Simulation studies of core heat transport in JT-60U plasmas with different toroidal rotation profiles
E. Narita1, M. Honda2, N. Hayashi2, H. Urano2, S. Ide2, T. Fukuda1
1Osaka Univ., 2JAEA
19th Numerical Experiment of Tokamak (NEXT) Meeting Kyoto Univ., Japan
29-30 August 2013
This work was carried out using the HELIOS supercomputer system at International Fusion Energy Research Centre, Aomori, Japan, under the Broader Approach collaboration between Euratom and Japan, implemented by Fusion for Energy and JAEA.
Improved confinement related to toroidal rotation
• The improved confinement mode with internal transport barriers (ITBs) has been observed in plasmas with the strong Er shear.
●co-NB □bal-NBI ▼ctr-NBI
[H. Shirai NF1999]
[H. Urano NF2008]
Introduction
Does toroidal rotation have little influence on core hear transport without the strong change in Er shear?
A) The pedestal temperature increases with co-toroidal rotation and profile stiffness.
B) Identical core temperature profiles have been observed for co- and counter- rotating plasmas with identical pedestal temperature.
Box type ITB
Conventional H-mode A) B)
1/14
-20
-15
-10
-5
0
5
0 0.2 0.4 0.6 0.8 1
Er_s46861_t09000_002
Er [kV/m]
E r [
kV/m
]
-20
-15
-10
-5
0
5
0 0.2 0.4 0.6 0.8 1
Er_s46861_t15000_002
Er [kV/m]
CoCtr
Influence of co-toroidal rotation on Te-ITB
[N. Oyama NF2007]
Parabolic type ITB
A) The slight difference in the core ne profile
B) Similar power deposition profiles
C) With a change in the toroidal rotation profile
– Pe increases larger in the core region
– Pi increases larger in the pedestal region and is maintained with similar profile
Points of these plasmas
0
1
2
3
4
5
0 0.2 0.4 0.6 0.8 1
s46861_t09000_TEM0-CDIF1_glf_exb_ibscop3_irotstab0_calden
ne [10^19 m^-3]
n e [10
19 m
-3]
Co46861 t9.0
0
1
2
3
4
5
0 0.2 0.4 0.6 0.8 1
s46861_t15000_TEM0-CDIF1_glf_exb_ibscop3_irotstab0_calden
ne [10^19 m^-3]
Ctr46861 t15.0
CoCtr
0
0.1
0.2
0.3
0 0.2 0.4 0.6 0.8 1
steady_s46861_t09000_002
SNBIE0 [MWm^-3]SNBIE1 [MWm^-3]
QN
B [
MW
m-3
]
0
0.1
0.2
0.3
0 0.2 0.4 0.6 0.8 1
steady_s46861_t15000_002
SNBIE0 [MWm^-3]SNBIE1 [MWm^-3]
ionco: 4.0517MWctr: 3.9127MW
electronco: 2.5248MW, ctr: 2.6829MW
Co46861 t9.0
Ctr46861 t15.0
CoCtr
0
10
20
30
0 0.2 0.4 0.6 0.8 1
steady_s46861_t09000_002
PRE0 [kPa]PRE1 [kPa]
P [k
Pa]
0
10
20
30
0 0.2 0.4 0.6 0.8 1
steady_s46861_t15000_002
PRE0 [kPa]PRE1 [kPa]
ion
electron
Co46861 t9.0
Ctr46861 t15.0
CoCtr
• The better Te-ITB with co-toroidal rotation has been observed.
• The difference in Er shear is small.
