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Increased understanding of the dynamics and transport in ITB plasmas from multi-machine comparisons

IOP Publishing
Nuclear Fusion
Authors:
Pruthvirajsinh Gohil at Parul Universiy
Pruthvirajsinh Gohil
J. Kinsey
J. Kinsey
J. Kinsey
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V. Parail
V. Parail
V. Parail
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X. Litaudon at EUROfusion
X. Litaudon
  • EUROfusion
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Abstract

Our understanding of the physics of internal transport barriers (ITBs) is being advanced by analysis and comparisons of experimental data from many different tokamaks worldwide. An international database consisting of scalar and two-dimensional profile data for ITB plasmas is being developed to determine the requirements for the formation and sustainment of ITBs and to perform tests of theory-based transport models in an effort to improve the predictive capability of the models. Analysis using the database indicates that: (a) the power required to form ITBs decreases with increased negative magnetic shear of the target plasma, and: (b) the E×B flow shear rate is close to the linear growth rate of the ion temperature gradient (ITG) modes at the time of barrier formation when compared for several fusion devices. Tests of several transport models (JETTO, Weiland model) using the two-dimensional profile data indicate that there is only limited agreement between the model predictions and the experimental results for the range of plasma conditions examined for the different devices (DIII-D, JET, JT-60U). Gyrokinetic stability analysis (using the GKS code) of the ITB discharges from these devices indicates that the ITG/TEM growth rates decrease with increased negative magnetic shear and that the E×B shear rate is comparable to the linear growth rates at the location of the ITB.
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by
P. Gohil
in collaboration with
J. Kinsey, V. Parail, X. Litaudon, T. Fukuda, T. Hoang
for the ITPA Group on Transport and ITB Physics and for the
International ITB Database Group
Presented at
the 19th IAEA Fusion Energy Conference
Lyon, France
October 14–19, 2002
INCREASED UNDERSTANDING OF THE DYNAMICS
AND TRANSPORT IN ITB PLASMAS FROM
MULTI-MACHINE COMPARISONS
256-02/PG/amw
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
AUTHOR LIST
256-02/PG/amw
P. Gohil,1 J. Kinsey,2 V. Parail,3 X. Litaudon,4 T. Fukuda,5 T. Hoang4
For the ITPA Group on Transport and ITB Physics: J. Connor,6 E. Doyle,7
Yu. Esipchuk,8 T. Fujita,5 T. Fukuda,5 P. Gohil,1 J. Kinsey,2 S. Lebedev,9 X. Litaudon,4
V. Mukhovatov,10 J. Rice,11 E. Synakowski,12 K. Toi,13 B. Unterberg,14 V. Vershkov,8
M. Wakatani,15 J. Weiland,16 and for the International ITB Database Working Group:
T. Aniel,4
Yu.F. Baranov,3E. Barbato,17A. Bécoulet,4C. Bourdelle,4 G. Bracco,17
R.V. Budny,12 P. Buratti,17 E. Doyle, L. Ericsson,487 Yu. Esipchuk, B. Esposito,17
T. Fujita,5 T. Fukuda,5 P. Gohil,1 C. Greenfield,1 M. Greenwald,11 T. Hahm,12
T. Hellsten,3 T. Hoang,4 D. Hogeweij,18 S. Ide,5 F. Imbeaux,4 Y. Kamada,5 J. Kinsey,2
N. Kirneva,8 X. Litaudon,4 P. Maget,4 A. Peeters,19 K. Razumova,8 F. Ryter,19
Y. Sakamoto,5 H. Shirai,5 G. Sips,19 T. Suzuki,5 E. Synakowski,12 T. Takizuka,5 and
R. Wolf19
1General Atomics, P.O. Box 85608, San Diego, California, 92186-5608 USA
email: gohil@fusion.gat.com
2Lehigh University, Bethlehem, Pennsylvania 18015 USA
3EFDA-JET CSU, Culham Science Centre, Abingdon, Oxon, UK
4Association Euratom-CEA, CEA de Cadarache, St Paul lez Durance, France
5JAERI, Naka Fusion Research Establishment, Naka, Japan
6EURATOM/UKAEA Association, Culham Science Centre, Abingdon, Oxon, UK
7University of California, Los Angeles, California 90095 USA
8Kurchatov Institute of Atomic Energy, Moscow, Russia
9Ioffe Institute, St. Petersburg, Russia
10ITER JWS, Naka, Japan
11Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 USA
12Plasma Physics Laboratory, Princeton University, Princeton, New Jersey 08543 USA
13National Institute of Fusion Science, Toki City, Japan
14Forschungszentrum Jülich, GmbH, EURATOM-Association, Jülich, Germany
15Kyoto University, Kyoto, Japan
16Chalmers University and EURATOM-VR association, Gothenburg, Sweden
17Associazione EURATOM-ENEA sulla Fusione, C.R. Frascati, Frascati, Italy
18FOM Insituut voor Plasmafisica, “Rijnhuizen”, Nieuwegein, the Netherlands
19Max-Planck-Institut für Plasmaphysik, EURATOM Association, Garching, Germany
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
● Our understanding of the physics of ITBs is being increased by analysis and
comparisons of experimental data from many tokamaks worldwide.
● An international ITB database consisting of scalar and 2-D profile data on ITB
plasmas has been developed
● Specific discharges from three major tokamaks (DIII–D, JET, JT-60U) were selected
to better understand the influence of the q-profile on ITBs
● Gyrokinetic stability analysis of the selected discharges indicates that the ITG mode
growth rates generally decrease with increased negative shear and that the E × B
shear rate is comparable to the linear growth rates at the location of the ITB
● Tests of several transport models (JETTO, Weiland model) using the 2-D profile data
indicate there is only limited agreement between model predictions and experimental
results for the selected discharges
SUMMARY
256-02/PG/amw
— To determine the requirements for formation and sustainment of ITBs
— To perform tests of theory-based transport models in an effort
to improve their predictive capability
— Selected a low shear or monotonic q-profile discharge together with
a high magnetic shear discharge from each machine
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
● Examination and compilation of experimental results on transport from many
machines worldwide to better understand the physics of ITB formation and
sustainment
● The development of an international database on ITB experimental results to
determine the requirements for the formation and sustainment of ITBs
● Determining and performing comprehensive tests of theory based transport
models and simulations using the international ITB database (ITBDB) – critical
for model validation and improving predictive capability
● Identifying experiments to address and resolve critical issues in transport
and ITB physics
● Facilitating inter-machine ITB experiments and comparisons
PURPOSE OF THE ITPA GROUP ON TRANSPORT
AND THE ITBDB WORKING GROUP
256-02/PG/amw
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
● There is a wide variety of experimental results on plasma transport and ITB's
from many machines worldwide
● Provide a depository for ITB data for access by experimentalists and modelers
● Improve predictive capability of transport models
● Find solutions to critical issues such as impurity transport, electron transport,
fueling, core-edge integration, profile control, etc.
