Numerical modelling of the RF plasma production in URAGAN-2М stellarator with crankshaft antenna
The qualitative technique of the analysis of the efficiency of the RF plasma production is presented in which the
 solution of boundary problem for Maxwell’s equations is only necessary. The analysis of the character of the plasma
 production process with the crankshaft antenna in Ur...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2006 |
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| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2006
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| Цитувати: | Numerical modelling of the RF plasma production in URAGAN-2М stellarator with crankshaft antenna / V.Е. Moiseenko, Yu.S. Stadnik, E.D. Volkov, O.M. Schvet // Вопросы атомной науки и техники. — 2006. — № 6. — С. 62-64. — Бібліогр.: 4 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860246474672046080 |
|---|---|
| author | Moiseenko, V.Е. Stadnik, Yu.S. Volkov, E.D. Schvets, O.M. |
| author_facet | Moiseenko, V.Е. Stadnik, Yu.S. Volkov, E.D. Schvets, O.M. |
| citation_txt | Numerical modelling of the RF plasma production in URAGAN-2М stellarator with crankshaft antenna / V.Е. Moiseenko, Yu.S. Stadnik, E.D. Volkov, O.M. Schvet // Вопросы атомной науки и техники. — 2006. — № 6. — С. 62-64. — Бібліогр.: 4 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | The qualitative technique of the analysis of the efficiency of the RF plasma production is presented in which the
solution of boundary problem for Maxwell’s equations is only necessary. The analysis of the character of the plasma
production process with the crankshaft antenna in Uragan-2M stellarator is carried out. The discussion of the
calculations results is presented.
Представлена качественная методика анализа эффективности создания плазмы высокочастотными полями, в
рамках которой необходимо только лишь решение уравнений Максвелла. Проведен анализ характера процесса
создания плазмы в установке Ураган-2М с помощью антенны типа коленвал. Приведено обсуждение
результатов расчетов.
Представлено якісну методику аналізу ефективності створення плазми високочастотними полями, в межах
якої необхідне лише розв`язання рівнянь Максвелла. Проведено аналіз характеру процесу створення плазми в
установці Ураган-2М за допомогою антени типу коленвал. Приведено обговорення результатів розрахунків.
|
| first_indexed | 2025-12-07T18:37:09Z |
| format | Article |
| fulltext |
NUMERICAL MODELLING OF THE RF PLASMA PRODUCTION IN
URAGAN-2М STELLARATOR WITH CRANKSHAFT ANTENNA
V.Е. Moiseenko, Yu.S. Stadnik, E.D. Volkov, O.M. Schvets
Institute of Plasma Physics, NSC “Kharkov Institute of Physics and Technology",
61108, Akademicheskaya Str.1, Kharkov, Ukraine
The qualitative technique of the analysis of the efficiency of the RF plasma production is presented in which the
solution of boundary problem for Maxwell’s equations is only necessary. The analysis of the character of the plasma
production process with the crankshaft antenna in Uragan-2M stellarator is carried out. The discussion of the
calculations results is presented.
PACS: 52.25.Jm, 52.50.Qt.
INTRODUCTION
Plasma production in the ion-cyclotron (IC) range of
frequencies is the major method for plasma generation in
Uragan-2M stellarator that starts to operate next year in
the Kharkov Institute of Physics and Technology.
The features of plasma production in IC range of
frequencies in toroidal magnetic devices are studied, and
the stages of the plasma production process with increase
of the plasma density are identified in Ref. [1].
In the paper [2] the crankshaft antenna is proposed,
and it is has been shown its efficiency in the experiments
on the radio-frequency (RF) plasma production on
Uragan-3M small-size torsatron [3].
In the present work the results of study of plasma
production in Uragan-2M stellarator with the crankshaft
antenna obtained numerically are presented.
DESCRIPTION OF THE MODEL OF
PLASMA PRODUCTION
The model of plasma production includes system of
the balance equations and the boundary problem for the
Maxwell equations. The system of the balance equations
of particles and energy reads:
( )
aeiHaeeHRFe
ee nnnnP
t
Tn υσευσε −−=
∂
∂
4
3
2
3
eeTn∇⋅+ ∇ χ ,
eaei
e nDnn
dt
dn ∇⋅∇+= υσ ,
constnVVndVn VVae ==+∫ , (1)
where en is the plasma density, an is the neutral atoms
density, eT is the electron temperature, RFeP is the RF
power density, Hε =13.6eV is the ionization threshold for
hydrogen atom, υσ e and υσ i are the excitation and
ionization rates, χ is the heat transport coefficient, D is
the diffusion coefficient, VV is the vacuum chamber
volume.
