RWM Control in FIRE and ITER

Gerald A. Navratilwith

Jim Bialek, Allen Boozer& Oksana Katsuro-Hopkins

MHD Mode Control WorkshopUniversity of Texas-Austin

3-5 November, 2003

OUTLINE

• REVIEW OF VALEN MODEL

• BENCHMARKING MARS & VALEN/DCON+ MAPPING OF ‘S’ TO bN: 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 COUPLINGOPTIMIZATION IN FIRE AND ITER

+ POWER REQUIREMENTS: INITIAL VALUE SIMULATIONS ANDEFFECTS OF NOISE

VALEN combines 3 capabilitiessee 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 feedbacklogic (smart shell and mode control)

X

Y

Z

VALEN Model

• All conducting structure, control coilsand sensors, are represented by afinite element integral formulation, wehave a matrix circuit equation: i.e.,

L[ ] I{ } + R[ ] I{ } = V(t){ }

• Unstable Plasma mode is modeled asa special circuit equation. We startwith a plasma equilibrium, use DCONwithout any conducting walls, toobtain δW, and the magneticperturbation represents the plasmainstability.

• The instability is represented via anormalized mode strength

s = −δW

LI2 / 2( ) , the equations are now

L' (s)[ ] I'{ } + R'[ ] I'{ } = V' (t){ }

VALEN predicts growth rate forplasma instability as function of

the instability strength parameter 's'

• 's' is a normalized mode energy

s = −δW

LI2 / 2( )• computed dispersion relation of

growth rate vs. 's' is an eigenvaluecalculation

1 0 01 0 - 11 0 - 210 0

10 1

10 2

10 3

10 4

10 5

10 6

normalized mode energy s

gro

wth

rat

e (1

/sec

)

ideal branch

resistive branchdetermined by geometry &resistance of structure

difference producedby coupling to

conducting structure

ITER Double Wall Vacuum Vessel Configuration

1 21 086420-6

-4

-2

0

2

4

6

r

z

• The ITER vacuum vessel is modeled as a double wall configurationwith 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 81 61 41 21 086420-1

0

1

Bn#1@0

arc length

Bn

#1

@0

Use B-normal to Compute EquivalentPlasma Surface Current

RWM Induces Stabilizing Image CurrentsLargely on the Inner Vessel Wall

• Vacuum Vessel Modeled with and without wall penetrations.

ITER Double Vacuum Vessel Passive RWM Dispersion Relation

1 0 01 0 - 11 0- 210 - 1

10 0

10 1

10 2

10 3

10 4

10 5

10 6

g-passive no ports 3.0

s - normalized mode energy

gro

wth

ra

te

(1/s

)

no blanketsno ports

• Shows usual transition from RWM to Ideal Branch at s~0.1

OUTLINE

• REVIEW OF VALEN MODEL

• BENCHMARKING MARS & VALEN/DCON+ MAPPING OF ‘S’ TO bN: 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 COUPLINGOPTIMIZATION IN FIRE AND ITER

+ POWER REQUIREMENTS: INITIAL VALUE SIMULATIONS ANDEFFECTS OF NOISE

DCON Benchmark with Series ofConformal Wall ITER Equilibria

1086422-6

-4

-2

0

2

4

6

ITER Inner VesselITER Blanket

EQDSK_512x512_a(series)

R [ m ]

Z [

m ]

p lasma

beta-n = 2.546

beta-n = 2.841

beta-n = 3.142

beta-n = 3.450

beta-n = 3.764

• Use series of ITER conformal wallequilibria as input into VALEN

Benchmark Calibration of VALEN with DCON

10010- 110- 210- 7

10- 6

10- 5

10- 4

10- 3

10- 2

10- 1

100

101

102

103

104

105

106

g a1.4 36x36g a1.3g a1.2g a1.1 36x36g a1.0

s

grow

th r

ate

[ 1/

s ] beta-n = 2.546

beta-n = 2.841

beta-n = 3.142

beta-n = 3.450

beta-n = 3.764

• DCON ideal bN limit found for series of conformal wall ITERplasmas.

• VALEN ideal s limit found for same conformal wall series.Use to calibrate bN vs s

Use DCON Computation of dW to Calibrate s to bN

0.80.60.40.20.0-0.22.0

3.0

4.0

5.0

s

beta

-nbased onconformal wallVALEN calcs based on PET

equilibria beta scan& δW calibration of 's'

based onBondeson equilibia beta scan & δW calibration of 's'

• 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.

