RWM CONTROL IN BP EXPERIMENTS CONTROL … · RWM CONTROL IN BP EXPERIMENTS: CONTROL COIL LOCATION,...
Transcript of RWM CONTROL IN BP EXPERIMENTS CONTROL … · RWM CONTROL IN BP EXPERIMENTS: CONTROL COIL LOCATION,...
RWM CONTROL IN BP EXPERIMENTS:CONTROL COIL LOCATION, PASSIVE STABILIZER
GEOMETRY; FEEDBACK LOOP DYNAMICS
Gerald A. Navratil[with Jim Bialek, Allen Boozer & Oksana Katsuro-Hopkins]
Columbia University
Third Meeting of ITPA MHD, Disruption, and Control GroupIoffe Institute, St. Petersburg, Russia
15-17 July 2003
OUTLINE
• REVIEW OF RWM FEEDBACK
• CRITICAL ISSUES IN CONTROL DESIGN+ PASSIVE STABILIZER PERFORMANCE
+ CONTROL COIL-PLASMA-STABILIZER COUPLING
+ REACTIVE VS RESISTIVE CONTROL COIL
• DIFFERENCES WITH LIU & BONDESON+ TRANSITION TO IDEAL BRANCH IN DISPERSION RELATION
+ MAPPING OF bN TO DISPERSION RELATION LIMITS
+ EFFECTIVENESS OF ITER ERROR FIELD CORRECTION COILSFOR RWM CONTROL
• RESOLVING DIFFERENCES: BENCHMARKS
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){ }
DCON computation of mode structureNSTX - derived from EFITreconstruction of #106165βn = 6.154, Fp = 2.2, n = 1
6 . 05 . 04 . 03 . 02 . 01 . 00 . 00 . 0-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
Mode #1 @ 0.
DCON mode for beta n = 6.154mode at 0.0 deg ( even )
arc length
B-n
orm
al
( ar
b
un
its
)
6 . 05 .04 .03 .02 .01 .00 .00 .0-0.4
-0.2
0.0
0.2
0.4
Mode #1 @ 90.
DCON mode for beta n = 6.154mode at 90.0 deg ( odd )
arc length
B-n
orm
al
( ar
b
un
its
)
from dcon_surf_Fp2.2_bn6.154 24 by 72 Equivalent Surface Current which produces mode field
Input to VALEN for NSTX ’s’= 2.0590e-1
X Y
Z
from dcon_surf_Fp2.2_bn6.154 unwrapped inboard cut Equivalent Surface Current which produces mode vacuum field
Input to VALEN for NSTX ’s’= 2.0590e-1
X Y
Z
VALEN 03/14/02 NSTX half of VV removed
NSTX geometry ( including sensors and ideal control coils )
X
Y
Z
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
passive performance for NSTX structurebasic dispersion relation from VALENData from "NSTX.02.2002"
normalized mode energy s
gro
wth
rat
e (
1 /
sec
)
ideal branch
resistive branchdetermined by geometry &resistance of structure
difference producedby coupling toconducting structure
VALEN predicts growth rate forplasma instability as function of 's'
•s = −δW
LI2 / 2( ) a normalized energy
• great agreement for different startingplasma equilibria !
1 001 0- 11 0 - 2100
101
102
103
104
105
106
g (5.182)
gamma - 5.182
gamma-6.154
gamma-7.112
g (6.154)
g (7.112)
passive performance for NSTX structureData from "NSTX.02.2002"
s
gro
wth
ra
te
( 1
/se
c
)
beta n = 5.182
beta n = 6.154
beta n = 7.112
resistive branchdetermined by geometry &resistance of structure
ideal branch
VALEN s = 0.31623 gamma = 573.3 betan(6.154)driver 03/01/02 10:05:40 EST artemis executable: xvps6
eddy currents ( passive only ) in NSTX structure
X
Y
Z
VALEN predicts growth rate forplasma instability as function of 's'
• examine limit of perfect conductors• connect s to βn
1 0 01 0 - 11 0 - 2100
101
102
103
104
105
106
passive performance for NSTX structurebasic dispersion relation from VALENData from "NSTX.02.2002"
normalized mode energy s
gro
wth
rat
e (
1 /
sec
)
ideal branch
r e s i s t i v ebranch
i d e a ll i m i t
beta n = 5.182
beta n = 6.154
beta n = 7.112
ColumbiaUniversity
ITERPASSIVE STABILIZER AND ACTIVE CONTROL COILS
Inner Vacuum Vessel Wall (6 cm-thick stainless steel)
Outer VV Wall
The ITER vessel is modeled as two walls.
