Particle transport simulations based on selfconsistency of pressure profiles in tokamaks
Simulation of particle and heat transport was performed with the ASTRA code. The equations for the electron temperature and density, ion temperature and current diffusion were solved. For the heat transport we used the canonical profiles model. Three T-10 pulses with toroidal magnetic field 2.5...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Цитувати: | Particle transport simulations based on selfconsistency of pressure profiles in tokamaks / A.V. Danilov, Yu. N. Dnestrovskij, V.F. Andreev, S.V. Cherkasov, A.Yu. Dnestrovskij, S.E. Lysenko, V.A. Vershkov // Вопросы атомной науки и техники. — 2006. — № 6. — С. 44-46. — Бібліогр.: 3 назв. — англ. |
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irk-123456789-817762015-05-21T03:02:19Z Particle transport simulations based on selfconsistency of pressure profiles in tokamaks Danilov, A.V. Dnestrovskij, Yu. N. Andreev, V.F. Cherkasov, S.V. Dnestrovskij, A.Yu. Lysenko, S.E. Vershkov, V.A. Magnetic confinement Simulation of particle and heat transport was performed with the ASTRA code. The equations for the electron temperature and density, ion temperature and current diffusion were solved. For the heat transport we used the canonical profiles model. Three T-10 pulses with toroidal magnetic field 2.5 T, plasma current 250…255 kA, initial average density 1.3, 2.4 and 3.2×10¹⁹ m⁻³ respectively, on-axis 900 kW ECRH and D₂ puffing were considered. The model proved to describe rather fast penetration of the density disturbance from the edge to the core during 15…20 ms after gas puffing. The simulation of the density profiles agrees with experiment in Ohmic and ECRH phases, and during the gas puffing, describing the particle pump-out after ECRH switch-on. The neutral influx at the plasma edge increases after ECRH switch-on in agreement with Da measurements. Both the effective diffusion coefficient and pinch velocity decrease slightly when the plasma density is increased. A set of two Ohmic and three NBI MAST pulses were considered for comparison. 2006 Article Particle transport simulations based on selfconsistency of pressure profiles in tokamaks / A.V. Danilov, Yu. N. Dnestrovskij, V.F. Andreev, S.V. Cherkasov, A.Yu. Dnestrovskij, S.E. Lysenko, V.A. Vershkov // Вопросы атомной науки и техники. — 2006. — № 6. — С. 44-46. — Бібліогр.: 3 назв. — англ. 1562-6016 PACS: 52.55.Fa; 52.25.Fi http://dspace.nbuv.gov.ua/handle/123456789/81776 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| language |
English |
| topic |
Magnetic confinement Magnetic confinement |
| spellingShingle |
Magnetic confinement Magnetic confinement Danilov, A.V. Dnestrovskij, Yu. N. Andreev, V.F. Cherkasov, S.V. Dnestrovskij, A.Yu. Lysenko, S.E. Vershkov, V.A. Particle transport simulations based on selfconsistency of pressure profiles in tokamaks Вопросы атомной науки и техники |
| description |
Simulation of particle and heat transport was performed with the ASTRA code. The equations for the electron
temperature and density, ion temperature and current diffusion were solved. For the heat transport we used the
canonical profiles model. Three T-10 pulses with toroidal magnetic field 2.5 T, plasma current 250…255 kA, initial
average density 1.3, 2.4 and 3.2×10¹⁹ m⁻³ respectively, on-axis 900 kW ECRH and D₂ puffing were considered. The
model proved to describe rather fast penetration of the density disturbance from the edge to the core during 15…20 ms
after gas puffing. The simulation of the density profiles agrees with experiment in Ohmic and ECRH phases, and during
the gas puffing, describing the particle pump-out after ECRH switch-on. The neutral influx at the plasma edge increases
after ECRH switch-on in agreement with Da measurements. Both the effective diffusion coefficient and pinch velocity
decrease slightly when the plasma density is increased. A set of two Ohmic and three NBI MAST pulses were
