Fast Alfvén wave propagation in milticomponent nonuniform plasmas
The problem of the conversion, reflection and transmission of the fast Alfvén wave propagating in multicomponent nonuniform plasmas is studied. The dependences of the wave scattering characteristics on the plasma composition and parallel wave number have been obtained. The results can be used to c...
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2008
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| Cite this: | Fast Alfvén wave propagation in milticomponent nonuniform plasmas / Ye.O. Kazakov, I.V. Pavlenko, I.O. Girka, B. Weyssow // Вопросы атомной науки и техники. — 2008. — № 4. — С. 99-103. — Бібліогр.: 9 назв. — англ. |
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| author | Kazakov, Ye.O. Pavlenko, I.V. Girka, I.O. Weyssow, B. |
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| citation_txt | Fast Alfvén wave propagation in milticomponent nonuniform plasmas / Ye.O. Kazakov, I.V. Pavlenko, I.O. Girka, B. Weyssow // Вопросы атомной науки и техники. — 2008. — № 4. — С. 99-103. — Бібліогр.: 9 назв. — англ. |
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| description | The problem of the conversion, reflection and transmission of the fast Alfvén wave propagating in multicomponent
nonuniform plasmas is studied. The dependences of the wave scattering characteristics on the plasma
composition and parallel wave number have been obtained. The results can be used to control the part of the
launched power converted to the slow short wavelength mode and to prevent the essential reflection of the wave
power back to the antenna.
Вивчається задача конверсії, відбиття та проходження швидкої магнітозвукової хвилі, яка поширюється
у багатокомпонентній неоднорідній плазмі. Отримано залежності характеристик проходження хвилі від
складу плазми та від паралельного хвильового вектора. Отримані результати можуть бути використані для
керування частиною енергії хвилі, яка конвертується у короткохвильову моду, та для запобігання суттєвого
відбиття енергії хвилі назад до антени.
Изучается задача конверсии, отражения и прохождения быстрой магнитозвуковой волны,
распространяющейся в многокомпонентной неоднородной плазме. Получены зависимости характеристик
прохождения волны от состава плазмы и от параллельного волнового вектора. Полученные результаты
могут быть использованы для управления частью энергии волны, которая конвертируется в
коротковолновую моду, и для предотвращения существенного отражения энергии волны назад к антенне.
|
| first_indexed | 2025-12-02T10:50:16Z |
| format | Article |
| fulltext |
___________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2008. № 4.
Серия: Плазменная электроника и новые методы ускорения (6), с.99-103. 99
FAST ALFVÉN WAVE PROPAGATION IN MILTICOMPONENT
NONUNIFORM PLASMAS
Ye.O. Kazakov, I.V. Pavlenko, I.O. Girka, B. Weyssow*
Kharkiv National University, Kharkiv, Ukraine;
*EFDA-CSU Garching, Boltzmannstr. 2, D-85748, Garching, Germany
E-mail: kazakov_evgenii@mail.ru
The problem of the conversion, reflection and transmission of the fast Alfvén wave propagating in multi-
component nonuniform plasmas is studied. The dependences of the wave scattering characteristics on the plasma
composition and parallel wave number have been obtained. The results can be used to control the part of the
launched power converted to the slow short wavelength mode and to prevent the essential reflection of the wave
power back to the antenna.
