Numerical modelling of plasma production with radio-frequency heating using four-strap π-phased antenna
Results of calculations of radio-frequency (RF) plasma production in the ion-cyclotron range of frequencies (ICRF) in the Uragan-2M stellarator using four-strap π-phased antenna are presented. The analysis carried out with usage of a self-consistent model that simulates plasma production with ICRF a...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2014 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2014
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| Цитувати: | Numerical modelling of plasma production with radio-frequency heating using four-strap π-phased antenna / Yu.S. Kulyk, V.Е. Moiseenko, T. Wauters, A.I. Lyssoivan // Вопросы атомной науки и техники. — 2014. — № 6. — С. 30-33. — Бібліогр.: 7 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859637402281181184 |
|---|---|
| author | Kulyk, Yu.S. Moiseenko, V.Е. Wauters, T. Lyssoivan, A.I. |
| author_facet | Kulyk, Yu.S. Moiseenko, V.Е. Wauters, T. Lyssoivan, A.I. |
| citation_txt | Numerical modelling of plasma production with radio-frequency heating using four-strap π-phased antenna / Yu.S. Kulyk, V.Е. Moiseenko, T. Wauters, A.I. Lyssoivan // Вопросы атомной науки и техники. — 2014. — № 6. — С. 30-33. — Бібліогр.: 7 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | Results of calculations of radio-frequency (RF) plasma production in the ion-cyclotron range of frequencies (ICRF) in the Uragan-2M stellarator using four-strap π-phased antenna are presented. The analysis carried out with usage of a self-consistent model that simulates plasma production with ICRF antennas.
Представлены результаты расчетов по ВЧ-созданию плазмы в ионно-циклотронном (ИЦ) диапазоне частот в стеллараторе Ураган-2М с использованием четырехполувитковой π-фазированной антенны. Теоретический анализ проводился с помощью самосогласованной модели, которая моделирует создание плазмы с использованием ИЦ-антенн.
Представлено результати розрахунків з ВЧ-створення плазми в іонно-циклотронному (ІЦ) діапазоні частот у стелараторі Ураган-2М з використанням чотирьохнапіввиткової π-фазованої антени. Теоретичний аналіз проводився за допомогою самоузгодженої моделі, що моделює створення плазми з використанням ІЦ-антен
|
| first_indexed | 2025-12-07T13:17:36Z |
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PLASMA HEATING AND CURRENT DRIVE
ISSN 1562-6016. ВАНТ. 2014. №6(94)
30 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2014, № 6. Series: Plasma Physics (20), p. 30-33.
NUMERICAL MODELLING OF PLASMA PRODUCTION WITH RADIO-
FREQUENCY HEATING USING FOUR-STRAP π-PHASED ANTENNA
Yu.S. Kulyk
1
, V.Е. Moiseenko
1
, T. Wauters
2
, A.I. Lyssoivan
2
1
Institute of Plasma Physics NSC KIPT, Kharkov, Ukraine;
2
Laboratory for Plasma Physics - ERM/KMS, Association EURATOM - BELGIAN STATE,
Brussels, Belgium
Results of calculations of radio-frequency (RF) plasma production in the ion-cyclotron range of frequencies
(ICRF) in the Uragan-2M stellarator using four-strap π-phased antenna are presented. The analysis carried out with
usage of a self-consistent model that simulates plasma production with ICRF antennas.
PACS: 52.50.Qt, 52.55.Hc.
INTRODUCTION
Plasma production in ICRF is most efficient if the
frequency is lower than the ion cyclotron frequency.
The features of plasma production in ICRF in toroidal
magnetic devices are studied, and the stages of the
plasma production process with an increase of the
plasma density are identified in Refs. [1, 2]. The
problem of RF plasma generation can be reformulated
as the problem of RF heating of a low-density low-
temperature plasma. The plasma density grows from the
value determined by the natural level of ionizing
radiation to the value corresponding to the full
ionization of the neutral gas. Since the range of plasma
densities is fairly wide, it is possible to distinguish three
stages of RF plasma generation that differ in both the
distribution of the electromagnetic field and the
character of the ionization process. In the first (wave-
less) stage (breakdown of the neutral gas), the plasma
density is very low and only slightly affects the
structure of the electromagnetic field. The second stage
is preliminary gas ionization; in this stage, waves can
already propagate in the plasma, but the plasma density is
still lower than the neutral gas density. The third stage is
the stage of neutral gas burnout; in this stage, the plasma
density becomes comparable with the neutral gas density.