ne[1019m-3]
Er[kV/m]
QNB[MWm-3]
P[kPa]
Co
Bal
Ctr
Co
Ctr
2/14
A)
B) C)
Investigation of toroidal rotation effects on core heat transport
Investigate effects of toroidal rotation on core heat transport in conventional H-mode and parabolic type ITB plasmas using
• Transport models implemented in the transport code TOPICS
• The flux-tube gyrokinetic code GS2
Parallel flow Toroidal flow
Including radial electric field effects
Focus on ExB shear representing toroidal rotation in this study
First order equilibrium flows in Tokamaks
objective 3/14
TOkamak Prediction and Interpretation Code System [N. Hayashi PoP2010]
- 1D transport & 2D MHD equilibrium
- Time-dependent / Steady-state analysis of JT-60U experiment
- Simulation with transport model
Neoclassical : MI method or NCLASS, Anomalous : CDBM, GLF23, BgB, MMM95
- Development of toroidal momentum eq. solver consistent with Er (M. Honda)
- Tuning of CDBM model to LH transition (M. Yagi, PET2011)
Components
- NB & High energy particle : 1D or 2D FP, 3D MC (F3D-OFMC)
- EC : Ray tracing & Relativistic FP (EC-Hamamatsu)
- IC : Full wave analysis (TASK/WM), LH : Bonoli module in ACCOME
- MHD stability : Kink / Ballooning / Peeling (MARG2D)
- Impurity : 1D transport (IMPACT)
- Neutral : 2D MC
- Radiation : Impurity line radiation model (Coronal eq.), Synchrotron (CYTRAN)
- SOL / Div. : Five-point model (D5PM), 2D Fluid & MC (SONIC)
- Pellet : Ablated Pellet with ExB drift (APLEX)
Integrated suite of codes TOPICS
・・・used in this study *
4/14
Transport models implemented in TOPICS
• Current Diffusive Ballooning Mode (CDBM) [e.g. A. Fukuyama PPCF1995]
• GLF23 [R. E. Waltz PoP1997, J. E. Kinsey PoP2005]
• Bohm/gyro-Bohm (BgB) [modified from M. Erba PPCF1997]
Given: The MHD equilibrium, the q profile, the density profile
Calculate: ion and electron temperatures in < 0.85
The anomalous heat diffusivity is given by following transport models.
Thermal pressure
− Mixing length formula is used to obtain the heat diffusivity with 10 wavenumbers for ion temperature gradient(ITG) and trapped electron mode(TEM) and 10 wavenumbers for electron temperature gradient(ETG) mode.
− ITG/TEM is stabilized by the effect of ExB shear.
5/14
-40
-30
-20
-10
0
10
20
0 0.2 0.4 0.6 0.8 1
Er_s46303_t07900_008_givenq
Er [kV/m]
E r [kV
/m]
-40
-30
-20
-10
0
10
20
0 0.2 0.4 0.6 0.8 1
Er_s46301_t07000_003_givenq
Er [kV/m]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46303_TEM0-CKAIAN1_cdbm_iexbcdbm2_modcdbm1_itorminit-3
Te [keV]Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46303_t07900_exp_plot
Te [keV]
T [k
eV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46303_t07900_exp_plot
Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46303_TEM0-CKAIAN1_cdbm_iexbcdbm2_modcdbm1
Te [keV]Ti [keV]
E46303, t=7.9s
electron
ion
CDBMExp.Exp. fit
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46301_TEM0-CKAIAN1_cdbm_iexbcdbm2_modcdbm1_itorminit-3
Te [keV]Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46301_t07000_exp_plot
Te [keV]
T [k
eV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46301_t07000_exp_plot
Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46301_TEM0-CKAIAN1_cdbm_iexbcdbm2_modcdbm1
Te [keV]Ti [keV]