PACS: 52.35.Bj
1. INTRODUCTION
The problems of the wave-particle interaction be-
come especially interesting when the electromagnetic
wave propagates in multi-component nonuniform plas-
mas. The plasma inhomogeneity leads to the appearance
of the ion-ion hybrid resonance and the evanescence
layer during the wave propagation when the plasma
consists of the ion species with different charge-to-mass
ratios [1-3]. When the plasma contains more than two
ion species the number of the ion-ion hybrid resonances
in plasmas can become greater. The launched electro-
magnetic wave will be transmitted through, reflected
from and converted near the evanescence layer in the
vicinity of each of the resonances. The interference pic-
ture of the fast waves reflected back to the antenna will
give the distribution of the wave field along the plasma
column. The information about the wave field distribu-
tion is important to study the wave-particle interaction
for both ion and electron subsystems. At the same time,
part of the fast wave power will be converted to the
slow short wavelength mode, which is effectively
damped on electrons. In such a way the power launched
by the antenna to the plasma will be distributed over
different wave modes. The fast wave is mainly absorbed
by ions through the cyclotron damping mechanisms
under the appropriate resonance conditions. The slow
wave will be absorbed locally by electrons if the plasma
temperature is of the order of the present day fusion
experimental data. If the wave-particle interaction is not
enough effective the essential part of the launched
power can be transmitted through and reflected from the
plasma column. When the reflection coefficient is large
the experimental conditions could be dangerous for the
antenna operation due to the large power flux back to
the antenna (the problem of power coupling). In such a
way, the antenna operation with the multi-component
nonuniform plasmas needs predicting the power distri-
bution between the different modes in plasmas as a
function of the experimental conditions. It will allow to
choose the safety antenna operation regime and the
dominant channel of the wave-particle interaction to
provide heating or pinch velocity for the selected
plasma component.
The simplest model of the fast wave propagation
through the nonuniform plasma column was proposed
by Budden [4]. The real dispersion curve was approxi-
mated by the simplified dependence, which did not take
into consideration the plasma density inhomogeneity.
The transmission, reflection and conversion coefficients
were obtained for two cases of the wave incidence. It
was shown that the conversion coefficient can not ex-
ceed the value 25% when the fast wave is launched
from the Low Magnetic Field Side (LMFS). Below only
this case will be discussed as more realistic for the pre-
sent day fusion experiments.
The more sophisticated model [5-7], which usually
is called as “the triplet configuration”, takes into con-
sideration the plasma density inhomogeneity at the edge
of the plasma column. The Budden dispersion curve
was corrected to take into account the wave reflection
from R-cutoff layer at the High Magnetic Field Side
(HMFS). Due to the reflection the second backward
propagating wave appears in the plasma column. As a
result the interference of two fast waves issues the wave
field distribution in the plasma column between the
evanescence layer and the antenna. But the interference
picture depends on the phase difference between the two
reflected waves. In the two limiting cases the launched
power can be either completely converted to the short
wavelength mode or completely reflected to the an-
tenna. The model considers R-cutoff at the HMFS as the
non-transparent barrier and, therefore, does not allow
the fast wave to be transmitted through the plasma col-
umn. In the framework of the model the phase differ-
ence can be controlled by choosing the parallel wave
number, the wave frequency or the plasma composition.
But the position of the barrier provided by R-cutoff can
be determined only approximately (it is always difficult
to measure and control the plasma density at the edge).
It leads to the uncertainty in the phase difference calcu-
lating. Since the barrier position can not be controlled
externally the model restricts the possibility to predict
the reflection and conversion fractions for the given
experimental conditions.
In this paper, the method is proposed to control the
wave field distribution in plasma by creating the addi-
tional semi-transparent barriers for the fast wave. New
barriers can be created by puffing the additional ion
species into the plasma. The launched fast wave will be
partially transmitted through and reflected from each of
the barriers. The interference picture will issue the wave
field distribution in some regions of the plasma column.
As a result, the general conversion, reflection and
transmission coefficients can be obtained. The proposed
model is preferable for wave field distribution control in
comparison with the triplet configuration model where
the second barrier is non-transparent and its position
depends on the plasma edge density profile. On the con-
trary, the properties of the second barrier in the pro-
posed model depend on the concentration of the second
ion species. Both the barrier transparency and the inter-
ference picture can be controlled by choosing the paral-
lel wave number and the wave frequency. In such a way
the most preferable wave field distribution (to create the
desired radial profiles of the ion pinch velocity and the
electron/ion heating) can be provided by changing the
concentration of the second ion species and choosing
the launched wave parameters.
2. MODE CONVERSION IN PLASMAS WITH
TWO ION-ION HYBRID RESONANCES
The three ion component plasma will be studied here
to show the effect of the semi-transparent barriers pro-
vided by the ion-ion hybrid resonances on the fast wave
propagation. The problem can be generalized for the
greater number of ion species in plasma but the more
complicated interference picture will not change a na-
ture of the physics processes. The propagation of the
fast Alfvén wave (FAW) through the fusion plasma col-
umn is usually considered within a slab approximation.
