Ion kinetics and ion sound generation under the development of modulation instability of an intense Langmuir wave in a plasma
The development of one-dimensional parametric instabilities of intense long-wave plasma waves is considered in terms of the so-called hybrid models, when electrons are treated as a fluid and ions are regarded as particles. The analysis is performed for both cases when the average plasma field energy...
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| Zitieren: | Ion kinetics and ion sound generation under the development of modulation instability of an intense Langmuir wave in a plasma / A.V. Kirichok, V.M. Kuklin, A.V. Pryimak, A.G. Zagorodny // Вопросы атомной науки и техники. — 2015. — № 4. — С. 258-263. — Бібліогр.: 25 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860264153409650688 |
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| author | Kirichok, A.V. Kuklin, V.M. Pryimak, A.V. Zagorodny, A.G. |
| author_facet | Kirichok, A.V. Kuklin, V.M. Pryimak, A.V. Zagorodny, A.G. |
| citation_txt | Ion kinetics and ion sound generation under the development of modulation instability of an intense Langmuir wave in a plasma / A.V. Kirichok, V.M. Kuklin, A.V. Pryimak, A.G. Zagorodny // Вопросы атомной науки и техники. — 2015. — № 4. — С. 258-263. — Бібліогр.: 25 назв. — англ. |
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| container_title | Вопросы атомной науки и техники |
| description | The development of one-dimensional parametric instabilities of intense long-wave plasma waves is considered in terms of the so-called hybrid models, when electrons are treated as a fluid and ions are regarded as particles. The analysis is performed for both cases when the average plasma field energy is lower (Zakharov's hybrid model − ZHM) or greater (Silin's hybrid model − SHM) than the plasma thermal energy. Reduced absorption of the high-frequency (HF) field leads to the retardation of the HF field burnout within plasma density cavities and to the broadening of the HF spectrum. At the same time, the ion velocity distribution tends to the normal distribution in both ZHM and SHM.
Аналізується розвиток 1D-параметричних нестійкостей інтенсивних довгохвильових ленгмюрівських хвиль у термінах так званих гібридних моделей, коли електрони описуються як рідина, а іони описуються частинками. Розглядаються випадки, коли середня енергія поля менше (гібридна модель Захарова) і більше (гібридна модель Силіна) теплової енергії плазми. Зменшення поглинання високочастотного поля відповідає уповільненню вигорання ВЧ-поля в утворених кавернах щільності плазми і уширенню спектра ВЧ-мод. При цьому функція розподілу іонів за швидкостями в моделях Захарова та Силіна за формою наближається до нормального розподілу.
Анализируется развитие 1D-параметрических неустойчивостей интенсивных длинноволновых ленгмюровских волн в рамках так называемых гибридных моделей, когда электроны описываются как жидкость, а ионы описываются частицами. Рассматриваются случаи, когда средняя плотность энергии поля меньше (гибридная модель Захарова) и больше (гибридная модель Силина) плотности тепловой энергии плазмы. Уменьшение уровня поглощения высокочастотного поля соответствует замедлению выгорания ВЧ-поля в образовавшихся кавернах плотности плазмы и уширению спектра ВЧ-мод. При этом функция распределения ионов по скоростям в моделях Захарова и Силина по форме приближается к нормальному распределению.
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| first_indexed | 2025-12-07T18:58:34Z |
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ISSN 1562-6016. ВАНТ. 2015. №4(98) 258
ION KINETICS AND ION SOUND GENERATION UNDER
THE DEVELOPMENT OF MODULATION INSTABILITY
OF AN INTENSE LANGMUIR WAVE IN A PLASMA
A.V. Kirichok1, V.M. Kuklin1, A.V. Pryimak1, A.G. Zagorodny2
1V.N. Karazin Kharkiv National University, Institute for High Technologies, Kharkov, Ukraine;
2Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine
The development of one-dimensional parametric instabilities of intense long-wave plasma waves is considered in
terms of the so-called hybrid models, when electrons are treated as a fluid and ions are regarded as particles. The
analysis is performed for both cases when the average plasma field energy is lower (Zakharov's hybrid model −
ZHM) or greater (Silin's hybrid model − SHM) than the plasma thermal energy. Reduced absorption of the high-
frequency (HF) field leads to the retardation of the HF field burnout within plasma density cavities and to the broad-
ening of the HF spectrum. At the same time, the ion velocity distribution tends to the normal distribution in both
ZHM and SHM.
