RESISTIVE WALL MODE STABILIZATION RESEARCH ON DIII D STATUS AND RECENT RESULTS

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1 RESISTIVE WALL MODE STABILIZATION RESEARCH ON STATUS AND RECENT RESULTS by A.M. Garofalo1 in collaboration with J. Bialek,1 M.S. Chance,2 M.S. Chu,3 T.H. Jensen,3 L.C. Johnson,2 R.J. La Haye,3 G.A. Navratil,1 M. Okabayashi,2 J.T. Scoville,3 E.J. Strait,3 and A.D. Turnbull3 1Columbia University, New York, New York. 2Princeton University, Princeton, New Jersey. 3General Atomics, San Diego, California. April 16, 21 Columbia University 77 1/AMG/wj

2 TWO STABILIZATION APPROACHES HAVE BEEN EXPLORED ON Rotational Stabilization Stable window exists when Ω >> Ω c Ω c a few percent of Alfvén transit frequency Growth Rate (γ) τ Α 1 RWM Regime (γ< ) Ideal Kink Regime Magnetic Feedback Stabilization Slow growth time makes feedback practical τ W 1 Increasing Rotation Improves Plasma Surface Wall Radius r c Ideal Kink Limit Originally proposed by Bondeson and D. Ward /jy

3 OUTLINE Rotational stabilization Rotation slowdown above no-wall beta limit 3 Unstable RWM and torque balance 3 Stable RWM and error field amplification Recent experimental results Magnetic feedback stabilization 1-D feedback model and comparison with experimental results 2-D model versus experiment 3-D model versus experiment Recent sensor upgrades and experimental results Summary Future plans 77 1/AMG/wj

4 EARLIER EXPERIMENTS SHOWED PLASMA ROTATION SLOWDOWN AT β N EXCEEDING NO WALL LIMIT 2 dω (ρ~.5) dt (khz/s) H mode ACCELERATION H mode What causes the slowdown? H mode ELMing H mode ELMing ELMing no-wall 1.5 E w = β N /β N DECELERATION 77-1/jy

5 INCREASING NEUTRAL BEAM TORQUE ONLY DELAYS INSTABILITY Rotation threshold shown by varying neutral beam torque Neutral beam torque increased by reducing voltage at constant power Greater torque gives faster initial rotation, identical profiles at transition 3 2 I p β N # of Neutral Beam Sources (15 rad/s) Plasma Toroidal Rotation t=12 ms 1 (gauss) (km/s) n=1 δbr at wall Plasma Toroidal Rotation ρ ~ Time (ms) (15 rad/s) Plasma Toroidal Rotation t=1325 ms t=137 ms ρ 77-1/jy

6 NONLINEAR MODEL ALLOWS SUDDEN CHANGES IN PLASMA ROTATION FREQUENCY AND MODE GROWTH RATES Plasma rotation Ω from torque balance is multivalued (depends on mode rotation) [C. G. Gimblett and R. J. Hastie, Phys. Plasmas 7, 258 (2)] Ω Ω UNSTABLE with slow growth rate (γ «1/τ w ) Growth rate is small (γ << τ 1 ) on the upper branch. Rotation slowly decreases as mode amplitude increases Ω 2 Ω 1 "forbidden" band of plasma rotation UNSTABLE with growth rate γ ~ 1/τ w δb r At the upper knee (if outside the stable window) torque balance is lost, and the rotation frequency drops to the lower branch Growth rate is much larger (γ ~ τ 1 ) on the lower branch Similar to "forbidden" frequency bands for tearing modes [D. Gates and T. Hender, Nucl. Fusion 36, 273 (1996)] Ω = plasma rotation frequency of unperturbed equilibrium 77-1/jy

7 MODEL IS QUALITATIVELY CONSISTENT WITH TRAJECTORY OF WALL-STABILIZED DISCHARGES Evolution at high beta has three phases: Slow mode growth with constant or slowly decreasing plasma rotation More rapid deceleration of rotation as slow mode growth continues Rapid mode growth v φ (km/s) at ρ = SHOT 9782, ms β exceeds β no-wall crit Rotation threshold for RWM in experiment is significantly higher than in Gimblett-Hastie model δb r (G) 77-1/jy