MOTIVATION FOR ITPA AND ITBDB WORKING GROUPS
256-02/PG/amw
— Need to assess large variety of results and improve our understanding
of important transport issues
— Define common definitions for ITBs
— Assess reactor compatibility and develop reactor scenarios
— Development of international ITB database
— Determine key trends from data, e.g., effect of q profile,
momentum input, etc.
— Need to test and validate models with experimental data
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
● The formation and sustainment of ITBs is very dependent on behavior
of the q-profile in many devices
● Determine the variation in the E × B shearing rate and the ITG/TEM mode
growth rates for the selected discharges in order to evaluate the relative
influence of the q-profiles
● Need to improve the predictive capability of transport models
● The work described in this paper is expandable
MOTIVATION FOR THIS PAPER
256-02/PG/amw
— Need to examine discharges with significant differences in q-profiles
(e.g., positive shear to strong negative shear from many devices
— Examine the level of agreement between model predictions and
experimental results for selected discharges with significantly
different q-profiles
— By increasing the number of models to be tested
— By examining more issues relevant for reactor scenarios
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
● Analysis of data from
ITB database [1]
● Plasmas with weak or negative
magnetic shear are more
favorable for ITB formation
TARGET PLASMAS WITH WEAK OR NEGATIVE MAGNETIC SHEAR
REQUIRE LOWER HEATING POWER FOR ITB FORMATION
256-02/PG/amw
● Heating power per particle
just prior to ion-ITB formation
(for dominantly ion heated
plasmas) (ne = plasma density;
V
p = plasma volume)
Positive Shear
1/ρ*
Weak Shear
Negative Shear
0.0
0.1
0.2
0.3
0.4
0.5
0.0 100 200 300 400 500
Pheat / (ne Vp) [10–19 MW]
[1] G.T. Hoang et al., Proc. 29th EPS Conference, Montreux, Switzerland (2002)
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
● For ion-ITB with dominant
ion heating
THE E × B SHEARING RATE IS CLOSE TO THE MAXIMUM
LINEAR GROWTH RATE AT THE TIME OF ITB FORMATION
256-02/PG/amw
● Using data from ITB database [1]
● Data at time of ITB formation
● Indicates strong influence of
E × B flow shear in several
devices
JT-60U ( for no ITB)
JET
TFTR
–2.0
0.10
1.00
–1.0 0.0 1.0
s at γL
max or ωE×Bmax
ωE×B/γL
[1] T. Fukuda et al., Proc. 29th EPS Conference, Montreux, Switzerland (2002)
^
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
● Used 2-D profile data from ITBDB for DIII–D, JET and JT-60U
● JETTO is based on an empirical mixed Bohm/gyroBohm transport model [1]
● Examined pairs of discharge from each device
PREDICTIVE SIMULATIONS USING TRANSPORT MODELS:
JETTO AND WEILAND MODEL
256-02/PG/amw
— With weak negative shear or monotonic q profile
— Strong negative shear
Bohm term:
GyroBohm term:
Where H (x) is a Heaviside step-function, s is magnetic shear, C is an adjustable
factor, γ is the growth rate, ωE×B is the shearing rate
q2HχBohm ∝∇nT ∇Te
T
nB
B2
ωE×B
γ
0.05 + s – C
()
3/2
χgyroBohm ∝∇Te s
1 + s
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
● Weiland model is an advanced fluid model [2] whereby
PREDICTIVE SIMULATIONS USING TRANSPORT MODELS:
JETTO AND WEILAND MODEL (CONTINUED)
256-02/PG/amw
Where H (x) is a Heaviside step-function, γk is the characteristic growth rate
and k is the characteristic perpendicular wave-vector
[1] G. Cennachi and A. Tami, JET-IR (88), 03 (1988)
[2] J. Weiland "Collective Modes in Inhomogeneous Plasmas"
Institute of Physics Publishing, Bristol and Philadelphia (2000)
H
χ ∝
k
γk – ωE×B ()
Σ
T
k2
γk – ωE×B
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
● DIII–D discharge 87031 – weak negative central shear
● DIII–D discharge 85989 – strong negative central shear (NCS)
● Only reasonable agreement with Ti profile for strong NCS case
JETTO PREDICTIVE MODELING FOR DIII–D DATA
256-02/PG/amw
0.0
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.0
0.5
1.0
1.5
2.0
0.0
2
4
6
8
2
4
6
8
10
2.0
4.0
6.0
8.0
0.0
1.0
2.0
3.0
4.0
103 eV
104 eV
103 eV
104 eV
EXP
EXP
EXP
EXP
EXP
EXP
DIII–D #87031
T=1.88 s, Ti
JETTO predict
DIII–D #87031
T=1.88 s, Te
JETTO predict
DIII–D #87031
T=1.88 s, q
JETTO predict
DIII–D #95989
T=1 s, Ti
JETTO predict
DIII–D #95989
T=1 s, Te
JETTO predict
DIII–D #95989
T=1 s, q
JETTO predict
C=0.8
C=1.2
C=1.5
C=1.0
C=1.5
(a) (b) (c)
(f)(e)(d)
ρρρ
C=0.8
C=1.2
C=1.5
C=1.0
C=1.5
High Negative
Shear
Weak Shear Model
Model
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
● JET discharge 46664 – weak positive shear
● JET discharge 53521 – strong negative shear
● Good agreement with Ti and Te profiles only for strong negative shear case
JETTO PREDICTIVE MODELING FOR JET DATA
256-02/PG/amw
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.0
1.0
2.0
3.0
104 eV
104 eV
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0
ρρρ
0.0
0.2
0.4
0.6
0.8
1.0
1.2
2.0
4.0
6.0
8.0
