Integrated Simulation of Hybrid Scenarios in Preparation for Feedback Control

Yong-Su Na, Hyun-Seok Kim, Kyungjin Kim,

Won-Jae Lee, Jeongwon Lee

Department of Nuclear Engineering

Seoul National University

◦ Simulation Setup- ELM

- NTM

- Momentum Transport

◦ Momentum Transport Simulation

◦ ELM Simulation- Sensitivity analysis- Small ELM event- Ideal MHD analysis

◦ NTM Simulation

◦ Real-time Control Simulation of NTM in KSTAR- Model validation- Feedback control simulation

◦ ELM Control by Pellets2

Contents

Ip 12 MA

BT 5.3 T

τP*/τE 5.0

fD/(fD+fT) 0.5

fBe 2 %

fAr 0.12 %

PNBI 33 MW

PICRF 20 MW

PEC 20 MW

Rb, zb for fixed boundary

Simulation Setup• Based on the hybrid benchmark guideline• Plasma in a flattop phase (as stationary as possible)• Density prescribed. Solving the heat transport in the whole plasma.

Solving momentum transport ρ = 0-0.9

χe,i = χe,iNEO + χe,i

ITG/TEM + χe,iRB + χe,i

KB

- In the pre-ELM phase

χe,i = χe,iNEO + χe,i

ITG/TEM + χe,iRB + χe,i

KB

- In the ELM burst phase

χe,i = Fχ,ELM (ELM transport Enhancement Factor)

: MMM95

: Arbitrary constant value

Simulation Setup• Heat transport coefficients

- Inside the magnetic island

χe,i = Fχ,NTM (NTM transport Enhancement Factor)

: Arbitrary constant value

- For ρ = 0.0-0.925

- For ρ = 0.925-1.0

- For ρ = 0.0-0.925

- For ρ = 0.925-1.0

χe,i = χe,iNEO

χe,i = χe,iNEO + χe,i

ITG/TEM + χe,iRB + χe,i

KB

- In the pre-ELM phase

χe,i = χe,iNEO + χe,i

ITG/TEM + χe,iRB + χe,i

KB

- In the ELM burst phase

χe,i = Fχ,ELM (ELM transport Enhancement Factor)

: MMM95

: Arbitrary constant value

Simulation Setup• Heat transport coefficients

- Inside the magnetic island

χe,i = Fχ,NTM (NTM transport Enhancement Factor)

: Arbitrary constant value

- For ρ = 0.0-0.925

- For ρ = 0.925-1.0

- For ρ = 0.0-0.925

- For ρ = 0.925-1.0

χe,i = χe,iNEO

Simulation Setup• ELM criterion

Hyunsun Han et al., ITPA IOS 2010, Seoul, Korea

𝛼𝑀𝐻𝐷≡−2𝜇0𝑅𝑞

2

𝐵2 ( 𝑑𝑝𝑑𝑟 )[2] Presented by C. Kessel in ITPA-SSO (2005)

[1] H.R Wilson et al., NF 40 713 (2000)

𝛼𝑐≡ 0.4 s (1+𝜅 95❑2 (1+5 𝛿95❑

2 ))[1]

, [2]

[3] A. Loarte et al., PPCF 45 1549 (2003)

[3]Fχ,ELM(ρ=0.925) ~ 200

Simulation Setup• ELM criterion

Simulation Setup• The Modified Rutherford Equation (MRE) for NTMs

Toroidal angular momentum transport equation[1]

Toroidal Reynolds stress[1]

Turbulent Equipartition pinch[3]

Residual stress[4,5]

[3] T.S. Hahm et al., PoP 14, 072302 (2007)[4] M. Yoshida et al., PRL 100 105002 (2008)

Momentum diffusivity[2]

[1] P.H. Diamond et al., NF 49 045002 (2009)[2] S.D. Scott et al., PRL 64 531 (1990

[5] M. Yoshida et al., 23rd IAEA-FEC, Dajeon Korea (Oct, 2010)

Momentum Transport Equation

Toroidal angular momentum transport equation[1]

Toroidal Reynolds stress[1]

Turbulent Equipartition pinch[3]

Residual stress[4,5]

[3] T.S. Hahm et al., PoP 14, 072302 (2007)[4] M. Yoshida et al., PRL 100 105002 (2008)

Momentum diffusivity[2]

[1] P.H. Diamond et al., NF 49 045002 (2009)[2] S.D. Scott et al., PRL 64 531 (1990

[5] M. Yoshida et al., 23rd IAEA-FEC, Dajeon Korea (Oct, 2010)

Momentum Transport Equation

What could be a reasonable boundary condition?