5.04.03.02.02.010 - 1

10 0

10 1

10 2

10 3

10 4

10 5

10 6

beta-n(new)

grow

th r

ate

[ 1

/ s

]

Without Blanket Modules

• Note absence of Ideal Kink Branch Transition when Cb ~ 1• In Liu, et al. twall ~ 0.188 s so g at Cb~1 is between 53 to 120 s-1

• In VALEN modeling g at Cb~1 is between 1000 to 104 s-1

• Growth rate disparity consistent with g twall in Liu, et al. toosmall for claimed values of Cb

VALEN vs MARS RWM Benchmarking

4.54.03.53.02.52.02.010 0

10 1

10 2

10 3

10 4

10 5

10 6

passive 3.764passive 3.764g no blanketgammagamma (3)gamma(1)

double walled ITER VV only passive structure

beta-n

grow

th r

ate

[1

/s ]

VALENpreviouss-to-betan map

VALENnews to betan map

originalMARSdata (est)

newMARSdata (est)

est MARSgamma-idealtau-a = 1.e-6 to 3.e-6 s

New MARS results and benchmarked VALEN results agree!

OUTLINE

• REVIEW OF VALEN MODEL

• BENCHMARKING MARS & VALEN/DCON+ MAPPING OF ‘S’ TO bN: 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 COUPLINGOPTIMIZATION IN FIRE AND ITER

+ POWER REQUIREMENTS: INITIAL VALUE SIMULATIONS ANDEFFECTS OF NOISE

Include ITER Ports & Blanket Modules inPassive RWM Stabilization Model

• Modeled as set of isolated plates above theinner vessel wall.

• Each blanket module adjusted to have 9 msradial field penetration time constant.

ITER Ports Cause Small Reduction in Ideal Limit

5.04.03.02.02.010 - 1

10 0

10 1

10 2

10 3

10 4

10 5

10 6

beta-n(new)

grow

th r

ate

[1/s

]

no blankets & no ports

no blankets45 ports

• No wall bN limit is 2.4; Ideal Wall Limit Drops to bN ~ 3.3

VALEN Model of ITER Double Wall Vessel and Blanket Modules

XY

Z

ITER Blanket Opens Up Large AT Regime

5.04.03.02.02.010 - 1

10 0

10 1

10 2

10 3

10 4

10 5

10 6

beta-n(new)

grow

th r

ate

[ 1/

s ]

with blankets45 ports

no blankets & no ports

no blankets45 ports

• No wall bN limit is 2.4; Ideal Wall Limit With Blanket is 4.9!

Amplifier:

Gp and Gd

Control Coils PlasmaResponse Bp Sensors

V B-radial ψψψψ

RWM

Basic Feedback Control Loop with Voltage Amplifiersand Sensors Uncoupled to Control Coils

no-coupling

Feedback Volts/Weber

ITER Base Case Feedback Control System Geometry

1 21 086420-6

-4

-2

0

2

4

6

r

z

• The ITER vacuum vessel is modeled as a double wall configurationusing design data provided by Gribov, with feedback control provided by3 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

5.04.03.02.02.010 - 2

10 - 1

10 0

10 1

10 2

10 3

10 4

10 5

10 6

g passive10^8 g10^8 10^8 g10^8 10^9 g10^9 10^10 gnbl_3.0

beta-n (new)

grow

th r

ate

[ 1

/ s

]

stable < 2.72

stable < 2.94

stable < 2.97

• Feedback Saturates at bN ~ 2.97 for Gp=108 V/W & Gd=109 V/V• Gp=108 V/W is Liu’s Ki=0.32 and Gd=109 V/V is Liu’s Kp=15.6

ITER Basic Coils: Use Liu & Bondeson Gain Parameters

5.04.03.02.02.010 - 2

10 - 1

10 0

10 1

10 2

10 3

10 4

10 5

10 6

g passivenbl_3.0g L&B

beta-n

grow

th r

ate

[ 1

/ s

]

stable < 2.78

• Liu uses Vf = - Lf bs/bos[Ki/s+Kp]; bo=28x10-7T/A; Lf=0.04H; bs=Fs/As

• VALEN uses Vf = - Lf/ boAs [Ki+Kpd/dt ] Fs = -1.4x108[Ki+Kpd/dt ]Fs

• Gp= 6x108 V/W is Liu’s Ki=4.318 and Gd= 2x108 V/V is Liu’s Kp=1.5• These values reduce bN ~ 2.78! Only 15% towards ideal limit!!