104 eV103 eV
2
3
4
5
2
4
6
8
10
EXP
EXP
EXP
EXP
EXP
EXP
JET #46664
T=6 s, Ti
JETTO predict
JET #53521
T=6 s, Ti
JETTO predict
JET #53521
T=6 s, Te
JETTO predict
JET #53521
T=6 s, q
JETTO predict
JET #46664
T=6 s, Te
JETTO predict
JET #46664
T=6 s, q
JETTO predict
(a)
(d) (e) (f)
(b) (c)
C=1.0
C=1.5
C=1.0
C=1.5
C=1.0
C=1.5
C=1.0
C=1.5
High Negative
Shear
Low Shear Model
Model
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
● JT-6OU discharge 34487 – weak positive shear
● JT-6OU discharge 39056 – strong negative shear
● Poor agreement for all cases
JETTO PREDICTIVE SIMULATIONS FOR JT-6OU DATA
256-02/PG/amw
2.0
4.0
6.0
8.0
103 eV
0.0
0.2
0.4
0.6
0.8
1.0
104 eV
0.2
0.4
0.6
0.8
1.0
1.2
0.0
0.5
1.0
1.5
2.0
104 eV
104 eV
2
3
4
5
4
6
8
10
q
q
0.0 0.2 0.4 0.6 0.8 1.0
ρ
0.0 0.2 0.4 0.6 0.8 1.0
ρρ
EXP
EXP
High Negative
Shear
EXP
EXP
EXP
JT60U #34487
T=5 s, Ti
JETTO predict
JT60U #39056
T=6.8 s, Ti
JETTO predict
JT60U #39056
T=6.8 s, Te
JETTO predict
JT60U #34487
T=5 s, Te
JETTO predict
JT60U #34487
T=5 s, q
JETTO predict
JT60U #39056
T=6.8, q
JETTO predict
(a) (b)
(d) (e) (f)
(c)
C=1.2
C=1.5
C=1.2
C=1.5
C=1.2
C=1.5
C=1.2
C=1.5
0.0 0.2 0.4 0.6 0.8 1.0
EXP
Low Shear
Model
Model
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
● For JET strong NCS discharge – 53521
● Increasing the toroidal rotation by factor of 4 produces the Ti ITB, but
grossly overestimates the Te profile
COMPARISON BETWEEN JETTO AND WEILAND MODELS
USING EXPERIMENTAL DATA FROM JET
256-02/PG/amw
● Weiland model fails to produce the Ti or Te ITBs
● Comparisons also performed for DIII–D and JT-60U discharges
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.0
0.5
1.0
1.5
104 eV
104 eV
0.0 0.2 0.4 0.6 0.8 1.0
ρ0.0 0.2 0.4 0.6 0.8 1.0
ρ
EXP EXP
Weiland
Weiland
Weiland with
4xVtor
Weiland with
4xVtor
JETTO
JETTO
JET #53521
T=6 s
Ti predict
JET #53521
T=6 s
Te predict
(a) (b)
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
● Overall there is limited agreement between the predictive simulations
and the experimental data
● Fair agreement is obtained in predicting the Ti profiles (c.f. to Te profiles)
by JETTO for strong NCS discharges
● Predictions for the Te profiles are very poor
● Weiland model is unable to produce the experimental Te and Ti profiles
for JET discharges
● JETTO overestimates both the Ti and Te profiles for low magnetic shear
discharges in DIII–D and JET
SIMULATION RESULTS
256-02/PG/amw
— JETTO does not include effects such as alpha stabilization
— Preference for reduced transport in the presence of low magnetic shear
and moderate levels of plasma rotation
THE E × B SHEARING RATE IS COMPARABLE TO THE MAXIMUM
LINEAR GROWTH RATE (ITG/TEM) AT THE LOCATION OF THE ITB
256-02/PG/amw
0.0
(b) (c)(a)
(f)(e)(d)
0.2 0.4 0.6 0.8 1.0
ρ
0.0 0.2 0.4 0.6 0.8 1.0
ρ
0.0 0.2 0.4 0.6 0.8 1.0
ρ
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0.0
0.5
1.0
1.5
2.0
2.5
3.0
ω, γ/105 (1/S) ω, γ/105 (1/S)
0.0
1.0
2.0
3.0
4.0
5.0
0.0
1.0
2.0
3.0
4.0
5.0
0.0
0.5
1.0
1.5
2.0
0.0
0.5
1.0
1.5
2.0
γmax
ωExB (Waltz)
γmax
ωExB (Waltz)
γmax
ωExB (Waltz)
ωExB (HB)
γmax
ωExB (Waltz)
DIII–D
#87031
T=1.76 s
DIII–D
#95989
T=0.88 s
JET
#46664
T=6.0 s
JT-60U
#34487
T=5.0 s
JET
#53521
T=6.0 s
JT-60U
#39056
T=6.8 s
γmax
ωExB (Waltz)
ωExB (HB) ωExB (HB)
ωExB (HB)
γmax
ωExB (W)
ωExB (HB)
γmax
ωExB
(W)
ωExB
(HB)
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
● ITG/TEM linear growth rates calculated using the GKS code [1]
● Generally the ITG growth rates tend to decrease with increased negative magnetic shear
● Differences between the Hahm-Burrell and Waltz shearing rates result from:
SUMMARY OF GYROKINETIC STABILITY ANALYSIS
256-02/PG/amw
● E × B shearing rates from Hahm and Burrell [2] and Waltz et al. [3]
[1] M. Kotschenreuther, et al., Comp., Phys. Comm. 88, 128 (1995)
[2] T.S. Hahm and K.H. Burrell, Phys. Plasmas 2, 1648 (1995)
[3] R.E. Waltz et al, Phys. Plasmas 4, 2482 (1997)
— Neoclassical vθ used in evaluation of Er
— More favorable for ITB formation for given E × B shearing rate
— Flux-surface averaged evaluation for Waltz and outside midplane for Hahm-Burrell
— Pre-derivative (r/q) factor for Waltz which can be significantly smaller in elongated
plasmas than the corresponding factor (RBp/B) used in Hahm-Burrell
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
CENTRAL BEAM DEPOSITION AND NEGATIVE
MAGNETIC SHEAR AID ITB FORMATION
256-02/PG/amw
#14180 / #14933: ASDEX Upgrade
0.0
0.0 0.2 0.4 0.6 0.8
5.0
10.0
15.0
20.0
Ti (keV)
ρ
3 On-axis Beams (7.5 MW)
2 On-axis/1 Off-axis (7.5 MW)
● Power requirements for ITB formation are very dependent on profile data such as
the power deposition and q profiles
— Makes scaling relationships very difficult to determine
1.5
0
5
10
15
20
2.0 2.5 3.0 3.5 4.0
Mark IIGB
Mark IIA
Ohmic Preheat
LHCD Preheat
ICRH Preheat
}Target q0 close to 2
(1999)
P (MW)
Toroidal Magnetic Field (T)
JET
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
● Constant Ne puff for t > 44s.
