rwm control in fire and iter - general atomics · rwm control in fire and iter gerald a. navratil...
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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