In this model the confining magnetic field is assumed to
be directed along the z-axis, the wave vector has the
components (k⊥, 0, k||) with k||-spectrum fixed by the Ion
Cyclotron Resonance Frequency (ICRF) antenna phas-
ing. The radial inhomogeneity of the plasma density and
the nonuniformity of the magnetic field lead to the par-
tial conversion of the launched FAW to the slow wave
near the ion-ion hybrid resonances. The slow wave is
effectively absorbed by electrons. In general, the propa-
gation of the FAW through the resonances and cutoffs
in nonuniform plasmas in the ion cyclotron frequency
range is described by the wave equation
0E)x(Q
xd
Ed
y2
y
2
=+ (1)
for the electric field component Ey. The potential Q(x) is
proportional to the square of perpendicular refraction
index, 2
2
2
n
c
)x(Q ⊥
ω
= , given by the cold plasma disper-
sion relation
2
||
2
||
2
||2
nS
)nL)(nR(
n
−
−−
=⊥ , (2)
where S, L=S–D and R=S+D are the components of the
plasma dielectric tensor in the Stix notation [8]:
∑ ω−ω
ω
−=
s
2
cs
2
2
ps1S , (3a)
∑ ω−ω
ω
ω
ω
=
s
2
cs
2
2
pscsD . (3b)
The equation (2) gives the ion-ion hybrid resonances
and L-cutoffs which form the eva-
nescence layers. The relation defines R-
cutoffs located at low plasma densities near the plasma
edge. The equation (1) is derived neglecting the electron
inertia and assuming the longitudinal component of the
electric field E
)nS( 2
||= )nL( 2
||=
)nR( 2
||=
z is small. The cold-plasma approxima-
tion can be used to describe the mode conversion if the
layers of the fundamental cyclotron resonances and ion-
ion hybrid resonance are well separated. When the
mode conversion is the dominated process the cyclotron
damping and direct minority heating are small, but the
enhanced electron damping is observed.
Historically, the first equation used to study the
propagation of the FAW through the single cutoff-
resonance pair was the Budden equation [4]. The wave
scattering characteristics depend on the tunneling pa-
rameter Δ=η Ak , the product of the wave vector far
from the resonance and the width of the evanescence
layer. The transmission coefficient does not depend on
the incidence side and is given by . It was
shown that in case of the LMFS incidence, when the
fast wave first approaches the L-cutoff, the maximal
mode conversion is 25% provided that η=0.22.
ηπ−= eT
Fig.1. The real part of as a function of normalized
distance x/a from the center of the plasma column.
The plasma consists of H, D, and
2
⊥n
3He ions
with the fractions 0.82, 0.14 and 0.02, respectively
In this paper, the wave propagation through the
plasma column with two cutoff-resonance pairs is stud-
ied. This scenario can be realized in plasma which con-
sists of three ion species with different charge-to-mass
ratios. As an example, the hydrogen plasma with the
fractions of deuterium and helium minorities, denoted as
(D,3He)H, is considered. Fig.1 shows the dispersion
relation for FAW and the spatial variance of magnetic
field and electron plasma density through the plasma
column. The ion-ion hybrid resonances associated with
3He and D minority are denoted as S1 and S2, respec-
tively. The L-cutoffs are denoted as L1 and L2. The fun-
damental cyclotron resonances of 3He and D species are
located at x/a = 0.2 and x/a −= 0.67, respectively. The
central electron density is assumed to be
. The confinement magnetic field at
the axis and the antenna operation frequency were cho-
sen to be B
313
0e cm105.2n −⋅=
0=3.6 T and f=34.7 MHz, respectively.
To study the propagation of the FAW in such plas-
100
mas the potential Q(x) is modeled by the expression:
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
Δ
−
−
Δ
−=
2S
2
1S
12
A xxxx
1k)x(Q . (4)
The parameters of the potential Q(x) are found numeri-
cally to fit them with the dispersion relation (Fig.1).
