RWM Control in FIRE and ITER - PDF Free Download

RWM Control in FIRE and ITER Gerald A. Navratil with Jim Bialek, Allen Boozer & Oksana Katsuro-Hopkins MHD Mode Control Workshop University of Texas-Austin 3-5 November, 2003

OUTLINE REVIEW OF VALEN MODEL BENCHMARKING MARS & VALEN/DCON + MAPPING OF S TO b N : IDEAL WALL BETA LIMIT + TRANSITION TO IDEAL BRANCH IN DISPERSION RELATION CRITICAL ISSUES IN RWM CONTROL DESIGN + ITER PASSIVE STABILIZER PERFORMANCE: IMPORTANT ROLE OF THE BLANKET MODULES + CONTROL COIL-PLASMA-STABILIZER COUPLING OPTIMIZATION IN FIRE AND ITER + POWER REQUIREMENTS: INITIAL VALUE SIMULATIONS AND EFFECTS OF NOISE

VALEN combines 3 capabilities see PoP 8 (5), 2170 (2001) Bialek J., et al. Unstable Plasma Model ( PoP Boozer 98) General 3D finite element electromagnetic code Arbitrary sensors, arbitrary control coils, and most common feedback logic (smart shell and mode control) Z X Y

VALEN Model All conducting structure, control coils and sensors, are represented by a finite element integral formulation, we have a matrix circuit equation: i.e., L {}= V(t) [ ] İ {}+ R [ ] I { } Unstable Plasma mode is modeled as a special circuit equation. We start with a plasma equilibrium, use DCON without any conducting walls, to obtain δw, and the magnetic perturbation represents the plasma instability. The instability is represented via a normalized mode strength s = δw LI 2 /2 [ L'(s) ]{ İ' }+ [ R' ]{ I' }= { V'(t) } ( ), the equations are now

VALEN predicts growth rate for plasma instability as function of the instability strength parameter 's' 's' is a normalized mode energy s = δw LI 2 /2 ( ) computed dispersion relation of growth rate vs. 's' is an eigenvalue calculation 10 6 ideal branch 10 5 growth rate (1/sec) 10 4 10 3 10 2 resistive branch determined by geometry & resistance of structure difference produced by coupling to conducting structure 10 1 10 0 10-2 10-1 normalized mode energy s 10 0

ITER Double Wall Vacuum Vessel Configuration 6 4 2 z 0-2 -4-6 0 2 4 6 8 10 12 r The ITER vacuum vessel is modeled as a double wall configuration with time constants for low order modes in range 0.15 s to about 0.3 s

DCON Calculation of ITER RWM: B-normal vs Poloidal Angle 1 Bn#1@0 0 Bn#1@0-1 0 2 4 6 8 10 12 14 16 18 arc length Use B-normal to Compute Equivalent Plasma Surface Current

RWM Induces Stabilizing Image Currents Largely on the Inner Vessel Wall Vacuum Vessel Modeled with and without wall penetrations.

ITER Double Vacuum Vessel Passive RWM Dispersion Relation 10 6 10 5 growth rate (1/s) 10 4 10 3 10 2 10 1 no blankets no ports g-passive no ports 3.0 10 0 10-1 10-2 10-1 10 0 s - normalized mode energy Shows usual transition from RWM to Ideal Branch at s~0.1

DCON Benchmark with Series of Conformal Wall ITER Equilibria EQDSK_512x512_a(series) 6 beta-n = 2.546 beta-n = 2.841 4 beta-n = 3.142 beta-n = 3.450 2 beta-n = 3.764 Z [ m ] 0 plasma ITER Inner Vessel ITER Blanket -2-4 -6 2 4 6 8 10 R [ m ] Use series of ITER conformal wall equilibria as input into VALEN