considered for comparison. |
| format |
Article |
| author |
Danilov, A.V. Dnestrovskij, Yu. N. Andreev, V.F. Cherkasov, S.V. Dnestrovskij, A.Yu. Lysenko, S.E. Vershkov, V.A. |
| author_facet |
Danilov, A.V. Dnestrovskij, Yu. N. Andreev, V.F. Cherkasov, S.V. Dnestrovskij, A.Yu. Lysenko, S.E. Vershkov, V.A. |
| author_sort |
Danilov, A.V. |
| title |
Particle transport simulations based on selfconsistency of pressure profiles in tokamaks |
| title_short |
Particle transport simulations based on selfconsistency of pressure profiles in tokamaks |
| title_full |
Particle transport simulations based on selfconsistency of pressure profiles in tokamaks |
| title_fullStr |
Particle transport simulations based on selfconsistency of pressure profiles in tokamaks |
| title_full_unstemmed |
Particle transport simulations based on selfconsistency of pressure profiles in tokamaks |
| title_sort |
particle transport simulations based on selfconsistency of pressure profiles in tokamaks |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2006 |
| topic_facet |
Magnetic confinement |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/81776 |
| citation_txt |
Particle transport simulations based on selfconsistency of pressure profiles in tokamaks / A.V. Danilov, Yu. N. Dnestrovskij,
V.F. Andreev, S.V. Cherkasov, A.Yu. Dnestrovskij, S.E. Lysenko, V.A. Vershkov // Вопросы атомной науки и техники. — 2006. — № 6. — С. 44-46. — Бібліогр.: 3 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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| fulltext |
44 Problems of Atomic Science and Technology. 2006, 6. Series: Plasma Physics (12), p. 44-46
PARTICLE TRANSPORT SIMULATIONS BASED ON SELF-
CONSISTENCY OF PRESSURE PROFILES IN TOKAMAKS
A.V. Danilov, Yu. N. Dnestrovskij,
V.F. Andreev, S.V. Cherkasov, A.Yu. Dnestrovskij, S.E. Lysenko, V.A. Vershkov
Nuclear Fusion Institute, RRC “Kurchatov Institute”, Moscow, Russia
Simulation of particle and heat transport was performed with the ASTRA code. The equations for the electron
temperature and density, ion temperature and current diffusion were solved. For the heat transport we used the
canonical profiles model. Three T-10 pulses with toroidal magnetic field 2.5 T, plasma current 250…255 kA, initial
average density 1.3, 2.4 and 3.2⋅1019 m-3 respectively, on-axis 900 kW ECRH and D2 puffing were considered. The
model proved to describe rather fast penetration of the density disturbance from the edge to the core during 15…20 ms
after gas puffing. The simulation of the density profiles agrees with experiment in Ohmic and ECRH phases, and during
the gas puffing, describing the particle pump-out after ECRH switch-on. The neutral influx at the plasma edge increases
after ECRH switch-on in agreement with Dα measurements. Both the effective diffusion coefficient and pinch velocity
decrease slightly when the plasma density is increased. A set of two Ohmic and three NBI MAST pulses were
considered for comparison.
PACS: 52.55.Fa; 52.25.Fi
1. INTRODUCTION
The plasma density profile plays an important role in
the plasma performance and that is why is being
intensively investigated in most current tokamaks. In
particular, the fusion power increases with plasma density
peaking, as does the bootstrap current fraction. On the
other hand, the density peaking may have negative effects
for MHD stability and central impurity accumulation.
Recently, significant experimental results in the field
of particle transport have been obtained. Evidence of an
anomalous pinch has been demonstrated in the non-
inductive current drive experiments with zero loop
voltage in TCV [1] and Tore Supra [2]. According to
current knowledge, the particle flux Γn can be presented
in the form
])//([ nTTCqqCnDnV eeTqwn ∇−∇+∇−=Γ , (1)
where the first term is the neoclassical Ware pinch, n and
Te are the electron density and temperature, Cq, and CT
are constants to be determined from experiment. The
terms in the round brackets present the anomalous pinch.
