ITER RWM benchmarkingVALEN modeling results

6th ITPA MHD topical group meeting

Tarragona, Spain 4 July 2005Presented by J. BialekColumbia University

outline

• RWM mode from CHEASE / DCON• Benchmarking techniques and models

– Current control with continuous external coil system– Voltage control with 6 coil external coil system– Effect of blanket modules

• Extended analysis, interior RWM coils withblanket modules, using voltage control

• summary

CHEASE equilibria for scenario 4 used in VALEN computations,the n=1 DCON B-normal distribution (Bn) on the plasma surfaceis shown below, Bn & dW are used as VALEN input, Color scale: from dark red, to green ( approx zero ) to dark blue.

Dominant field perturbationon outside ( large R ) of plasma

Field perturbation on inside( small R ) is not important

-6

-4

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0

2

4

6

0 2 4 6 8 10 12

ITER RWM benchmarkingplasma, walls, control coils,

& Bp sensorin Zvv[m]out Zvv[m]Zsep(m)coils Z[m]sensor Z[m]

Z [m

]

R [m]ITER.RWM.comparison

Benchmarking modelcontinuous external RWM coilaxisymmetric VVno blanket modules

Extended ITER modeldiscrete interior RWM coilspenetrations in VVsegmented blanket modules

-6

-4

-2

0

2

4

6

0 2 4 6 8 10 12

extended ITER RWM analysisplasma, walls, control coils,

blanket modules, & Bp sensorsin Zvv[m]out Zvv[m]Zsep(m)ext coils Z[m]int coils Z[m]sensor Z[m] int coilsZ bl [m]

Z[m

]

R[m] ITER.RWM.comparison

10-1

100

101

102

103

104

105

106

10-2 10-1 100

VALEN passive growth rates

real & ideal wallspassive growth rate (bench)passive g PBMpassive g ABMg ideal a1.4search g ideal PBMg ideal ABM

pass

ive g

rowt

h ra

te [

1/s]

s ( normalized mode energy ) tarragona.2005

benchmarkmodelno portsno shielding

alternative designswith 45 vv penetrationsall outboard modulesmost outboard modules

idealwallresults

ideal wall bn3.54.865.21

10-1

100

101

102

103

104

105

106

2.5 3 3.5 4 4.5 5 5.5 6

VALENpassive growth rates

real & ideal wallspassive growth rate (bench)passive g PBMpassive g ABMg ideal a1.4search g ideal PBMg ideal ABM

pass

ive g

rowt

h ra

te [1

/s]

bn

3.50 4.86 5.21

tarragona.2005

benchmarkmodelno portsno shielding

alternative designswith 45 vv penetrationsall outboard shieldingmost outboard shielding

VALEN calculation of ITER passive RWM growth ratesHigh conductivity wall allows estimate of ideal wall bn limitNo wall and ideal wall bn limit define Cb scale

no wall bn limit = 2.52

ITER baseline external RWM coils shownCut away view of axisymmetric vacuum vesselVALEN blanket modules visible without VVExternal RWM coils cover only 2/3 of perimeter Coil pairs have

28 turns L/R = 10. s !

Each blanket moduleHas a ‘L/R’ = 0.009 s

20 degreegap betweenext RWM coils

VALEN benchmark RWM coil and cut away viewof axisymmetric vacuum vessel modelContinuous RWM coils system shown

60 picture frame coilswith no overlap. Thetotal gap between allCoils = 1 degree

Each coil has adifferent current,this resultsi n a n=1 distributionof current

No blanketModules !

Approximatecurrent control !

Extended ITER models use internal coilsand have penetrations in the vacuum vessel

Internal coilbehind blanketmodules

Gapsbetweenblanketmodules

Vacuum vessel

Vacuum vessel

Technique:RWM control coilsModel continuous RWMcoil system by many small(non overlapping)‘picture frame’ coils

VALEN implements feedback via voltage control.Sensor signals to control logic determines thevoltage applied to the RWM coils.

VALEN benchmark model approximates MARScontinuous RWM control coil-axisymmetric walls- ignore blanket modules-continuous external RWM coil-approximate current control in feedback logic

Technique:current controlMake each sub-coil have fast (L/R) time constantso that requested coil current is obtained with minimaldelay

-1

-0.5

0

0.5

1

0 60 120 180 240 300 360

VALEN approximationto n=1 current distributionin 60 control coil basis set

norm current

norm

alize

d cu

rrent

s in

bas

is se

t

toroidal current f [deg]

y = m1*sin(m0+m2)ErrorValue

0.0031781-0.99889m1 0.1823-95.497m2

NA0.16181ChisqNA0.9991R

n=1 curve fitshown in red

currents in60 control coilbasis setshown in blue

VALEN can approximateA continuous RWM coil

One coil Twocoils

60 coils

60 coilsHide verticalPart of coils

Mode control feedback in VALEN RWM modelSensors track Bp inside VV & have area = 10-4 m2