Benchmark Calibration of VALEN with DCON 10 6 10 5 10 4 growth rate [ 1/s ] 10 3 10 2 10 1 10 0 10-1 10-2 10-3 10-4 10-5 10-6 10-7 10-2 10-1 beta-n = 2.546 beta-n = 2.841 beta-n = 3.142 beta-n = 3.450 beta-n = 3.764 g a1.4 36x36 g a1.3 g a1.2 g a1.1 36x36 g a1.0 10 0 s DCON ideal b N limit found for series of conformal wall ITER plasmas. VALEN ideal s limit found for same conformal wall series. Use to calibrate b N vs s

Use DCON Computation of dw to Calibrate s to b N 5.0 based on conformal wall VALEN calcs based on PET equilibria beta scan & δw calibration of 's' beta-n 4.0 based on Bondeson equilibia beta scan & δw calibration of 's' 3.0 2.0-0.2 0.0 0.2 s 0.4 0.6 0.8 Error found in DCON dw to VALEN s conversion! This NEW calibration used to replot passive response.

[From ITPA Meeting July 2003] Physics of Ideal Kink Transition Seems Absent in Liu, et al. 10 6 10 5 Without Blanket Modules growth rate [ 1 / s ] 10 4 10 3 10 2 10 1 10 0 10-1 2.0 3.0 4.0 5.0 beta-n(new) Note absence of Ideal Kink Branch Transition when C b ~ 1 In Liu, et al. t wall ~ 0.188 s so g at C b ~1 is between 53 to 120 s -1 In VALEN modeling g at C b ~1 is between 1000 to 10 4 s -1 Growth rate disparity consistent with g t wall in Liu, et al. too small for claimed values of C b

VALEN vs MARS RWM Benchmarking growth rate [1/s ] 10 6 10 5 10 4 10 3 10 2 10 1 10 0 2.0 double walled ITER VV only passive structure VALEN previous s-to-betan map 2.5 3.0 original MARS data (est) beta-n 3.5 new MARS data (est) 4.0 4.5 VALEN new s to betan map est MARS gamma-ideal tau-a = 1.e-6 to 3.e-6 s passive 3.764 passive 3.764 g no blanket gamma gamma (3) gamma(1) New MARS results and benchmarked VALEN results agree!

Include ITER Ports & Blanket Modules in Passive RWM Stabilization Model Modeled as set of isolated plates above the inner vessel wall. Each blanket module adjusted to have 9 ms radial field penetration time constant.

ITER Ports Cause Small Reduction in Ideal Limit 10 6 no blankets & no ports 10 5 growth rate [1/s] 10 4 10 3 10 2 10 1 no blankets 45 ports 10 0 10-1 2.0 3.0 4.0 beta-n(new) No wall b N limit is 2.4; Ideal Wall Limit Drops to b N ~ 3.3 5.0

VALEN Model of ITER Double Wall Vessel and Blanket Modules Z Y X

ITER Blanket Opens Up Large AT Regime 10 6 no blankets & no ports 10 5 growth rate [ 1/s ] 10 4 10 3 10 2 10 1 no blankets 45 ports with blankets 45 ports 10 0 10-1 2.0 3.0 4.0 beta-n(new) No wall b N limit is 2.4; Ideal Wall Limit With Blanket is 4.9! 5.0

Basic Feedback Control Loop with Voltage Amplifiers and Sensors Uncoupled to Control Coils Feedback Volts/Weber Amplifier: Gp and Gd V Control Coils B-radial Plasma ψ Response RWM Bp Sensors no-coupling

ITER Base Case Feedback Control System Geometry 6 4 2 z 0-2 -4-6 0 2 4 6 8 10 12 r The ITER vacuum vessel is modeled as a double wall configuration using design data provided by Gribov, with feedback control provided by 3 n=1 pairs of external control coils on the mid-plane.

VALEN Model of ITER Vessel and Control Coils: Base Case Feedback Control System Vacuum Vessel Modeled with and without wall penetrations.