When the resonances are well separated the position of
L-cutoffs are determined by the expressions:
2n⊥
2S1S
21
11S1L xx
xx
−
ΔΔ
+Δ+≈ , (5a)
2S1S
21
22S2L xx
xx
−
ΔΔ
−Δ+≈ . (5b)
In this case two back-to-back cutoff-resonance pairs are
characterized by the tunneling parameters η1,2 = kA Δ1,2.
In general, the tunneling parameters must be evaluated
numerically:
. (6) dx))x(Q(
2L,1L
2S,1S
2/1
1,2 ∫ −=η
The wave equation with the potential Q(x) in the
form (4) was studied analytically using the phase-
integral method [5,9]. It is the generalization of the
WKB method to find the approximate solutions of wave
equation for the given potential Q(x) in the complex
plane. This method is based on the Stokes phenomena:
the coefficient of the subdominant WKB term must be
discontinuously changed upon crossing the so-called
Stokes lines. The WKB solutions from each side of the
resonances are matched not by passing along the real
axis but tracing the evolution of the WKB solutions
along the contour in the complex plane crossing the
Stokes lines. Using this method, the mode conversion
coefficient C was derived
).2/(sin)T1)(T1(T4)TT1(TTC 2
2112121 ϕΔ−−+−= (7)
In this formula are Budden transmission
coefficients of each evanescence layer. The total trans-
mission coefficient is T=T
2,1eT 2,1
ηπ−=
1T2.
In the vicinity of L1-cutoff the FAW is partially re-
flected and partially transmitted through the first layer.
The transmitted wave is partially reflected from L2-
cutoff. This reflected wave tunnels through the first
layer. Finally, there is the interference of two waves
with the different amplitudes and phases, which deter-
mines the reflection R and the mode conversion C coef-
ficients. The phase difference Δϕ is the sum of three
terms:
122 Ψ−Ψ+Φ=ϕΔ , (8)
,dx)x(Q
1S
2L
x
x
2/1∫=Φ
.2/ik,
)k1()k(
))1k(lnk2exp(i2
Arg 2,12,1
2,12,1
2,12,1
2,1 η−=⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+ΓΓ
−π
=Ψ
The phases Ψ1,2 appear due to the additional phase shift-
ing under the reflection from L-cutoffs. It can be shown
for small values of tunneling parameters η1,2, that
))(ln116.1( 2,12,12,1 η−η≈Ψ . (9)
For large values η1,2 these phases tend to π/2 as for the
case of the isolated cutoff. The phase 2Φ appears due to
the double pass of the second reflected wave from
S1 resonance to L2 cutoff.
As a function of a phase, the mode conversion will
be maximal possible
)T1)(T1(T4)TT1(TTC 2112121opt −−+−= , (10)
if the phase difference Δϕ is equal to the odd values of π
.Zn),1n2( ∈+π=ϕΔ (11)
The contours of the constant Copt as a function of the
tunneling parameters η1 and η2 are plotted in Fig.2. It is
clear that the mode conversion can be effective in plas-
mas with 22.01 ≈η and 0.1~2η . In such plasmas the
second evanescence layer acts similar to R-cutoff in the
theory of triplet configuration [5-7]. If 12 >>η our ex-
pression reduces to that obtained in [5]:
)2/(sin)T1(T4C 2
11trip ϕΔ−= . (12)
Fig.2. The contours of the maximal possible mode
conversion coefficient Copt as a function of the tunneling
parameters η1 and η2
The physics of the enhancement of the mode con-
version is the same: due to the interference of the re-
flected waves the total reflection coefficient R can be
minimized. Compared to the triplet configuration case,
the proposed scenario has the certain advantage: the
location of the cutoff is primarily determined by the
plasma composition rather than the edge plasma density
profile.
