The parametric excitation of ion Bernstein modes at the ICR plasma heating in the U-3M torsatron
The results of theoretical and experimental investigations of oscillatory and wave processes at the stellarator plasma edge are presented. Experimental results were interpreted using the kinetic theory of the electron-ion parametrical instability. It is shown that the interaction between plasma an...
Збережено в:
| Дата: | 2009 |
|---|---|
| Автори: | , , , , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2009
|
| Назва видання: | Вопросы атомной науки и техники |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/88220 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | The parametric excitation of ion bernstein modes at the ICR plasma heating in the U-3M torsatron / V.V. Olshansky, K.N. Stepanov, I.K. Tarasov, M.I. Tarasov, D.A Sitnikov, A.I. Skibenko, E.D. Volkov // Вопросы атомной науки и техники. — 2009. — № 1. — С. 46-48. — Бібліогр.: 6 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-88220 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-882202015-11-10T03:02:13Z The parametric excitation of ion Bernstein modes at the ICR plasma heating in the U-3M torsatron Olshansky, V.V. Stepanov, K.N. Tarasov, I.K. Tarasov, M.I. Sitnikov, D.A. Skibenko, A.I. Volkov, E.D. Магнитное удержание The results of theoretical and experimental investigations of oscillatory and wave processes at the stellarator plasma edge are presented. Experimental results were interpreted using the kinetic theory of the electron-ion parametrical instability. It is shown that the interaction between plasma and the alternating electric field under conditions carried out in given experiment makes possible a parametric excitation of the ion cyclotron oscillations. Представлені результати теоретичних та експериментальних досліджень осциляторних й хвильових процесів в периферійній стелараторній плазмі. Експериментальні результати інтерпретуються на основі кінетичної теорії електрон-іонної параметричної нестійкості. Показано, що дія змінного електричного поля на плазму в умовах даного експерименту робить можливим параметричне збудження іонних циклотронних коливань. Представлены результаты теоретических и экспериментальных исследований колебательных и волновых процессов в периферийной стеллараторной плазме. Экспериментальные результаты интерпретируются на основе кинетической теории электрон-ионной параметрической неустойчивости. Показано, что воздействие переменного электрического поля на плазму в условиях данного эксперимента делает возможным параметрическое возбуждение ионных циклотронных колебаний. 2009 Article The parametric excitation of ion bernstein modes at the ICR plasma heating in the U-3M torsatron / V.V. Olshansky, K.N. Stepanov, I.K. Tarasov, M.I. Tarasov, D.A Sitnikov, A.I. Skibenko, E.D. Volkov // Вопросы атомной науки и техники. — 2009. — № 1. — С. 46-48. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 52.55.Fa; 52.35.B http://dspace.nbuv.gov.ua/handle/123456789/88220 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Магнитное удержание Магнитное удержание |
| spellingShingle |
Магнитное удержание Магнитное удержание Olshansky, V.V. Stepanov, K.N. Tarasov, I.K. Tarasov, M.I. Sitnikov, D.A. Skibenko, A.I. Volkov, E.D. The parametric excitation of ion Bernstein modes at the ICR plasma heating in the U-3M torsatron Вопросы атомной науки и техники |
| description |
The results of theoretical and experimental investigations of oscillatory and wave processes at the stellarator plasma
edge are presented. Experimental results were interpreted using the kinetic theory of the electron-ion parametrical
instability. It is shown that the interaction between plasma and the alternating electric field under conditions carried out