RWM Dispersion Relation withMode Control Feedback*

* A. Boozer, Phys. Plasmas 5, 3350 (1998)

Apply Voltage to Control Coil, Vf(t) = - Lf

Mfp [gw Gp + Gd

ddt ] Fsensor

Gp = Proportional Gain Gd = Derivative Gaingw = Rwall/Lwall gf = Rcontrol coil/Lcontrol coil t= feedback delay

a3g3 + a2g2 + a1g + a0 = 0

a0/gw = – gf + gw Gp

a1 = gf D(s) + gw [Gd + cf Gp – s]/sa2 = D(s) + cf Gd/s a3 = t D(s)

For Stability all four Coefficients must be Positive!D(s) = c[(1+s)/s] -1 where c = [MpwMwp]/[LmodeLwall]

At Ideal Wall b Limit: D(scrit) = 0Feedback Coupling Constant, cf = 1 – [MpwMfw]/[LwallMfp]

For Feedback to Stabilize up toIdeal Wall b Limit cf must be ≥ 0

Want small Mfw and large Mfp to insure cf > 0

If Control Coils Outside Stabilizer then:Mwf > Mfp and cf < 0

Why is Basic ITER Control Coil Set aPoor Feedback System?

D(s) = c[(1+s)/s] -1 where c = [MpwMwp]/[LmodeLwall]

At Ideal Wall b Limit: D(scrit) = 0

ITER Basic System has scrit = 0.35 [or bN ~ 4.9]Therefore c = 0.26 for ITER

Feedback Coupling: cf = 1 – [MpwMfw]/[LwallMfp]Boozer shows that feedback fails when

D(s) + cf = 0

Using VALEN model results shows ITERFeedback Saturates ats = 0.063 therefore:

ITER Basic System: cf = - 3.39

Physically: cf = 1–[Vplasma from Iw]/[Vplasma from If]

Says Plasma Mode is more than 4 times bettercoupled to wall eddy currents thanexternal Basic ITER Control Coils.

VALEN Model Geometry: Resistive Wall & Control CoilSimple 1-turn Control Coil: Examine Control Fields with Wall Behind & in Front of Coil

z=0

z=-0.1

z=0.5z=-0.5

plate 130.e-08 ohm m2 x 2 x 0.0254 thick

coilR=0.5 m

sensor #50.01 x 0.01

sensor #80.01 x 0.01

Frequency Dependence of Control FieldMagnitude of Control Field vs Frequency

10 410 310 210 110 010 - 5

10 - 4

10 - 3

10 - 2

BB #5 gauss/ampBB #8 gauss/amp

Data from "FRdemo2a"t = 0.0254 rho = 130.e-08 ohm m

h z

gaus

s (

at s

enso

r )

/ (a

mp

in c

oil

)

sensor #8( 0.5 m left of coil )plate between coil & sensor

sensor #5( 0.5 m right of coil )

Phase of Control Field vs Frequency

10 410 310 210 110 0-270

-240

-210

-180

-150

-120

-90

-60

-30

0

BB ph - driverBB ph max plateBB #5 phaseBB #8 phase

Data from "FRdemo2a"t = 0.0254 m rho = 130.e-08 ohm m

hz driving frequency

phas

e re

lati

ve

to

driv

ing

volt

age

coil,

pla

te,

r. &

l.

sens

or(d

egre

es)

current in coil

sensor #5right of coil

sensor #8left of coil

current in plate

At High Frequency: Destabilizing Wall Image CurrentsPhase of Control Field vs Frequency

10 410 310 210 110 0-270

-240

-210

-180

-150

-120

-90

-60

-30

0

BB ph - driverBB ph max plateBB #5 phaseBB #8 phase

Data from "FRdemo2a"t = 0.0254 m rho = 130.e-08 ohm m

hz driving frequency

phas

e re

lati

ve

to

driv

ing

volt

age

coil,

pla

te,

r. &

l.

sens

or(d

egre

es)

current in coil

sensor #5right of coil

sensor #8left of coil

current in plate

Magnitude of Currents vs Frequency

10 410 310 210 110 0.1

1

10

100

BB I - driverBB max plate I

Data from "FRdemo2a"t= 0.0254 rho = 130.e-08 ohm m

hz driving frequency

curr

ent

in

coil

(am

p)

net

curr

ent

in p

late

( a

mp)

currentin coil

net currentin plate

Optimizing Resistive Wall Mode Control: FIRE Approach

Allows Ideal Beta Limit to be Achieved thru Cf > 0 Improved Plasma/Coil Coupling

1st Vacuum Shell

2nd Vacuum Shell

Copper Stabilizing Shell(backing for PFCs)

horizontal port (1.3 m x 0.65 m)

port shield plug (generic)

resistive wall modestabilization coil

(embedded in shield plug)

Try FIRE RWM Control Scheme in ITER

• Add Control Coils inVacuum Vessel Ports:Good Coupling to Plasma

• Use Poloidal Sensors onMidplane Behind BlanketArmor

ITER Internal Coils in Port Plugs Easily Reach Ideal Limit

5.04.03.02.02.010 - 2

10 - 1

10 0

10 1

10 2

10 3

10 4

10 5

10 6

g passivenbl_3.0g wbl 10^8 cs5_3.0

beta-n (new)

grow

th r

ate

[ 1

/ s

]

stable < 4.93

• Ideal Beta Limit Reached with only Proportional Gain Gp=108 V/W• Control Coils use only three n=1 pairs in 6 port plugs!