3. NUMERICAL RESULTS AND
DISCUSSIONS
101
The dependence of the maximal possible mode con-
version coefficient on both tunneling parameters is
shown in Fig.2. Theoretically the fast wave can be con-
verted completely to the slow short wavelength mode if
the second barrier is non-transparent and the phase dif-
ference (8) is equal to odd values of π. In Fig.2 it corre-
sponds to the vertical dashed line at η1=0.22 (the opti-
mal mode conversion condition for two-component
plasmas according to the Budden model) when η2 goes
to an infinity. The solid lines show the levels of the
maximal possible mode conversion coefficient when the
second barrier is semi-transparent. The value of the
mode conversion coefficient lays somewhere in the
range from )TT1(TT 2121 − to Copt (the precise value is
defined by the phase difference). The dot lines are the
constant levels of the transmission coefficient T. Since
the power conservation law can be written in the form
T+R+C=1 the fraction of the wave power reflected back
to the antenna can also be obtained from the figure. As a
result, the range of the experimental conditions can be
obtained when the reflection coefficient R is enough
high to damage the antenna. Also the operational paths
for the waves with the parallel wave vectors in the range
from 0 to 5 m-1 are shown in Fig.2 for three concentra-
tions of 3He species. It can be seen that for 2% concen-
tration of 3He the mode conversion coefficient for all
waves from the range can reach but does not exceed the
value of 85%. But the real value of the mode conversion
coefficient for each wave with the particular k|| will be
defined by the phase difference between the reflected
waves. This difference depends on the experimental
conditions and will be discussed below.
Fig.3. The phase difference Δϕ as the function of the
parallel wave number k|| for different 3He fractions
When the maximal possible value of the mode con-
version coefficient is known, the dependence of the
phase difference on the experimental conditions should
be discussed. Fig.3 shows the dependence of the phase
difference between two reflected waves (8) on the paral-
lel wave vector for different values of 3He concentra-
tion. The phase difference (the vertical axis) is normal-
ized on π. When the phase difference is equal to odd
values of π the mode conversion coefficient is equal to
the maximal possible value Copt (presented in Fig.2).
When the phase difference is equal to even values of π
the mode conversion coefficient is minimal possible
and goes to zero for the considered con-
ditions. In other words, the phase difference defines a
multiplier (Fig.4) for C
)TT1(TT 2121 −
opt that must be used to find the
mode conversion coefficient C.
Fig.4 shows this multiplier for three values of 3He
concentrations as a function of the parallel wave vector.
The shaded areas correspond to different concentrations
(1%, 2%, 3%, from the left to the right) and cover the k||
range from 0 to 5 m-1. As it can be seen from Fig.4, the
multiplier approaches to 1 for the case of 2% concentra-
tion and it is enough small for concentration of 1% for
the selected experimental conditions. The value of the
multiplier for 3% concentration changes from 0.1 for
k||=0 m-1 to 0.9 for k||=5 m-1.
Figs.2-4 demonstrate three typical but different cases
of the launched power distribution between the modes
in the plasma column.
The first case is optimal for the wave conversion
(2% of 3He concentration). The maximal possible value
of the conversion coefficient Copt slightly depends on
the parallel wave vector and is equal to Copt ≈ 85%.
Fig.4. The multiplier for the maximal possible mode
conversion coefficient Copt for different 3He fractions
The phase multiplier (Fig.4) is enough large (in the
range from 0.6 to 1.0). As a result, the conversion coef-
ficient is in the range from 50% to 85%. The main part
of the launched power is converted to the slow mode.
This case can be used to provide the local electron heat-
ing through the effective damping of the converted
mode on the electrons.
The second case is optimal for the wave reflection
(1% of 3He concentration). The maximal possible value
of the conversion coefficient changes from 95% for
k||=0 m-1 to 90% for k||=5 m-1. But due to the antiphase
the phase multiplier is very small and lays in the range
0.0…0.3. Therefore the conversion coefficient is very
small. It is in the range from 0% to 25%. The main part
of the launched power is reflected back to the antenna.
This case would be used to realize the fast wave interac-
tion with plasma ions if there is the cyclotron damping
mechanisms somewhere between the first evanescence
layer and the antenna.
