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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
Contents
◦ 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 Pellets
2
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
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
• Heat transport coefficients
- Inside the magnetic island
χe,i = Fχ,NTM (NTM transport Enhancement Factor)
: Arbitrary constant value
- In the pre-ELM phase
- For ρ = 0.0-0.925
χe,i = χe,iNEO + χe,iITG/TEM + χe,iRB + χe,iKB
- For ρ = 0.925-1.0
χe,i = χe,iNEO
: MMM95
- In the ELM burst phase
- For ρ = 0.0-0.925
χe,i = χe,iNEO + χe,iITG/TEM + χe,iRB + χe,iKB
- For ρ = 0.925-1.0
χe,i = Fχ,ELM (ELM transport Enhancement Factor)
: Arbitrary constant value
Simulation Setup
• Heat transport coefficients
- Inside the magnetic island
χe,i = Fχ,NTM (NTM transport Enhancement Factor)
: Arbitrary constant value
- In the pre-ELM phase
- For ρ = 0.0-0.925
χe,i = χe,iNEO + χe,iITG/TEM + χe,iRB + χe,iKB
- For ρ = 0.925-1.0
χe,i = χe,iNEO
: MMM95
- In the ELM burst phase
- For ρ = 0.0-0.925
χe,i = χe,iNEO + χe,iITG/TEM + χe,iRB + χe,iKB
- For ρ = 0.925-1.0
χe,i = Fχ,ELM (ELM transport Enhancement Factor)
: Arbitrary constant value
Simulation Setup
• ELM criterion
Hyunsun Han et al., ITPA IOS 2010, Seoul, Korea
Simulation Setup
[1] H.R Wilson et al., NF 40 713 (2000)
[2] Presented by C. Kessel in ITPA-SSO (2005)
[3] A. Loarte et al., PPCF 45 1549 (2003)
• ELM criterion
𝛼𝑀𝐻𝐷
2𝜇0 𝑅𝑞 2 𝑑𝑝
≡−
𝐵2
𝑑𝑟
2
2
𝛼𝑐 ≡ 0.4s 1 + 𝜅95 1 + 5𝛿95
[1]
[2]
𝜅95 = 1.75, 𝛿95 = 0.50
Fχ,ELM(ρ=0.925) ~ 200
[3]
Simulation Setup
• The Modified Rutherford Equation (MRE) for NTMs
t R dw
rs dt
= D'0 + D BS + DGGJ + D ECCD + D ECH
2
é
L
w
t R dw
jbs q
jec
w PechH ù
marg
= D'0 rs + dD'rs + a2
- K1 - a H FH
ê1ú
2
rs dt
j|| w êë 3w
jbs
wdep I ec úû
Momentum Transport Equation
 Toroidal angular momentum transport equation[1]
 Toroidal Reynolds stress[1]
 Momentum diffusivity[2]
 Turbulent Equipartition pinch[3]
 Residual stress[4,5]
[1]
[2]
[3]
[4]
[5]
P.H. Diamond et al., NF 49 045002 (2009)
S.D. Scott et al., PRL 64 531 (1990
T.S. Hahm et al., PoP 14, 072302 (2007)
M. Yoshida et al., PRL 100 105002 (2008)
M. Yoshida et al., 23rd IAEA-FEC, Dajeon Korea (Oct, 2010)
Momentum Transport Equation
 Toroidal angular momentum transport equation[1]
 Toroidal Reynolds stress[1]
 Momentum diffusivity[2]
 Turbulent Equipartition pinch[3]
 Residual stress[4,5]
[1] P.H. Diamond et al., NF 49 045002 (2009)
[2] S.D. Scott et al., PRL 64 531 (1990
What[3]could
be
a reasonable
boundary condition?
T.S. Hahm
et al.,
PoP 14, 072302 (2007)
[4] M. Yoshida et al., PRL 100 105002 (2008)
[5] M. Yoshida et al., 23rd IAEA-FEC, Dajeon Korea (Oct, 2010)
Turbulence driven convective pinch velocity
TEP(Turbulent Equipartition Pinch) velocity
Fballoon quantifies the ballooning mode
structure of the turbulence.
Typical outward ballooning
flucturations(peaked at the low-B side),
Fballoon ~1>0
CTh(Curvature driven Thermal) flux
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
MA = vtor/CA
• No NBI or negligible
momentum input
• ßN =1.9 ~ 2.2
J.E. Rice et al, NF 47 1618 (2007)
Intrinsic Rotation :
Rice scaling for ITER extrapolation
MA = vtor/CA
• No NBI or negligible
momentum input
• ßN =1.9 ~ 2.2
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
TCV
r/a ~0.6-0.7 (q=2 surface)
JT-60U
r/a ~0.25
J.E. Rice et al, NF 47 1618 (2007)
(q=2 surface)
(flat profile)
Intrinsic Rotation :
Rice scaling for ITER extrapolation
MA = vtor/CA
• 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)
B.C. Scan for Rice Scaling
MA
q
0.10
8
0.08
B.C.
B.C.
B.C.
0.06
0.014
0.01
0.006
• Without NBI torque
Used for scans
6
 MA ~ 0.025
near q=2 surface
4
 B.C. at ρ=0.9
0.04
2
0.02
0.00
0.0
0.2
0.4
0.6
ρ
0.8
0
1.0
→ MA0.9 ~ 0.01
ω = 14.5 kRad/s
vTOR = 90 km/s
accords with the
scaling
B.C. Scan for RWM Suppression
MA
 RWM suppression
requirements:
- MA ~ 0.02-0.05
at the centre for
peaked profiles
0.10
0.08
0.06
B.C.
B.C.
B.C.
B.C.
0.01
0.006
0.004
0.002
Used as reference
0.04
0.02
0.00
0.0
0.2
0.4
0.6
0.8
ρ
Yueqiang Liu et al, NF 44 232 (2004)
 MA0.9 ≥ 0.0034
ω ≥ 4.8 kRad/s
vTOR ≥ ~ 30 km/s
for suppression
of RWM
→ Enough rotation
to suppress RWM
1.0
with MA0.9 ~ 0.01?
Prandtl Number Scan
MA
ω (kRad/s)
0.10
0.08
Pr 0.5
Pr 1.0
Pr 1.5
120
0.06
90
0.04
60
30
0.02
0.00
0.0
0.2
0.4
0.6
ρ
0.8
0
1.0
 Profile NOT
sensitive to
Prandtl number
due to pinching
flux
Convective Momentum Pinch Scan
MA
ω (kRad/s)
0.10
0.08
Fballoon
Fballoon
Fballoon
2.0
1.5
1.0
120
0.06
90
0.04
60
0.02
30
0.00
0.0
0.2
0.4
0.6
ρ
0.8
0
1.0
 Profile sensitive
to Convective
momentum pinch
Residual Stress Scan
MA
ω (kRad/s)
0.10
0.08
αk
αk
αk
0
0.5α
1.0α
120
0.06
90
0.04
60
30
0.02
0.00
0.0
0.2
0.4
0.6
ρ
0.8
0
1.0
 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 minority
concentration is not clear but the poloidal shear
force
is
strongly
depend
on
minority
concentration.
Counter Torque by ICRH
0.25
0.4
0.2
0.3
0.2
0.15
 /2
0.1
toroidal force at (  =1) [N]
toroidal force at (  =1) [N]
TOROIDAL
Force on last flux surface
-/2