8 DISCOVERY OF ERROR FIELD AMPLIFICATION CAN EXPLAIN PLASMA ROTATION SLOWDOWN ABOVE NO-WALL β LIMIT Merginally stable RWM can be excited to finite amplitude by resonant, un-corrected error field [A.H. Boozer, Phys. Rev. Lett. (21)] Incremental external error field pulsed on and off in discharges with β N well below and close to the no wall limit Larger n=1 plasma response measured at higher β N (Gauss) (km/s) (Gauss) β N B Error Field at q=2 n=1 δb r at Wall (plasma response only) Plasma Toroidal Rotation (ρ~.4) Time (ms) 77-1/jy

9 RATE OF DECAY OF PLASMA ROTATION REDUCED WITH REDUCED ERROR FIELD Previous error correction algorithum obsolete when β N > β N no wall Onset of n=1 RWM delayed to rotation 6 khz at q=2 β N - β N no wall increases with delay of RWM, eventual γτw is larger C Coil79 (A) (khz) Reduced static n=1 error field n=1 δb r (gauss) β N Critical Rotation for onset of RWM No wall limit (approx.) Time (ms) 77-1/jy

10 β N MAINTAINED 5% ABOVE CALCULATED n=1 NO-WALL LIMIT FOR ~1.5 SECONDS Error field minimization and increased injected power allow complete, quasi-stationary RWM stabilization Ip (A) β N Plasma Toroidal Rotation (Km/s) Mirnov Amplitude (T/s) n=1 δbr (gauss) P beam (kw) β N no wall ~ 2.4 l i Time (ms) 77-1/jy

11 ERROR CORRECTION WAVEFORMS SUGGESTED BY FEEDBACK USING INTERNAL POLOIDAL FIELD SENSORS ALLOW ROTATIONAL STABILIZATION UP TO β N =2 β N no wall I p (MA) p inj *1 (kw) betan 2.4*l i Ideal limit with wall? 1. Approximate no-wall limit -Eigenvalue (No Wall) Ideal MHD n=1 eigenvalue (~ g 2 ) with no wall.1 Stable eigenvalues Time (ms)

12 BRAKING EXPERIMENT AT DIFFERENT βs GIVES EXPERIMENTAL BENCHMARKING OF CALCULATED NO-WALL LIMIT Error field correction turned off at β N just above and just below the calculated no-wall limit RWM strongly stable below β N no wall -> small error field drag amplification RWM weakly stable with rotation above β N no wall -> large amplification C-coil current (A) β N β N no wall Plasma Toroidal Rotation (km/s) n=1 δbr (gauss) Time (ms) 77-1/jy

13 SAME PHYSICS OF ERROR FIELD-RWM INTERACTION OBSERVED FOR PLASMAS WITH β N NO-WALL ~4li OR ~2.4li C-coil current (A) β N Plasma Toroidal Rotation (km/s) n=1 δbr (gauss) β N no wall ~ 4 l i /jy

14 RWM FEEDBACK EXPERIMENT ON Six midplane coils (C-Coil) Six Sensors } Connected in anti-parallel for n=1 control Three Power supplies dc - 1 Hz, 5 ka Shared with error field correction Vacuum Vessel τ w 5 ms o Sensor Loops Active Coil (C-Coil) x Active Coil (C-Coil) 77-1 jy

15 1-D FEEDBACK MODEL GIVES QUANTITATIVE PREDICTIONS OF FEEDBACK DYNAMICS Symmetry assuption: Toroidal / y = ik ; Poloidal / z = ; φ(x,y) = φ(x)eiky Dispersion relation: 1 - G Cntrl = G f comp G 1 + iωτ f α = iωτw α = 1 G P + G D iωτd G + i 1 + iωτ p 1 + iωτd 1 + iωτi e 2kD 1 e 2kD G = G Cntrl G Hdw G Hdw Ω = 1 Ω1 + i ω x Ω 2 Ω 2 + i Plasma properties described in one number: D = distance from resistive wall at which ideal wall gives marginal stability Wall properties described in one number: τ w = resistive wall time constant Linear electronics Exact modeling of proportional, derivative, integral gains for smart shell, mode control, fake rotating shell, etc. Realistic model of amplifier + coils frequency response function (Ω 1, Ω 2 determined from fit to measurements of the amplifier + coil transfer function) Feedback problem reduced to finding roots of 7th order polynomial with complex coefficients Model successfully benchmarked against experiments ω 77 1/AMG/wj