Central zeff = 3.5 at t= 46.9 s
(dominated by Ni)
● Steep impurity density gradients
are inboard of the location of the
T
i gradients
IMPURITY ACCUMULATION IS A CRITICAL PROBLEM
FOR ITB DISCHARGES
256-02/PG/amw
● Before ITB formation, impurity
density profiles are hollow or
slightly peaked
● Data from JET
● On ITB formation, impurity density
peaking increases with impurity
charge Z (weakest for C and
strongest for Ni)
#51976 JET
3.1 3.3 3.5 3.7
Ni
Ne
C
ne
Ti
45.8 s
46.2 s
46.6 s
46.8 s
+
2
10
20
30
0
2
4
6
8
10
0
1
2
0
1
0
2
4
5
3
1
(keV)
(1019 m–3)
(1017 m–3)
(1017 m–3)(1017 m–3)
R [Z=Zmag] (m)
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
● Central ECH/ECCD decreases the central electron density and Zeff (from Ni and Cu)
decreases by a factor of 2
● QDB plasmas have peaked density profiles
CENTRAL ECH/ECCD CAN BE USED TO CONTROL THE
ELECTRON DENSITY AND IMPURITY DENSITY PROFILES IN ITBs
256-02/PG/amw
0ρ
.1 .2 .3 .4 .5 .6 .7 .8 .9 1.0
110874 ECCD at ρ=.2
t=2.45s - before ECH
t=3.45s - at end of ECH
0
.05
.10
.15
.20
.25
.30
.35
.40
.45
Electron Density –1020 m–3
0.1*<JECCD>
Zeff Profile 110874.2450
Zeff
ρ
0.0
0
2
4
6
8
0.2 0.4 0.6 0.8
Total
High Z
Z=28
Z=29
C+6
Before ECH
Zeff Profile 110874.2700
Zeff
ρ
0.0
0
2
4
6
8
0.2 0.4 0.6 0.8
Total
High Z
Z=28
Z=29
C+6
During ECH
Discharge 11084
Ni XXV 117 ph/cm2/str/s
Time (ms)
8.0
1.6
0.3
3.0
5.0
1.6
2.0
0.0
0.0
0.0
0.0
0.0
0.0
1000 2000 3000 4000
Central Electron Density (1019 m–3)
Central Visible Bremsstrahlung (10–7 W/cm2/str/)
Central Carbon Density (1019 m–3)
Central ECH Power (MW)
Ni XXVI 165 ph/cm2/str/s
Divertor Dα ph/cm2/str/s
DIII–D
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
STRONG ITBs WITH Te = Ti HAVE BEEN FORMED
IN REVERSE MAGNETIC SHEAR DISCHARGES
256-02/PG/amw
ne
Dα
(a.u.)
Pabs
(MW)
fEH
T
(keV)
Wdia
(MJ)
PEC, N-NB
(MW)
Ip
(MA)
P-NB
(MW)
E36646: Bt0 = 3.68 T
N-NB
ECH
Te
Ti
Time (s)
JT-60U
345678
0
2
4
0
10
0
5
10
0
2
4
0
1
(1019 m–3)
0
2
4
0
0.5
0
2
4
0
10
20
ρ
ρ
7.0 s
5.6 s
5.6 s 7.0 s
q
ρ
7.0 s
5.6 s
0
1
2
3
4
5
0 0.5 1
0 0.5 1
ρ
0 0.5 1
0
2
4
6
8
10
ne (1019 m–3)T
e, i (keV)
Te, i (keV)
0
2
4
6
8
10
2
3
4
5
6
7
0 0.5 1
Ti
Te
TeTiTi
TiTe
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
REAL TIME CONTROL OF ITB'S AND q-PROFILE HAVE BEEN
DEMONSTRATED ON JET
256-02/PG/amw
1.8MA / 3.4T
Time (s)
Pulse No:
53697
Active Control
Vs(V)
4
6
2
0.8
5
10
15
1.0
2.0
3.0
0
0
0
0
0.8
0
Ip (MA) PLHCD (MW)
PNBI
MW
PICRH
(RNT) ref = 0.9×1016s–1
1016 Neutron/s
Norm. Te Gradient (×10–2)
(ρTe*)ref=2.5×10–2
24681012
0
1
2
3
4
5
6
7
Normalized Radius
t = 44 s (ohmic ramp)
t = 54 s (end of control)
PIh = 1.6 MW
t = 49.5 s (undershoot)
JET Pulse #55873
Safety Factor
00.20.4 0.6 0.8 1
3.0
2.5
2.0
1.5
1.0
0.5
0.0
3.0
2.5
2.0
1.5
1.0
0.5
0.0
3.0
2.5
2.0
1.5
1.0
0.5
0.0
3.5
2.5
3.0
2.0
1.5
1.0
0.5
0.0
Time (s)
qref
q(x=0.2) q(x=0.4)
56545250484644
Time (s)
56545250484644
Time (s)
Without LH
56545250484644
Time (s)
565452504846
Time (s)
56545250484644
JET #55873 JET #55873 JET #55873 JET #55873 JET #55873
Plhcd (a.u.) Plhcd (a.u.)
qref
Plhc (MW)
qref
qref
q(x=0.5)
Plhcd (a.u .)
q(x=0.6)
Plhcd (a.u.)
5
4
3
2
1
0
q(x=0.8)
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
● Tests of transport models (JETTO, Weiland model) have been performed
using profile data from the international ITB database
● Overall there is limited agreement between the model predictions and
the experimental data from DIII–D, JET and JT-60U
● Much more interaction between experimentalists and modelers is needed
to improve the predictive capability of the models
● Gyrokinetic stability analysis of ITB discharges from DIII–D, JET and JT-60U
indicates that the E × B shear rate is comparable to the maximum linear
growth rates at the location of the ITB
CONCLUSIONS
256-02/PG/amw
— Using data from several machines allows for model validation over a large
range of conditions (reveals deficiencies and areas for improvement)
— Important for improving predictive capability of models
SAN DIEGO
DIII–D
NATIONAL FUSION FACILITY
● More work and greater interaction between modelers
and experimentalists is required to perform further tests of
transport models and to improve the models
● Increased focus on critical issues for burning plasmas
and reactor compatibility
● More multi-machine collaborative experiments and comparisons
of experimental data, e.g., similarity experiments
FUTURE WORK
256-02/PG/amw
— Test more transport models (GLF23, Multi-mode, etc.)
— Examine more linear stability codes (FULL, GS2, etc.)
— Design experiments to test models
— Motivate model development from experimental results
— Electron transport, core heating and fueling, impurity
accumulation, profile control, stability, etc.