E46301, t=7.0s
electron
ion
CDBMExp.Exp. fit
Calculations with CDBM for H-mode shots
Co Ip =1.16MA Bt=2.56T H=1.074 We=0.7705MJ Wi=0.5778MJ
Co H=0.8518
Ctr Ip=1.16MA Bt=2.56T H=1.049 We=0.6741MJ Wi=0.4551MJ
Ctr H=0.8587
Test of transport models against JT-60U plasmas
We=0.5593MJ
Wi=0.5111MJ
We=0.5027MJ
Wi=0.4219MJ
ne[1019m-3] q
Er[kV/m]
CDBM model
Ion Ti similar to exp. for > 0.3
Electron Te lower than exp. with high ce
Comparisons between co and ctr Little difference
0
1
2
3
4
5
0 0.2 0.4 0.6 0.8 1
steady_s46303_t07900_008
ne [10^19 m^-3]
ne [
10
19 m
-3]
0
1
2
3
4
5
0 0.2 0.4 0.6 0.8 1
steady_s46301_t07000_003
ne [10^-19 m^-3]
Co46303 t7.9
Ctr46301 t7.0
CoCtr
0
1
2
3
4
5
0 0.2 0.4 0.6 0.8 1
s46303_QQT-BP
QQT
q
0
1
2
3
4
5
0 0.2 0.4 0.6 0.8 1
s46301_QQT-BP
QQT
Co46303 t7.9
Ctr46301 t7.0
CoCtr
6/14
0
2
4
6
8
0 0.2 0.4 0.6 0.8 1
s46303_TEM0-CKAIAN1_cdbm_iexbcdbm2_modcdbm1_itorminit-3
CKAIAN0 CKAIAN1
0
2
4
6
8
0 0.2 0.4 0.6 0.8 1
s46303_chiano
chie_neochii_neo
can
o [
m2/s
]
E46303, t=7.9s
electron
ion
cCDBM
cexp
- cneo
ionelectron
0
2
4
6
8
0 0.2 0.4 0.6 0.8 1
s46301_TEM0-CKAIAN1_cdbm_iexbcdbm2_modcdbm1_itorminit-3
CKAIAN0 CKAIAN1
0
2
4
6
8
0 0.2 0.4 0.6 0.8 1
s46301_chiano
chie_anochii_ano
can
o [
m2/s
]
E46301, t=7.0s
electron
ion
cCDBM
cexp
- cneo
ionelectron
Calculations with GLF23 for H-mode shots
Ion similar Ti profile to exp. for > 0.2 Better agreement for ctr case
Electron lower Te than exp., especially for < 0.5
Comparisons between co and ctr
• Predicted ci for co rotation is larger than that for ctr rotation.
• However, the difference in ci is not caused by ExB shear effect.
Co H=0.8533 Ctr H=0.9307
We=0.5712MJ
Wi=0.5004MJ
We=0.5448MJ
Wi=0.4554MJ
Test of transport models against JT-60U plasmas
Co Ctr Calculations w/o ExB shear effects
7/14
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46301_TEM0-CKAIAN1_glf_exb_ibscop3_irotstab0_itorminit-3
CKAIAN0 CKAIAN1
can
o [
m2/s
]
E46301, t=7.0s
electron
ion
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46303_TEM0-CKAIAN1_glf_exb_ibscop3_irotstab0_itorminit-3
CKAIAN0 CKAIAN1
can
o [
m2/s
]
electron
ion
E46303, t=7.9s0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46303_TEM0-CKAIAN1_glf_exb_ibscop3_irotstab0_itorminit-3
Te [keV]Ti [keV]
T [k
eV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46303_t07900_exp_plot
Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46303_t07900_exp_plot
Te [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46303_TEM0-CKAIAN1_glf_exb_ibscop3_irotstab0
Te [keV]Ti [keV]
electron
ion GLF23 w ExBExp.Exp. fit
46303
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46301_TEM0-CKAIAN1_glf_exb_ibscop3_irotstab0_itorminit-3
Te [keV]Ti [keV]
T [k
eV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46301_t07000_exp_plot
Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46301_t07000_exp_plot
Te [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46301_TEM0-CKAIAN1_glf_exb_ibscop3_irotstab0
Te [keV]Ti [keV]
electron
ion GLF23 w ExBExp.Exp. fit
46301
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46303_TEM0-CKAIAN1_glf_noexb_ibscop3_itorminit-3
CKAIAN0 CKAIAN1
can
o [
m2/s
]
E46303, t=7.9s
electron
ion
w/o ExB