Turbulence driven convective pinch velocity

TEP(Turbulent Equipartition Pinch) velocity

CTh(Curvature driven Thermal) flux

Fballoon quantifies the ballooning mode structure of the turbulence.Typical outward ballooning fluctura-tions(peaked at the low-B side), Fballoon ~1>0

GTh quantifies the relative strength of contributions from ion temperature fluctuations related to the curvature driven thermoelectric effect.

T. S. Hahm et al., PoP 14 072302 (2007)

Intrinsic Rotation : Rice scaling for ITER extrapolation

J.E. Rice et al, NF 47 1618 (2007)

MA = vtor/CA

• No NBI or negligible momentum input

• ßN =1.9 ~ 2.2

Intrinsic Rotation : Rice scaling for ITER extrapolation

J.E. Rice et al, NF 47 1618 (2007)

Measurement point

JET r/a ~0.35

C-Mod r/a ~0.0 (flat profile)

Tore Supra r/a <0.17

DIII-D r/a ~0.8 (q=2 surface)

TCV r/a ~0.6-0.7 (q=2 surface)

JT-60U r/a ~0.25 (flat profile)

MA = vtor/CA

• No NBI or negligible momentum input

• ßN =1.9 ~ 2.2

Intrinsic Rotation : Rice scaling for ITER extrapolation

• No NBI or negligible momentum input

• ßN =1.9 ~ 2.2

• MA ~ 0.025 near q = 2 surface

• Find expected boundary condition for the ITER intrinsic rotation velocity

J.E. Rice et al, NF 47 1618 (2007)

MA = vtor/CA

0

2

4

6

8

0.0 0.2 0.4 0.6 0.8 1.00.00

0.02

0.04

0.06

0.08

0.10

ρ

q

MA ~ 0.025

near q=2 surface

B.C. at ρ=0.9

→ MA0.9 ~ 0.01

ω = 14.5 kRad/s vTOR = 90 km/s

accords with the scaling

B.C. 0.014B.C. 0.01B.C. 0.006

MA

B.C. Scan for Rice Scaling

• Without NBI torque

Used for scans

0.0 0.2 0.4 0.6 0.8 1.00.00

0.02

0.04

0.06

0.08

0.10

MA0.9 ≥ 0.0034

ω ≥ 4.8 kRad/s vTOR ≥ ~ 30 km/s

for suppression of RWM

ρ

RWM suppression requirements:

- MA ~ 0.02-0.05

at the centre for peaked profiles

B.C. 0.01B.C. 0.006B.C. 0.004B.C. 0.002

Yueqiang Liu et al, NF 44 232 (2004)

MA

→ Enough rotation to suppress RWM with MA0.9 ~ 0.01?

B.C. Scan for RWM Suppression

Used as reference

Profile NOT sensitive to Prandtl number due to pinching flux

ρ

0.0 0.2 0.4 0.6 0.8 1.00.00

0.02

0.04

0.06

0.08

0.10

0

30

60

90

120

Pr 0.5Pr 1.0Pr 1.5

ω (kRad/s)

Prandtl Number Scan

MA

Profile sensitive to Convective momentum pinchρ

0.0 0.2 0.4 0.6 0.8 1.00.00

0.02

0.04

0.06

0.08

0.10

0

30

60

90

120

Fballoon 2.0

Fballoon 1.5

Fballoon 1.0

ω (kRad/s)MA

Convective Momentum Pinch Scan

0.0 0.2 0.4 0.6 0.8 1.00.00

0.02

0.04

0.06

0.08

0.10

0

30

60

90

120

ρ

αk 0

αk 0.5α

αk 1.0α

Residual Stress Scan

ω (kRad/s)MA

Profile not so sensitive to the coefficient of the Residual stress term

Counter Torque by ICRH

Work being done by Dr. B.H. Park (NFRI)

We calculated the momentum transfer from RF waves.

The total toroidal force is much larger than the total poloidal force.

Even though the total poloidal force is negligible there is strong shear torque near MC layer.

The total force is almost proportional to the toroidal wave number and the RF power.

The direction of the force is strongly dependent on antenna phase.

In toroidal force, the dependence on the minor-ity concentration is not clear but the poloidal shear force is strongly depend on minority con-centration.