In Uragan-2M stellarator plasma is regularly
produced by the frame antenna. However, the frame
antenna cannot generate plasma with high enough
density. Numerical calculations have shown the
effectiveness of the frame antenna for low density
plasma production [3, 4]. Starting from the plasma
density ne0~10
12
cm
-3
the power deposition becomes
periphery located and this cannot be avoided by
changing of antenna sizes and other parameters. For this
reason plasma density can be obtained with such an
antenna is not high that is confirmed by first
experiments in Uragan-2M device [4]. The resulting
plasma density is of order ne0~2·10
12
cm
-3
. However,
there is a need to operate with plasma of the density of
at least several times higher. Further increase of plasma
density to ne0~10
13
cm
-3
could be provided by RF
heating with another antenna system.
The four-strap antenna is oriented to the Alfvén
heating in the short wavelength regime [5]. Therefore,
the antenna is π -phased. Of course, the k|| range of this
antenna is not optimal for plasma production and it does
not allow such an antenna to produce plasma. To
operate successfully, the four-strap antenna needs initial
plasma with noticeable density.
In this paper we investigate whether four-strap
antenna is able to increase the plasma density in
Uragan-2M stellarator. In our scenario, the frame
antenna produces plasma with partial ionization with the
density, which it is able to produce. The four-strap
antenna increases plasma density and provide full
neutral gas ionization.
The self-consistent model of the RF plasma
production in stellarators [2] is applied to this problem.
NUMERICAL MODEL
The model of the RF plasma production includes the
system of the balance equations and the boundary
problem for the Maxwell’s equations. It is assumed that
the gas is atomic hydrogen. The stellarator plasma
column is modeled as a straight plasma cylinder with
identical electric fields at its ends (periodicity
condition). The plasma is assumed to be axisymmetric,
radially non-uniform and uniformly distributed along
the plasma column.
The system of the balance equations of particles and
energy reads:
,
1v
2
3
vv
4
3
2
3
2
re
e
eeee
B
n
ieB
aieeeiB
aeiHBaeeHBRF
eeB
Ee
r
T
nTqr
rr
k
Tnk
)(CTTnk
nnknnkP
t
Tnk
,
1
v e
n
e
aei
e r
rr
n
nn
dt
dn
(1)
,0 constVnVndVn VVae
where ne is the plasma density, na is the neutral gas
density, n0 is the initial neutral gas density, Te is the
electron temperature, PRFe is the RF power density of
electron heating, kB is the Boltzmann constant,
εH=13.6 eV is the ionization energy threshold of a
hydrogen atom, τn is the particle confinement time, the
coefficient 3/4 is the ratio of the excitation energy to the
ISSN 1562-6016. ВАНТ. 2014. №6(94) 31
ionization energy, VV is the vacuum chamber volume,
‹σev› is the rate of electron-impact excitation of an
atom, ‹σiv› is the rate of electron-impact ionization of
an atom, ‹σeiv› is the rate of electron-ion energy
exchange via Coulomb collisions, and Ca=eΦa/Te≈3.5 is
the ratio of the electron energy in the ambipolar
potential to the electron thermal energy. Only electrons
with energies higher than the potential energy eΦa leave
the plasma. Accordingly, energy losses per electron
increase by a factor of Ca in average.
The neoclassical particle flux Γe and energy flux qe
are
,
1
2
31
1
2
1
r
T
TD
D
Tk
eE
r
n
n
Dn e
eeB
re
e
ee
.
1
2
31
2
3
2
r
T
TD
D
Tk
eE
r
n
n
DTnq e
eeB
re
e
eee
In this formulas
,4...1
2
11
21
0
lDKedKD l
e
K
en
e
,
v
,
v
,,
2
v
0
1111
2
B
E
rDD
Tk
m
K
e
r
e
e
eB
ee
e
where D11 is the monoenergetic diffusion coefficient, me
is the electron mass, ve is the electron velocity, νe is the
collision frequency, and Er is the radial component of
the electric field.
The RF field produces plasma both inside and
outside the confinement region. Charged particle losses
outside the confinement region are caused not only by
diffusion, but also convection, because the plasma
particles escape onto the chamber wall along the
magnetic field lines, as is the case in open traps [6]. The
model takes into account this process in the τ-
approximation with τn=ΠL/2vs. Here, Π is the mirror
ratio, which was assumed to be unity in our simulations,
L is the length of a magnetic field line, and vs is the ion-
acoustic velocity. This formula describes plasma
expansion along the magnetic field with the speed of
sound. Expression is applicable only to plasma located
outside the confinement region. Inside the confinement
region, the characteristic time of convective losses is
infinite.