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46301_TEM0-CKAIAN1_glf_noexb_ibscop3_itorminit-3
CKAIAN0 CKAIAN1
can
o [
m2/s
]
E46301, t=7.0s
electron
ion
w/o ExB
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46303_TEM0-CKAIAN1_bgbc_wF_itorminit-3
Te [keV]Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46303_t07900_exp_plot
Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46303_TEM0-CKAIAN1_cdbm_iexbcdbm2_modcdbm1
Te [keV]Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46303_t07900_exp_plot
Te [keV]
T [k
eV]
E46303, t=7.9s
electron
ion
BgBExp.Exp. fit
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46301_TEM0-CKAIAN1_bgbc_wF_itorminit-3
Te [keV]Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46301_t07000_exp_plot
Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46301_TEM0-CKAIAN1_cdbm_iexbcdbm2_modcdbm1
Te [keV]Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46301_t07000_exp_plot
Te [keV]
T [k
eV]
E46301, t=7.0s
electron
ion
BgBExp.Exp. fit
Calculations with BgB for H-mode shots
Ion overestimated Ti with much smaller ci than exp., especially for 0.4 < < 0.8
Electron Te similar to exp. for > 0.3
Comparisons between co and ctr Little difference
Co H=1.107 Ctr H=1.103
Test of transport models against JT-60U plasmas
We=0.7348MJ
Wi=0.6519MJ
We=0.6495MJ
Wi=0.5324MJ
8/14
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46303_TEM0-CKAIAN1_bgbc_wF_itorminit-3
CKAIAN0 CKAIAN1
can
o [
m2/s
]
E46303, t=7.9s
electron
ion
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46301_TEM0-CKAIAN1_bgbc_wF_itorminit-3
CKAIAN0 CKAIAN1
can
o [
m2/s
]
E46301, t=7.0s
electron
ion
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t09000_TEM0-CKAIAN1_cdbm_iexbcdbm2_modcdbm1_itorminit-3
Te [keV]Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t09000_exp_plot
Te [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t09000_exp_plot
Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t09000_TEM0-CKAIAN1_cdbm_iexbcdbm2_modcdbm1
Te [keV]Ti [keV]
T [k
eV]
electron
ion
CDBMExp.Exp. fit
Co46861 t9.0
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t15000_TEM0-CKAIAN1_cdbm_iexbcdbm2_modcdbm1_itorminit-3
Te [keV]Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t15000_exp_plot
Te [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t15000_exp_plot
Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t15000_TEM0-CKAIAN1_cdbm_iexbcdbm2_modcdbm1
Te [keV]Ti [keV]
T [k
eV]
electron
ion
CDBMExp.Exp. fit
Ctr46861 t15.0
Calculations with CDBM for parabolic ITB shots
Ion similar to exp. for > 0.3
Electron similar Te for > ITB
lower Te with high ce for > ITB, especially for co case
Co H=0.9352
Co Ip=0.9MA Bt=1.60T H=1.133 We=0.5233MJ Wi=0.3252MJ
Ctr H=0.8642
Ctr Ip=0.9MA Bt=1.59T H=0.9128 We=0.4698MJ Wi=0.2268MJ
Test of transport models against JT-60U plasmas
0
1
2
3
4
5
0 0.2 0.4 0.6 0.8 1
s46861_t09000_TEM0-CDIF1_glf_exb_ibscop3_irotstab0_calden
ne [10^19 m^-3]
ne [
10
19 m
-3]
Co46861 t9.0
0
1
2
3
4
5
0 0.2 0.4 0.6 0.8 1
s46861_t15000_TEM0-CDIF1_glf_exb_ibscop3_irotstab0_calden
ne [10^19 m^-3]
Ctr46861 t15.0
CoCtr
ne[1019m-3]
Er[kV/m]
q
We=0.3914MJ
Wi=0.3055MJ
0
1
2
3
4
5
0 0.2 0.4 0.6 0.8 1
s46861_t09000_QQT-SHA
QQT
q
0
1
2
3
4
5
0 0.2 0.4 0.6 0.8 1
s46861_t15000_QQT-SHA