The third case is the intermediate between the first
and the second cases (3% of 3He concentration). The
maximal possible value of the conversion coefficient is
changed in the range 65…70% but the phase multiplier
covers the wide range of values 0.1…0.85 giving the
conversion coefficient somewhere between 5% and
60%. In this case there is a big difference in the proc-
esses of the reflection and conversion for the waves
with different parallel wave vectors. Therefore it is im-
portant to know how the generator power is distributed
over the k||-spectra of the ICRF antenna. The relation
between the converted and reflected fractions can be
changed in the wide range.
The presented numerical data has been obtained for
the enough wide second barrier. For all the discussed
cases the transmission coefficient T does not exceed
10%. It allows to speak only about the conversion and
reflection channels of the launched power distribution.
But the cases with the essential power transmission can
also be studied in a similar way. The transmission will
become important if the D concentration will be de-
creased or the parallel wave number will be increased.
The case of the substantial wave transmission could be
interesting to provide the partial wave absorption near
the cyclotron resonance layer behind the second ion-ion
hybrid resonance.
102
103
CONCLUSIONS
Puffing the additional ion species into the plasma
can be used to create the additional ion-ion hybrid reso-
nance layers. These layers play an important role for the
fast wave propagation through the plasma column. It
can be used to control the processes of fast wave trans-
mission through, reflection from and conversion in the
plasma. These processes define the distribution of the
launched power between the transmitted, reflected and
converted modes. In turn, the modes will define the
structure of the electromagnetic field in plasma. Finally,
the local field polarization defines the efficiency of the
wave-particle interaction. The properties of the semi-
transparent wave barriers depend on the plasma compo-
sition and therefore they can be controlled by maintain-
ing the needed concentration of the additional ions.
From the other point of view, the barrier transparencies
depend on the parallel wave vector value and the wave
frequency. Choosing the antenna phasing and the oper-
ating frequency is a key to obtain the preferable distri-
bution of the launched power between the modes and, as
a result, the structure of the electromagnetic field
through the plasma column.
The problem has an essential dependence on the ex-
perimental conditions: plasma density profile, nonuni-
formity of the magnetic field, plasma ion composition.
Due to the obtained results the dominant channel of the
launched power going (transmission, reflection or con-
version) can be identified for the given experimental
conditions and for the particular antenna phasing and
operating frequency. The scenarios with large reflection
have to be avoided because of the essential backward
power flux to the antenna. The scenarios with large
conversion can be used for the effective local electron
heating through the slow wave damping on electrons.
The scenarios with large transmission can be useful, for
example, to realize (simultaneously with the partial
mode conversion) the minority heating mechanism for
the ions behind the second ion-ion hybrid resonance
layer at the HMFS. The intermediate scenarios can be
used to get a preferable partition of the launched power
between the wave modes.
The processes of the wave-particle interaction are
not considered here. Therefore the used approximations
will be realistic if there are not the effective mecha-
nisms of the fast wave interaction with the plasma parti-
cles. Usually it is realized when there is not the effective
ion cyclotron damping. When the damping mechanisms
become essential and they can not be neglected the fast
wave amplitude will be changed essentially along the
propagation path. As a result, the interference picture
will be the other but it can be calculated in a similar way
taking into consideration the damping mechanisms.
Here the possibility to control the launched power dis-
tribution between the wave modes has been demon-
strated. It can be used to optimize the wave-particle in-
teraction according to the goals of the experiments.
Acknowledgements. The work is partially supported by
the Science and Technology Center in Ukraine, project
№3685.
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Статья поступила в редакцию 15.05.2008 г.
РАСПРОСТРАНЕНИЕ БЫСТРОЙ МАГНИТОЗВУКОВОЙ ВОЛНЫ В МНОГОКОМПОНЕНТНОЙ
НЕОДНОРОДНОЙ ПЛАЗМЕ
Е.О. Казаков, И.В. Павленко, И.А. Гирка, Б. Вейссов
Изучается задача конверсии, отражения и прохождения быстрой магнитозвуковой волны,
распространяющейся в многокомпонентной неоднородной плазме. Получены зависимости характеристик
прохождения волны от состава плазмы и от параллельного волнового вектора. Полученные результаты
могут быть использованы для управления частью энергии волны, которая конвертируется в
коротковолновую моду, и для предотвращения существенного отражения энергии волны назад к антенне.