The problem of particle and energy transfer requires
setting the following regularity conditions at the
cylinder axis
.0
)(
,0
00 r
ee
r
e
r
Tn
r
n
(2)
The boundary conditions at the chamber wall,
0,0
areeare Tnn (3)
correspond to a zero plasma density and plasma energy
at the wall.
To make the system of the equations (1) closed, it is
necessary to determine RF power density,
,Im
2
,nm
mnmnRFP DE (4)
where m and n are the azimuthal and toroidal mode
numbers, respectively. This quantity can be found from
the solution of the boundary problem for the Maxwell’s
equations
,02
2
extir
c
jEE (5)
where E is the temporal Fourier harmonics of the
electric field and jext is the density of the external RF
current. The plasma dielectric tensor is a function of the
plasma density and electron temperature,
.
00
0
0
,
//
ig
ig
tr
All components of the plasma dielectric tensor, except
for ε||, are taken in the cold plasma approximation. For
the ion and electron temperatures of T~2…20 eV, which
are typical of the initial stage of plasma production, the
particle gyroradius is much smaller than the wavelength
and the finite-Larmor-radius corrections to the tensor
can be ignored. At the same time, the value of k||vTe can
be comparable with the frequency ω (in particular, when
generating plasma in small stellarators), which indicates
that it is necessary to take into account electron Landau
damping and use the expression for the tensor
component ε|| in the hot plasma approximation.
In cylindrical geometry the Fourier series could be
used
.)(
,
tiikzim
nm
mn eeeE rE (6)
The Maxwell’s equations are solved at each time
moment for current plasma density and temperature
distributions.
EXAMPLES OF CALCULATIONS
The following parameters of calculations for the
Uragan-2M stellarator are chosen: the major radius of
the torus is R=1.7·10
2
cm; the radius of the plasma
column is rpl=22 cm; the radius of the metallic wall is
a=34 cm; the toroidal magnetic field is B=5 kG. The
radial coordinate of the front surface of four-strap
antenna (Fig. 1) is rant=28 cm; the distance between
antenna strap elements in z-direction is lz=20 cm.
Antenna is simulated by external RF currents jext which
obey to the condition ·jext=0. The explicit expressions
for the Fourier harmonics of the antenna currents are
substituted to the Maxwell’s equations.
For this antenna the leading value of parallel wave-
number is k||=0.16 cm
-1
. The most efficient Landau
damping occurs when k||vTe~ω this corresponds to the
electron temperature of 35 eV. The lower k|| modes of
antenna spectrum need higher electron temperature to
be damped efficiently.
Simulation results are presented in Figs.2-7. The
parameters of numerical calculations were as follows:
the initial electron temperature was Te=2 eV; the ion
temperature was taken to be independent of the radius
and time, Ti=3 eV; the frequency of heating was
ω=4·10
7
s
-1
.
32 ISSN 1562-6016. ВАНТ. 2014. №6(94)
Fig. 1. Four-strap antenna layout
The first numerical experiments have shown that the
four-strap antenna cannot create plasma if initial plasma
density is lower than ne0=5·10
11
cm
-3
, where ne0=ne|r=0
[7]. In current numerical experiments initial plasma
density was ne0~10
12
cm
-3
; the antenna current for the
matched load was I0=800 A. The initial density of
neutral atoms was in the range n0=1·10
12
…4·10
12
cm
-3
.
Figures 2-4 display the time evolution of average
plasma density, average electron temperature and
average density of neutral atoms. Figures 5-7 display
the profiles of plasma density, electron temperature and
deposited power at the time moment t=1.5 ms.
Just after the start, the plasma density begins to
increase (see Fig. 2). The first two stages of plasma
production (the wave-less and preionization stages) pass
very rapidly.
0 0.0004 0.0008 0.0012 0.0016
t, s
0.0E+000
4.0E+012
8.0E+012
1.2E+013
<
n
e>
,
cm
-3
Fig. 2. Time evolution of the average plasma density for
different values of the initial density of the neutral
atoms n0=1·10
12
cm
-3
(unmarked curve), n0=2·10
12
cm
-3
(circles), n0=4·10
12
cm
-3
(triangles)
At the initial stage of the plasma production the
average electron temperature is low. This is due to low
coupling of antenna to plasma. Further, the antenna
loading improves and plasma production is accelerated.
The electron temperature increases (see Figs. 2, 3).
At the end of the ionization process the density of the
neutral gas decreases to a value determined by particle
recycling (see Fig. 4).
The generated plasma density profile has a maximum
in the center of the plasma column (see Fig. 5). The
electron temperature and the power deposition are low
at the center of the plasma column (see Figs. 6, 7).