QQT
Co46861 t9.0
Ctr46861 t15
CoCtr
CDBM model
-20
-15
-10
-5
0
5
0 0.2 0.4 0.6 0.8 1
Er_s46861_t09000_002
Er [kV/m]
E r [
kV/m
]
-20
-15
-10
-5
0
5
0 0.2 0.4 0.6 0.8 1
Er_s46861_t15000_002
Er [kV/m]
CoCtr
We=0.4132MJ
Wi=0.2414MJ
9/14
0
2
4
6
8
0 0.2 0.4 0.6 0.8 1
s46861_t09000_TEM0-CKAIAN1_cdbm_iexbcdbm2_modcdbm1_itorminit-3
CKAIAN0 CKAIAN1
can
o [
m2/s
]
CDBM LH tuned
ion, electron
0
2
4
6
8
0 0.2 0.4 0.6 0.8 1
s46861_t09000_chiano
chie_neochii_neo
ion
electron
cCDBM
cexp
- cneo
0
2
4
6
8
0 0.2 0.4 0.6 0.8 1
s46861_t15000_TEM0-CKAIAN1_cdbm_iexbcdbm2_modcdbm1_itorminit-3
CKAIAN0 CKAIAN1
can
o [
m2/s
]
CDBM LH tunedCtr 46861 t15.0
0
2
4
6
8
0 0.2 0.4 0.6 0.8 1
s46861_t15000_chiano
chie_neochii_neo
ion,electron
ion
electron
cCDBM
cexp
- cneo
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t09000_TEM0-CKAIAN1_glf_exb_ibscop3_irotstab0_itorminit-3
Te [keV]Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t09000_exp_plot
Te [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t09000_exp_plot
Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t09000_TEM0-CKAIAN1_glf_exb_ibscop3_irotstab0
Te [keV]Ti [keV]
T [k
eV]
electron
ion GLF23 w ExBExp.Exp. fit
Co46861 t9.0
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t15000_TEM0-CKAIAN1_glf_exb_ibscop3_irotstab0_itorminit-3
Te [keV]Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t15000_exp_plot
Te [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t15000_exp_plot
Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t15000_TEM0-CKAIAN1_glf_exb_ibscop3_irotstab0
Te [keV]Ti [keV]
T [k
eV]
electron
ion GLF23 w ExBExp.Exp. fit
Ctr46861 t15.0
Calculations with GLF23 for parabolic ITB shots
Ion
similar Ti gradient, but overestimated Ti with much smaller ci than exp .
Electron
Co: similar Te for > ITB
Ctr: similar Te
Failure of Te-ITB reproduction may be due to ETG mode
[cf. J. E. Kinsey PoP2005]
Co H=1.212 Ctr H=1.058
Test of transport models against JT-60U plasmas
We=0.4626MJ
Wi=0.4321MJ
We=0.4654MJ
Wi=0.3256MJ
Calculations w/o ExB shear effects
Co Ctr
10/14
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t09000_TEM0-CKAIAN1_glf_exb_ibscop3_irotstab0_itorminit-3
CKAIAN0 CKAIAN1
can
o [
m2/s
]
GLF23 w ExBCo 46861 t9.0
electron
ion0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t15000_TEM0-CKAIAN1_glf_exb_ibscop3_irotstab0_itorminit-3
CKAIAN0 CKAIAN1
can
o [
m2/s
]
GLF23 w ExBCtr 46861 t15.0
electron
ion
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t09000_TEM0-CKAIAN1_glf_noexb_ibscop3_itorminit-3
CKAIAN0 CKAIAN1
can
o [
m2/s
]
Co 46861 t9.0 w/o ExB
electron
ion
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t15000_TEM0-CKAIAN1_glf_noexb_ibscop3_itorminit-3
CKAIAN0 CKAIAN1
can
o [
m2/s
]
Ctr 46861 t15.0
electron
ion
w/o ExB
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t09000_TEM0-CKAIAN1_bgbc_wF_itorminit-3
Te [keV]Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t09000_exp_plot
Te [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t09000_exp_plot
Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t09000_TEM0-CKAIAN1_bgbc_wF
Te [keV]Ti [keV]
T [k
eV]
electron
ion
BgBExp.Exp. fit
Co46861 t9.0
Calculations with BgB for parabolic ITB shots
Ion
Co: similar to exp.