Time Dependent Feedback Model of ITER Internal Coils

0.040.030.020.010.000.0e+0

2.0e-8

4.0e-8

6.0e-8

8.0e-8

1.0e-7

sensor 6 #2s 6 #4 G=10^7s 6 #3 G=10^8

time (s)

sens

or f

lux

(v*s

)

passive onlyGp=0.1 V/G

Gp=1 V/G

turn FBon at10 milli s

0.040.030.020.010.00-1.0e+3

0.0e+0

1.0e+3

2.0e+3

3.0e+3

4.0e+3

4287 #3 G=10^84288 #3 G=10^84289 #3 G=10^8

Gp = 10^8 s = 0.1

time (s)

cont

rol c

oil c

urre

nt [

amp]

• At Moderate Beta (s=0.1) we observe simple damped suppressionin 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

0.040.030.020.010.00-1.0e-8

0.0e+0

1.0e-8

2.0e-8

3.0e-8

4.0e-8

5.0e-8

6.0e-8

7.0e-8

8.0e-8

9.0e-8

1.0e-7

sensor 6sensor 6 #6

βN = 4.9 Gp = 1 V/G

time (s)

flux

in B

p se

nsor

[v*

s]

turn on FB here

0.040.030.020.010.00-1000

-500

0

500

1000

1500

2000

4287 #64288 #64289 #6

time (s)

cont

rol

coil

curr

ent

[am

p]

• 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

0.30.20.10.00.0e+0

2.0e-8

4.0e-8

6.0e-8

8.0e-8

flux s#5

time [s]

flux

in B

p se

nsor

[v*

s]

0.30.20.10.0-1000

-750

-500

-250

0

250

500

750

1000

e 4287e 4288e 4289

time [s]

cont

rol c

oil c

urre

nt [

amp]

• Beta chosen to be near predicted limit of bN ~ 2.9 which isonly 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 ofFeedback System: Stable only up to ~ 20% above No-wall Beta Limit. Voltage requirements at coiloperating limits (1.1 kV) degrade feedbackperformance and multi-MW reactive power required.

• Inclusion of Blanket Modules Significantly IncreasesIdeal Wall Beta Limit from about bN of ~3.4 to ~4.9

• Use of Single Turn Modular Coils in 6 of the 18 ITERMidplane Ports allows the feedback system to reachthe Ideal Wall Beta Limit for the double wall ITERvacuum vessel plus blanket modules. Timedependent modeling shows only 5 Volts at 1.5 kA ofcurrent 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 (Wmode < 1/twall): smallstabilizing effect

+ Use MARS and/or DCON+ to find s(Wp)

Simulated RWM Noise on DIII-D with ELMs

To the low level noise ELMs (Edge Localized Modes) were addedas small group of Gaussian random numbers from 6 to 16 Gaussapproximately every 0.01 sec with different signs +/- chosen with

50% probability

-20

-10

0

10

20

2.80 2.85 2.90 2.95 3.00

time (sec)

[Gau

ss]

0.01

0.10

1.00

0.01 0.10 1.00 10.00

f(kHz)

PS

D

DIII-D I-Coil Feedback model for theControl Coils L=60 mH and R=30 mOhm

with Proportional Gain Gp=7.2Volts/Gauss

Control coil current

-1200

-1000

-800

-600

-400

-200

0

200

400

600

800

0.00 0.05 0.10 0.15 0.20 0.25

time [sec]

Cu

rren

t C

C #

2 [

Am

p]

s=.15849

s=.156335

s=.14987-400

-300

-200

-100

0

100

200

300

0.00 0.05 0.10 0.15 0.20 0.25

time [sec]C

urr

en

t C

C #

2 [

Am

p]

s=.14987

s=.12589

s=.1

Maximum control coil current and voltagewith noise in DIII-D as function of bN

0

200

400

600

800

60% 70% 80% 90% 100%Beta, %

Max C

urr

en

t o

n C

C,

#7

[A

mp

]

020406080

100120140160180200

60% 70% 80% 90% 100%

Beta, %

Maxim

um

Vo

ltatg

e a

pp

lied

to

CC

#

2 [

V]

Effects of Noise on Feedback Dynamics for L=60 mHand R=30 mOhm DIII-D I-Coil Feedback model

with Proportional Gain Gp=7.2Volts/Gauss

Sensor Flux

-10

-5

0

5

10

15

20

25

0.000 0.002 0.004 0.006 0.008 0.010

time [sec]

Sen

sor

#7

Flu

x [

Gau

ss]

FB on with NoiseNo FB with NoiseFB on w/o NoiseNo Fb w/o Noise

turn on FBat t = 1.65 ms