Self-consistent modelling of plasma density increase with radio-frequency heating
The self-consistent model of the radio-frequency (RF) plasma production in stellarators is described in this work. With this model of plasma production, one can perform calculations for different antenna systems. The selfconsistent model includes the system of the particle and energy balance equatio...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2012
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| Cite this: | Self-consistent modelling of plasma density increase with radio-frequency heating / V.Е. Moiseenko, Yu.S. Stadnik, A.I. Lyssoivan // Вопросы атомной науки и техники. — 2012. — № 6. — С. 46-48. — Бібліогр.: 3 назв. — англ. |
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| author | Moiseenko, V.Е. Stadnik, Yu.S. Lyssoivan, A.I. |
| author_facet | Moiseenko, V.Е. Stadnik, Yu.S. Lyssoivan, A.I. |
| citation_txt | Self-consistent modelling of plasma density increase with radio-frequency heating / V.Е. Moiseenko, Yu.S. Stadnik, A.I. Lyssoivan // Вопросы атомной науки и техники. — 2012. — № 6. — С. 46-48. — Бібліогр.: 3 назв. — англ. |
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| description | The self-consistent model of the radio-frequency (RF) plasma production in stellarators is described in this work. With this model of plasma production, one can perform calculations for different antenna systems. The selfconsistent model includes the system of the particle and energy balance equations and the boundary problem for the Maxwell’s equations. The numerical calculations of RF plasma production with four-strap antenna in the Uragan-2M stellarator are presented.
Описана самосогласованная модель высокочастотного (ВЧ) создания плазмы в стеллараторах. С помощью этой модели создания плазмы можно проводить расчеты для различных антенных систем. Модель включает в себя систему уравнений баланса частиц и энергии, и краевую задачу для уравнений Максвелла. Представлены результаты численных экспериментов по ВЧ-созданию плазмы в стеллараторе Ураган-2М с использованием четырехполувитковой антенны с помощью разработанной модели.
Описано самоузгоджену модель високочастотного (ВЧ) створення плазми в стелараторах. За допомогою цієї моделі створення плазми можна проводити розрахунки для різних антенних систем. Модель включає в себе систему рівнянь балансу частинок та енергії, та крайову задачу для рівнянь Максвелла. Представлено результати числових експериментів з ВЧ-створення плазми в стелараторі Ураган-2М з використанням чотиринапіввиткової антени за допомогою розробленої моделі.
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46 ISSN 1562-6016. ВАНТ. 2012. №6(82)
SELF-CONSISTENT MODELLING OF PLASMA DENSITY INCREASE
WITH RADIO-FREQUENCY HEATING
V.Е. Moiseenko1, Yu.S. Stadnik1, A.I. Lyssoivan2
1Institute of Plasma Physics NSC “Kharkov Institute of Physics and Technology”, Kharkov,
Ukraine;
2Laboratory for Plasma Physics - ERM/KMS, Association EURATOM - BELGIAN STATE,
1000 Brussels, Belgium
The self-consistent model of the radio-frequency (RF) plasma production in stellarators is described in this work.
With this model of plasma production, one can perform calculations for different antenna systems. The self-
consistent model includes the system of the particle and energy balance equations and the boundary problem for the
Maxwell’s equations. The numerical calculations of RF plasma production with four-strap antenna in the Uragan-2M
stellarator are presented.
PACS: 52.50.Qt, 52.55.Hc.
INTRODUCTION
The physical base of plasma production is the
electron impact ionization of a neutral gas. For
electrons, the maximum of the cross-section takes place
for the energies several times exceeding the threshold ε
( eVH 6.13=ε for hydrogen atom). One can perform
rough estimates for plasma production time
eHa man ε
τ
0
1~ and the net power τε /~ VnP HaRF
(here V is the plasma volume). For the magnetic fusion
parameters the plasma production time appears very
short and the power is much higher that is usual for
plasma auxiliary heating. Because the plasma
production time is not a parameter of primary
importance, it can be extended up to the hot plasma
confinement time. This allows one to decrease the RF
power level. In this regime, the majority of the electron
population have the energy below the ionization
threshold. The ionization is performed by the tail of the
electron distribution function.