Ctr: overestimated
Electron
similar to exp. for ctr case, but no gradient like exp. for both co and ctr cases
Co H=1.202 Ctr H=1.120
Test of transport models against JT-60U plasmas
We=0.5139MJ
Wi=0.3803MJ
We=0.5413MJ
Wi=0.3044MJ
11/14
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t09000_TEM0-CKAIAN1_bgbc_wF_itorminit-3
CKAIAN0 CKAIAN1
can
o [
m2/s
]
BgB w F
ion
electron
Co 46861 t9.0
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t15000_TEM0-CKAIAN1_bgbc_wF_itorminit-3
Te [keV]Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t15000_exp_plot
Te [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t15000_exp_plot
Ti [keV]
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t15000_TEM0-CKAIAN1_bgbc_wF
Te [keV]Ti [keV]
T [k
eV]
electron
ion
BgBExp.Exp. fit
Ctr46861 t15.0
0
2
4
6
8
10
0 0.2 0.4 0.6 0.8 1
s46861_t15000_TEM0-CKAIAN1_bgbc_wF_itorminit-3
CKAIAN0 CKAIAN1
can
o [
m2/s
]
BgB w F
ion
electron
Ctr 46861 t15.0
GS2 code
GS2 code [M. Kotschenreuther CPC1995, W. Dorland PRL2000] is
• the local flux-tube gyrokinetic code
• solving the gyrokinetic equations for the perturbed distribution functions df
• able to carry out linear and nonlinear
• able to calculate both electrostatic and electromagnetic cases, including nonadiabatic (kinetic) electrons
• calculating initial value problems using the Lorentz collision operator
• able to work with s-a model equilibrium, Miller equilibrium and the equilibrium obtained experiments(G EQDSK)
• incorporating effects of sheared flow by forcing radial wavenumber kx to depend linearly on time
Toroidal angular velocity
: Parallel flow shear
12/14
Effects of the flow shear
• Cyclone base case
• ITG mode is stabilized by increasing gE for 0 < gE < 0.3.
• ITG and parallel velocity gradient (PVG) drive for 0.3 < gE < gE
(c).
10-6
0.0001
0.01
1
100
0 10 20 30 40 50 60 70
gs2-case391_heatflux
heat fluxes:
Q/(n
iTiv
th
i2/R
2)
t/(R/vth
)
gE/(v
th/R) = 0.0
10-6
0.0001
0.01
1
100
0 10 20 30 40 50 60 70
gs2-case391_heatflux
heat fluxes:
y = 1.5901e-7 * e^(0.31236x) R= 0.99981
g*/(vth
/R) = 0.1560
0.05
0.1
0.15
0.2
0.25
0 0.2 0.4 0.6 0.8
gs2-case391-397_barnes2011PRL
gamma*_cs
g*/(c s/R
)
gE/(v
th/R)
Barnes PRL2011 Fig.1R/L
T = 6.9
[Barnes PRL 2011]
GS2
• The effects of the flow shear are confirmed.
• The growth rate is estimated by time dependence of the heat flux at linear phase. [C. M. Roach PPCF2009]
gE =0.0 gE =0.2 gE =0.5 10
-6
10-5
0.0001
0.001
0.01
0.1
1
0 100 200 300
gs2-case393_heatflux
heat fluxes:
Q/(n
iTiv
th
i2/R
2)
t/(R/vth
)
10-6
10-5
0.0001
0.001
0.01
0.1
1
0 100 200 300
gs2-case393_heatflux
heat fluxes:
gE/(v
th/R) = 0.2
g*/(vth
/R) = 0.0173
y = 4.1473e-6 * e^(0.034452x) R= 0.97233
10-6
10-5
0.0001
0.001
0.01
0.1
1
10
0 50 100 150 200
gs2-case396_heatflux
heat fluxes:
Q/(n
iTiv
th
i2/R
2)
t/(R/vth
)
10-6
10-5
0.0001
0.001
0.01
0.1
1
10
0 50 100 150 200
gs2-case396_heatflux
heat fluxes:
y = 1.2287e-6 * e^(0.077493x) R= 0.99127
gE/(v
th/R) = 0.5
g*/(vth
/R) = 0.0387
13/14
Conclusions and future works
• Estimated Ti using CDBM and GLF23 is similar to exp.
• CDBM and BgB predict little differences between co and ctr cases.
Conventional H-mode
• CDBM and GLF23 predict similar Te and Ti for > ITB .
• CDBM, GLF23 and BgB do not show the difference in Te profile between co and ctr cases observed in the experiment.
Parabolic ITB
Future works
Calculations using GS2 with the equilibrium obtained experiments
Estimation of ExB shear effects using the transport model TGLF [G. M. Staebler PoP2005, PoP2007, J. E. Kinsey PoP2008]
14/14
Transport models
Gyrokinetic code GS2
• ExB shear stabilization and PVG destabilization are able to investigate with GS2