ITER Basic Coils: Scan of Proportional & Derivative Gain 10 6 10 5 growth rate [ 1 / s ] 10 4 10 3 10 2 10 1 10 0 10-1 g passive 10^8 g 10^8 10^8 g 10^8 10^9 g 10^9 10^10 g nbl_3.0 stable < 2.72 stable < 2.94 stable < 2.97 10-2 2.0 3.0 4.0 5.0 beta-n (new) Feedback Saturates at b N ~ 2.97 for G p =10 8 V/W & G d =10 9 V/V G p =10 8 V/W is Liu s K i =0.32 and G d =10 9 V/V is Liu s K p =15.6

ITER Basic Coils: Use Liu & Bondeson Gain Parameters 10 6 10 5 growth rate [ 1 / s ] 10 4 10 3 10 2 10 1 10 0 g passive nbl_3.0 g L&B stable < 2.78 10-1 10-2 2.0 3.0 4.0 5.0 beta-n Liu uses V f = - L f b s /b o s[k i /s+k p ]; b o =28x10-7 T/A; L f =0.04H; b s =F s /A s VALEN uses V f = - L f / b o A s [K i +K p d/dt ] F s = -1.4x10 8 [K i +K p d/dt ]F s G p = 6x10 8 V/W is Liu s K i =4.318 and G d = 2x10 8 V/V is Liu s K p =1.5 These values reduce b N ~ 2.78! Only 15% towards ideal limit!!

RWM Dispersion Relation with Mode Control Feedback* * A. Boozer, Phys. Plasmas 5, 3350 (1998) Apply Voltage to Control Coil, V f (t) = - L f Mfp [g w G p + Gd d dt ] F sensor Gp = Proportional Gain Gd = Derivative Gain g w = Rwall/Lwall g f = Rcontrol coil/lcontrol coil t= feedback delay a 1 a 3 g 3 + a 2 g 2 + a 1 g + a 0 = 0 a 0 /g w = g f + g w G p = g f D(s) + g w [G d + c f G p s]/s a 2 = D(s) + c f G d /s a 3 = t D(s) For Stability all four Coefficients must be Positive! D(s) = c[(1+s)/s] -1 where c = [M pw M wp ]/[L mode L wall ] At Ideal Wall b Limit: D(s crit ) = 0 Feedback Coupling Constant, c f = 1 [M pw M fw ]/[L wall M fp ] For Feedback to Stabilize up to Ideal Wall b Limit c f must be 0 Want small M fw and large M fp to insure c f > 0 If Control Coils Outside Stabilizer then: M wf > M fp and c f < 0

Why is Basic ITER Control Coil Set a Poor Feedback System? D(s) = c[(1+s)/s] -1 where c = [M pw M wp ]/[L mode L wall ] At Ideal Wall b Limit: D(s crit ) = 0 ITER Basic System has s crit = 0.35 [or b N ~ 4.9] Therefore c = 0.26 for ITER Feedback Coupling: c f = 1 [M pw M fw ]/[L wall M fp ] Boozer shows that feedback fails when D(s) + c f = 0 Using VALEN model results shows ITER Feedback Saturates at s = 0.063 therefore: ITER Basic System: c f = - 3.39 Physically: c f = 1 [V plasma from I w ]/[V plasma from I f ] Says Plasma Mode is more than 4 times better coupled to wall eddy currents than external Basic ITER Control Coils.

VALEN Model Geometry: Resistive Wall & Control Coil Simple 1-turn Control Coil: Examine Control Fields with Wall Behind & in Front of Coil plate 130.e-08 ohm m 2 x 2 x 0.0254 thick coil R=0.5 m sensor #8 0.01 x 0.01 sensor #5 0.01 x 0.01 z=-0.5 z=0.5 z=0 z=-0.1

Frequency Dependence of Control Field Magnitude of Control Field vs Frequency Data from "FRdemo2a" t = 0.0254 rho = 130.e-08 ohm m Phase of Control Field vs Frequency Data from "FRdemo2a" t = 0.0254 m rho = 130.e-08 ohm m 10-2 sensor #5 ( 0.5 m right of coil ) 0-30 current in coil gauss ( at sensor ) / (amp in coil ) 10-3 10-4 sensor #8 ( 0.5 m left of coil ) plate between coil & sensor BB #5 gauss/amp BB #8 gauss/amp phase relative to driving voltage coil, plate, r. & l. sensor (degrees) -60-90 -120-150 -180-210 -240 current in plate sensor #5 right of coil sensor #8 left of coil BB p BB p BB # BB # 10-5 10 0 10 1 10 2 10 3 10 4-270 10 0 10 1 10 2 10 3 10 4 hz hz driving frequency