VALEN solution variables are currents in model

i.e., {I(t)} and {dI/dt} for each wall element & coil & plasma

Voltage control is used to specify feed back in VALEN:

†

sensors : Fs t( ){ } = MsI[ ] I(t){ } and - ˙ F s t( ){ } = - MsI[ ] ˙ I (t){ }voltage feedback : Vcc (t) = SGpFs t( ) + SGd - ˙ F s t( )( )

To approximate ideal current controlwe adjusted Rcc so Lcc/Rcc of coil is fast.We keep Lcc fixed and increase Rcc.Studied Lcc/Rcc < 1ms and < 1 ms !Each increase in Rcc required anincrease in gain to match performance.We obtain requested current =Vcc/Rcc in ~ Lcc/Rcc sec

We also examine voltagecontrol with actual externalcoil parameters, i.e.,L/R|cc(pairs) = 39.2e-3H /3.92e-3W = 10. s

VALEN RWM dispersion relationFor ITER benchmark model with fast L/R<1 ms

[approximates current control]

10-2

10-1

100

101

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103

104

2.5 3 3.5

tarragona.2005

passive growth rate (bench)#2 g e+9#2 g e+10#2 g+ e+10#2 g e+11#2 g+ e+11#2 g p/d =+10/+7#2 g+ p/d =+10/+7

grow

th ra

te [1

/s]

bn tarragona.2005

idea

l wal

l lim

it

best resultsC

b = 69% ( 2.52 / 3.0 )

bn = 3.196

passive

Can stabilize up togpassive = 43.88 [1/s]

#1 #2#3

#1 Gp=1012[v/w] (real)@ 1 gaussIcc=0.518 KA

#2 Gp=1013(complex c. pairs)@ 1 gaussIcc = 5.18 KA

#3 Gp=1014(complex c pairs)@ 1 gaussIcc = 51.8 KA

( L/R = 16.8 mH/19.29 W= 0.87 ms for each coil)

Best results useGp/Gd =103 (2.52 / 3.5 )

10-1

100

101

102

1012 1013 1014

VALEN resultsITER RWM benchmarking

fine scan in Gp

max growth ratesingle real #3 values, 1 real & 2 cc2 cc answersang frequency

g [1/

s]

gro

wth

rate

Gp [v/weber] keeping s=0.1 fixedITER.s.beta.benchmark

eigenvalue isa real number

eigenvalues arecomplex conjugatepairs

rad/secfor cc pairs

100

101

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103

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105

0 100 2 109 4 109 6 109 8 109 1 1010

VALEN resultsITER RWM benchmarking model

scan in Gd with fixed 's' & Gps=0.1, Gp=1013 [v/weber]

#1 Re g#1 Im g#2 Re g#2 Im g

g [1

/s]

gro

wth

rate

Gd [v/v]

growth rate

angular frequency

new unstable evgrowth rate

new unstable evangular frequency[rad/s]

Investigate RWM feedback performance limits asgain applied to sensor flux & sensor voltage is variedLook at bn = 3.22, Cb = 72% (2.52 / 3.50), (or s=0.1)Can not stabilize this growth rate ( gpassive = 50.8 [1/s] )

#1

#2

#3

Performance with 6 external coils with 10 s time constantsCan not stabilize RWM with only Gp[v/w] in ITER Baseline Design

Vcc = ( gain * sensor flux) still no blanket modules

10-1

100

101

102

103

2.5 3 3.5

tarragona.2005

passive growth rate (bench)G Gp=e+9G+ Gp=e+9G Gp=e+10G+ Gp=e+10

grow

th ra

te [

1/s]

bn

idea

l wal

l lim

it

passive

Vcc

= 109 * (sensor flux)

Vcc

= 1010 * (sensor flux)

tarragona.2005

No stabilizedRegionsUsing only Gp

only Vcc = sensor flux * gain VALEN results voltage control6 external coils with L/R = 10. sno ports, no blanket modules

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10-1

100

101

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103

108 109 1010 1011 1012

tarragona.2005

g for Gp scan

grow

th ra

te [

1/s]

Gp [v/weber] scan @ bn = 3.22

tarragona.2005

passive growth rateat b

n = 3.22 ( s=0.1 )

scan in Gp (proportional gain)VALEN results voltage control6 external coils with L/R = 10. Sno ports, no blanket modules

No stabilizationwith only Gp(gain onsensor flux)