The calculations have shown that optimal value of
the initial neutral gas density is atoms n0=2·10
12
cm
-3
.
The power deposition occurs within the plasma volume
in this case (see Fig. 7). As in the case of the frame-type
antenna [2], by using the four-strap antenna, the peripheral
0 0.0004 0.0008 0.0012 0.0016
t, s
0
20
40
60
80
100
<
T
e>
,
eV
Fig. 3.Time evolution of the average electron
temperature for different values of the initial density of
the neutral atoms n0=1·10
12
cm
-3
(unmarked curve),
n0=2·10
12
cm
-3
(circles), n0=4·10
12
cm
-3
(triangles)
0 0.0004 0.0008 0.0012 0.0016
t, s
0
1E+012
2E+012
3E+012
4E+012
<
n
a>
,
cm
-3
Fig. 4. Time evolution of the average density of neutral
atoms for different values of the initial density of the
neutral atoms n0=1·10
12
cm
-3
(unmarked curve),
n0=2·10
12
cm
-3
(circles), n0=4·10
12
cm
-3
(triangles)
0 10 20 30 40
r, cm
0.0E+000
4.0E+012
8.0E+012
1.2E+013
1.6E+013
n
e,
c
m
-3
Fig. 5. Plasma density profile at t=1.5 ms for different
values of the initial density of the neutral atoms
n0=1·10
12
cm
-3
(unmarked curve), n0=2·10
12
cm
-3
(circles), n0=4·10
12
cm
-3
(triangles)
plasma
l z
ISSN 1562-6016. ВАНТ. 2014. №6(94) 33
0 10 20 30 40
r, cm
0
200
400
600
800
T
e,
e
V
Fig. 6. Electron temperature profile at t=1.5 ms for
different values of the initial density of the neutral
atoms n0=1·10
12
cm
-3
(unmarked curve), n0=2·10
12
cm
-3
(circles), n0=4·10
12
cm
-3
(triangles)
0 10 20 30 40
r, cm
0
0.2
0.4
0.6
p
R
F
,
a.
e.
Fig. 7. Power deposition profile at t=1.5 ms for
different values of the initial density of the neutral
atoms n0=1·10
12
cm
-3
(unmarked curve), n0=2·10
12
cm
-3
(circles), n0=4·10
12
cm
-3
(triangles)
plasma is also heated to high temperatures (see Fig. 6).
It can be explained by the Landau damping of the slow
wave at the plasma periphery. Unlike the frame-type
antenna slow wave is excited by the conversion of the
fast wave field in the Alfvén resonance layer. When the
neutral gas density increases, the resulting plasma
density is somewhat higher (see Fig. 5), the power
deposition profile is shifted toward the antenna (see
Fig. 7), whereby the electron temperature within the
plasma column decreases (see Fig.6).
DISCUSSION
The numerical calculations for Uragan-2M
stellarator indicated that using the four-strap antenna
plasma density can be increased by an order of
magnitude during the pulse. For chosen discharge
parameters, the optimal value of the initial neutral gas
density is n0=2·10
12
cm
-3
.
REFERENCES
1. A.I. Lysojvan, V.E. Moiseenko, O.M. Schvets,
K.N. Stepanov // Nuclear Fusion. 1992, v. 32, p. 1361.
2. V.E. Moiseenko, Yu.S. Stadnik, A.I. Lyssoivan //
Plasma Physics Reports. 2013, v. 39, № 11, p. 978-986.
3. Yu.S. Stadnik et al. Theoretical Analysis of RF
Plasma Production in Uragan-2M Torsatron // 34th EPS
Conference on Plasma Phys. Warsaw, Poland, 2-6 July
2007, ECA 2007, v.31F, p. -4.157.
4. V.E. Moiseenko et al. RF Plasma Production in
Uragan-2M Torsatron // AIP Conf. Proc. 2007, v. 933,
p. 115-118.
5. V.E. Moiseenko, Ye.D. Volkov, V.I. Tereshin,
Yu.S. Stadnik // Plasma Physics Reports. 2009, v. 35,
№ 10, p. 828-833.
6. V.V. Mirnov, D.D. Ryutov. Itogi Nauki Tekh. Ser.
“Fiz. Plazmy”, 1988, v. 8, p. 77 (in Russian).
7. V.E. Moiseenko, Yu.S. Stadnik. A.I. Lyssoivan //
Problems of Atomic Science and Technology. Series
“Plasma Physics”. 2012, № 6, p. 46-48.