To make the system of the equations (1) closed it is
necessary to determine the single external parameter in it,
RFeP . This parameter can be found from the solution of
the boundary problem for the Maxwell’s equations:
( ) jiEr
c
E
02
2
ω µεω =−×∇×∇
∧
, (2)
where E
is the electric field, ( )r
∧
ε is the dielectric tensor,
extj
is the external RF currents.
The system (1) describes the following physical
processes during the plasma production. The electrons are
heated by the RF field owing to collisional and Landau
wave damping. The characteristic value of temperature is
lower than the ionization threshold HeT ε< . In such
conditions the ionization is made mainly by the “tail” of
the electron distribution function. At low plasma density
ae nn < < the system of the balance equations has a self-
similar solution
( )rTT ere = , ( ) ( ) ( )rnttrn ere νexp, = , constna = ,
and
( ) ( )rPtP RFRF νexp= . (3)
From the self-similar solution follows that
( )rf
n
P
S
re
RF ==
= 0
. (4)
Such self-similar solution describes the mostly
efficient plasma production. The degree of satisfying of
the criterion (4) is used as an estimate of the plasma
production performance.
The quantity (4) is analysed in the series of the
calculations for the RF heating of plasma with the same
density profile and increasing density values. Such a
procedure allows one to avoid the long and labour-
consuming solving the self-consistent problem (1, 2).
The crankshaft antenna (see Fig. 1) has three strap
elements. The currents in the side straps are equal and co-
phased. The current in the twisted central strap is double
and directed opposite to the currents in the side straps.
62 Problems of Atomic Science and Technology. 2006, № 6. Series: Plasma Physics (12), p. 62-64
Fig. 1. Crankshaft antenna layout
RESULTS OF CALCULATIONS
The Maxwell’s equations are solved using the 1D
computer code that is based on the uniform finite
elements method [4]. The parameters of calculations for
Uragan-2M stellarator are chosen the following: the major
radius of the torus is R =1.5 × 102cm, the radius of the
plasma column is r =20 cm, the radius of the metallic
wall is a =30 cm, the toroidal magnetic field is B =5 ×
103G, the radial coordinate of the antenna strap rl =20 cm,
the electron temperature is eT =8eV. In the numerical
experiments certain parameters are varied in the following
range: the frequency of heating ω =3 × 107…4 × 107s-1,
the amplitude of crankshaft twisting of the central
conductor in the toroidal direction aϑ =0…0.04, the
distance between the side straps of the antenna zl
=30...50cm. The quantity S is analyzed in the range of
the plasma densities 0en =108…1013cm-3, where
00 == ree nn .
0 20 0 20 0 20
10
10
10
10
10
10
13
12
11
10
9
8
n
e0
cm [
]
-3
r [cm] r [cm] r [cm]
Fig. 2. Contours S as a function of plasma density at the
centre of the plasma column 0en and radial coordinate r
for different values of amplitude of crankshaft twisting of
the central conductor, aϑ =0 (left figure), aϑ =0.02
(central figure), aϑ =0.04 (right figure)
In Fig. 2 the quantity S is shown for different
crankshaft twisting of the central strap. In the left figure
this parameter equals zero. The power deposition is small
at low plasma densities. The power deposition appears at
0en >3 × 1012cm-3 and reaches its optimum at 0en ~1 ×
1013сm-3. The maximum of the power deposition is at r
=5 сm in this case. At higher values of plasma density
parameter S decreases and its distribution worsens.
With the introduction of the crankshaft twisting the
power deposition increases at low plasma densities. At
higher values of plasma density the power deposition
shifts to the plasma edge and for high densities it is
located in the vicinity of the antenna. At high plasma
densities the power deposition into the centre of the
plasma column remains the same as at aϑ =0.
The calculations with varying aϑ have shown that it
is not possible to achieve constancy of the quantity S
with increase of the plasma density. The noticeable
problem appears at the plasma densities 0en ~1 × 1011сm-3
at which the RF power does not reach the plasma core for
reasonable values of aϑ .
The variation of the distance between the side straps
does not influence on the low density plasma production
(see Fig. 3). With the increase of this distance, the plasma
density at which the power deposition is optimum
decreases.
The variation of the heating frequency (see Fig. 4)
gives the similar result: The optimum plasma density
decreases with frequency.