10-1

100

101

102

103

2.5 3 3.5

tarragona.2005

passive growth rate (bench)g Gp/Gd=e8/e8g+ Gp/Gd=e8/e8g Gp/Gd=e9/e9g+ Gp/gd=e9/e9

grow

th ra

te [

1/s]

bn

tarragona.2005

idea

l wal

l lim

it

passive

Gp [v/w] = 108

Gd [v/v] = 108

Gp [v/w] = 109

Gd [v/v] = 109

3.18

100

101

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108 109 1010

tarragona.2005

g Gd scan Gp=e+9 s=0.1

grow

th ra

te [

1/s]

Gd [v/v] scan @ fixed bn = 3.22 & Gp [v/w] = 109

tarragona.2005

Performance with 6 external coils with 10 s time constantsInvestigate combined Gp [v/w] & Gd [v/v] gainVcc = Gp x(sensor flux ) + Gd x( sensor voltage), still no blanket modules

Stabilized to bn = 3.18When both Gp & Gd used

Could not reachbn = 3.22 with different Gd

Selectedgains

10-1

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101

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106

2.5 3 3.5 4 4.5 5 5.5 6

tarragona.2005

passive growth rate (bench)passive g PBMpassive g ABMg pWB p9 d9g+ pWB p9 d9g ABM p9 d9g+ ABM p9 d9

grow

th ra

te [1

/s]

bn

tarragona.2005

Performance with 6 external coils with 10 s time constantsSame Gp & Gd, add blanket modules to model ( no ports)

Gain settings:Gp = 109 [v/w]Gd = 109 [v/v]

passiveBest bn = 3.177( with all blanket modules)

Best bn = 3.189( with blanket modulesremoved from mid planeports)

BestResultsAbout same as benchmark !

3.5 4.86 5.21

Recall ideal wall bn limits

Extended ITER RWM analysis6 interior coils

6 internal coilsin symmetrical arrangement( 3 pairs )

Blanket modules andInterior RWM coils shown above

Extended ITER RWM analysis7 internal coils

7 internal coilsno symmetry

7 internal coilsand all blanket modulesshown

Neutralbeams here ?

Extended ITER RWM analysisRemove blanket modules at mid plane ports

7 internal coilsno symmetry

7 internal RWM coilsand blanket modulesshown, blanket modules removedat all radial ports

Neutralbeams here ?

10-1

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104

2.5 3 3.5 4 4.5 5 5.5

tarragona.2005

passive g ABMintcg #4 ABM e+7intc g #4 ABM e+8intc g #4 ABM e+9intc g+ #4 ABM e+9

grao

wth

rate

[1/s

]

bn

tarragona.2005

idea

l wal

l lim

it

best resultsb

n = 3.62

Cb = 41% (2.52 / 5.21)

Performance with 6 internal coils, all blanket modulesOne coil in every third radial port (symmetrical)Exceeds best performance with exterior coils

passive

#1

#2

#3

#1 Gp=107 [v/w]

#2 Gp = 108

#3 Gp = 109

6 internalcoils connectedInto 3 pairsEach pair hasL/R = 7.2e-6 H /360.e-6 W= 20. ms

Stabilize up to bn = 3.62

No optimizationwas done.Only Gp used !

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tarragona.2005

passive g ABMintc g #5 ABM e+7intc g #5 ABM e+8intc g+ #5 ABm e+8intc g #5 ABM e+9intc g+ #5 ABM e+9

grow

th ra

te [

1/s]

bn

tarragona.2005

best resultsb

n = 3.94

Cb = 53% ( 2.52 / 5.21 )

idea

l wal

l lim

it

Performance with 7 internal coils, again better thanexternal coils, one coil every other radial portHas best performance with all blanket modules

#1 Gp=107 [v/w]

#2 Gp = 108

#3 Gp = 109

7 single coils Each coil hasL/R = 3.6e-6 H /180.e-6 W= 20. ms

passive

#1

#2

#3

Stablize up tobn = 3.94

No optimizationwas done.Only Gp used !

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100

101

102

103

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105

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tarragona.2005

passive g PBMintc g 005PBM e+7intc g #5 PBM e+8intc g+ #5 PBM e+8intc g 005PBM e+9intc g+ 005PBM e+9

grow

th ra

te [

1/s]

bn

tarragona.2005

idea

l wal

llim

it

best resultsb

n = 4.83

Cb = 98.7%

Removing blanket modules in front of internal coilsGives best of all cases Cb = 98.7% ( 2.52 / 4.86), 7 interior coils with one coil every other radial port

#1 Gp=107 [v/w]

#2 Gp = 108

#3 Gp = 109

7 single coils each coil hasL/R = 3.6e-6 H /180.e-6 W= 20. ms

All blanket modulesIn front of radial portswere removed, this lowers passive performance

passive

#1

#2

#3

Stablize up tobn = 4.83

No optimizationwas done.Only Gp used !