Article received 18.09.2014
САМОСОГЛАСОВАННОЕ МОДЕЛИРОВАНИЕ ВОЗРАСТАНИЯ ПЛОТНОСТИ ПЛАЗМЫ
С ВЫСОКОЧАСТОТНЫМ НАГРЕВОМ
Ю.С. Кулик, В.Е. Моисеенко, Т. Вотерс, А.И. Лысойван
Представлены результаты расчетов по ВЧ-созданию плазмы в ионно-циклотронном (ИЦ) диапазоне
частот в стеллараторе Ураган-2М с использованием четырехполувитковой π-фазированной антенны.
Теоретический анализ проводился с помощью самосогласованной модели, которая моделирует создание
плазмы с использованием ИЦ-антенн.
САМОУЗГОДЖЕНЕ МОДЕЛЮВАННЯ ЗРОСТАННЯ ГУСТИНИ ПЛАЗМИ
ВИСОКОЧАСТОТНИМ НАГРІВОМ
Ю.С. Кулик, В.Є. Моісеєнко, Т. Вотерс, А.І. Лисойван
Представлено результати розрахунків з ВЧ-створення плазми в іонно-циклотронному (ІЦ) діапазоні
частот у стелараторі Ураган-2М з використанням чотирьохнапіввиткової π-фазованої антени. Теоретичний
аналіз проводився за допомогою самоузгодженої моделі, що моделює створення плазми з використанням
ІЦ-антен.
32
|
| id | nasplib_isofts_kiev_ua-123456789-81189 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T13:17:36Z |
| publishDate | 2014 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Kulyk, Yu.S. Moiseenko, V.Е. Wauters, T. Lyssoivan, A.I. 2015-05-13T15:05:12Z 2015-05-13T15:05:12Z 2014 Numerical modelling of plasma production with radio-frequency heating using four-strap π-phased antenna / Yu.S. Kulyk, V.Е. Moiseenko, T. Wauters, A.I. Lyssoivan // Вопросы атомной науки и техники. — 2014. — № 6. — С. 30-33. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 52.50.Qt, 52.55.Hc https://nasplib.isofts.kiev.ua/handle/123456789/81189 Results of calculations of radio-frequency (RF) plasma production in the ion-cyclotron range of frequencies (ICRF) in the Uragan-2M stellarator using four-strap π-phased antenna are presented. The analysis carried out with usage of a self-consistent model that simulates plasma production with ICRF antennas. Представлены результаты расчетов по ВЧ-созданию плазмы в ионно-циклотронном (ИЦ) диапазоне частот в стеллараторе Ураган-2М с использованием четырехполувитковой π-фазированной антенны. Теоретический анализ проводился с помощью самосогласованной модели, которая моделирует создание плазмы с использованием ИЦ-антенн. Представлено результати розрахунків з ВЧ-створення плазми в іонно-циклотронному (ІЦ) діапазоні частот у стелараторі Ураган-2М з використанням чотирьохнапіввиткової π-фазованої антени. Теоретичний аналіз проводився за допомогою самоузгодженої моделі, що моделює створення плазми з використанням ІЦ-антен en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Нагрев плазмы и поддержание тока Numerical modelling of plasma production with radio-frequency heating using four-strap π-phased antenna Самосогласованное моделирование возрастания плотности плазмы с высокочастотным нагревом Самоузгоджене моделювання зростання густини плазми високочастотним нагрівом Article published earlier |
| spellingShingle | Numerical modelling of plasma production with radio-frequency heating using four-strap π-phased antenna Kulyk, Yu.S. Moiseenko, V.Е. Wauters, T. Lyssoivan, A.I. Нагрев плазмы и поддержание тока |
| title | Numerical modelling of plasma production with radio-frequency heating using four-strap π-phased antenna |
| title_alt | Самосогласованное моделирование возрастания плотности плазмы с высокочастотным нагревом Самоузгоджене моделювання зростання густини плазми високочастотним нагрівом |
| title_full | Numerical modelling of plasma production with radio-frequency heating using four-strap π-phased antenna |
| title_fullStr | Numerical modelling of plasma production with radio-frequency heating using four-strap π-phased antenna |
| title_full_unstemmed | Numerical modelling of plasma production with radio-frequency heating using four-strap π-phased antenna |
| title_short | Numerical modelling of plasma production with radio-frequency heating using four-strap π-phased antenna |
| title_sort | numerical modelling of plasma production with radio-frequency heating using four-strap π-phased antenna |
| topic | Нагрев плазмы и поддержание тока |
| topic_facet | Нагрев плазмы и поддержание тока |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/81189 |
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