Counter Torque by ICRH ne = 5×1019 m-3

0 5 10 15 20 25 30-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

Hydrogen concentration [%]

toro

idal

for

ce a

t (

=1)

[N

]

/2

-/2

0 5 10 15 20 25 30-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

3He concentration [%]

toro

idal

for

ce a

t (

=1)

[N

]

/2

-/2

0 5 10 15 20 25 30-0.01

-0.005

0

0.005

0.01

0.015

0.02

Hydrogen concentration [%]

toro

idal

for

ce a

t (

=1)

[N

]

/2

-/2

0 5 10 15 20 25 30-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

3He concentration [%]

pol

oid

al f

orce

at

(=

1) [

N]

/2

-/2

Force on last flux surface

H-minority

3He-minority

3He-minority

H-minority

Toroidal force strongly depend on antenna phase and large than poloidal force.

TO

RO

IDA

LP

OLO

IDA

L

Counter Torque by ICRH

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

nornalized minor radius

F(

) [N

]

0 = /2

1% H

2% H

5% H

10% H

20% H

30% H

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

nornalized minor radius

F(

) [N

]

0 =

1% H

2% H

5% H

10% H

20% H

30% H

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.25

-0.2

-0.15

-0.1

-0.05

0

nornalized minor radius

F(

) [N

]

0 = -/2

1% H

2% H

5% H

10% H

20% H

30% H

Toroidal & Poloidal Force Profile

H-minority

Toroidal force is smooth function of minor radius and almost monotonically in-creases as y increases. Input poloidal force is small but it possibly makes strong shear flow near MC regime.

ne = 5×1019 m-3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.14

-0.12

-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

nornalized minor radius

F(

) [N

]

0 = /2

1% H

2% H

5% H

10% H

20% H

30% H

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

nornalized minor radius

F(

) [N

]

0 =

1% H

2% H

5% H

10% H

20% H

30% H

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.2

-0.15

-0.1

-0.05

0

0.05

nornalized minor radius

F(

) [N

]

0 = -/2

1% H

2% H

5% H

10% H

20% H

30% H

TO

RO

IDA

LP

OLO

IDA

L

@ ~550 s

Plasma Profiles with NTM and ELM

After ELM burst

Time Trace of ELMs

550.2 550.4 550.6 550.8 551.0 551.2

1

2

3

4

550.2 550.4 550.6 550.8 551.0 551.2

1

2

3

4

Simulation Time [s]

Te [keV]

Ti [keV]

Fχ,ELM(ρ=0.925)

= 200, 400, 600, 800, 1000

1. Scan of ELM enhancement factor; Fχ,ELM(ρ=0.925)

ELM Characteristics Studies

1. Scan of ELM enhancement factor; Fχ,ELM(ρ=0.925)

2. Scan of ELM crash duration; tELM,Crash

ELM Characteristics Studies

Simulation Time [s]

tELM,Crash

tbetween ELMs

550.6 550.8

1

2

3

4

tELM,Crash

Te [keV]

: 1 ms, 2 ms

Results of ELM characteristics (1)

@ ~550 s@ ~550 s

Results of ELM characteristics (2)

@ ~550 s@ ~550 s

@ ~550 s

eff

n0/<

n>

vol

ITER

H. Weisen et al, IAEA (2006)C. Angioni et al, NF 47 1326 (2007)

Density Profile Scan

Density peaking factor ~ 1.7

Flat ne Pro-file

Peaked ne

Profile

unit

Vtor

Pr 1 1

Fballoon 4 4

Residual 0.5 0.5

B.C. @ ρ=0.9 0.004 0.004

Ti / Te @ ρ=0.0 24.5 / 31.3 21.3 / 24.7 keV

Ti / Te @ ρ=0.925 3.66 / 4.17 5.63 / 6.32 keV

ne @ ρ=0.0 9.5 13.4 1019 m-3

ne @ ρ=0.925 8.68 5.3 1019 m-3

βN 2.19 2.27

Q 5.2 5.2

IBS 3.48 3.95 MA

INBI 1.33 1.46 MA

IECR 0.408 0.409 MA

IPL 12 12 MA

q(0) 0.702 0.714

Density Profile Scan@ ~550 s

Small ELM Event

αc and αMHD During the Events

Effect of Loop Voltage Variation

550.80 550.85 550.90 550.95 551.00

1

2

3

4

① ② ③ ④ ⑤

Te [keV]

Simulation Time [s]

@ ~550 s @ ~550 s

Ideal MHD Stability Analysis

• ELITE[2]

- 2D eigenvalue code using the energy principle- Difficult to handle reversed shear configurations

• MISHKA[3]