The turbulent thermodiffusion generates a pinch velocity,
inwards or outwards, proportional to ∇Te/Te. On the other
hand, the turbulent equipartition due to the curvature of
the magnetic field lines drives an inward pinch
proportional to ∇q/q, called curvature pinch.
2. CANONICAL PROFILE PARTICLE
TRANSPORT MODEL
Recent analysis of the plasma pressure profiles from
various tokamaks confirmed the conservation of relative
pressure profiles in the gradient zone under the variation
of plasma density and deposited power [3]. Usually these
profiles are close to the canonical ones, introduced by
B. Coppi, B. Kadomtsev and others in 1980s. The
conservation of pressure profiles means that the density
and temperature profiles are consistently correlated under
different external actions on the plasma. A simple
transport model for the plasma density based on the self-
consistency of the pressure profiles is proposed and
validated for a number of T-10 and MAST pulses. The
model naturally develops the canonical profiles model,
used for simulations of the heat transport:
nrrHDppppD
nnnnDnDnV
sstccp
ccnwn
∇−−∇−∇−
−∇−∇−∇−=Γ
)()/(
)/(0 , (2)
where p=nTe is the electron pressure. The second term in
(2) is linked with background diffusion, the next two -
with canonical profiles, and the last term describes the
sawtooth mixing in the central zone (rs is the radius of the
surface q=1, H(z) is the Heaviside function). For the T-10
tokamak with circular cross-section and large aspect ratio,
the Kadomtsev’s canonical profiles of density and
pressure nc and pc were used. In the case of the spherical
tokamak MAST the canonical profiles derived in [3] were
used. The diffusion coefficients D0, Dn and Dp were
assumed to be proportional to the heat diffusivity
coefficient used in the canonical profile model for the
heat transport.
Simulations of particles and heat transport were
performed with the ASTRA code. The equations for
electron temperature and density, ion temperature and
current diffusion were solved.
In order to compare the model (2) with the general
form of the particle flux (1) it may be presented in another
form. To do this we express p and pc through n, Te and nc,
Tec respectively, separate terms with n, nc and Te, Tec and
use the approximate expression: ∇nc/nc≈1/3∇pc/pc =
= -2/3∇qc/qc, valid for circular cylindrical plasmas. Thus
we obtain
nVnTTTTDDD
qqnnDD
wececeenpp
ccpnn
+∇−∇+−
−∇+∇+−=Γ
]//)(/(
)/3/2/)[((
. (3)
The first term in square brackets is quite similar to
corresponding expression in (1), especially taking into
account the value Cq≈0.8, obtained in [2] for the gradient
zone, but the terms responsible for thermodiffusion are
rather different. This term in (3) contains the difference of
two large values, which may be positive or negative.
Obviously, it is impossible to describe such a behaviour
of the flux using a single factor CT. The different signs of
CT in the central and gradient zones, observed by the
authors of [2] are in agreement with this statement.
45
b
3. RESULTS OF MODELLING
3.1 T-10
Three T-10 pulses with the toroidal magnetic field
2.5 T, plasma current 250-255 kA, initial average density
1.3, 2.4 and 3.2⋅1019 m-3 respectively, on-axis 900 kW
ECRH and D2 puffing were considered. The model proved
to describe a rather fast penetration of the density
disturbance from the edge to the core during 15-20 ms
after the gas puffing start. The simulations of the density
profiles agree with experiments in Ohmic and ECRH
phases, and during the gas puffing, describing the particle
pump-out after ECRH switch-on (Fig.1a). The subroutine
adjusting the density of incoming cold neutrals in order to
provide a required average electron density was used. The
neutral influx at the plasma edge, determined in such a
way, was increased after ECRH switch-on in agreement
with Dα measurements (Fig. 1b). The effective diffusion
coefficient and the pinch velocity decreased slightly when
the plasma density was increased.