— Need solutions to issues
● Improvements could result from more accurate and reliable treatment
of transport suppression mechanisms such as E × B flow shear,
negative magnetic shear, and alpha stabilization
... This problem has been reviewed by Burrel (1994), Connor and Wilson (2000), Connor et al. (2004), Doyle et al. (2007), Garbet (2006), , Gohil (2006), and Wolf (2003). The role of rational magnetic surface in the formation of transport barriers has been discussed by Austin et al. (2006), Brakel et al. (2002), Eriksson et al. (2002), Garbet et al. (2003), Gohil et al. (2003), Hogeweij where e r , e τ , e ψ are unit vectors along the coordinates r, τ, ψ, respectively. The corresponding components, j r , j τ , and j ψ , are defined as ...
... The existence of gaps in the density of rational tori has been pointed out already in a number works, for example, byAustin et al. (2006),Brakel et al. (2002),Eriksson et al. (2002),Garbet et al. (2003),Gohil et al. (2003),Hogeweij et al. (2004),,Joffrin et al. (2003), Lopes Cardozo (2004, andRazumova et al. (2003Razumova et al. ( , 2008. However, to my knowledge no quantitative estimations have been given. ...
... This mechanism, particularly has been discussed byAustin et al. (2006),Brakel et al. (2002),Eriksson et al. (2002),Garbet et al. (2003),Gohil et al. (2003),Hogeweij et al. (2004),,Joffrin et al. (2003), Lopes Cardozo (2004, andRazumova et al. (2003Razumova et al. ( , 2008. ...
Magnetic Field Perturbations
Chapter
Full-text available
  • Nov 2014
In real tokamak plasmas magnetic field deviates from the ideal equilibrium field. In typical situations the deviation of magnetic field from the equilibrium field is small. The magnetic perturbations may have a diverse nature: error fields produced by imperfect technical installation of poloidal and toroidal field coils, helical magnetic fields generated by MHD instabilities, magnetic fields created by external coils etc.
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... At present it is widely accepted that in addition to the mean E × B shear flow, the nonlinearly self-generated poloidal flow in saturated turbulence states known as ZFs [20][21][22], can act as an effective role in reducing the turbulent transport. The former has been examined on many devices such as TFTR [23], JET [24], DIII-D [25] and JT-60U [26] and its shearing rate (ω E×B ) was found to be close to the linear growth rate of the ITG modes (γ ITG ) at the time of barrier formation when compared with several tokamaks [27]. For instance, analysis of the DIII-D discharge has shown that ω E×B > γ ITG holds across the whole plasma [28]. ...
Impact of fast ions on microturbulence and zonal flow dynamics in HL-2A internal transport barriers
Article
Full-text available
  • Sep 2023
The turbulent transport properties and dynamics of zonal flows (ZFs) in the presence of fast ions (FIs) are investigated for a typical internal transport barrier (ITB) plasma based on the gyrokinetic approach, focusing on the role of fast ion temperature and the effects of the toroidal rotation, including the EB rotational shear, parallel velocity gradient (PVG) as well as the rotation velocity itself. Linear GENE simulations have shown that the core ITB plasma on HL-2A is dominated by ion temperature gradient (ITG) modes and trapped electron modes (TEMs), where the former is stabilized by FIs whereas destabilized by the PVG. Neither of the FIs or the PVG has observable effect on TEMs. The ion heat transport generally decreases at large FI temperature due to the nonlinear electromagnetic stabilization of turbulence with increased total plasma  until electromagnetic modes are excited. The transport fluxes peak around a certain FI temperature and the ZF shearing rate is significantly higher at such value compared with that in the absence of FIs, and the heat flux reduction is a result of the synergistic interaction between turbulence, ZFs and the external rotational shear. The E×B shear stabilizing and PVG destabilizing is not obvious at low normalized ion temperature gradient R/LTi, indicating they are less important in determining the stiffness level in the relatively low density and rotation scenarios regarding the HL-2A ITB discharges. The turbulence suppression is predominated by the nonlinear stabilization of ITG turbulence as well as enhanced zonal flows simultaneously in the presence of FIs. These results have also provided the possible way to reduce the turbulence transport through increasing the fast ion temperature in the off-axis neutral beam heated plasmas such as in HL-2A.
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... Scalings of turbulent diffusion in both CSDX and larger devices characterized by higher temperature follow the same trend. 46,47 When the axial to azimuthal flow coupling is weak, the axial flow is mainly driven by the turbulent Reynolds stress, particularly by the parallel residual part. The reduced 4-field model can thus be simplified to a 2-field predator-prey model which evolves v y and n. ...
The ecology of flows and drift wave turbulence in CSDX: A model
Article
Full-text available
  • Feb 2018
This paper describes the ecology of drift wave turbulence and mean flows in the coupled drift-ion acoustic wave plasma of a CSDX linear device. A 1D reduced model that studies the spatiotemporal evolution of plasma mean density n¯, and mean flows v¯y and v¯z, in addition to fluctuation intensity ε, is presented. Here, ε=〈ñ2+(∇⊥ϕ̃)2+ṽz2〉 is the conserved energy field. The model uses a mixing length lmix inversely proportional to both axial and azimuthal flow shear. This form of lmix closes the loop on total energy. The model self-consistently describes variations in plasma profiles, including mean flows and turbulent stresses. It investigates the energy exchange between the fluctuation intensity and mean profiles via particle flux 〈ñṽx〉 and Reynolds stresses 〈ṽxṽy〉 and 〈ṽxṽz〉. Acoustic coupling breaks parallel symmetry and generates a parallel residual stress Πxzres. The model uses a set of equations to explain the acceleration of v¯y and v¯z via Πxyres∝∇n¯ and Πxyres∝∇n¯. Flow dynamics in the parallel direction are related to those in the perpendicular direction through an empirical coupling constant σVT. This constant measures the degree of symmetry breaking in the 〈kmkz〉 correlator and determines the efficiency of ∇n¯ in driving v¯z. The model also establishes a relation between ∇v¯y and ∇v¯z, via the ratio of the stresses Πxyres and Πxzres. When parallel to perpendicular flow coupling is weak, axial Reynolds power PxzRe=−〈ṽxṽz〉∇v¯z is less than the azimuthal Reynolds power PxyRe=−〈ṽxṽy〉∇v¯y. The model is then reduced to a 2-field predator/prey model where v¯z is parasitic to the system and fluctuations evolve self-consistently. Finally, turbulent diffusion in CSDX follows the scaling: DCSDX=DBρ⋆0.6, where DB is the Bohm diffusion coefficient and ρ⋆ is the ion gyroradius normalized to the density gradient |∇n¯/n¯| −1.