- Can handle reversed shear configurations- Not enough poloidal harmonic number m:

weakness of the edge calculation

[1] G.T.A. Huysmans et al, Proc. CP90 Conf. Computational Physics, Amsterdam (1991)[2] P.B. Snyder et al PoP 9 2037 (2002)[3] A.B. Mikhailovskii et al, Plasma Phys. Rep. 23 844 (1997)

• Helena[1]

- 2D fixed boundary equilibrium solver using finite element method

• 5 equilibrium point in an ELM cycle → j – α scan for stability analysis

Ideal MHD Stability Analysis

3 4 5 6 7

0.5

0.6

0.7

0.8

0.9

1.0

1.1

γ/ω0 = 0.01

1

2 34

5

α

<j>

max

Ideal MHD Stability Analysis

Simulation Setup• ELM criterion

Hyunsun Han et al., ITPA 2010, Seoul, Korea

0

1.5

0 0.3i *

pe

(rs/L

p)

JETDIII-DASDEX UITER

ITER scenario 2operation point

Regression fitagainst i

* alone:

Pe=5.5i*1.08

* Buttery R.J. et al 2004 IAEA FEC (Vilamoura, 2004) (Vienna: IAEA) CD-ROM file EX/7-1

cf) ITER ops. point → ITER H-mode scenario 2

NTM Onset Criteria & Stability Diagram

0

1.5

0 0.3i *

pe

(rs/L

p)

JETDIII-DASDEX UITER

ITER scenario 2operation point

Regression fitagainst i

* alone:

Pe=5.5i*1.08

* Buttery R.J. et al 2004 IAEA FEC (Vilamoura, 2004) (Vienna: IAEA) CD-ROM file EX/7-1

At ,

𝛽𝑝𝑒(𝑟 𝑠

𝐿𝑝

) 1.00541

with ITER simul.point

cf) ITER ops. point → ITER H-mode scenario 2

NTM Onset Criteria & Stability Diagram

At ,

NTM Onset Criteria & Stability Diagram

Time Evolution of the Island Width

42

• TCV: (2,1) stabilisation by ECH in OH plasmas

Validation of the Modelling Tool

0.0 0.5 1.0 1.5 2.0-100

-50

0

50

100

0.00

0.25

0.50

0.75

0.0

0.1

0.2

0.3

MHD

N

PECRH/2 (MW)

Ip (MA)

Time (s)

#40539

Time (s)

#40543

0.0 0.5 1.0 1.5 2.0-100

-50

0

50

100

0.00

0.25

0.50

0.75

0.0

0.1

0.2

0.3

MHD

N

PECRH/2 (MW)

Ip (MA)

K.J. Kim et al, EPS (2011)

43

• ASDEX Upgrade: (3,2) stabilisation by ECCD

0

1

2

3

4

0

1

2

3

0 1 2 3 4 5 6-3.0

-1.5

0.0

1.5

3.0

0.0

0.5

1.0

1.5

H98

BT (T)

PECRH (MW)

EvenN

OddN

Ip (MA)

PNB

/15 (MW)

#21133

Time (s)

0

1

2

3

0

2

4

6

0 1 2 3 4 5 6

-2-1012

0.0

0.4

0.8

1.2

H98

launching angle (o)

PECRH (MW)

EvenN

OddN

Ip (MA)

PNB

/10 (MW)

#25845

Time (s)

Validation of the Modelling Tool

Yong-Su Na et al, IAEA (2010)

44

• ASDEX Upgrade: (3,2) stabilisation by ECCD

0.0

1.0

2.0

3.0

4.0

5.0

Lo

g

0

5

10

15

20

25

30

Freq

uenc

y (k

Hz)

1.0 1.5 2.0 2.5 3.0 3.5 4.00.00

0.02

0.04

0.06

0.08

Simul.

Exp.

Isla

nd

Wid

th, w

(m

)

Time (s)

0

5

10

15

20

25

30

Freq

uenc

y (k

Hz)

0.0

1.0

2.0

3.0

4.0

5.0

Lo

g

1.0 1.5 2.0 2.5 3.0 3.5 4.00.00

0.02

0.04

0.06

0.08

0.10

Isla

nd

Wid

th, w

(m

)

Time (s)

Simul.

Exp.