0.05
H-minority
0
-0.05
-0.1
0.1
0
-0.1
-0.2
-0.3
-0.15
-0.4
-0.2
-0.5
-0.25
ne = 5×1019 m-3
 /2
3He-minority
-/2
0
5
10
15
20
Hydrogen concentration [%]
25
-0.6
30

0
5
10
15
20
He concentration [%]
25
30
25
30
3
0.02
0.16
 /2
0.12
poloidal force at ( =1) [N]
toroidal force at (  =1) [N]
POLOIDAL
-/2

H-minority
 /2
0.14
- /2
0.015
0.01
0.005
0

0.1
3He-minority
0.08
0.06
0.04
0.02
-0.005
0
-0.01
0
5
10
15
20
Hydrogen concentration [%]
25
30
-0.02
0
5
10
15
20
He concentration [%]
3
Toroidal force strongly depend on antenna phase and large than poloidal force.
H-minority
ne = 5×1019 m-3
Counter Torque by ICRH
Toroidal & Poloidal Force Profile
0.2
 =
0.1
0
0
F  ( ) [N]
0.12
1% H
2% H
5% H
10% H
20% H
30% H
0.1
0.08
0.06
0.04
0
-0.05
1% H
2% H
5% H
10% H
20% H
30% H
-0.1
-0.15
0.02
0
F  ( ) [N]
0.05
 = /2
0.14
0
0.1
0.2
0.3 0.4
0.5 0.6 0.7
nornalized minor radius 
0.8
0.9
-0.2
1
0.06
-0.15
-0.25
0
0.1
0.2
0.3 0.4
0.5 0.6 0.7
nornalized minor radius 
0.8
0.9
1
 = -/2
0
0
0.1
0.2
0.3 0.4
0.5 0.6 0.7
nornalized minor radius 
0.8
0.9
1
0.05
0.05
0.02
0
-0.04
1% H
2% H
5% H
10% H
20% H
30% H
 = /2
-0.06
F  ( ) [N]
-0.02
0
-0.08
-0.1
-0.05
1% H
2% H
5% H
10% H
20% H
30% H
 =
-0.1
F  ( ) [N]
0
0
F  ( ) [N]
-0.1
-0.2
0.1
0.04
0
-0.15
-0.05
1% H
2% H
5% H
10% H
20% H
30% H
-0.1
 = -/2
-0.15
0
-0.2
-0.12
-0.14
1% H
2% H
5% H
10% H
20% H
30% H
-0.05
0.16
F  ( ) [N]
TOROIDAL
0.18
POLOIDAL
0
0.15
0
0.1
0.2
0.3 0.4
0.5 0.6 0.7
nornalized minor radius 
0.8
0.9
1
-0.25
0
0.1
0.2
0.3 0.4
0.5 0.6 0.7
nornalized minor radius 
0.8
0.9
1
-0.2
0
0.1
0.2
0.3 0.4
0.5 0.6 0.7
nornalized minor radius 
0.8
Toroidal force is smooth function of minor radius and almost monotonically
increases as y increases. Input poloidal force is small but it possibly makes
strong shear flow near MC regime.
0.9
1
Plasma Profiles with NTM and ELM
@ ~550 s
After ELM burst
Time Trace of ELMs
4
Te [keV]
3
Ti [keV]
2
1
550.2
550.4
550.6
550.8
551.0
Simulation Time [s]
551.2
ELM Characteristics Studies
1. Scan of ELM enhancement factor; Fχ,ELM(ρ=0.925)
Fχ,ELM(ρ=0.925)
= 200, 400, 600,
800, 1000
ELM Characteristics Studies
1. Scan of ELM enhancement factor; Fχ,ELM(ρ=0.925)
2. Scan of ELM crash duration; tELM,Crash
tELM,Crash : 1 ms, 2 ms
tELM,Crash
tbetween ELMs
4
Te [keV]
3
2
1
550.6
550.8
Simulation Time [s]