PACS: 52.35.-g, 52.65.-y
INTRODUCTION
Considerable experimental and computational effort
has been directed toward parametrically excited Lang-
muir turbulence over recent decades in several different
arenas, including ionospheric modification, space phys-
ics, and inertial confinement fusion. The interest to the
parametric instability of intense Langmuir waves, which
can be easily excited in the plasma by various sources [1
- 9] was stipulated, in particular, by new possibilities in
heating electrons and ions in a plasma.
The theoretical concepts proposed by V.P. Silin [10]
were confirmed by the early numerical experiments on
the one-dimensional simulation of the parametric decay
of plasma oscillations[11]. However, the greatest exper-
imenters' interest was provoked by the mechanism of
wave-energy dissipation discovered by V.E. Zakharov.
The modulation instability of intense Langmuir waves
in non-isothermal plasmas also leads to collective ion
perturbations, in particular, to the generation of ion-
sound waves [12 - 16].
In Zakharov's model [13] that describes the instabil-
ity of intense long-wave Langmuir waves in a non-
isothermal plasma, just the modulation instability results
in the excitation of a range of short-wave oscillations. In
Silin's model, a strong Langmuir wave in a cold plasma
leads to intense oscillations of the electron velocity with
the amplitudes comparable to the wavelengths of the
excited modes.
In the works [17, 18] an attempt was made to com-
pare these models, which have similar physical nature, by
the example of one-dimensional description. Of particular
interest is the process of ion heating, so in this paper we
use the particle description for ions because the account
of inertial effects can be significant just at the nonlinear
stage of the process [19]. It was observed in [19, 20] that
simulation in terms of the so-called hybrid model (incor-
porating one of Zakharov's equations for the HF waves
and using particle simulation for ions) demonstrates that
fluctuations of ion density are rather significant and
favor the development of parametric instability. The
non-resonant interaction between ions and HF plasma
oscillations, along with ion trapping by the potential
wells produced by these oscillations, lead to an instabil-
ity of density cavities resulting from the modulation
instability and produce fast particle groups.
In papers [17, 18] the simulation of one-dimensional
ion dynamics was performed in terms of the particle
method [23, 24]. The number of particles used in nu-
merical calculations was 42 10⋅ , which is equivalent to
the number of ions, about 4 3 13(2 10 ) 10⋅ , in the three-
dimensional case, in agreement with the conditions of
most experiments. Thus, the interaction between model-
ing particles and plasma oscillations in this simulation is
in rather good accordance with the interaction between
real particles and plasma waves, naturally with regard to
the inherent limitations of the one-dimensional descrip-
tion. Nevertheless, there is reason to believe that the
description of field energy transfer to ions within the
framework of the hybrid model represents the real con-
ditions of ion heating by intense Langmuir oscillations
in plasmas. Moreover, the one-dimensional description
makes it possible to select arbitrary electron-to-ion mass
ratios.
Below, we discuss the efficiency of energy transfer
from Langmuir oscillations to ions and ion density per-
turbations under the development of the modulation
instability in both cases of non-isothermic hot and cold
one-dimensional plasmas within the framework of hy-
brid models and for different values of the electron-to-
ion mass ratio. The attention is mainly concentrated on
the effect of HF field burnout within density cavities
accompanied by energy transfer to the ion component of
the plasma.
1. STATEMENT OF THE PROBLEM
AND THE INITIAL CONDITIONS
The purpose of this paper is to clarify the efficiency
of the energy transfer to ions and ion density perturba-
tions in the course of development of modulation insta-
bility for the cases of both non-isothermal hot and cold
plasmas in terms of the hybrid models. The equations,
governing the nonlinear dynamics of the parametric
instability of an intense plasma wave, were derived in
the work [21]. Both SHM and ZHM were considered for
two cases of light and heavy ions. The parameters of the
simulation are presented in Table 1. It is also interesting
to elucidate the effect of HF spectrum damping and sub-
sequent burnout of the Langmuir field within density
cavities on the energy transfer to plasma ions.
ISSN 1562-6016. ВАНТ. 2015. №4(98) 259
ZHM, light ions
SHM, light ions
ZHM, heavy ions
SHM, heavy ions
Fig. 1. Time evolution of relative values of: energy of the main Langmuir wave (1), energy of low-scale plasma
wave spectrum (2), energy transferred to electrons (3) and ions (4)
Below we employ, unless otherwise specified in the
text, the following initial conditions and parameters.