Graphical summary VALEN RWM best resultsInternal RWM coils perform significantly better than external RWM coils

passiveext coilsno blanketmodules

Interiorcoils withall blanketmodules6

7

7 interiorcoils with blanket modulesremovedat midplane ports

Ideal wallbn limits

ports blankets RWM coils bn Cb g[1/s] (passive)

VALEN RWM active control performance limits in ITER

no no continuous 3.196 69% 43.9 (benchmark) ( 2.52 / 3.50)

no no 6 ext. coils 3.18 67.6% 40.9 ( 2.52 / 3.50)

no 9.ms 6 ext coils 3.177 24.4 % 16.38 ( 2.52 / 5.21)

yes 9.ms 6 int. coils 3.62 41% 52.5 ( 2.52 / 5.21)

yes 9.ms 7 int. coils 3.94 53% 110.8 ( 2.52 / 5.21)

yes 9.ms* 7 int. coils 4.83 98.7% 4061. *(except at ports ) ( 2.52 / 4.86 )

Conclusions VALEN benchmarking

• VALEN RWM continuous coil benchmark model reachesbn = 3.196 or Cb = 69% (2.52 / 3.50) [only the double wallvacuum vessel in this model].

• Presence of all blanket modules ( 9 ms each) extend theideal bn limit from 3.50 to 5.21

• ITER baseline design (no blankets, 6 ext coils with L/R=10. s & voltage control) requires both Gp & Gd (sensorflux and sensor voltage) gain, this model has aboutsame performance as continuous coil benchmark model

• Extended ITER models with internal RWM coils performssignificantly better than baseline ITER design: bn = 3.94with all blanket modules and bn = 4.83 with blanketmodules removed on mid plane radial ports

2.5

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5.5

0 0.1 0.2 0.3 0.4 0.5

mapping from VALEN 's' to bn

use conservative fitbeta-n DCONlinear2.52+7.45*s + s8s(-4.08)

b n

s (VALEN) tarragona.2005

points derivedfrom CHEASEequilibria

linear fitbn = 2.5668 + 6.5044 *s

quad fit is conservativebn = 2.5232 + 7.4545*s - 4.0841*s*s

Mapping from s to bn

VALEN parameter s = - dW / (LI2/2)no wall bn limit = 2.52 from conservative fit

Here LI2/2 isthe energyof the currentdistribution thatproduces Bn

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ITER RWM benchmarkingplasma, walls, control coils,

blanket modules, & Bp sensorsin Zvv[m]out Zvv[m]Zsep(m)int coils Z[m]sensor Z[m] int coilsZ bl [m]ext coils Z[m]

Z [m

]

R [m]ITER.RWM.comparison

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0

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1

1.5

2

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radial view of mid plane port

& interior RWM coilz rwm coilz mid plane port

z [m

]

local 'y' [m](toroidal)

0.174 [m]

0.1

[m]

0.22

[m]

each internal RWMcoil covers 9.05 degrees(in toroidal direction)

10-5

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6 6.5 7 7.5 8 8.5 9 9.5 10

Br ext(pairs) @z=0.45Br int(pairs) @ z=0.61Br int(single) @ z=0.61

Br [

T ]

fro

m 1

KA

curre

nt

R [m]

28 turnscoil pairs

internal coils ( 1 turn )singles or coil pairshave ~ same field

michio.06.2005

RWM Coil Concept for ITER

• Baseline RWM coils located outside TF coils

Applying FIRE-Like RWM Feedback Coils to ITER Increases b-limit for n = 1 from bN = 2.5 to ~4

• Integration and Engineering feasibility of internal RWM coils is under study.

VALEN Analysis Columbia University

No-walllimit

FIRE-like RWM coils would havelarge stabilizing effect on n=1

RWM Coils in every thirdport, no shield module

G. Navratil, J. Bialek Columbia University

5.04.03.02.02.010 - 2

10- 1

10 0

10 1

102

10 3

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105

10 6

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

Data from "ITER.09.2003"

beta-n (new)gr

owth

rat

e [

1 /

s ]

stable < 4.93

• FIRE-like RWM coils would be locatedinside the vacuum vessel behind shieldmodule but inside the vacuum vessel on theremovable port plugs.

BaselineRWM Coils

Outboard First Wall for FIRE

Be Cu Tile SS VV

WallCu

Cladding

ITER First Wall Panel

Be Cu Tile

SS Back plate

0 10 20 30 40 50 60 70mm

80 90

steady-state

Prad = 0.5 MW/m2

FIRE and ITER First Wall Design Concepts are Similar

60 sinertial

SS VV

WallSteel-water

shield

H2O Cooled Shield Module

TF

TF

~ 50 cm, not to scale

SS VV1

SS VV2

37 cm, not to scale

Gn = 2.2 MW/m2

Prad = 0.5 MW/m2

Gn = 0.5 MW/m2

+

+