Results of ELM characteristics (1)
@ ~550 s
@ ~550 s
Results of ELM characteristics (2)
@ ~550 s
@ ~550 s
Density Profile Scan
ITER
n0/<n>vol
@ ~550 s
eff
Density peaking factor ~ 1.7
H. Weisen et al, IAEA (2006)
C. Angioni et al, NF 47 1326 (2007)
Density Profile Scan
@ ~550 s
Flat ne
Profile
Peaked ne
Profile
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
Vtor
unit
Small ELM Event
αc and αMHD During the Events
Effect of Loop Voltage Variation
@ ~550 s
@ ~550 s
①②③ ④
⑤
4
3
Te [keV]
2
1
550.80
550.85
550.90
550.95
Simulation Time [s]
551.00
Ideal MHD Stability Analysis
• Helena[1]
- 2D fixed boundary equilibrium solver using finite element method
• 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)
Ideal MHD Stability Analysis
• 5 equilibrium point in an ELM cycle → j – α scan for stability analysis
Ideal MHD Stability Analysis
1.1
<j>max
1.0
1
0.9
0.8
5
4
2 3
0.7
0.6
γ/ω0 = 0.01
0.5
3
4
5
α
6
7
Simulation Setup
• ELM criterion
Hyunsun Han et al., ITPA 2010, Seoul, Korea
NTM Onset Criteria & Stability Diagram
 pe (r s /L p )
1.5
JET
DIII-D
ASDEX U
ITER
Regression fit
against i* alone:
1.08
Pe=5.5i*
ITER scenario 2
operation point
0
0
 i*
0.3
cf) ITER ops. point
→ ITER H-mode scenario 2
* Buttery R.J. et al 2004 IAEA FEC (Vilamoura, 2004) (Vienna: IAEA)
CD-ROM file EX/7-1
NTM Onset Criteria & Stability Diagram
 pe (r s /L p )
1.5
JET
DIII-D
ASDEX U
ITER
ITER simul.
point
At 𝑡 = 520 𝑠,
Regression fit
against i* alone:
1.08
Pe=5.5i*
𝑟𝑠
𝛽𝑝𝑒 ( )~1.00541
𝐿𝑝
∗
with 𝜌𝑖𝜃 ~0.001
ITER scenario 2
operation point
0
0
 i*
0.3
cf) ITER ops. point
→ ITER H-mode scenario 2
* Buttery R.J. et al 2004 IAEA FEC (Vilamoura, 2004) (Vienna: IAEA)
CD-ROM file EX/7-1
NTM Onset Criteria & Stability Diagram
At 𝒕 = 𝟓𝟐𝟎 𝒔,
Time Evolution of the Island Width
Validation of the Modelling Tool
• TCV: (2,1) stabilisation by ECH in OH plasmas
0.3
0.2
#40539
Ip (MA)
0.1
0.3
0.2
PECRH/2 (MW)
0.1
0.0
0.0
0.75
0.75
N
0.50
0.25
0.00
0.00
MHD
50
0
0
-50
-50
-100
0.0
N
100
MHD
50
PECRH/2 (MW)
0.50
0.25
100
#40543
Ip (MA)
0.5
1.0
1.5
Time (s)
2.0
-100
0.0
0.5
1.0
1.5
Time (s)
42
K.J. Kim et al, EPS (2011)
2.0
Validation of the Modelling Tool
• ASDEX Upgrade: (3,2) stabilisation by ECCD
1.5
#21133
Ip (MA)
1.0
1.2
0.5
#25845
Ip (MA)
0.8
0.4
PNB/15 (MW)
PNB/10 (MW)
0.0
0.0
3
6
2
4
BT (T)
1
o
launching angle  ( )
0
0
4
3

