Development of 2D discharge initiation model in tokamaks
In this paper the increase of the region of the avalanche breakdown was taken into account while considering of the breakdown voltage as the function of gas pressure. The plasma column form is determined from the 2D equilibrium condition. Plasma conductivity was determined from 0D model particles an...
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| Date: | 2005 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2005
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| Cite this: | Development of 2D discharge initiation model in tokamaks / E.A. Azizov, A.D. Barkalov, G.G. Gladush, R.R. Khayrutdinov // Вопросы атомной науки и техники. — 2005. — № 2. — С. 14-16. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860258810855161856 |
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| author | Azizov, E.A. Barkalov, A.D. Gladush, G.G. Khayrutdinov, R.R. |
| author_facet | Azizov, E.A. Barkalov, A.D. Gladush, G.G. Khayrutdinov, R.R. |
| citation_txt | Development of 2D discharge initiation model in tokamaks / E.A. Azizov, A.D. Barkalov, G.G. Gladush, R.R. Khayrutdinov // Вопросы атомной науки и техники. — 2005. — № 2. — С. 14-16. — Бібліогр.: 8 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | In this paper the increase of the region of the avalanche breakdown was taken into account while considering of the breakdown voltage as the function of gas pressure. The plasma column form is determined from the 2D equilibrium condition. Plasma conductivity was determined from 0D model particles and heat balance. The dynamics of transition of plasma configuration with the open magnetic surfaces to the closed one is demonstrated.
У роботі враховується вплив збільшення області лавинного пробою на величину напруги пробою з ростом тиску газу. Форма плазмового шнура визначається з умови двовимірної рівноваги, провідність з 0-мірних рівнянь балансу тепла і часток. Показано динаміку переходу від плазмової конфігурації з розімкнутими магнітними поверхнями до конфігурації з замкнутими поверхнями.
В работе учитывается влияние увеличения области лавинного пробоя на величину напряжения пробоя с ростом давления газа. Форма плазменного шнура определяется из условия двумерного равновесия, проводимость из 0-мерных уравнений баланса тепла и частиц. Показана динамика перехода от плазменной конфигурации с разомкнутыми магнитными поверхностями к конфигурации с замкнутыми поверхностями.
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| first_indexed | 2025-12-07T18:52:54Z |
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DEVELOPMENT OF 2D DISCHARGE INITIATION MODEL IN TOKAMAKS
E.A. Azizov, A.D. Barkalov, G.G.Gladush, R.R. Khayrutdinov
SRC of RF TRINITI, Troitsk, Moscow Reg., Russia
In this paper the increase of the region of the avalanche breakdown was taken into account while considering of
the breakdown voltage as the function of gas pressure. The plasma column form is determined from the 2D equilibrium
condition. Plasma conductivity was determined from 0D model particles and heat balance. The dynamics of transition
of plasma configuration with the open magnetic surfaces to the closed one is demonstrated.
PACS: 52.55.Fa
1. INTRODUCTION
The study of breakdown physics and current ramp-up
in tokamaks is still far from completion. Meanwhile, this
issue is of a great importance because of its practical
applications. Knowing the location of plasma column
formation is crucial for development of tokamaks and
accurate description of the process of current ramp-up.
The stage of transition from the avalanche breakdown
to plasma column formation in the case of plasma being
generated in the region of either closed or non-closed
magnetic surfaces remains the most obscure. Currently
the plasma column formation and current ramp-up at this
stage is analyzed within the homogeneous (0D) model
when the transverse column dimension a, as well as the
major radius R are derived from the avalanche breakdown
condition and considered constant throughout the entire
stage [1-3]. In [8] the early stage of plasma formation is
considered in 1D model, where column dimension equals
dimension of vacuum chamber.
After avalanche phase plasma minor and major radii
can change. So, it will be more accurate to calculate all
plasma parameters from condition of 2D plasma
equilibrium in the external poloidal magnetic fields. Our
work is devoted to this issue.
2. EQUATIONS FOR QUASINEUTRAL
PLASMA
However, we firstly want to study the properties of
this 0D model, i.e. analyze the regularities induced by the
bulk processes accompanying current ramp during the
early stage of plasma column formation. In this work we
apply the approach developed in [1,2] following the
original notation. The energy balance equations for
electrons and ions in 0D approximation are written in the
form:
3
2
d
dt
ne kT e =POH−P Δ−P ion−
3
2
ne kT e
τ E
(1)
3
2
d
dt
ne kT i =P Δ−Pcx−
3
2
ne kT i
τ E
(2)
Particle balance: electrons ne and neutrals n0 respectively:
dne
dt
=n0ne S i−
ne
τ p
(3)
V V
dn0
dt
=
n0 V p
τ p
−n0 ne S i V p (4)
Circuit equation for plasma current Ip:
L
dI p
dt
Rpl I p=U , (5)
where L is column inductance and U is the loop voltage.