16 EXPERIMENTAL PARAMETER SCAN SHOWS QUANTITATIVE AGREEMENT WITH 1-D FEEDBACK MODEL 1 2 Diamagnetic Flux (mv s) Gd scan 1415 / 1418 / 1411 G d = 11 G p = 5 G i = G d = 14 G p = 5 G i = 3 No Feedback Time (ms) 155 ω (Rad/s) Derivative gain is stabilizing Gd Scan 14 G p = Stable γ (1/s) Plasma Mode Vacuum Mode Unstable /jy

17 EXPERIMENTAL PARAMETER SCAN SHOWS QUANTITATIVE AGREEMENT WITH 1-D FEEDBACK MODEL 1 2 Diamagnetic Flux (mv s) Gi Scan G d = 14 G p = 5 G i = 31 τ i = 1 ms Gd scan / 1415 / 1418 / 1411 G d = 11 G p = 5 G i = G d = 14 G p = 5 G i = ω (Rad/s) 3 No Feedback Time (ms) Derivative gain is stabilizing Gd Scan 14 G p = Stable γ (1/s) Plasma Mode Vacuum Mode Unstable The integral gain is destabilizing G p = 5, G d = 14 Gi Scan Stable τ i = 1 ms γ (1/s) Unstable /jy

18 EXPERIMENTAL PARAMETER SCAN SHOWS QUANTITATIVE AGREEMENT WITH 1-D FEEDBACK MODEL 1 2 Diamagnetic Flux (mv s) Gi Scan G d = 14 G p = 5 G i = 31 τ i = 1 ms τ i = 1 ms / / 1415 / 1418 / 1411 Gd scan G d = 11 G p = 5 G i = G d = 14 G p = 5 G i = ω (Rad/s) 3 No Feedback Time (ms) Derivative gain is stabilizing Gd Scan 14 G p = Stable γ (1/s) Plasma Mode Vacuum Mode Unstable The integral gain is destabilizing G p = 5, G d = 14 Gi Scan 31 Stable τ i = 1 ms τ i = 1 ms γ (1/s) 31 Unstable /jy

19 COUPLED GATO-VACUUM CODES PREDICT MODE STRUCTURE IS NOT CHANGED SIGNIFICANTLY WITH FEEDBACK Self-consistent 2-D MHD calculation including feedback field Coil Coverage Eddy Pattern on the Wall Without Feedback 1. Internal Radial Displacement on Midplane Without Feedback ξ r With Feedback With Feedback o o Toroidal Direction 36. ρ. 1. With midplane coil only, the total eddy current pattern was not changed significatly Internal mode structure was unchanged, except slightly peaked with feedback 77-1/jy

20 EXPERIMENT SHOWS MODE STRUCTURE OUTSIDE THE WALL IS NOT CHANGED SIGNIFICANTLY WITH/WITHOUT FEEDBACK Toroidal Array Three Toroidal Arrays of Saddle Loops Provide Poloidal Mode Structure Upper Array Midplane Array 1 Lower Array Time (ms) Mode Structure Relative to Midplane θ = θ = Qualitatively consistent with VACUUM/GATO prediction Without Feedback (13353) With Feedback (13353) Relative Toroidal Angle θ = Supports rigid displacement assumption used in lumped parameter formulation and 3D feedback codes 268-/jy

21 VALEN 3D FEEDBACK CONTROL MODEL PREDICTS IMPROVED β LIMIT WITH EXISTING 6 COIL SET Existing 6 coil set can increase RWM stability limit by ~ 2% towards ideal wall β N limit for basic smart shell control algorithm Three control system improvements: shorter sensor coils internal sensor coils internal Bp sensors Base Six-Element C-Coil can reach 5% towards ideal wall beta using internal Bp sensor Growth Rate (s -1 ) No Feedback Base C-Coil 1 4 ideal kink resistive wall mode Short, internal Br sensors Internal Bp sensors β N - β N no-wall β N ideal-wall - β N no-wall ideal wall limit 77-1/jy