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... Study of the physics underlying ITBs via international multimachine comparisons has been facilitated using the profile database. 100 In particular, this analysis has reported two important findings. First, in conditions where ITBs can be generated, a threshold input power P th is required to generate the ITB, and this is reduced with negative magnetic shear s, where s ϭ r0q dq0dr. ...
Chapter 11: Data Validation, Analysis, and Applications for Fusion Plasmas
Article
Full-text available
  • Feb 2008
Principal techniques and trends in the validation and analysis of data in magnetic fusion research are described and examples of applications are given. Well-established methods to obtain key physical quantities are outlined, as well as newer techniques employing integrated analysis of multiple diagnostics to improve quality and extract additional information from the data. Plasma control, confinement scaling, and transport studies, including model validation and development, are presented as important examples of applications of validated data. Finally, aspects essential to successful operation of future devices, which bring challenges due to a harsher environment for diagnostics, increased real-time requirements, and a geographically more distributed user community, are highlighted.
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Gyrokinetic simulations of zonal flows and ion temperature gradient turbulence in HL-2A ITB plasmas
Article
  • Jan 2022
The characteristics of zonal flows (ZFs) in ion temperature gradient (ITG) turbulence during the formation of internal transport barrier (ITB) have been investigated by nonlinear gyrokinetic simulations for the HL-2A tokamak experiment. The turbulent ion heat transport and zonal flow dynamics are investigated in the local turbulence limit for a neutral beam heated L-mode plasma. Linear stability analyses have shown that the maximum growth rate, γmax, is decreased across the whole confinement region during the formation of ITB although the critical parameter, ηi, is increased, which is identified to be due to the stabilizing of ITG with an increased ion-to-electron temperature ratio τ. The entropy generated by ion heat flux is significantly decreased together with the enhanced ZF amplitude and reduced ion heat transport when ITB has been fully developed, especially the modes with intermediate radial wavenumbers, implying that the long and medium radial scale turbulences are strongly suppressed by the ZF shear. Meanwhile, the long-range correlation and relative energy of the self-generated ZF are increased while the turbulent energy is decreased when ITB is triggered, indicating that the ZF gains more energy from background turbulence. It is found that the ratio between τ and ηi is a key parameter in determining the ZF shearing rate ωE×BZF and γmax. The value of ωE×BZF>γmax occurs around τ/ηi > 1.4, which is suggested to be responsible for the reduction of ion heat transport and hence the ITB formation.
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Generation of E × B flow shear by finite orbit width effects from heat sources in tokamaks
Article
  • Jan 2022
We present a possible mechanism for the generation of strong E × B flow shear relevant to internal transport barrier formation in tokamak plasmas. From gyrokinetic calculations, we show that strong E × B flow shear can be generated by finite orbit width (FOW) effects associated with a non-uniform heat source and is sufficient to lead to transport barrier formation in the core region with a moderate power level. Two FOW effects inducing neoclassical polarization are shown to be responsible for this: 1) the radial drift of particle orbit center due to the variation of the heat source within orbit width and 2) the non-uniformly evolved orbit width by the non-uniform heating.
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Internal transport barrier in tokamak and helical plasmas
Article
  • Mar 2018
The differences and similarities between the internal transport barriers (ITBs) of tokamak and helical plasmas are reviewed. By comparing the characteristics of the ITBs in tokamak and helical plasmas, the mechanisms of the physics for the formation and dynamics of the ITB are clarified. The ITB is defined as the appearance of discontinuity of temperature, flow velocity, or density gradient in the radius. From the radial profiles of temperature, flow velocity, and density the ITB is characterized by the three parameters of normalized temperature gradient,R/LT, the location, PITB, and the width, W/a, and can be expressed by 'weak' ITB (small R/LT) or 'strong' (large R/LT), 'small' ITB (small PITB) or 'large' ITB (large PITB), and 'narrow' (small W/a) or 'wide' (large W/a). Three key physics elements for the ITB formation, radial electric field shear, magnetic shear, and rational surface (and/or magnetic island) are described. The characteristics of electron and ion heat transport and electron and impurity transport are reviewed. There are significant differences in ion heat transport and electron heat transport. The dynamics of ITB formation and termination is also discussed. The emergence of the location of the ITB is sometimes far inside the ITB foot in the steady-state phase and the ITB region shows radial propagation during the formation of the ITB. The non-diffusive terms in momentum transport and impurity transport become more dominant in the plasma with the ITB. The reversal of the sign of non-diffusive terms in momentum transport and impurity transport associated with the formation of the ITB reported in helical plasma is described. Non-local transport plays an important role in determining the radial profile of temperature and density. The spontaneous change in temperature curvature (second radial derivative of temperature) in the ITB region is described. In addition, the key parameters of the control of the ITB and future prospects are discussed.
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Transport modelling of JT-60U and JET plasmas with internal transport barriers towards prediction of JT-60SA high-beta steady-state scenario
Article
  • Aug 2017
Transport modelling of plasmas with internal transport barriers in JT-60U and JET tokamaks has been carried out using integrated modelling codes TOPICS and CRONOS for the prediction of high-beta steady-state scenario in JT-60SA, which shares important characteristics with both tokamaks. Typical models of anomalous heat transport, which is one of major uncertainties in the prediction, have been validated for the experimental data in JT-60U and JET, and TOPICS and CRONOS equipped with the models are used for the model verification. It is found that CDBM model predicts temperatures close to experiments or underestimates them, and thus can be used for the conservative prediction, which considers a lower bound of plasma performance. By using the CDBM model, a JT-60SA high-beta steady-state plasma has been conservatively predicted within the machine capability. The conservative prediction shows that the JT-60SA has enough capability to explore high-beta steady-state plasmas and their controllability. Model modifications related with an E × B shear effect to improve the prediction capability are discussed. © 2017 National Institutes for Quantum and Radiological Science and Technology.