3
PECRH (MW)
2
PECRH (MW)
2

2
H98
1
H98

1
0
0
3.0
1.5
2
1
0
-1
-2
EvenN
0.0
OddN
-1.5
-3.0
0
1
2
3
4
Time (s)
5
EvenN
OddN
0
6
1
2
43
Yong-Su Na et al, IAEA (2010)
3
Time (s)
4
5
6
Validation of the Modelling Tool
• ASDEX Upgrade: (3,2) stabilisation by ECCD
30
4.0
20
3.0
15
2.0
10
5
1.0
0
0.10
0.0
5.0
25
4.0
20
3.0
Log
Frequency (kHz)
5.0
25
Log
Frequency (kHz)
30
15
2.0
10
1.0
5
0
0.08
Island Width, w (m)
Island Width, w (m)
0.0
Exp.
0.08
0.06
0.04
Simul.
0.02
0.00
1.0
1.5
2.0
2.5
Time (s)
3.0
3.5
4.0
44
Exp.
0.06
0.04
Simul.
0.02
0.00
1.0
1.5
Yong-Su Na et al, IAEA (2010)
2.0
2.5
Time (s)
3.0
3.5
4.0
Real-time Feedback Control of NTMs in KSTAR
plasma
Launcher angle
response
controller
PECH
Island width
Location of Island
ECH & ECCD
Te
jECCD
q
jbs
jOH
j
Alignment
between NTM and
ECCD
To control the NTM
Replacing the missing bootstrap current inside island
by localised external current drive
System Identification
Defining the input and the output parameter
The input parameter: the poloidal angle of the ECCD launcher
The output parameter: the width of the (3,2) island
Simulation by ASTRA with/without modulation of the input parameter
Pseudobinary noise modulation applied
Creating a database for the difference between with and without modulation case
Reference case: without ECCD as well as without modulation
the poloidal angle
of the ECCD launcher
plasma
response
the width
of the (3,2) island
System Identification - Estimation
4
2
0
-2

