integrated simulation of hybrid scenarios in preparation for feedback control yong-su na, hyun-seok...
TRANSCRIPT
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)