz odd-n observed core n=1 triggered, RWM locks

11. NSTX S. A. Sabbagh RWM sensor data taken during XP407  Detail of RWM slow rotation, mode locking underway J. Menard A. Sontag  B p = 4G  B p = 10G upper array lower array