. Three sets of six saddle coils, outside the vessel, but the upper and lower coils couple weakly to the RWM. .
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.
ITER Vacuum Vessel Mode Analysis
n ~ 0 and m ~ 0
toroidal
polo
idal
outboardmidplane
inb oardmidplane
inb oardmidplane
• Modeled with 3906 elements.
• Longest Time Constant: 0.39897 s
ITER Vacuum Vessel Mode Analysis
n ~ 1 and m ~ 1(2 fold degenerate)
toroidal
pol
oida
l
or toroidal
pol
oida
l
• Modeled with 3906 elements.
• 1/1 Time Constant: 0.18762 s.
Whole Family of ITER Vessel Modesthe n=0, m=0 'OH response mode' 0.39897 s, 0.39804 s
[red = 3906 elements ; black = 2970 elements]
toroidal
polo
idal
outboardmidplane
inb oardmidplane
inb oardmidplane
the n=1, m=0 horizontal field mode ( 2 fold degenerate ) 0.31114 s, 0.31729 s
toroidal
pol
oida
l
toroidalpo
loid
al
the n=0, m=0 toroidal flux response 0.24513 s, 0.25216 s
toroidal
po
loid
al
the n=0, m=1 response to vertical plasma displacement 0.23113 s, 0.22753 s
toroidal
pol
oida
l
the n=2, m=0 mode ( which is 2 fold degenerate ) 0.19377 s , 0.20166 s
toroidal
po
loid
al
toroidal
polo
idal
the n=1, m=1 mode ( which is 2 fold degenerate ) 0.18762 s, 0.18937 s
toroidal
pol
oida
l
toroidal
pol
oida
l
VALEN Model of ITER Vessel and Control Coils:Base Case Feedback Control System
• Vacuum Vessel Modeled with and without wall penetrations.
DCON Calculation of ITER RWM:B-normal vs Poloidal Angle
1 81 61 41 21 086420-1
0
1
Bn#1@0
Data from "iter_at_129.sgfile"
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 Vacuum Vessel Penetrations HaveLittle Effect on Passive RWM Stabilization
1 0 01 0 - 11 0- 210 - 1
10 0
10 1
10 2
10 3
10 4
10 5
10 6
nbl_3.0
g-passive no ports 3.0
Data from "ITER.10.2002"Scen4_bn3.0 ( 129 by 129 )
s - normalized mode energy
gro
wth
ra
te
( 1
/s
)
no blanketsno ports
no blankets45 ports
• Relatively small reduction in the ideal wall beta limit.
Include ITER Blanket Modules in PassiveRWM Stabilization Model
• Modeled as set of isolated plates above theinner vessel wall.
• Each blanket module adjusted to have 9 msradial field penetration time constant.
VALEN Model of ITER Double Wall Vessel and Blanket Modules
XY
Z
ITER Blanket Modules Substantially Increasethe Passive RWM Stabilization Limits
1 0 01 0 - 11 0 - 210 - 1
10 0
10 1
10 2
10 3
10 4
10 5
10 6
passive character different modelsData from "ITER.10.2002"based on Scen4_bn4.0 ( 129 x 129 )from Y. Gribov
s - normalized mode energy
gro
wth
ra
te
( 1
/se
c
)
no blankets & no ports
no blankets45 ports
with blankets45 ports
ports are:18 top18 midplane9 divertor
• Offers prospect of much higher beta limit with anoptimized feedback control coil system.
Use DCON Computation of dW to Calibrate s to bN
0.60.40.20.0-0.2-0.22.0
2.5
3.0
3.5
4.0
4.5
beta-nbeta-n
s
beta
-n
• This calibration can then be used to replot passive response.