Fig. 1. a) Density profile, experiment (dashed)
and simulation (solid);
b) Neutral influx at the plasma edge and Dα signal
3.2 MAST
A set of two Ohmic and three NBI MAST pulses were
considered for comparison with the same proportionality
coefficients between D0, Dn, Dp and the heat diffusivity.
The calculations proved to describe adequately the temperature
and density profiles in these pulses, as presented in Fig. 2a.
Fig. 2. a) The comparison of experimental and calculated
density profiles for two MAST shots;
b) Profiles of effective diffusion coefficient for Ohmic and
NBI shots;
c) The profiles of anomalous and neoclassical Ware pinch
velocities
0.0 0.1 0.2 0.3
0
1
2
3
4
5 a)
OH+ECRH+GAS PUFFING
OH+ECRH
OH
n, OH
nex
n, OH+ECRH
nex
n, ECRH+puff
nex
T-10, #39652
n
(1
019
m
-3
)
r (m)
500 550 600
0
200
400
Qna
Q
na
(1
019
s
-1
)
t (ms)
0
20
40
60
80
ECRH
b) #40694
D
α
D
α
0.0 0.2 0.4 0.6 0.8
0
2
4
Vp
Vw
#11458
NBI
#11445 OH
v p, v
w
(m
/s
)
ρ
0.0 0.2 0.4 0.6 0.8 1.0
0
1
2
3
4
b)
OH
NBI
#11456
#11458
#11459
#11445
#11447
D ef
f (
m
2 /s
)
ρ
0.2 0.4 0.6 0.8 1.0 1.2 1.4
0
1
2
3
4
5
a)
#11447
#11445
MAST
n
(1
019
m
-3
)
Major radius (m)
a
c
a
b
46
Figure 2b shows the effective diffusion coefficients for
Ohmic and NBI shots. We see that in the high-density
Ohmic shot (#11447) the diffusion is minimal over the all
plasma cross-section, while for another Ohmic shot
(#11445) the diffusion is small only in the core. Note that
for the NBI shot #11456 the beam was switched off at
t = 290 ms just before the density measurements at
t = 300 ms. Therefore in calculations at the time instant
t = 300 ms we have no beam particle source. As a result,
the value of Deff in the region 0 < ρ < 0.7 becomes much
lower in comparison with its previous level and with the
level of Deff in other NBI shots at t = 300 ms.
Figure 2c shows the profiles of anomalous and Ware
pinch velocities for Ohmic and NBI shots. It can be seen
that for low-density shots, when the electron temperature
is high, the anomalous pinch velocity in the gradient zone
is much higher (in a factor of 3-4) than the neoclassical
pinch velocity.
4. CONCLUSIONS
1. A simple model for particle transport in tokamaks
based on self-consistency of pressure profiles is proposed.
The model reasonably describes three T-10 pulses in
ohmic, ECRH and gas puffing stages and five MAST
pulses, with ohmic and NBI heating, thus proving to be
promising for further investigations.
2. The anomalous pinch velocity in the gradient zone is
3-4 times higher than the neoclassical one both in T-10
and MAST pulses under consideration.
3. Results of T-10 pulses modeling are in qualitative
agreement with the increase of neutral influx at the
plasma edge manifested in Dα increase. Absolute
measurements of neutral influx at the plasma edge are
needed for proper model calibration.
The work is supported by Rosatom, Grant NSh
2264.2006.2 and Consultancy Agreement N 3000043145,
UKAEA, UK.
REFERENCES
1. A. Zabolotsky, H. Weisen et. al. //Plasma Phys.
Control. Fusion. 2003, v.45, p. 735.
2. G.T. Hoang et. al. //Phys. Rev. Lett. 2003, v.90,
155002.
3. Yu. N. Dnestrovskij, K. A. Razumova et. al. Self-
consistency of pressure profiles in tokamaks. // Nuclear
Fusion. 2006, v.46, N11, p.953-965.
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