Validation of the Modelling Tool

Yong-Su Na et al, IAEA (2010)

Real-time Feedback Control of NTMs in KSTAR

Launcher angle

ECH & ECCD

j

qTe

PECH

jECCD

jOH

Island widthLocation of Island

controller

Alignment between NTM

and ECCDTo control the NTM

Replacing the missing bootstrap current inside island by localised external current drive

plasma

re-sponse

jbs

System Identification

Defining the input and the output parameter

The input parameter: the poloidal angle of the ECCD launcherThe output parameter: the width of the (3,2) island

Simulation by ASTRA with/without modulation of the input parameter

Pseudobinary noise modulation appliedCreating a database for the difference between with and without modulation caseReference case: without ECCD as well as without modulation

plasma

response

the poloidal angleof the ECCD launcher

the widthof the (3,2) is-land

System Identification - Estimation

Estimating the linear/nonlinear mathematical models of the dynamic system

Computing using various parametric modelsChoosing the best estimated and stable model for the NTM control

100ˆ

1(%)

yy

yyaccuracyFit

P2DIZ model : 77.24 %P1D1 model : 73.51 %n4s9 model : 65.98 %

-4

-2

0

2

4

4.0 4.5 5.0 5.5 6.0 6.5

-3

0

3

6

n4s9 model

P2DIZ model

ASTRA

P1D1 model

Time (s)

Δ(I

slan

d w

idth

) Fit Accuracy

System Identification - Validation

P1D1 model : 97.98%P2DIZ model : 88.74%n4s9 model : -31.66%

-1

0

1

2

3

4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7-4

-2

0

2

ASTRA

P1D1 model

P2DIZ modeln4s9 model

Time (s)

Δ(P

oloi

dal a

ngle

)Δ

(Isl

and

wid

th) Fit Accuracy

Validating the estimated model

Test the model with another form of the modulation

100ˆ

1(%)

yy

yyaccuracyFit

Real-time Feedback Control Simulation

The poloidal angle controlled to deposit the ECCD on the exact location of the (3,2) island about 0.2 ˚ per 20 ms in real time

ECCD

2.85 2.90 2.95 3.00 3.05 3.10 3.1588

89

90

91

92

93

94

ECCD w/o control

ECCD w control

Po

loid

al a

ng

le (°)

Time (s)1 2 3 4 5 6 7

0.00

0.02

0.04

0.06

0.08

0.10

0.12

ECCDw control

ECCDw/o control

no ECCD

Isla

nd

Wid

th, w

(m

)

Time (s)

no ECCD

The ECCD is applied at 2.85 sThe initial launcher misaligned (toroidal angle of 190˚, poloidal angle of 90˚)

ELM Pacing by Pellets in KSTAR and ITER

Ki Min Kim et al, NF 51 063003 (2011)Ki Min Kim et al, NF 50 055002 (2010)

◦ Simulation Setup- ELM

- NTM

- Momentum Transport

◦ Momentum Transport Simulation

◦ ELM Simulation- Sensitivity analysis- Small ELM event- Ideal MHD analysis

◦ NTM Simulation

◦ Real-time Control Simulation of NTM in KSTAR- Model validation- Feedback control simulation

◦ ELM Control by Pellets51

Contents

The modified Rutherford equation for NTM stability

3rd : Destabilisation from perturbed bootstrap current:

fitted by inferred size of saturated NTM island from ISLAND or estimated by experiments2a

1st : Conventional tearing mode stability:assumed as for NTM 0 sr m m/n

2nd : Tearing mode stability enhancement by ECCD: Westerhof’s model with no-island assumption3 2

2

5

32( )

/q ec

sec

L jr a F e

j

∥

2 31 2 43 1 40 0 23( ) . . .F e e e e , where the misalignment function

assumed as for NTM in ohmic phases* 0 w m/n

22

2

dww

w

for ohmic phases* (The bootstrap current term can be increased when the heating is added.)

R. J. La Haye et al., Nuclear Fusion 46 451 (2006)* O. Sauter et al., Physics of Plasmas 4,1654 (1997)

The modified Rutherford equation for NTM stability

R. J. La Haye et al., Nuclear Fusion 46 451 (2006)

4th : Stabilisation from small island & polarization threshold (Glasser-Green-Johnson (GGJ) term ):

5th : Stabilisation from replacing bootstrap current by ECCD:

1 22 /marg iw (= twice ion banana width)

calculated from improved Perkins’ current drive model1K

**D. De Lazzari et al., Nuclear Fusion 49, 075002 (2009)

6th : Stabilisation by the ECH effect**:

for ohmic phases*22 2.0 d

GGJ

ww

a

andwhere

* O. Sauter et al., Physics of Plasmas 4,1654 (1997)