At High Frequency: Destabilizing Wall Image Currents Phase of Control Field vs Frequency Data from "FRdemo2a" t = 0.0254 m rho = 130.e-08 ohm m Magnitude of Currents vs Frequency Data from "FRdemo2a" t= 0.0254 rho = 130.e-08 ohm m 0-30 current in coil 100 current in coil phase relative to driving voltage coil, plate, r. & l. sensor (degrees) -60-90 -120-150 -180-210 -240 current in plate sensor #5 right of coil sensor #8 left of coil BB ph - driver BB ph max plate BB #5 phase BB #8 phase current in coil (amp) net current in plate ( amp) 10 1 net current in plate BB I - BB ma -270 10 0 10 1 10 2 10 3 10 4.1 10 0 10 1 10 2 10 3 10 4 hz driving frequency hz driving frequency

Optimizing Resistive Wall Mode Control: FIRE Approach Allows Ideal Beta Limit to be Achieved thru Cf > 0 Improved Plasma/Coil Coupling horizontal port (1.3 m x 0.65 m) Copper Stabilizing Shell (backing for PFCs) 1st Vacuum Shell 2nd Vacuum Shell port shield plug (generic) resistive wall mode stabilization coil (embedded in shield plug)

Try FIRE RWM Control Scheme in ITER Add Control Coils in Vacuum Vessel Ports: Good Coupling to Plasma Use Poloidal Sensors on Midplane Behind Blanket Armor

ITER Internal Coils in Port Plugs Easily Reach Ideal Limit 10 6 10 5 growth rate [ 1 / s ] 10 4 10 3 10 2 10 1 10 0 g passive nbl_3.0 g wbl 10^8 cs5_3.0 stable < 4.93 10-1 10-2 2.0 3.0 4.0 5.0 beta-n (new) Ideal Beta Limit Reached with only Proportional Gain G p =10 8 V/W Control Coils use only three n=1 pairs in 6 port plugs!

Time Dependent Feedback Model of ITER Internal Coils sensor flux (v*s) 1.0e-7 8.0e-8 6.0e-8 4.0e-8 2.0e-8 0.0e+0 0.00 turn FB on at 10 milli s 0.01 passive only 0.02 0.03 Gp=0.1 V/G Gp=1 V/G 0.04 sensor 6 #2 s 6 #4 G=10^7 s 6 #3 G=10^8 control coil current [amp] 4.0e+3 3.0e+3 2.0e+3 1.0e+3 0.0e+0-1.0e+3 0.00 Gp = 10^8 s = 0.1 0.01 0.02 0.03 0.04 4287 #3 G=10^8 4288 #3 G=10^8 4289 #3 G=10^8 time (s) time (s) At Moderate Beta (s=0.1) we observe simple damped suppression in 20 to 30 ms Peak Current in Control Coils reaches peak of 3.5 ka Peak voltage on single turn control coils is only 5 volts Reactive power requirements only ~5 kw in each coil pair

Time Dependent Feedback Model of ITER Internal Coils flux in Bp sensor [v*s] 1.0e-7 9.0e-8 8.0e-8 7.0e-8 6.0e-8 5.0e-8 4.0e-8 3.0e-8 2.0e-8 1.0e-8 0.0e+0-1.0e-8 0.00 β N = 4.9 0.01 turn on FB here Gp = 1 V/G 0.02 0.03 0.04 sensor 6 sensor 6 #6 control coil current [amp] 2000 1500 1000 500 0-500 -1000 0.00 0.01 0.02 0.03 0.04 4287 #6 4288 #6 4289 #6 time (s) time (s) At Ideal Beta Limit (s=0.35) highly damped suppression in ~ 6 ms Peak Current in Control Coils reaches peak of only 1.5 ka Peak voltage on single turn control coils is only 5 volts Reactive power requirements only ~7 kw in each coil pair