ПОШИРЕННЯ ШВИДКОЇ МАГНІТОЗВУКОВОЇ ХВИЛІ У БАГАТОКОМПОНЕНТНІЙ
НЕОДНОРІДНІЙ ПЛАЗМІ
Є.О. Казаков, І.В. Павленко, І.О. Гірка, Б. Вейссов
Вивчається задача конверсії, відбиття та проходження швидкої магнітозвукової хвилі, яка поширюється
у багатокомпонентній неоднорідній плазмі. Отримано залежності характеристик проходження хвилі від
складу плазми та від паралельного хвильового вектора. Отримані результати можуть бути використані для
керування частиною енергії хвилі, яка конвертується у короткохвильову моду, та для запобігання суттєвого
відбиття енергії хвилі назад до антени.
|
| id | nasplib_isofts_kiev_ua-123456789-110357 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-02T10:50:16Z |
| publishDate | 2008 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Kazakov, Ye.O. Pavlenko, I.V. Girka, I.O. Weyssow, B. 2017-01-03T16:55:52Z 2017-01-03T16:55:52Z 2008 Fast Alfvén wave propagation in milticomponent nonuniform plasmas / Ye.O. Kazakov, I.V. Pavlenko, I.O. Girka, B. Weyssow // Вопросы атомной науки и техники. — 2008. — № 4. — С. 99-103. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 52.35.Bj https://nasplib.isofts.kiev.ua/handle/123456789/110357 The problem of the conversion, reflection and transmission of the fast Alfvén wave propagating in multicomponent nonuniform plasmas is studied. The dependences of the wave scattering characteristics on the plasma composition and parallel wave number have been obtained. The results can be used to control the part of the launched power converted to the slow short wavelength mode and to prevent the essential reflection of the wave power back to the antenna. Вивчається задача конверсії, відбиття та проходження швидкої магнітозвукової хвилі, яка поширюється у багатокомпонентній неоднорідній плазмі. Отримано залежності характеристик проходження хвилі від складу плазми та від паралельного хвильового вектора. Отримані результати можуть бути використані для керування частиною енергії хвилі, яка конвертується у короткохвильову моду, та для запобігання суттєвого відбиття енергії хвилі назад до антени. Изучается задача конверсии, отражения и прохождения быстрой магнитозвуковой волны, распространяющейся в многокомпонентной неоднородной плазме. Получены зависимости характеристик прохождения волны от состава плазмы и от параллельного волнового вектора. Полученные результаты могут быть использованы для управления частью энергии волны, которая конвертируется в коротковолновую моду, и для предотвращения существенного отражения энергии волны назад к антенне. The work is partially supported by the Science and Technology Center in Ukraine, project №3685. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Термоядерный синтез (коллективные процессы) Fast Alfvén wave propagation in milticomponent nonuniform plasmas Поширення швидкої магнітозвукової хвилі у багатокомпонентній неоднорідній плазмі Распространение быстрой магнитозвуковой волны в многокомпонентной неоднородной плазме Article published earlier |
| spellingShingle | Fast Alfvén wave propagation in milticomponent nonuniform plasmas Kazakov, Ye.O. Pavlenko, I.V. Girka, I.O. Weyssow, B. Термоядерный синтез (коллективные процессы) |
| title | Fast Alfvén wave propagation in milticomponent nonuniform plasmas |
| title_alt | Поширення швидкої магнітозвукової хвилі у багатокомпонентній неоднорідній плазмі Распространение быстрой магнитозвуковой волны в многокомпонентной неоднородной плазме |
| title_full | Fast Alfvén wave propagation in milticomponent nonuniform plasmas |
| title_fullStr | Fast Alfvén wave propagation in milticomponent nonuniform plasmas |
| title_full_unstemmed | Fast Alfvén wave propagation in milticomponent nonuniform plasmas |
| title_short | Fast Alfvén wave propagation in milticomponent nonuniform plasmas |
| title_sort | fast alfvén wave propagation in milticomponent nonuniform plasmas |
| topic | Термоядерный синтез (коллективные процессы) |
| topic_facet | Термоядерный синтез (коллективные процессы) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110357 |
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