22 (G) GATING FEEDBACK OFF DEMONSTRATES STABILIZATION AT β N JUST ABOVE STABILITY BOUNDARY 2 1 Large instability in comparison case without feedback n=1 δb r (G) without Feedback with Feedback β N Time (ms) Feedback Gain Relative Displacement (SXR) (cm) Feedback Current (C79) (ka) with Feedback without Feedback ρ= Time (ms) Rapid RWM growth when feedback is switched off Prompt suppression of RWM when feedback resumes 77-1/jy

23 NEW RWM SENSORS AVAILABLE FOR FY1 FEEDBACK EXPERIMENTS New saddle loops inside the vessel measure the radial field closer to plasma New Mirnov probes increase to 4 the number of diametrically opposed measurements of the poloidal field inside the vessel C Coil External δb r Internal δb r Internal B r Loops o Internal δb p Internal B p Loops External B r Loops C Coil x 325-/AMG/jy

24 PLASMA DISPLACEMENTS DEDUCED FROM X-RAY DATA AGREE WITH MAGNETIC PERTURBATIONS MEASURED BY δb r AND δb p SENSORS X-RAY INTENSITY (arb) º Camera 195º Camera ρ =.29 ρ =.42 ρ =.55 R(195º) R(45º) (cm) ρ =.29 ρ =.42 ρ =.55 #16179 MODE AMPLITUDE (gauss) δb p δb r x TIME (ms) db (gauss) δb p (195º) δb p (45º) [δb r (285º) δb r (135º)] x TIME (ms) 77-1/jy

25 INTERNAL LOOPS ARE MORE EFFECTIVE THAN EXTERNAL LOOPS FOR STABILIZATION OF RWM; CONSISTENT WITH VALEN PREDICTIONS β N *1 NO FEEDBACK Internal B r Loops o 1 n=1 δbr (gauss) External B r Loops C-Coil β N *1 FEEDBACK WITH EXTERNAL SENSOR LOOPS x 2 1 n=1 δbr (gauss) β N *1 FEEDBACK WITH INTERNAL SENSOR LOOPS 2 1 n=1 δbr (gauss) Time (ms) 77-1/jy

26 SUMMARY RWM and plasma rotation Discovery of error field amplification by marginally stable RWM, suggested by theory, provides mechanism for rotation slowdown above no-wall β limit Minimizing error field enables demonstration of rotational stabilization at β N ~ 5% above β N no-wall RWM detection on SXR and magnetics in excellent agreement RWM feedback modeling 1-D feedback simulation code describes feedback system dynamics GATO-VACUUM 2-D codes predict little effect of feedback on plasma eigenfunction VALEN 3-D code used for optimization studies of feedback configurations 3 Predicts large gain in stable beta with internal RWM sensors RWM feedback experiments no-wall Clear demonstration of RWM suppression by feedback for β N just above β N Observation of rigid RWM structure when feedback is applied Comparison of different sensors agrees qualitatively with predictions 77 1/AMG/wj

27 EXTENDED 18 COIL SET CAN INCREASE RWM STABILITY LIMIT TO 8% OF INCREMENTAL PERFORMANCE OF IDEAL WALL Active coil can be extended with 6 coils above and 6 coils below existing C-coil Extended 18-element C-coil can reach 8% towards ideal wall beta limit using internal B p sensors Expanded Coil Set (22) Growth Rate (s 1) Existing six Coils No Feedback Base C-Coil 1 4 Ideal kink 1 Resistive wall mode 18-coil with short, internal B r sensors 18-coil with internal B p sensors Ideal wall limit no-wall β N β N β N ideal-wall no-wall β N 77 1/AMG/wj

28 FUTURE PLANS Short-range plans Explore correction of error field amplification by feedback control Continue comparison of feedback performance with different sensor locations 3 External B r, internal B r, internal B p Quantitative benchmarking of VALEN versus experiment Finalize design of 18-element active coil set Begin integration of RWM control with advanced tokamak scenarios Long-range plans Install C coil extension Compare 6-coil versus 18-coil control system Extend advanced tokamak operating range through RWM control 77 1/AMG/wj

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