in given experiment makes possible a parametric excitation of the ion cyclotron oscillations. |
| format |
Article |
| author |
Olshansky, V.V. Stepanov, K.N. Tarasov, I.K. Tarasov, M.I. Sitnikov, D.A. Skibenko, A.I. Volkov, E.D. |
| author_facet |
Olshansky, V.V. Stepanov, K.N. Tarasov, I.K. Tarasov, M.I. Sitnikov, D.A. Skibenko, A.I. Volkov, E.D. |
| author_sort |
Olshansky, V.V. |
| title |
The parametric excitation of ion Bernstein modes at the ICR plasma heating in the U-3M torsatron |
| title_short |
The parametric excitation of ion Bernstein modes at the ICR plasma heating in the U-3M torsatron |
| title_full |
The parametric excitation of ion Bernstein modes at the ICR plasma heating in the U-3M torsatron |
| title_fullStr |
The parametric excitation of ion Bernstein modes at the ICR plasma heating in the U-3M torsatron |
| title_full_unstemmed |
The parametric excitation of ion Bernstein modes at the ICR plasma heating in the U-3M torsatron |
| title_sort |
parametric excitation of ion bernstein modes at the icr plasma heating in the u-3m torsatron |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2009 |
| topic_facet |
Магнитное удержание |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/88220 |
| citation_txt |
The parametric excitation of ion bernstein modes
at the ICR plasma heating in the U-3M torsatron / V.V. Olshansky, K.N. Stepanov, I.K. Tarasov, M.I. Tarasov, D.A Sitnikov,
A.I. Skibenko, E.D. Volkov // Вопросы атомной науки и техники. — 2009. — № 1. — С. 46-48. — Бібліогр.: 6 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT olshanskyvv theparametricexcitationofionbernsteinmodesattheicrplasmaheatingintheu3mtorsatron AT stepanovkn theparametricexcitationofionbernsteinmodesattheicrplasmaheatingintheu3mtorsatron AT tarasovik theparametricexcitationofionbernsteinmodesattheicrplasmaheatingintheu3mtorsatron AT tarasovmi theparametricexcitationofionbernsteinmodesattheicrplasmaheatingintheu3mtorsatron AT sitnikovda theparametricexcitationofionbernsteinmodesattheicrplasmaheatingintheu3mtorsatron AT skibenkoai theparametricexcitationofionbernsteinmodesattheicrplasmaheatingintheu3mtorsatron AT volkoved theparametricexcitationofionbernsteinmodesattheicrplasmaheatingintheu3mtorsatron AT olshanskyvv parametricexcitationofionbernsteinmodesattheicrplasmaheatingintheu3mtorsatron AT stepanovkn parametricexcitationofionbernsteinmodesattheicrplasmaheatingintheu3mtorsatron AT tarasovik parametricexcitationofionbernsteinmodesattheicrplasmaheatingintheu3mtorsatron AT tarasovmi parametricexcitationofionbernsteinmodesattheicrplasmaheatingintheu3mtorsatron AT sitnikovda parametricexcitationofionbernsteinmodesattheicrplasmaheatingintheu3mtorsatron AT skibenkoai parametricexcitationofionbernsteinmodesattheicrplasmaheatingintheu3mtorsatron AT volkoved parametricexcitationofionbernsteinmodesattheicrplasmaheatingintheu3mtorsatron |
| first_indexed |
2025-07-06T15:58:50Z |
| last_indexed |
2025-07-06T15:58:50Z |
| _version_ |
1836913820132442112 |
| fulltext |
THE PARAMETRIC EXCITATION OF ION BERNSTEIN MODES
AT THE ICR PLASMA HEATING IN THE U-3M TORSATRON
V.V. Olshansky, K.N. Stepanov, I.K. Tarasov, M.I. Tarasov, D.A Sitnikov,
A.I. Skibenko, E.D. Volkov
NSC “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine,
E-mail: itarasov@ipp.kharkov.ua
The results of theoretical and experimental investigations of oscillatory and wave processes at the stellarator plasma
edge are presented. Experimental results were interpreted using the kinetic theory of the electron-ion parametrical
instability. It is shown that the interaction between plasma and the alternating electric field under conditions carried out
in given experiment makes possible a parametric excitation of the ion cyclotron oscillations.