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Modelling the Ohmic L-mode ramp-down phase of JET hybrid pulses using JETTO with Bohm-gyro-Bohm transport
Article
  • Sep 2016
The empirical Bohmgyro-Bohm (BgB) transport model implemented in the JETTO code is used to predictively simulate the purely Ohmic (OH), L-mode current-ramp-down phase of three JET hybrid pulses, which combine two different ramp rates with two different electron densities (at the beginning of the ramp). The modelling is discussed, namely the strategy to reduce as much as possible the number of free parameters used to benchmark the model predictions against the experimental results. Hence, keeping the gas puffing rate as measured whilst controlling the line-averaged electron density via the recycling coefficient (which in the modelling is taken at the separatrix instead of the wall), one of the many possible ways to fix the total particle source, it is shown that the BgB model reproduces well the experimental data, as far as both average quantities (plasma internal inductance and volume-averaged electron temperature) and profiles (electron density and temperature) are concerned, with relative errors remaining mostly below 20%. The sensitivenesses with respect to the recycling coefficient, the ion effective charge, the energy of neutrals entering the plasma through the separatrix and the need to introduce a particle pinch are assessed; the necessity for a proper sawtooth model if experimental results are to be reproduced is also shown. The strong non-linear coupling in a OH plasma between density, temperature and current (essentially via interplay between the powerbalance equation, Joules heating with a temperature-dependent resistivity and the dependence of BgB transport coefficients on profile gradients) is put in evidence and analyzed in light of modelling results. It is still inferred from the modelling that the real value of the recycling coefficient at the separatrix (basically, the so-called fuelling efficiency times the actual recycling coefficient at the wall) must become close to one in the final stages of the discharges, when the gas puffing is switched off and so recycling comes to be the only source of particles. If the wall recycling remains close to one (as standard for tokamaks), this may indicate that the fuelling efficiency also approaches unity, apparently consistent with the observed fact that the plasma is pushed towards the machine wall at the end of the current ramps.
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Absorption of lower hybrid wave power by -particles in ITER-FEAT scenarios
Article
Full-text available
  • Aug 2004
Many experiments have proved the effectiveness of lower hybrid waves for current drive (CD) and current density profile control in tokamaks. However, fusion generated α-particles may be accelerated well beyond their birth velocity and may damp the wave energy, thus reducing the CD efficiency. This effect is absent at high frequency (8 GHz), but such a high frequency is undesirable for technical reasons. Therefore in this paper we calculate, at different frequencies (<8 GHz), the competition in the absorption between alphas and electrons in ITER-FEAT scenarios using a quasi-linear (QL) model for the α distribution function and full ray tracing in toroidal plasmas for the lower hybrid propagation. The use of the QL model for α-particles is mandatory to evaluate the tail in the distribution function, which, if very energetic, could affect the ITER first wall. The results of the present calculation show that, to limit the α absorption to few percents, a bottom frequency of 5 GHz is required. The CD efficiency provided for these scenarios by our numerical model is also presented.
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A gyro-Landau-fluid transport model
Article
Full-text available
  • Jul 1997
A physically comprehensive and theoretically based transport model tuned to three-dimensional (3-D) ballooning mode gyrokinetic instabilities and gyrofluid nonlinear turbulence simulations is formulated with global and local magnetic shear stabilization and E×B rotational shear stabilization. Taking no fit coefficients from experiment, the model is tested against a large transport profile database with good agreement. This model is capable of describing enhanced core confinement transport barriers in negative central shear discharges based on rotational shear stabilization. The model is used to make ignition projections from relative gyroradius scaling discharges.
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Dynamics and control of internal transport barriers in reversed shear discharges
Article
Full-text available
  • Apr 1998
Transitions to an enhanced confinement regime in tokamak plasmas with negative central magnetic shear have been observed in a number of devices. A simple model incorporating the nonlinear coupling between the turbulent fluctuations and the sheared radial electric field is added to a transport model in order to investigate the dynamics of the transition to this enhanced confinement mode. In this model, by incorporating both the instability growth rate profiles and particle and/or power deposition profiles, a rich variety of transition dynamics is uncovered. Transition dynamics and their concomitant thresholds are examined within the context of these models. In the course of investigating these transitions, potential methods for triggering and controlling these enhanced confinement regimes have been discovered and are discussed. © 1998 American Institute of Physics.
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Ion temperature gradient turbulence simulations and plasma flux surface shape
Article
Full-text available
  • Nov 1999
A generalization of the circular ŝ-α local magnetohydrodynamic (MHD) equilibrium model to finite aspect ratio (A), elongation (κ), and triangularity (δ) has been added to a gyrokinetic stability code and our gyrofluid nonlinear ballooning mode code for ion temperature gradient (ITG) turbulence. This allows systematic studies of stability and transport for shaped flux surfaces with the same minor midplane radius label (r), plasma gradients, q, ŝ, and α while varying A, κ, and δ. It is shown that the (linear, nonlinear, and sheared) E×B terms in the equation of motion are unchanged from a circle at radius r with an effective field Bunit = B0ρdρ/rdr, where χ = B0ρ2/2 is the toroidal flux, r is the flux surface label, and B0 is the magnetic axis field. This leads to a “natural gyroBohm diffusivity” χnatural, which at moderate q = 2 to 3 is weakly dependent on shape (κ) at fixed Bunit. Since Bunit/B0∝κ and 〈∣∇r∣2〉 ≈ (1+κ2)/(2κ2), the label independent χITER = χnatural/〈∣∇r∣2〉 at fixed B0 scales as 2/(1+κ2) with much weaker scaling at high-q and stronger at low-q where increased κ is stabilizing. The generalized critical E×B shear rate to be compared to the maximum linear growth rate is a flux surface quantity (r/q)d/dr(cq/rBunitdϕ0/dr) = (r/q)d(Ex0/BpR)/dr. © 1999 American Institute of Physics.