In (1-5) the following notations are applied: Vp is the
volume of plasma region, Vv represents the vacuum
chamber volume, Te и Ti are the electrons and ions
temperatures respectively, POH describes ohmic heating
specific power, P∆ is equilibration specific power between
electrons and ions in plasma, Pion is neutral gas ionization
specific losses, Pcx describes charge exchange specific
losses, τЕ and τР are the energy and particles confinement
times. For simplicity we put τЕ= τР.
The value of breakdown voltage as a function of
parameters under consideration represents our major
interest [4]. Fig.1 shows that Ub increases linearly with
the gas pressure.
Allowing for the fact that charge exchange represents
the major energy loss channel during breakdown and
assuming Ti ≈ Te analytic expression for breakdown
voltage can be found Ub [5]:
U b=102 RV V ln L
aT K
0,1 n0
0 (6)
In Fig. 1 one can see the comparison of numerical
simulation results obtained for transient system (1-5) with
formula (6) where a fairly good agreement is observed.
Fig. 1. Comparison of simulation results for breakdown
voltage depending on hydrogen pressure: 1 – theory,
2 – simulation, 3 – simulation with taking into account
dependence of plasma radius from pressure (КТМ);
4 – theory, 5 – simulation, × – experiment (Т-11М)
14 Problems of Atomic Science and Technology. Series: Plasma Physics (11). 2005. № 2. P. 14-16
Fig.1 demonstrates pressure dependent linear growth
of breakdown voltage similar to that during the avalanche
breakdown (high pressure limit [6]). However, the
breakdown voltage at quasi-neutral stage is substantially
higher (within an order of magnitude) than the
corresponding value at the avalanche.
With increase of gas pressure breakdown conditions
become easier, because Taunsend coefficient α rises with
pressure. It is known that with increase of pressure the
permissible value of poloidal field increases, and
consequently, the area where conditions of breakdown are
fulfilled is broadened. Accurate consideration of electrons
movement along magnetic line let us to obtain detailed
shape of this region (Fig. 2).
60 70 80 90 100 110 120 130 140
-60
-50
-40
-30
-20
-10
0
10
20
R, cм
Z,
см 1
2
10
20
Fig. 2. Boundaries of region for avalanche breakdown at
КТМ tokamak for different pressures: p =1, 2, 10, 20mPa
It is seen that with increase of pressure the region,
favorable for breakdown is widened. If we determine the
size of plasma column through the size of this area and
substitute it’s value into formula (6), then we obtain
correlated value for breakdown voltage (see Fig. 1).
3. 2D MODEL OF PLASMA COLUMN
FORMATION
In 0D model major and minor plasma radii are
required, which can be determined from equilibrium
conditions for plasma column at external poloidal
magnetic fields. Plasma equilibrium in tokamaks is
described by Grad-Shafranov equation. At our case part
of magnetic field lines where plasma flows are closed and
part of them are opened and they end at the vessel walls.
This situation is similar to the picture of Halo-currents
formation during disruption [7].
At the Grad-Shafranov equation the condition that
plasma pressure is constant along magnetic surfaces is
used. In our case plasma pressure is small, so this
requirement is not important. Plasma conductivity was
determined from 0D model, electric field was calculated
from solution of 1D diffusion of magnetic field equation
self-consistently with shape of magnetic surfaces.
Poloidal current function F is calculated using averaged
Grad-Shafranov equation and it is used further as part of
toroidal current density to solve 2D equilibrium and to
find structure of magnetic surfaces.
At the Fig. 3 examples of magnetic field structure at
different plasma currents are shown. It is seen that at
small value of plasma current significant part of it flows
along opened field lines. With the increase of plasma
current practically all current flows inside closed
magnetic surfaces. Plasma columns in both cases are in
equilibrium state. Thus, for studying of initial plasma
column formation, the hybrid 0D-2D model can be used.
a
15
b
Fig. 3. Magnetic surfaces cross section of КТМ tokamak
during breakdown (а) - 3 кА, (b) – 60 кА. Dark region
corresponds the plasma column
4. CONCLUSIONS
At the 0D homogeneous model it was shown that
value of voltage to overcome radiation barrier increases
with the increase of hydrogen pressure and decreases with
the increase of minor plasma radius. The self-consistent
model of initial plasma formation with 2D equilibrium
and 0D transport is presented. The dynamics of transition
of plasma configuration with opened magnetic surfaces to
closed one is demonstrated. Next stage will consist of in
developing 2D transport and 2D equilibrium and use
scenario for Null formation and PF coils current
waveforms from TRANSMAK code.
REFERENCES
1. B. Lloyd, G.L. Jackson, T.S. Taylor et al.// Nuclear
Fusion (31). 1991, № 11.
2. B. Lloyd, P.G. Carolan, C.D. Warrick.// Plasma
Phys. and Controlled Fusion (38). 1996, p. 1627.
3. V.А. Belyakov, V.I. Vasiliev, К.I. Lobanov et al.//
Proc. of VII Int. Conf. Engineering Problems of
Termonuclear Reactors, Oct. 28-31, 2002,
St.Petersburg. p. 178.