In stellarator type machines, besides the electron-
cyclotron method, the plasma production in the ion-
cyclotron range of frequencies is practiced (see [1]).
The self-consistent model of the RF plasma production
[2] in stellarators is applied for this problem. With this
model one can perform calculations for different
antenna systems. The self-consistent model includes the
system of the particle and energy balance equations and
the boundary problem for the Maxwell’s equations.
Solution of the Maxwell’s equations determines a local
value of the electron RF heating power, which
influences on the ionization rate and, in this way, on the
evolution of plasma density.
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 system of the balance
equations of particles and energy reads:
( )
( ),1v
2
3
vv
4
3
2
3
2
ee
E
eeB
aeeeiB
aeiHBaeeHBRFe
eeB
Tnχ
τ
Tnk)(CTnσk
nnσεknnσεkP
t
Tnk
∇⋅∇++−−
−−−=
∂
∂
e
E
e
aei
e nDnnn
dt
dn
∇⋅∇+−=
τ
σ v , (1)
constVnVndVn VVae ==+∫ 0 ,
where en is the plasma density, an is the neutral gas
density, eT is the electron temperature, RFeP is the RF
power density that is coupled to the electrons, Bk is the
Boltzmann’s constant, eVH 6.13=ε is the ionization
energy threshold for the hydrogen atom, χ is the heat
transport coefficient, D is the diffusion coefficient, Eτ
is the particle confinement time, VV is the vacuum
chamber volume, veσ , viσ are the excitation and
ionization rates, veiσ is the energy exchange rate with
ions via Coulomb collisions, and 5.3/ ≈Φ= eaa TeC is
the ratio of the ambipolar potential energy to the
electron temperature.
To make the system of the equations (1) closed, it is
necessary to determine RF power density, RFeP . This
quantity can be found from the solution of the boundary
problem for the Maxwell’s equations:
( ) extir
c
jEE 02
2
ˆ ωμεω
=⋅−×∇×∇ , (2)
where E is the electric field, extj is the external RF
currents. The dielectric tensor reads:
( )
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
−= ⊥
⊥
//00
0
0
,ˆ
ε
ε
ε
ε ig
ig
tr .
In cylindrical geometry the Fourier series could be used:
tiikzim
nm
eeeE ωϕ −∑=
,
)(rE . (3)
The Maxwell’s equations are solved at each time
moment for current plasma density and temperature
distributions.
ISSN 1562-6016. ВАНТ. 2012. №6(82) 47
EXAMPLE OF CALCULATIONS
The following parameters of calculations for the
Uragan-2M stellarator are chosen: the major radius of
the torus is cm107.1 2⋅=R , the radius of the plasma
column is cm22=r , the radius of the metallic wall is
cm34=a , the toroidal magnetic field is kG5=B , the
frequency of heating -17 s104 ⋅=f . The radial
coordinate of the front surface of four-strap antenna
(Fig. 1) is cm28=rl , the distance between antenna
strap elements in z-direction is cm20=zl . Antenna is
simulated by external RF currents extj which obeys to
the condition 0=⋅∇ extj . The explicit expressions for
the Fourier harmonics of the antenna currents are
substituted to the Maxwell’s equations.
Fig. 1. Four-strap antenna layout
The numerical experiments have shown that the
four strap antenna cannot create plasma if initial plasma
density is lower than -311
0 cm105 ⋅=en (here
00 =
=
ree nn ). For higher initial densities the fully ionized
plasma is built-up.
The results of calculations of RF plasma production
in the Uragan-2M stellarator with the four-strap antenna
are presented in figures 2 and 3 which display the
profiles of plasma density, electron temperature and
deposited power at the time moment ms0.5=t . Figures
4-6 display the time evolution of electron temperature,
plasma density and density of neutral gas.
0 10 20 30 40
r, cm
0.0E+000
2.0E+012
4.0E+012
6.0E+012
8.0E+012
n e
, c
m
-3
Fig. 2. Profile of plasma density in t=0.5 ms
The power deposition and the electron temperature
(see Fig. 3) are low at the center of the plasma column.