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Effects of E × B velocity shear and magnetic shear on turbulence and transport in magnetic confinement devices
Article
  • May 1997
  • PHYS PLASMAS
One of the scientific success stories of fusion research over the past decade is the development of the EÃB shear stabilization model to explain the formation of transport barriers in magnetic confinement devices. This model was originally developed to explain the transport barrier formed at the plasma edge in tokamaks after the L (low) to H (high) transition. This concept has the universality needed to explain the edge transport barriers seen in limiter and divertor tokamaks, stellarators, and mirror machines. More recently, this model has been applied to explain the further confinement improvement from H (high) mode to VH (very high) mode seen in some tokamaks, where the edge transport barrier becomes wider. Most recently, this paradigm has been applied to the core transport barriers formed in plasmas with negative or low magnetic shear in the plasma core. These examples of confinement improvement are of considerable physical interest; it is not often that a system self-organizes to a higher energy state with reduced turbulence and transport when an additional source of free energy is applied to it. The transport decrease that is associated with EÃB velocity shear effects also has significant practical consequences for fusion research. The fundamental physics involved in transport reduction is the effect of EÃB shear on the growth, radial extent, and phase correlation of turbulent eddies in the plasma. The same fundamental transport reduction process can be operational in various portions of the plasma because there are a number of ways to change the radial electric field E{sub r}. An important theme in this area is the synergistic effect of EÃB velocity shear and magnetic shear. Although the EÃB velocity shear appears to have an effect on broader classes of microturbulence, magnetic shear can mitigate some potentially harmful effects of EÃB velocity shear and facilitate turbulence stabilization. (Abstract Truncated)
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Flow shear induced fluctuation suppression in finite aspect ratio shaped tokamak plasma
Article
  • May 1995
The suppression of turbulence by the E×B flow shear and parallel flow shear is studied in an arbitrary shape finite aspect ratio tokamak plasma using the two point nonlinear analysis previously utilized in a high aspect ratio tokamak plasma [Phys. Plasmas 1, 2940 (1994)]. The result shows that only the E×B flow shear is responsible for the suppression of flute‐like fluctuations. This suppression occurs regardless of the plasma rotation direction and is, therefore, relevant for the very high (VH) mode plasma core as well as for the high (H) mode plasma edge. Experimentally observed in–out asymmetry of fluctuation reduction behavior can be addressed in the context of flux expansion and magnetic field pitch variation on a given flux surface. The adverse effect of neutral particles on confinement improvement is also discussed in the context of the charge exchange induced parallel momentum damping. © 1995 American Institute of Physics.
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Microinstability properties of negative magnetic shear discharges in the Tokamak Fusion Test Reactor and DIII-D
Article
  • Sep 1997
The microinstability properties of discharges with negative (reversed) magnetic shear in the Tokamak Fusion Test Reactor (TFTR) [R. J. Hawryluk et al., Plasma Physics and Controlled Nuclear Fusion Research, 1994 (International Atomic Energy Agency, Vienna, 1995), Vol. 1, p. 11] and DIII-D [R. D. Stambaugh for the DIII-D Team, Plasma Physics and Controlled Nuclear Fusion Research, 1994 (International Atomic Energy Agency, Vienna, 1995), Vol. 1, p. 83] experiments with and without confinement transitions are investigated. A comprehensive kinetic linear eigenmode calculation employing the ballooning representation is employed with experimentally measured profile data, and using the corresponding numerically computed magnetohydrodynamic (MHD) equilibria. The instability considered is the toroidal drift mode (trapped-electron-ηi mode). A variety of physical effects associated with differing q-profiles are explained. In addition, different negative magnetic shear discharges at different times in the discharge for TFTR and DIII-D are analyzed. The effects of sheared toroidal rotation, using data from direct spectroscopic measurements for carbon, are analyzed using comparisons with results from a two-dimensional calculation. Comparisons are also made for nonlinear stabilization associated with shear in Er/RBθ. The relative importance of changes in different profiles (density, temperature, q, rotation, etc.) on the linear growth rates is considered. © 1997 American Institute of Physics.
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Bootstrap current and neoclassical transport in tokamaks of arbitrary collisionality and aspect ratio
Article
  • Sep 1997
A multi-species fluid model is described for the steady state parallel and radial force balance equations in axisymmetric tokamak plasmas. The bootstrap current, electrical resistivity, and particle and heat fluxes are evaluated in terms of the rotation velocities and friction and viscosity coefficients. A recent formulation of the neoclassical plasma viscosity for arbitrary shape and aspect ratio (including the unity aspect ratio limit), arbitrary collisionality, and orbit squeezing from strong radial electric fields is used to illustrate features of the model. The bootstrap current for the very low aspect ratio National Spherical Torus Experiment [J. Spitzer et al., Fusion Technol. 30, 1337 (1996)] is compared with other models; the largest differences occur near the plasma edge from treatment of the collisional contributions. The effects of orbit squeezing on bootstrap current, thermal and particle transport, and poloidal rotation are illustrated for an enhanced reverse shear plasma in the Tokamak Fusion Test Reactor [D. Meade and the TFTR Group, Plasma Physics and Controlled Nuclear Fusion Research, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. I, p. 9]. Multiple charge states of impurities are incorporated using the reduced ion charge state formalism for computational efficiency. Because the force balance equations allow for inclusion of external momentum and heat sources and sinks they can be used for general plasma rotation studies while retaining the multi-species neoclassical effects. © 1997 American Institute of Physics.
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Stability analysis of improved confinement discharges: Internal transport barriers in Tore Supra and radiative improved mode in TEXTOR
Article
  • Jul 2002
Results of stability analysis are presented for two types of plasma with good confinement: internal transport barriers (ITBs) on Tore Supra and the radiative improved (RI) mode on TEXTOR. The stability analysis has been performed with an electrostatic linear gyrokinetic code, evaluating the growth rates of microinstabilities. The code developed, KINEZERO, is aimed at systematic microstability analysis. Therefore the trade-off between having perfect quantitative agreement and minimizing computation time is made in favour of the latter. In the plasmas analysed, it is found that the onset of the confinement improvement involves a trigger. For the ITB discharges, negative magnetic shear is involved, whereas for the RI discharges, the triggering role is played by the increase of the impurity concentration. Once the improved confinement is triggered, the simultaneous increases of temperature and density gradients imply an increase in both the growth rate and the rotation shearing rate. The rotation shear is found to be high enough to maintain an improved confinement through the stabilization of the large scale modes.
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Development of a non-local model for tokamak heat transport in L-mode, H-mode and transient regimes
Article
  • Jan 1999
Non-local effects have recently been observed in many transient experiments in different tokamaks. These effects have been modelled by introducing a non-local dependence in the Bohm part of a previously introduced model for L-mode, so that good simulations are obtained for L - H transitions, cold pulses, sawteeth and ELMs. This model also explains the improvement of core transport in the whole high-performance phase of H-mode ELM-free discharges.
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Comparison of initial value and eigenvalue codes for kinetic toroidal plasma instabilities
Article
  • Aug 1995
  • COMPUT PHYS COMMUN
In plasma physics, linear instability calculations can be implemented either as initial value calculations or as eigenvalue calculations. Here, comparisons between comprehensive linear gyrokinetic calculations employing the ballooning formalism for high-n (toroidal mode number) toroidal instabilities are described. One code implements an initial value calculation on a grid using a Lorentz collision operator and the other implements an eigenvalue calculation with basis functions using a Krook collision operator. An electrostatic test case with artificial parameters for the toroidal drift mode destabilized by the combined effects of trapped particles and an ion temperature gradient has been carefully analyzed both in the collisionless limit and with varying collisionality. Good agreement is found. Results from applied studies using parameters from the Tokamak Fusion Test Reactor (TFTR) experiment are also compared.
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