PACS: 52.55.Fa; 52.35.B
INTRODUCTION
It is well known that the relative motion of plasma
components across the magnetic field lines appears to be
a reason of a number of instabilities with a transversal
current. If the relative motion velocity is lower or equal to
the thermal velocity of ions the frequencies and
increments of the mentioned instabilities are in order of
ion cyclotron frequency. The reason of such motion of the
plasma components presumably lays in the low-frequency
electromagnetic wave influence, centrifugal force
influence in rotating plasma or strong heterogeneity of
plasma density in the transition region between plasma
volume and vacuum. If the frequency of the
electromagnetic field (pumping wave) is in order of the
ion cyclotron frequency the phenomenon acquires a signs
of parametrical instability. The theory of ion cyclotron
instability of plasma with a transverse current was studied
in the great number of works references to which may be
found in [1]. The nonlinear theory of the ion cyclotron
instability with the transverse current was developed in
[2,3]. For the parametric kinetic ion cyclotron instability
one could expect that its characteristics are equal to those
of the current ion cyclotron instability by the order of
magnitude [3].
EXPERIMENTAL SETUP
Experiments were performed on U-3M device. U-3M is
a l = 3, m = 9 torsatron with open helical divertor. The main
parameters of plasma and magnetic field are R = 1 m, a =
0.13 m, B0 ≤ 1.6 T, rotational transform i/2π(a) = 0.4. In this
experiment the magnetic field was B0 = 0.72 T. Plasma in
U-3M is produced by absorption of RF power (f =
8…8.6 MHz, PRF ≤ 200 kW) from 2 antennas placed inside
of the helical winding near the last closed magnetic surface.
Frame aerials are used to excite the RF wave in plasma.
DIAGNOSTIC ELEMENTS
A set of capacitive probes (3 probes) was used as the
signal detectors. The probes were placed at the periphery
of the confinement volume Fig.1. The signals from each
of detectors were transmitted by the microwave coaxial
cable to the spectrum analyzer. A constant bias voltage
was applied on the probes through the same coaxial lines
using a stabilized voltage source. The magnitudes of
plasma density and temperature on the periphery of the
confining volume were obtained using a microwave
diagnostics and probe measurements. The density in the
probe area was determined using an X-wave
interferometry [4].
Fig.1. The scheme of experimental measurements
EXPERIMENTAL RESULTS
The results of experimental study of the oscillatory
processes observed at the edge of plasma confined in
U-3M torsatron are presented here. The plasma was
created by the RF discharge with the frequencies located
near the ion cyclotron resonance. To study the nature of
observed oscillations a number of spectrograms were
obtained.
a b
c d
Fig.2. The dynamics of oscillations spectra for different
values of RF pumping power (H =7 kOe, Δt =12…22 ms):
a) U= 5kV, b) U=6 kV, c) U=7 kV, d) U=8 kV
The measurements were carried out with the different
magnitudes of the RF power introduced into the plasma
46 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2009. № 1.
Series: Plasma Physics (15), p. 46-48.
volume (Fig. 2), magnitudes and polarities of potential
applied to the diagnostic probes (Fig. 3), time intervals
constituent to the RF pumping pulse (Fig. 4). To consider
the spatial dynamics of the oscillations spectrum a
comparison of signals obtained from different spatially
separated probes was made. The oscillations spectrum
was analyzed right up to the ninth harmonic component of
the ion cyclotron frequency.
47
a b
c
Fig.3. The probe potential magnitude and polarity
influence on the oscillations spectrum (H = 7 kOe,
Δt =12…22 ms, UA = 8 kV): a) UPR = 0 V,
b) UPR = +200V, c) UPR = -200 V
a b
c d
Fig.4. The dynamics of oscillations spectra for different
temporal zones of RF pumping pulse (H = 7 kOe,
UA = 8 kV): a) Δt = 0…12 ms, b) Δt = 12…22 ms,
c) Δt = 22…32 ms, d) Δt = 32…42 ms
THEORETICAL ESTIMATES
AND NUMERICAL SIMULATION
Comparison of the results of the linear analysis of
parametric electron-ion instability with the obtained from
numerical simulation spectral characteristics and
experimental data allows us to perform frequencies
identification and shows that the oscillation frequencies,
derived from the linear dispersion equation, predominate
in the numerical and experimental spectra, where
maximums of the intensity correspond to them.