y  yˆ 
Fit accuracy (%)  1 
 100
y  y 

Δ(Island width)
-4
Fit Accuracy
6
ASTRA
3
0
P1D1 model : 73.51 %
P2DIZ model
-3
4.0
P2DIZ model : 77.24 %
P1D1 model
n4s9 model
4.5
5.0
5.5
6.0
n4s9 model : 65.98 %
6.5
Time (s)
Estimating the linear/nonlinear mathematical models
of the dynamic system
Computing using various parametric models
Choosing the best estimated and stable model for the NTM control
Δ(Island width)
Δ(Poloidal angle)
System Identification - Validation
3
2
1
0

y  yˆ 
Fit accuracy (%)  1 
 100
y  y 

-1
2
Fit Accuracy
n4s9 model
P2DIZ model
P1D1 model : 97.98%
0
P2DIZ model : 88.74%
P1D1 model
-2
-4
4.0
n4s9 model : -31.66%
ASTRA
4.1
4.2
4.3
4.4
4.5
4.6
Time (s)
Validating the estimated model
Test the model with another form of the modulation
4.7
0.12
ECCD
w/o control
0.10
94
Poloidal angle (°)
Island Width, w (m)
Real-time Feedback Control Simulation
0.08
0.06
0.04
ECCD
w control
0.02
0.00
no ECCD
1
2
3
4
93
92
91
90
6
ECCD
7
ECCD w/o control
89
88
2.85
5
ECCD w control
2.90
2.95
3.00
3.05
3.10
3.15
Time (s)
Time (s)
The ECCD is applied at 2.85 s
The initial launcher misaligned
(toroidal angle of 190˚, poloidal angle of 90˚)
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
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)
Contents
◦ 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 Pellets
51
The modified Rutherford equation for NTM stability
t R dw
rs dt
= D'0 + D BS + DGGJ + D ECCD + D ECH
2
jbs Lq é wmarg
jec
w PechH ù
= D'0 rs + dD'rs + a2
- K1 - a H FH
ê1ú
2
rs dt
j|| w êë 3w
jbs
wdep I ec úû
t R dw
1st : Conventional tearing mode stability: assumed as 0rs   m for m/n NTM
assumed as   0   w for m/n NTM in ohmic phases*
2nd : Tearing mode stability enhancement by ECCD: Westerhof’s model with no-island assumption
j
5 3 / 2 Lq
 rs  
a2
F (e ) ec  , where the misalignment function F (e)  1  2.43e  1.40e 2  0.23e 3
32
 ec
j∥
3rd : Destabilisation from perturbed bootstrap current:
a2 fitted by inferred size of saturated NTM island from ISLAND or estimated by experiments
w2
w2  wd2
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
t R dw
rs dt
= D'0 + D BS + DGGJ + D ECCD + D ECH
2
jbs Lq é wmarg
jec
w PechH ù
= D'0 rs + dD'rs + a2
- K1 - a H FH
ê1ú
2
rs dt
j|| w êë 3w
jbs
wdep I ec úû
t R dw
4th : Stabilisation from small island & polarization threshold
(Glasser-Green-Johnson (GGJ) term ):
wmarg  2 1/ 2  i (= twice ion banana width)
aGGJ
w  0.2w
2
2
d
where aGGJ =
6DR
bp
and wd » wmarg for ohmic phases*
5th : Stabilisation from replacing bootstrap current by ECCD:
K1 calculated from improved Perkins’ current drive model
6th : Stabilisation by the ECH effect**:
rs D'H ,CD =
16m0 Lq PhH ,CD
FH,CD (w*, xdep, D)
2
p Bp wH,CD
R. J. La Haye et al., Nuclear Fusion 46 451 (2006)
* O. Sauter et al., Physics of Plasmas 4,1654 (1997)
**D. De Lazzari et al., Nuclear Fusion 49, 075002 (2
009)
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