The number of particles simulating the dynamics of ions
is 0 < = 20000s S≤ . The particles are distributed uni-
formly over the interval 1/ 2 < < 1/ 2ξ− , 0= / 2k xξ π ,
initial ion velocities are set as =0 =0/ | = | = 0s sd d vτ τξ τ ,
the number of spectrum modes is < <N n N− ,
= /100N S , / eM m is the ion-to-electron mass ratio,
= /θ δΘ is the damping rate θ normalized to the linear
increment of the parametric instability δ , peω is the
plasma frequency.
The development of the instability was considered in
terms of hybrid models in our previous papers [17, 18].
Here we give some results. The rate of damping of HF
modes governs the rate of the field energy burnout in
density caverns, from where the HF field has forced out
charged particles The main part of the instability energy
is initially concentrated in the HF Langmuir oscillations
in parallel with the formation of the LF spectrum of
density perturbations. Then the energy of the HF spec-
trum is transferred mainly to electrons. Thus, the shaped
density cavities collapse, the trajectories of ions inter-
cross, ion density perturbations become smoother and
their characteristic scale growths with time. The rela-
tionship between ionic perturbations and the HF field is
weakened and the instability is saturated. The amplitude
of the main wave stabilizes after several oscillations at
rather low level. The bulk energy is now contained in
the perturbations of the electron component of the plas-
ma. Some small portion of the initial energy transforms
into the kinetic energy of ions. The estimate of the ener-
gy density transmitted to ions kinE can be obtained from
the expression
2
2
0
0.27 ,kin
pe
E MI
W m
δ
ω
≈ ⋅ ⋅ ⋅
(1)
where 0W is the initial energy density of the intense
Langmuir wave, 2= ( / )ss
I d dξ τ∑ is normalized ion
kinetic energy and δ is the rate of the linear instability.
The portion of energy transferred from the intense
Langmuir wave to ions is determined by the ratio
0 0/ eW n T for the case of non-isothermic plasma (ZHM)
and by the ratio 1/3( / )m M for the case of cold plasma
(SHM).
Table 1
Simulation parameters for the hybrid models
The model
Light ions Heavy ions
3/ = 2 10eM m ⋅ 6/ = 8 10em M −⋅
SHM
2 2( / )( / ) = 0.43e pm M ω δ 2 2( / )( / ) = 0.1e pm M ω δ
1/3
0/ = 0.44 ( / ) = 0.034em Mδ ω ⋅ 1/3
0/ = 0.44 ( / ) = 0.0088em Mδ ω ⋅
0 / / = 29.4peω δ ω δ≈ 0 / / = 113.6peω δ ω δ≈
ZHM
2 2
0( / )( / ) = 2 / = 20e p em M n T Wω δ 2 2
0( / )( / ) = 2 / = 20e p em M n T Wω δ
( )1/2 1/2
0 0/ = 2 / ( / ) = 282.6e en T W M mω δ 1/2 1/2
0 0/ = 2( / ) ( / ) = 2234.4e en T W M mω δ
3
0/ = / = 3.5 10peδ ω δ ω −⋅ 4
0/ = / = 4.5 10peδ ω δ ω −⋅
ISSN 1562-6016. ВАНТ. 2015. №4(98) 260
ZHM, light ions
SHM, light ions
ZHM, heavy ions
SHM, heavy ions
Fig. 2. Dependence of the amplitude of the LF modes nM (1) and the frequency /nd dτΦ (2)
on the wave-number at the stage of developed instability
Below we consider more closely the nature of the
energy redistribution with time and especially the pro-
cess of energy transfer to the LF perturbations. We also
discuss the specific features of the excitation of LF ion-
sound waves in both non-isothermic and cold plasmas.
More attention will be focused on the role of absorption
of HF spectrum that is responsible for the burnout of the
HF field in the density cavities. We investigate the ef-
fect of this process on the excitation of the LF spectrum
and most importantly on the kind of ion velocity distri-
bution function and on the proportion of the total energy
transferred to ions.
2. THE RESULTS OF NUMERICAL
SIMULATION
Fig. 1 shows the energy redistribution between the
main Langmuir wave, the small-scale plasma wave
spectrum and plasma electrons and ions.