The numerical solution of the linear parametric
dispersion equation is depicted in Fig. 5. This dispersion
equation is derived from the solvability condition for the
system of difference equations [5]
( ) ( ) ( ) ( )
( ) ( ) (
,
0 0
1
,
i n E n m
n m
e
J a J a
m n Q
δε ω η ω
)
E
δε ω ω η ω ω ω
∞
+
=−∞
+ +⎡ ⎤⎣ ⎦
× + − =
∑ × (1)
where eδε and iδε are the contributions of electrons and
ions to the plasma permittivity, are Bessel functions,
is the relative displacement of electrons in the field of
the pumping wave. Equating of the infinite determinant of
the system (1) to zero gives
nJ
Ea
0det =mnA , (2)
where the matrix elements appear as follows
( ) ( ) ( )
( )
0
0
1
1
.
mn mn p m p n
pe
e
A J
m
p
α α
α
δ
δε ω ω
δε ω ω
∞
+ +
=−∞
a J a= + ×
+ +
× +
∑ ∑
The case of the strong non-isothermal plasma,
ie TT ⋅= 10 , are presented in Fig. 5 for the pumping field
frequency 0ω =0.8 ciω . The oscillations frequency and
growth rate dependencies against the transverse wave
number are shown in the instability regions. We note that
two instability regions exist: the short-wavelength region
with 1≥ikρ (Fig. 5) and the more long-wavelength
region with 1<ikρ , (not shown here). It is clear that the
spectrum of Bernstein modes considerably varies due to
particles oscillations in the pumping wave filed. Splitting
of each Bernstein mode occurs on two branches with the
same growth rate. Near the splitting point oscillations
become unstable and have maximum growth
rate 3105.1 −⋅≈ciωγ .
2 2.5 3 3.5 4 4.5
0
1
2
3
4
5
6
kρ i
ω
/ ω
ci
2.0 2.5 3.0 3.5 4.0 4.5 5.0
0.0000
0.0005
0.0010
0.0015
0.0020
γ/
ω
ci
kρi
a b
Fig.5. Frequency (а) and growth rate (b) against the
transversal wave number with ie TT =10 ( ik ρ|| =0.003)
Numerical simulation of ion cyclotron parametric
instability is curried out using the code based on macro
particles technique [6]. For the computations the
numerical parameters, which correspond to the
experimental parameters, were chosen: plasma density
n=3⋅1010 cm-3; magnetic field BB0=7 kG; E0=1.5 V/cm,
pumping wave frequency =9 MHz, antenna size
L
0f
a=40 cm, electron temperature Te=30 eV. It is assumed
that at the plasma boundary ion temperature is
considerably less than electron temperature Ti=0.1Te. At
that the relation of the pumping field frequency to the ion
cyclotron one is equal to ciωω0 =0.8, and the relation of
the electron plasma frequency to the electron cyclotron
one comes to cepe ωω =0.09, i.e. electrons are strongly
magnetized. The initial particles distribution over
velocities is maxwellian one and it is uniform in the
space. The numerical simulation results show that in this
case the weak parametric instability appears with not
large growth rate ≈ciωγ 0.0012. The electric field
energy slow increases and becomes saturated at the level
which agrees with the estimate (1). Comparison of the
frequency spectrum of the most unstable mode
( ik ρ⊥ =0.9, ik ρ|| =0.003) with the experimental one for
the input power 7 kV reveals that they are similar. It
follows from Fig. 6, which is obtained by superposition of
the numerical simulation spectrum (white color) and the
experimental one (in black). A difference appears
beginning with the fifth harmonic which amplitude
disproportionately decreases in the numerical simulation.
Development of the instability results in unsubstantial
growth of the longitudinal electron temperature (about
2%) and the transversal ion temperature. At the same time
the longitudinal ion temperature remains at the initial
level. It agrees well with the theoretical estimate (2).