4. E.A. Azizov, Yu. S. Cherepnin, V.N. Dokouka et al.//
Proc. of the 21-st Symp. on Fusion Techn, Madrid,
Spain, Sept. 11-15, 2000.
5. E.A. Azizov, A.D. Barkalov, G.G. Gladush, R.R.
Khairutdinov // Proc. of the Int. Conf. and School on
Plasma Phys. and Controlled Fusion, Alushta,
Ukraine, Sept. 16 – 21, 2002.
6. Von Engel. Ionized gases (2-nd ed.). Oxford:
Claredon Press, 1965.
7. V.E. Lukash, R.R. Khayrutdinov // Fiz. Plasmy (22).
1996, p. 99.
8. Yu. N. Dnestrovsky, D.P. Kostomarov, G.V. Pereverzev,
K.N. Tarasyan: Preprint 2980. Moscow: RRC
Kurchatov Institute, 1978.
РАЗВИТИЕ 2D МОДЕЛИ ИНИЦИИРОВАНИЯ РАЗРЯДА В ТОКАМАКЕ
Э.A. Aзизов, A.Д. Баркалов, Г.Г. Гладуш, Р.Р. Хайрутдинов
В работе учитывается влияние увеличения области лавинного пробоя на величину напряжения пробоя с
ростом давления газа. Форма плазменного шнура определяется из условия двумерного равновесия,
проводимость из 0-мерных уравнений баланса тепла и частиц. Показана динамика перехода от плазменной
конфигурации с разомкнутыми магнитными поверхностями к конфигурации с замкнутыми поверхностями.
РОЗВИТОК 2D МОДЕЛІ ІНІЦІЮВАННЯ РОЗРЯДУ В ТОКАМАЦІ
Е.A. Aзізов, A.Д. Баркалов, Г.Г. Гладуш, Р.Р. Хайрутдінов
У роботі враховується вплив збільшення області лавинного пробою на величину напруги пробою з
ростом тиску газу. Форма плазмового шнура визначається з умови двовимірної рівноваги, провідність з 0-мірних
рівнянь балансу тепла і часток. Показано динаміку переходу від плазмової конфігурації з розімкнутими
магнітними поверхнями до конфігурації з замкнутими поверхнями.
16
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| id | nasplib_isofts_kiev_ua-123456789-79311 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:52:54Z |
| publishDate | 2005 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Azizov, E.A. Barkalov, A.D. Gladush, G.G. Khayrutdinov, R.R. 2015-03-31T08:09:26Z 2015-03-31T08:09:26Z 2005 Development of 2D discharge initiation model in tokamaks / E.A. Azizov, A.D. Barkalov, G.G. Gladush, R.R. Khayrutdinov // Вопросы атомной науки и техники. — 2005. — № 2. — С. 14-16. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 52.55.Fa https://nasplib.isofts.kiev.ua/handle/123456789/79311 In this paper the increase of the region of the avalanche breakdown was taken into account while considering of the breakdown voltage as the function of gas pressure. The plasma column form is determined from the 2D equilibrium condition. Plasma conductivity was determined from 0D model particles and heat balance. The dynamics of transition of plasma configuration with the open magnetic surfaces to the closed one is demonstrated. У роботі враховується вплив збільшення області лавинного пробою на величину напруги пробою з ростом тиску газу. Форма плазмового шнура визначається з умови двовимірної рівноваги, провідність з 0-мірних рівнянь балансу тепла і часток. Показано динаміку переходу від плазмової конфігурації з розімкнутими магнітними поверхнями до конфігурації з замкнутими поверхнями. В работе учитывается влияние увеличения области лавинного пробоя на величину напряжения пробоя с ростом давления газа. Форма плазменного шнура определяется из условия двумерного равновесия, проводимость из 0-мерных уравнений баланса тепла и частиц. Показана динамика перехода от плазменной конфигурации с разомкнутыми магнитными поверхностями к конфигурации с замкнутыми поверхностями. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Magnetic confinement Development of 2D discharge initiation model in tokamaks Розвиток 2D моделі ініціювання розряду в токамаці Развитие 2D модели инициирования разряда в токамаке Article published earlier |
| spellingShingle | Development of 2D discharge initiation model in tokamaks Azizov, E.A. Barkalov, A.D. Gladush, G.G. Khayrutdinov, R.R. Magnetic confinement |
| title | Development of 2D discharge initiation model in tokamaks |
| title_alt | Розвиток 2D моделі ініціювання розряду в токамаці Развитие 2D модели инициирования разряда в токамаке |
| title_full | Development of 2D discharge initiation model in tokamaks |
| title_fullStr | Development of 2D discharge initiation model in tokamaks |
| title_full_unstemmed | Development of 2D discharge initiation model in tokamaks |
| title_short | Development of 2D discharge initiation model in tokamaks |
| title_sort | development of 2d discharge initiation model in tokamaks |
| topic | Magnetic confinement |
| topic_facet | Magnetic confinement |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79311 |
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