At the center of the plasma column the plasma density
has a hollow profile (see Fig. 2). Since the power
deposition profile has a maximum near the plasma edge,
the ionization rate is higher there and plasma density
growth at the center is owing to plasma diffusion from
the periphery to the center.
RF power is also deposited out of the plasma
confinement volume. Therefore low density plasma is
sustained there.
0 10 20 30 40
r, cm
0
4
8
12
16
20
T e,
eV
0 10 20 30 40
r, cm
0
0.02
0.04
0.06
0.08
p R
F,
a.
e.
Fig. 3. Profile of electron temperature (upper chart)
and power deposition profile (lower chart) in time
moment t=0.5 ms
0 0.2 0.4 0.6 0.8 1
t, ms
0
10
20
30
<T
e>
, e
V
Fig.4. Time evolution of average electron temperature
evolution of input RF power
plasma
l z
48 ISSN 1562-6016. ВАНТ. 2012. №6(82)
0 0.2 0.4 0.6 0.8 1
t, ms
0.0E+000
2.0E+012
4.0E+012
6.0E+012
8.0E+012
<n
e>
, c
m
-3
Fig. 6. Time evolution of average plasma density
0 0.2 0.4 0.6 0.8 1
t, ms
0
4E+011
8E+011
1.2E+012
1.6E+012
2E+012
<n
a>
, c
m
-3
Fig. 7. Time evolution of average neutral gas density
At the initial stage of the plasma production the
average electron temperature is low (Fig. 4). This is due
to low coupling of antenna to plasma. Sharp peaks in
input RF power are observed (see Fig. 5). These peaks
are associated with the sharp increase of the antenna
loading resistance. It occurs when the slow wave global
resonance conditions in a plasma column is met. Thus,
these peaks are associated with poor antenna matching
with the generator in the chosen regime. For this
specific calculation the antenna loading resistance at
which the antenna-generator matching takes place is
chosen 4 Ohm, while the actual antenna loading
resistance does not exceed 1 Ohm. This indicates that
some generator antenna mismatch.
Starting from ms0.4=t the antenna loading
improves and plasma production is accelerated. The
electron temperature increases (Fig. 6).
At the end of the ionization process the density of
the neutral gas (Fig. 7) decreases to a value determined
by particle recycling.
CONCLUSIONS
Using the self-consistent model for the ICRF
plasma production the numerical calculations for the
Uragan-2M stellarator with the four-strap antenna are
carried out.
The numerical calculations have shown that the
four-strap antenna is the able to produce plasma. But
there is density threshold -311
0 cm105 ⋅=en below which
the plasma production process stagnate. If the initial
density is higher than the threshold, the neutral gas
burns out fully and the centrally peaked plasma density
profile is formed.
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, V.L. Berezhnyj,
V.N. Bondarenko, P.Ya. Burchenko, et al. RF
plasma production and heating below ion-cyclotron
frequencies in Uragan torsatrons // Nuclear Fusion.
2011, v. 51, p. 083036.
3. V.E. Moiseenko. Numerically stable Modeling of
Radio-Frequency Fields in Plasma // Problems of
Atomic Science and Technology. Series “Plasma
Physics“ (7). 2002, № 4, p. 100.
Article received 10.10.12
САМОСОГЛАСОВАННОЕ МОДЕЛИРОВАНИЕ ВОЗРАСТАНИЯ ПЛОТНОСТИ ПЛАЗМЫ
С ВЫСОКОЧАСТОТНЫМ НАГРЕВОМ
В.Е. Моисеенко, Ю.С. Стадник, А.И. Лысойван
Описана самосогласованная модель высокочастотного (ВЧ) создания плазмы в стеллараторах. С
помощью этой модели создания плазмы можно проводить расчеты для различных антенных систем. Модель
включает в себя систему уравнений баланса частиц и энергии, и краевую задачу для уравнений Максвелла.
Представлены результаты численных экспериментов по ВЧ-созданию плазмы в стеллараторе Ураган-2М с
использованием четырехполувитковой антенны с помощью разработанной модели.