Fig. 6. Comparison of the experimental spectrum (in
black) and the spectrum of the most unstable mode (in
white)
CONCLUSIONS
The oscillations spectrum form changing is closely
connected with the pumping power increasing. Higher
harmonics become more pronounced. The appearance of
additional spectral components near the primary
harmonics may be considered as a threshold phenomenon.
The appearance of a higher harmonics corresponds to the
plasma density increasing. The results of numerous
experiments have shown the possibility of ion and
electron contributions separation by applying a bias
voltage on the measuring probe. The behavior of ion
spectral component differed from those of electron
component. The numerical simulation of the electron-ion
parametric instability shows the following. The frequency
spectra of the ion cyclotron oscillations considerably vary
even when amplitude of the oscillation velocity of the
electrons with regard to the ions is less than the ion
thermal velocity. In the instability region the ion
Bernstein modes break up into two branches. Maximum
value of the growth rate is about 1.5⋅10-3· ciω . Computed
values of the frequencies and the growth rates
qualitatively agree with the analytical results. For the
electron-ion parametric instability the level of the
oscillations at the quasi-stationary stage corresponds well
to the estimate (2) which was derived in [3] from the
condition of the instability saturation due to the nonlinear
broadening of the cyclotron resonances. Obtained with the
numerical simulation frequency spectra conform to the
experimental data. It allows to think that in the
experiment the electron-ion parametric instability
occurred. It conditions the character of the obtained
experimental spectra.
REFERENCES
1. K.N. Stepanov //Plasma Phys. And Contr. Fusion.
1996, v. 38, N 12, p. A13.
2. V.S. Mikhailenko, K.N. Stepanov. //Plasma Phys.
Control. Fusion. 1981, V. 23, No. 12, p. 1165.
3. V.S. Mikhailenko, K.N. Stepanov //JETP. 1984, v. 87,
N 1, p. 161.
4. A.I. Skibenko, O.S. Pavlichenko, V.L. Berezhnyj et al//
Problems of Atomic Science and Technology. Series
”Plasma Physics” (12). 2006, N 6, p. 65-67.
5. A.B. Kitsenko et al //Nuclear Fusion. 1973, v. 13,
p. 557.
6. V.V. Olshansky // National Academy of Sciences of
Ukraine Reports. 1999, N 2, p. 95.
Article received 13.10.08
ПАРАМЕТРИЧЕСКОЕ ВОЗБУЖДЕНИЕ ИОННЫХ БЕРШТЕЙНОВСКИХ МОД
ПРИ ИЦР- НАГРЕВЕ ПЛАЗМЫ В ТОРСАТРОНЕ У-3М
В.В. Ольшанский, К.Н. Степанов, И.К. Тарасов, М.И. Тарасов, Д.А. Ситников, А.И. Скибенко, Е.Д. Волков
Представлены результаты теоретических и экспериментальных исследований колебательных и волновых
процессов в периферийной стеллараторной плазме. Экспериментальные результаты интерпретируются на
основе кинетической теории электрон-ионной параметрической неустойчивости. Показано, что воздействие
переменного электрического поля на плазму в условиях данного эксперимента делает возможным
параметрическое возбуждение ионных циклотронных колебаний.
ПАРАМЕТРИЧНЕ ЗБУЖДЕННЯ ІОННИХ БЕРНШТЕЙНІВСЬКИХ МОД
ПРИ ІЦР- НАГРІВАННІ ПЛАЗМИ В ТОРСАТРОНІ У-3М
В.В. Ольшанський, К.М. Степанов, І.К. Тарасов, М.І. Тарасов, Д.А. Ситников, А.І. Скибенко, Є.Д. Волков
Представлені результати теоретичних та експериментальних досліджень осциляторних й хвильових
процесів в периферійній стелараторній плазмі. Експериментальні результати інтерпретуються на основі
кінетичної теорії електрон-іонної параметричної нестійкості. Показано, що дія змінного електричного поля на
плазму в умовах даного експерименту робить можливим параметричне збудження іонних циклотронних
коливань.
48
|