If the parabolic density profile is changed to the
hollow one, character of plasma production is altered (see
Fig. 5). The radical change of the power deposition
indicates the sensitivity of this method of plasma
production to the radial distribution of plasma density. In
the case of hollow plasma density profile the power
deposition is more central at the plasma densities 0en
~ 1 × 1011 сm-3. At higher densities then 0en > 1 ×
1012 сm-3 it worsens.
10
10
10
10
10
10
13
12
11
10
9
8
n e
0
cm[
]
-3
0 20 0 20
r [cm] r [cm]
Fig. 3. The same as in Fig.2 for different values of
distance between side straps, zl =30cm (left figure), zl
=50cm (right figure)
10
10
10
10
10
10
13
12
11
10
9
8
n e
0
cm[
]
-3
0 20 0 20
r [cm] r [cm]
Fig. 4. The same as in Fig.2 for different values of
frequency of heating, ω =3 × 107s-1 (left figure), ω =4 ×
107s-1 (right figure)
10
10
10
10
10
10
13
12
11
10
9
8
n
e0
cm[
]
-3
0 20 0 20
r [cm] r [cm]
63
Fig. 5. The same as in Fig.2 for parabolic density profile
(left figure) and for hollow density profile (right figure)
The results of the numerical experiments may be
explained in the following way. At small values of the
plasma density only the slow wave (SW) can propagate.
The antenna without the crankshaft twisting cannot excite
it, but even a small crankshaft twisting results in the
efficient SW excitation. With increase of the plasma
density the SW is strongly damped propagating to the
centre of the plasma column. At 0en ~1 × 1013 сm-3 it is
absorbed nearby the antenna.
The Alfvén resonances come to play at the plasma
densities 0en ~1 × 1012 сm-3. Three-half-turn part of the
antenna excites the Alfvén resonances efficiently. The
overlapping between the direct SW generation and the
Alfvén resonances excitation does not occur. There is the
range of plasma densities 0en ~1011…1012сm-3 where the
power deposition is minimal. In part, this can be
improved by increasing of the frequency value, and also
the power deposition is better for hollow density profile.
If the frequency is higher the maximum plasma density
which can be produced with crankshaft antenna will be
lower.
CONCLUSIONS
Aiming to describe the RF plasma production in the
Uragan-2M stellarator with the crankshaft antenna, the
power deposition to the plasma with varying densities is
analyzed numerically. At high plasma densities 0en
~1012…1013сm-3 and at low plasma densities 0en ~108…
1010сm-3 the power deposition is acceptable for efficient
plasma production. At high plasma densities there is some
power deposition out of plasma column. At intermediate
densities, the RF field does not deliver the energy to the
plasma centre. The situation improves if plasma has a
hollow radial profile.
The calculations show that the reasonable choice for
antenna parameters is the following: amplitude of
crankshaft twisting of the central conductor in toroidal
direction aϑ =0.04, the distance between the side straps of
the antenna zl =30cm number of the periods of the
crankshaft twisting cn =4, the frequency of heating ω =4
× 107s-1. The estimate show that such an antenna is the
able to produce plasma with the density 0en =2 × 1012сm-3
with the RF power P =600kW.
REFERENCES
1. A. I. Lysojvan, V. E. Moiseenko, O. M. Schvets,
K.N. Stepanov. Analysis of ICRF ( ciωω < ) plasma
production in large-scale tokamaks// Nuclear Fusion
1992. v. 32, p.1361.
2. V.E. Moiseenko, S.V. Kasilov, A.I. Lyssoivan,
V.V. Plyusnin. A Study of Antenna Coupling During
ICRF Plasma Build-up// 21st EPS Conf. on Contr.
Fusion and Plasma Phys., Montpellier, France, 1994.
v.18B, part I, p.980.
3. V.E. Moiseenko, V.V. Plyusnin, A.I. Lyssoivan et al.
Plasma Production Below the Ion Cyclotron
Frequency with Crankshaft Type Antenna// 23rd EPS
Conf. on Contr. Fusion and Plasma Phys., Kyiv,
Ukraine, 1996. v.20C, part II, p.926.
4. V.E. Moiseenko. Modelling of Maxwell's equations
using uniform finite elements// Problems of Atomic
Science and Technology, Series “Plasma Physics“
(9). 2003, N 1, p. 82-84.
ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ ВЫСОКОЧАСТОТНОГО СОЗДАНИЯ ПЛАЗМЫ
В СТЕЛЛАРАТОРЕ УРАГАН-2М С ПОМОЩЬЮ АНТЕННЫ КОЛЕНВАЛЬНОГО ТИПА
В.Е. Моисеенко, Ю.С. Стадник, Е.Д. Волков, О.М. Швец
Представлена качественная методика анализа эффективности создания плазмы высокочастотными полями, в
рамках которой необходимо только лишь решение уравнений Максвелла. Проведен анализ характера процесса
создания плазмы в установке Ураган-2М с помощью антенны типа коленвал. Приведено обсуждение
результатов расчетов.
ЧИСЕЛЬНЕ МОДЕЛЮВАННЯ ВИСОКОЧАСТОТНОГО СТВОРЕННЯ ПЛАЗМИ У СТЕЛАРАТОРІ
УРАГАН-2М ЗА ДОПОМОГОЮ АНТЕНИ КОЛЕНВАЛЬНОГО ТИПУ
В.Є. Моісеєнко, Ю.С. Стаднік, Є.Д. Волков, О.М. Швець
Представлено якісну методику аналізу ефективності створення плазми високочастотними полями, в межах
якої необхідне лише розв`язання рівнянь Максвелла. Проведено аналіз характеру процесу створення плазми в
установці Ураган-2М за допомогою антени типу коленвал. Приведено обговорення результатів розрахунків.
64
|
| id | nasplib_isofts_kiev_ua-123456789-81782 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:37:09Z |
| publishDate | 2006 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Moiseenko, V.Е. Stadnik, Yu.S. Volkov, E.D. Schvets, O.M. 2015-05-20T15:55:47Z 2015-05-20T15:55:47Z 2006 Numerical modelling of the RF plasma production in URAGAN-2М stellarator with crankshaft antenna / V.Е. Moiseenko, Yu.S. Stadnik, E.D. Volkov, O.M. Schvet // Вопросы атомной науки и техники. — 2006. — № 6. — С. 62-64. — Бібліогр.: 4 назв. — англ. 1562-6016 PACS: 52.25.Jm, 52.50.Qt. https://nasplib.isofts.kiev.ua/handle/123456789/81782 The qualitative technique of the analysis of the efficiency of the RF plasma production is presented in which the
 solution of boundary problem for Maxwell’s equations is only necessary. The analysis of the character of the plasma
 production process with the crankshaft antenna in Uragan-2M stellarator is carried out. The discussion of the
 calculations results is presented. Представлена качественная методика анализа эффективности создания плазмы высокочастотными полями, в
 рамках которой необходимо только лишь решение уравнений Максвелла. Проведен анализ характера процесса
 создания плазмы в установке Ураган-2М с помощью антенны типа коленвал. Приведено обсуждение
 результатов расчетов. Представлено якісну методику аналізу ефективності створення плазми високочастотними полями, в межах
 якої необхідне лише розв`язання рівнянь Максвелла. Проведено аналіз характеру процесу створення плазми в
 установці Ураган-2М за допомогою антени типу коленвал. Приведено обговорення результатів розрахунків. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Magnetic confinement Numerical modelling of the RF plasma production in URAGAN-2М stellarator with crankshaft antenna Численное моделирование высокочастотного создания плазмы в стеллараторе УРАГАН-2М с помощью антенны коленвального типа Чисельне моделювання високочастотного створення плазми у стелараторі УРАГАН-2М за допомогою антени коленвального типу Article published earlier |
| spellingShingle | Numerical modelling of the RF plasma production in URAGAN-2М stellarator with crankshaft antenna Moiseenko, V.Е. Stadnik, Yu.S. Volkov, E.D. Schvets, O.M. Magnetic confinement |
| title | Numerical modelling of the RF plasma production in URAGAN-2М stellarator with crankshaft antenna |
| title_alt | Численное моделирование высокочастотного создания плазмы в стеллараторе УРАГАН-2М с помощью антенны коленвального типа Чисельне моделювання високочастотного створення плазми у стелараторі УРАГАН-2М за допомогою антени коленвального типу |
| title_full | Numerical modelling of the RF plasma production in URAGAN-2М stellarator with crankshaft antenna |
| title_fullStr | Numerical modelling of the RF plasma production in URAGAN-2М stellarator with crankshaft antenna |
| title_full_unstemmed | Numerical modelling of the RF plasma production in URAGAN-2М stellarator with crankshaft antenna |
| title_short | Numerical modelling of the RF plasma production in URAGAN-2М stellarator with crankshaft antenna |
| title_sort | numerical modelling of the rf plasma production in uragan-2м stellarator with crankshaft antenna |
| topic | Magnetic confinement |
| topic_facet | Magnetic confinement |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/81782 |
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