XP407: Passive Stabilization Physics of the RWM in High b N ST Plasmas – 4/13/04

1. XP407: Passive Stabilization Physics of the RWM in High bN ST Plasmas – 4/13/04 • Goals • Define RWM stability boundary in (Vf, bN) space • Use past XP experience and new theories to determine boundary • Present theory and NSTX data suggests: Wcrit/wA ~ 1/4q2 • Define the operating space and criteria for active stabilization • Measure n > 1 resistive wall modes • Present high bN 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 bN ST plasmas to compare to theory • Critical rotation frequency: XP by A. Sontag • Rotation damping physics: XP408 by W. Zhu

2. Stability boundary probed and modes observed • q and pressure peaking variation were main techniques • q variation through slow Bt reduction • Bt reduction placed discharge in stabilized high wf/wA region • Bt 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 btargets reached at high toroidal rotation speed • wf/wA = 0.48; bN = 6.7 (highest value at constant Ip); bt = 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. Past experiments show Wcrit depends on q • Chu/Bondeson critical rotation Wcrit/wA = 1/(4q2) applies across the profile in CY02 plasmas

4. Approaches to probing (Vf, bN) stability boundary • Rapidly drive across increasing growth rate contours • This is the standard approach • Destabilize RWM by increasing Wcrit • Decrease Bt slowly in stable discharge • Stabilize RWM once triggered • Decrease Wcrit by increasing Bt slowly in unstable discharge • NBI step-down after destabilization • Drop out of H mode with bN >> bNNo-wall • Vary timing of NBI and Bt variation to change position in (Vf, bN ) space

5. Schematic approach to probing stability boundary Unstable bN wall drop bN no-wall 4 increased q bN decreased q 2 Unstable • Technique 3 was most extensively used • Technique 4 occurred as pressure peaking increased at lower Bt 1 3 bN no-wall w/wA

6. XP407 Passive RWM - Waveforms: 4/13/04 Use setup shot 111957 LSN • Aspect ratio in 110184 increased in time – vary A in similar way Plasma current Toroidal field 6 X10 4.5 1.0 Optional delayed Ip ramp 4.0 Amps 0.5 3.5 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 6 Default NBI timing Run NBI at max power Source C (start with this source delayed) 4 (arb) Source A 2 Source B 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Time (Seconds)

7. XP407 Passive RWM - Run plan: 4/13/04 • Scan boundary of passive stabilization space (Ff, bN) Task Number of Shots A) Restore shot 111957, k ~ 2.1 LSN (or newer similar target) (Ip ramped to 0.9 MA Bt = 4.4 kG (or above), k =2.1, li ~ 0.65) (i) 3 NBI sources (rerun 111957 with 3rd source at t = 0.4s) 1 (ii) 2 NBI + delayed 1 NBI if collapse occurs before 0.5 s 2 B) Use toroidal field ramp to influence rotation evolution (i) Bt = 4.4 kG, reduced to Bt = 3.5 kG, vary start time of ramp 3 (ii) Bt = 4.4 kG, reduced to Bt ~ 4.0 kG, vary start time of ramp 3 (iii) choose best Bt ramp, vary start time (2 or 3 unique times) 4 (iv) Bt ~ 4.0 kG, reproduce collapse time, ramp Bt up to delay crash 4 C) Vary NBI timing to best cover (Ff, bN) space (i) 3 NBI sources with source step-down / vary TS laser timing 5 D) Take plasma out of H-mode (ramp PF2) for high bN / bNNo-wall4 Total shots: 26

8. 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. Global rotation collapse when core n=1 is triggered rotation profile evolution core n=1 triggered, RWM locked 440 Hz odd-n observed PRELIMINARY rapid global collapse • 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 Vf = 1kHz (> 440 Hz) Radius (cm)

10. Slower collapse – RWM near marginal stability? rotation profile evolution core n=1 triggered, RWM locks PRELIMINARY 370 Hz odd-n observed • 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 Radius (cm)

11. RWM sensor data taken during XP407 lower array dBp = 10G upper array dBp = 4G • Detail of RWM slow rotation, mode locking underway J. Menard A. Sontag