The analysis of the numerical simulation results
shows that the energy of intense long-wave Langmuir
waves is first transferred to short-wave Langmuir oscilla-
tions. Just at this stage the cavities of plasma density,
filled with HF plasma oscillations, are formed. After that,
the HF field burns out due to the damping on electrons
that is included in the hybrid models phenomenological-
ly. The energy of the HF field therewith converts into
the energy of plasma electrons. Under these conditions,
the cavities collapse and thus excite LF waves, the ion
trajectories intercross, and the energy of both collapsed
caverns and LF spectrum is transferred to ions.
The root-mean-square velocity of ions,
2( ) = /ss
v v Sσ ∑ , at the final stage of the numerical
simulation is equal to ( ) = 0.015vσ for the case of light
ions and ( ) = 0.006vσ for heavy ions in ZHM and, re-
spectively, to ( ) = 0.002vσ for light ions and
( ) = 0.0005vσ for heavy ions in SHM. The total kinetic
energy of ions in assumed units 2= ( / )ss
I d dξ τ∑ is
equal to 4.689 for the case of light ions and 0.808 for
heavy ions in ZHM and ( ) = 0.086vσ for light ions and
0.005 for heavy ions in SHM. The variations in the
values of the total energy are caused by different linear
growth rates in the two models under consideration, and
by different ion masses in the simulation of light and
heavy ions. The final ion velocity distribution can be
fitted by the normal curve with the use of the values of
rms velocity. The particles outside the normal distribu-
tion (mainly in the so-called "tails") possess 13.8% of
the total energy for light ions and 9.2% for heavy ions in
ZHM model and much more in SHM: 25.6% for heavy
ions and 13% for light ions, respectively. It means that
in the case of instability of the intense wave in a cold
plasma, a significantly greater proportion of fast parti-
cles should be expected.
We are interested not only in the ion kinetic energy
distribution, but also in the collective excitation of ion
oscillation (Fig. 2), hence we define the frequency of
the mode with the wave vector 0nk associated with
these oscillations, i.e.
2 2 2 2
= ,n nr ni
nr ni nr ni
d M Md
dd M M M Mττ
Φ −
+ +
(2)
where the phases of LF modes can be found from the
expression
2 2= = exp ( ).n nr ni nr ni nM M iM M M i+ + ⋅ Φ
It should be noticed that the intensity of the LF spec-
trum in the case of a non-isothermal plasma (ZHM) is
quite high in a wide range of wave numbers, that corre-
sponds to the spectrum of ion sound after the destruc-
tion of density cavities detected in numerical experi-
ments [15]. In a cold plasma (SHM), in contrast, the
long-wave oscillations dominate in the spectrum.
ISSN 1562-6016. ВАНТ. 2015. №4(98) 261
ZHM, light ions
SHM, light ions
ZHM, heavy ions
SHM, heavy ions
Fig. 3. Evolution of 1) the ion kinetic energy and 2) LF field energy, multiplied by factor 70, with time
For both models, the ion kinetic energy in the as-
sumed units can be written as
21/2
0
1/2
1 ,
2
s
s
d
d
d
ξ
ξ
τ−
∫
(3)
and the energies of collective excitations for ZHM and
SHM, respectively, reduce to
2
2 2
2 2 2
0 22 2
1 1 | | ,
8
1 1 21 ( ) ( ) | | .
38
n
npeM
n n n
n
m M
M n
m J a J a M
M n
δ
ωπ
π
− +
∑
∑
(4)
Note that in Zakharov's model these oscillations are
referred to as ion-sound waves.
Fig. 3 demonstrates the time evolution of the ion ki-
netic energy and LF field energy. It should be noted that
the energy of the LF field is far smaller than ion ener-
gies in all cases. Reducing the field energy with time is
caused by the energy transfer to ions as well as by the
destruction of plasma density cavities [15].
The rate of the HF field burnout within density cavi-
ties is determined by the value = /θ δΘ . It is of inter-
est how the simulation results depend on this parameter.
Obviously, the decrease of this parameter not only in-
hibits the burnout of the HF field in the cavities, but also
broadens the spectrum of HF modes, i.e. it increases the
contribution of small-scale components that leads to the
deepening of plasma density cavities and to the growth
of the kinetic energy of ions ejected from the cavities.
Note that for both models the ion velocity distribu-
tion function approaches the Maxwellian curve with
decreasing damping rate of HF modes, as may be seen
from Fig. 4.
Table 2 demonstrates the extent of deviation of the
ion velocity distribution function, obtained by numerical
modeling, from the fitted Maxwellian curve for the cas-
es shown in Fig. 2.