ITER Passive Dispersion Relation
4.03.02.010- 2
10- 1
100
101
102
103
104
105
106
beta-n
grow
th r
ate
[ 1
/ s
]
Without Blanket Modules
With BlanketModules
• No wall bN limit is 2.5; Ideal Wall Limit With Blanket is 3.7
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 Basic Coils: Scan of Proportional & Derivative Gain
4.03.53.02.52.02.010- 2
10- 1
100
101
102
103
104
105
106
g passive10^8 g10^8 10^8 g10^8 10^9 g10^9 10^10 gnbl_3.0
beta-n
grow
th r
ate
[ 1
/ s
]
stable < 2.643
stable < 2.743
stable < 2.759
• Feedback Saturates at bN ~ 2.76 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
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 ~ 3.7]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)
ITER Internal Coils in Port Plugs Easily Reach Ideal Limit
4.03.02.010- 2
10- 1
100
101
102
103
104
105
106
g passiveg wbl 10^8 cs5_3.0nbl_3.0
beta-n
grow
th r
ate
[ 1
/ s
]
stable < 3.647
• Ideal Beta Limit Reached with pure 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
Data from "ITER.cs5"
time ( s )
sens
or 6
flux
( v*
s)
passiveonly cs#5
Gp=10^7
cs#5Gp=10^8
turn FBon at10 milli s
0.040.030.020.010.00-1000
-500
0
500
1000
1500
2000
4287 #64288 #64289 #6
Data from "ITER.cs5" s = 0.35 Gp = 10^8
time ( s )
curr
ent
in c
ontr
ol c
oils
[ a
mp
]
• At Ideal Beta Limit simple damped suppression in 20 to 30 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 7.5 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
Data from "Untitled Data #1"
time [ s ]
flux
in B
p se
nsor
#5
[ v
*s ]
0.30.20.10.0-1000
-750
-500
-250
0
250
500
750
1000
e 4287e 4288e 4289
Data from "Untitled Data #1"
time [ s ]
curr
ent
in c
ontr
ol c
oils
[
amp
]
• Beta chosen to be near predicted limit of bN ~ 2.7 which isonly about 20% between no-wall limit and ideal limit.
• 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
ITER Basic Coils: Use Liu & Bondeson Gain Parameters
4.03.02.010- 2
10- 1
100
101
102
103
104
105
106
g passivenbl_3.0g L&B
beta-n
grow
th r
ate
[ 1
/s ]
stable < 2.674
• 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 best bN ~ 2.67
Time Dependent Feedback With Liu, et al. Parameters
0.40.30.20.10.0-6.0e-8
-4.0e-8
-2.0e-8
0.0e+0
2.0e-8
4.0e-8
6.0e-8
8.0e-8
1.0e-7
s 5
Data from "ITER.tran.07.14.2003"
time [ s ]
flux
in B
p se
nsor
#5
[
v*s
]
0.40.30.20.10.0-400
-200
0
200
400
600
e 4287e 4288e 4289
Data from "ITER.tran.07.14.2003"
time [ s ]
curr
ent
in c
ontr
ol c
oils
[
amp
]
• Beta chosen to be near predicted limit of bN ~ 2.6 which is only about 10%between no-wall limit and ideal limit. Vmax ~ 200 V
• Time history similar to Liu, et al.
Physics of Ideal Kink Transition Seems Absent in Liu, et al.
4.03.02.010- 2
10- 1
100
101
102
103
104
105
106
beta-n
grow
th r
ate
[ 1
/ s
]
Without Blanket Modules
With BlanketModules
• 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
Use DCON Computation of dW to Calibrate s to bN
0.60.40.20.0-0.2-0.22.0
2.5
3.0
3.5
4.0
4.5
beta-nbeta-n
s
beta
-n
• Liu, et al. analysis seems constrained to small s values.
Limitation of Performance Due to cf Effects Seems Absent
4.03.53.02.52.02.010- 2
10- 1
100
101
102
103
104
105
106
g passive10^8 g10^8 10^8 g10^8 10^9 g10^9 10^10 gnbl_3.0
beta-n
grow
th r
ate
[ 1
/ s
]
worse than passive
stable < 2.643
stable < 2.743
stable < 2.759
• cf =1–[MpwMfw]/[LwallMfp] = 1–[Vplasma from Iw]/[Vplasma from If]• For ITER Basic External Coils is clear that cf < 0 [est. was –3.4]• Effect of Coil Toroidal Discreteness + Wall Modes May Play Role• Growth rate disparity consistent with g twall in Liu, et al. too
small for claimed values of Cb
Summary & Conclusions• Basic ITER External Control Coils with Double-wall Vacuum
Vessel in ITER Reduces Effectiveness of Feedback System:Stable only up to ~ 20% above No-wall Beta Limit. Voltagerequirements at coil operating limits (1.1 kV) degrade feedbackperformance and MW reactive power required.
• Inclusion of Blanket Modules Significantly Increases Ideal WallBeta Limit from about bN of ~2.7 to ~3.7
• Use of Single Turn Modular Coils in 6 of the 18 ITER MidplanePorts allows the feedback system to reach the Ideal Wall BetaLimit for the double wall ITER vacuum vessel plus blanketmodules. Time dependent modeling shows only 5 Volts at 1.5kA of current or 7.5 kW of reactive power needed.
• Unresolved discrepancies exist between VALEN analysis andLiu & Bondeson MARS analysis of Basic ITER ExternalControl Coils:
+ Program to benchmark two codes against common equilibria andgeometry needs to be established.
+ A common set of transfer functions needs to be established.