САМОУЗГОДЖЕНЕ МОДЕЛЮВАННЯ ЗРОСТАННЯ ГУСТИНИ ПЛАЗМИ
З ВИСОКОЧАСТОТНИМ НАГРІВОМ
В.Є. Моісеєнко, Ю.С. Стаднiк, А.І. Лисойван
Описано самоузгоджену модель високочастотного (ВЧ) створення плазми в стелараторах. За допомогою
цієї моделі створення плазми можна проводити розрахунки для різних антенних систем. Модель включає в
себе систему рівнянь балансу частинок та енергії, та крайову задачу для рівнянь Максвелла. Представлено
результати числових експериментів з ВЧ-створення плазми в стелараторі Ураган-2М з використанням
чотиринапіввиткової антени за допомогою розробленої моделі.
|
| id | nasplib_isofts_kiev_ua-123456789-109098 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-11-30T09:41:23Z |
| publishDate | 2012 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Moiseenko, V.Е. Stadnik, Yu.S. Lyssoivan, A.I. 2016-11-20T18:51:25Z 2016-11-20T18:51:25Z 2012 Self-consistent modelling of plasma density increase with radio-frequency heating / V.Е. Moiseenko, Yu.S. Stadnik, A.I. Lyssoivan // Вопросы атомной науки и техники. — 2012. — № 6. — С. 46-48. — Бібліогр.: 3 назв. — англ. 1562-6016 PACS: 52.50.Qt, 52.55.Hc. https://nasplib.isofts.kiev.ua/handle/123456789/109098 The self-consistent model of the radio-frequency (RF) plasma production in stellarators is described in this work. With this model of plasma production, one can perform calculations for different antenna systems. The selfconsistent model includes the system of the particle and energy balance equations and the boundary problem for the Maxwell’s equations. The numerical calculations of RF plasma production with four-strap antenna in the Uragan-2M stellarator are presented. Описана самосогласованная модель высокочастотного (ВЧ) создания плазмы в стеллараторах. С помощью этой модели создания плазмы можно проводить расчеты для различных антенных систем. Модель включает в себя систему уравнений баланса частиц и энергии, и краевую задачу для уравнений Максвелла. Представлены результаты численных экспериментов по ВЧ-созданию плазмы в стеллараторе Ураган-2М с использованием четырехполувитковой антенны с помощью разработанной модели. Описано самоузгоджену модель високочастотного (ВЧ) створення плазми в стелараторах. За допомогою цієї моделі створення плазми можна проводити розрахунки для різних антенних систем. Модель включає в себе систему рівнянь балансу частинок та енергії, та крайову задачу для рівнянь Максвелла. Представлено результати числових експериментів з ВЧ-створення плазми в стелараторі Ураган-2М з використанням чотиринапіввиткової антени за допомогою розробленої моделі. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Нагрев плазмы и поддержание тока Self-consistent modelling of plasma density increase with radio-frequency heating Самосогласованное моделирование возрастания плотности плазмы с высокочастотным нагревом Самоузгоджене моделювання зростання густини плазми з високочастотним нагрівом Article published earlier |
| spellingShingle | Self-consistent modelling of plasma density increase with radio-frequency heating Moiseenko, V.Е. Stadnik, Yu.S. Lyssoivan, A.I. Нагрев плазмы и поддержание тока |
| title | Self-consistent modelling of plasma density increase with radio-frequency heating |
| title_alt | Самосогласованное моделирование возрастания плотности плазмы с высокочастотным нагревом Самоузгоджене моделювання зростання густини плазми з високочастотним нагрівом |
| title_full | Self-consistent modelling of plasma density increase with radio-frequency heating |
| title_fullStr | Self-consistent modelling of plasma density increase with radio-frequency heating |
| title_full_unstemmed | Self-consistent modelling of plasma density increase with radio-frequency heating |
| title_short | Self-consistent modelling of plasma density increase with radio-frequency heating |
| title_sort | self-consistent modelling of plasma density increase with radio-frequency heating |
| topic | Нагрев плазмы и поддержание тока |
| topic_facet | Нагрев плазмы и поддержание тока |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/109098 |
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