Time Dependent Feedback Model of Basic ITER Coils flux in Bp sensor [v*s] 8.0e-8 6.0e-8 4.0e-8 2.0e-8 0.0e+0 0.0 0.1 0.2 time [s] 0.3 flux s#5 control coil current [amp] 1000 750 500 250 0-250 -500-750 -1000 0.0 0.1 0.2 time [s] 0.3 e 4287 e 4288 e 4289 Beta chosen to be near predicted limit of b N ~ 2.9 which is only 20% between no-wall limit (2.4) and ideal limit (4.9). Voltage limited to 40 V/turn times 28 turns = 1120 Volts Peak Current in Control Coils reaches peak of 28 ka-turns Reactive power requirements exceed 1 MW per coil pair!

SUMMARY OF RESULTS Basic ITER External Control Coils with Double-wall Vacuum Vessel in ITER Reduces Effectiveness of Feedback System: Stable only up to ~ 20% above Nowall Beta Limit. Voltage requirements at coil operating limits (1.1 kv) degrade feedback performance and multi-mw reactive power required. Inclusion of Blanket Modules Significantly Increases Ideal Wall Beta Limit from about b N of ~3.4 to ~4.9 Use of Single Turn Modular Coils in 6 of the 18 ITER Midplane Ports allows the feedback system to reach the Ideal Wall Beta Limit for the double wall ITER vacuum vessel plus blanket modules. Time dependent modeling shows only 5 Volts at 1.5 ka of current or 7.5 kw of reactive power needed.

Next Steps for ITER Modeling Continue Benchmark with MARS on Feedback Limits Add Noise to Estimate Power Requirements and Performance Limits. Extend VALEN to Include Rotation Effects: + Mode Rotation Relative to Wall: torque balance (W mode < 1/t wall ): small stabilizing effect + Use MARS and/or DCON+ to find s(w p )

Simulated RWM Noise on DIII-D with ELMs 20 1.00 10 [Gauss] 0 PSD 0.10-10 -20 2.80 2.85 2.90 2.95 3.00 0.01 0.01 0.10 1.00 10.00 time (sec) f(khz) To the low level noise ELMs (Edge Localized Modes) were added as small group of Gaussian random numbers from 6 to 16 Gauss approximately every 0.01 sec with different signs +/- chosen with 50% probability

DIII-D I-Coil Feedback model for the Control Coils L=60 mh and R=30 mohm with Proportional Gain G p =7.2Volts/Gauss Current CC #2 [Amp] 800 600 400 200 0-200 -400 s=.15849-600 -800 s=.156335-1000 s=.14987-1200 0.00 0.05 0.10 0.15 0.20 0.25 time [sec] Current CC #2 [Amp] 300 200 100 0-100 s=.14987-200 s=.12589-300 s=.1-400 0.00 0.05 0.10 0.15 0.20 0.25 time [sec] Control coil current

Maximum control coil current and voltage with noise in DIII-D as function of b N Max Current on CC, #7 [Amp] 800 600 400 200 0 60% 70% 80% 90% 100% Beta, % Maximum Voltatge applied to CC #2 [V] 200 180 160 140 120 100 80 60 40 20 0 60% 70% 80% 90% 100% Beta, %

Effects of Noise on Feedback Dynamics for L=60 mh and R=30 mohm DIII-D I-Coil Feedback model with Proportional Gain G p =7.2Volts/Gauss Sensor #7 Flux [Gauss] 25 20 15 10 5 0-5 -10 0.000 0.002 0.004 0.006 0.008 0.010 turn on FB at t = 1.65 ms time [sec] Sensor Flux FB on with Noise No FB with Noise FB on w/o Noise No Fb w/o Noise