Fig. 5 shows that in the case of a non-isothermal
plasma the maximum energy of ion-sound oscillations
remains practically unchanged as the damping rate of
HF field decreases, whereas the formation of the LF
spectrum occurs with higher rate. In a cold plasma, on the
contrary, the intensity of LF oscillations grows with the
decrease of the damping rate of the HF field. After that,
the LF spectrum is suppressed and its energy is trans-
ferred to ions. As might be expected, the energy, trans-
mitted to ions, increases with the decrease of the damping
rate of HF oscillations almost in the same proportion in
both non-isothermal and cold plasmas (Fig. 6).
Table 2
Deviation of the ion velocity distribution function,
obtained by numerical simulation,
from the fitted Maxwellian curve
Damping rate ZHM SHM
= 0.05Θ 19.9% 13%
= 0.015Θ 9.9% 13.4%
= 0.001Θ 6.9% 8.8%
It should be noted in conclusion that the ion-density
perturbations with spatial scale smaller than the Debye
radius = /Di Ti pir v ω do not contribute to the formation of
LF electric fields by virtue of the screening effect. The
Debye radius can be estimated from the expression [25]
1/2
0
0
1/2
/ 2 = =
2
< > .
i
Di Di
L pe e
s
pe e
v k Mr k R
m
Mv
m
δπ
πγ ω
δ
ω
∝
=
(5)
At the stage of developed instability this value is of
the order of 310DiR −≤ and the number of spatial spec-
tral modes of ion density does not exceed 1/ DiR that is
in agreement with the previous analysis.
CONCLUSIONS
In the case of a non-isothermic plasma (ZHM), the
amplitudes of modes of the LF spectrum (ion-sound
waves) are of the same order in a wide range of wave
numbers. In a cold plasma (SHM), the long-wave oscil-
lations dominate in the LF spectrum. The energy of the
LF field is found to be much lower than the total kinetic
energy of ions for all the cases discussed above. Reduc-
ing the energy of the LF field with time happens due to
the energy transfer to ions.
ISSN 1562-6016. ВАНТ. 2015. №4(98) 262
ZHM, = 0.05Θ
SHM, = 0.05Θ
ZHM, = 0.015Θ
SHM, = 0.015Θ
ZHM, = 0.001Θ
SHM, = 0.001Θ
Fig. 4. The ion velocity distribution for the case of light ions
ZHM
SHM
Fig. 5. Time evolution of the LF spectrum energy for the case of light ions,
1 – = 0.05Θ , 2 – = 0.015Θ , 3 – = 0.001Θ
ZHM
SHM
Fig. 6. Time evolution of the ion kinetic energy for the case of light ions:
1 – = 0.05Θ ; 2 – = 0.015Θ ; 3 – = 0.001Θ
The decrease of the damping rate of the HF field
corresponds to the slowing of the HF field burnout in
the cavities and leads to the broadening of the HF spec-
trum that causes the deepening of the cavities and in-
crease of the kinetic energy of ions ejected from them. It
should be noted that as the absorption rate of the HF
field decreases, the ion velocity distribution function
approaches the Maxwellian distribution in both models
under consideration. In a cold plasma, the intensity of
the long-wave LF oscillations is high and it increases
with the decrease of the absorption of HF modes. It is
important to note that the total energy transferred to ions
increases as the absorption of the HF spectrum reduces.
ISSN 1562-6016. ВАНТ. 2015. №4(98) 263
ACKNOWLEDGEMENTS
This paper was partially supported by the grant of
the State Fund for Fundamental Research (project
No. Φ 58/175-2014). The authors thank Prof.
V.I. Karas' for helpful comments.
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Article received 12.05.2015
ДИНАМИКА ИОНОВ И ГЕНЕРАЦИЯ ИОННОГО ЗВУКА ПРИ РАЗВИТИИ МОДУЛЯЦИОННОЙ
НЕУСТОЙЧИВОСТИ ИНТЕНСИВНЫХ ЛЕНГМЮРОВСКИХ ВОЛН В ПЛАЗМЕ
А.Г. Загородний, А.В. Киричок, В.М. Куклин, А.В. Приймак
Анализируется развитие 1D-параметрических неустойчивостей интенсивных длинноволновых ленгмюровских волн
в рамках так называемых гибридных моделей, когда электроны описываются как жидкость, а ионы описываются части-
цами. Рассматриваются случаи, когда средняя плотность энергии поля меньше (гибридная модель Захарова) и больше
(гибридная модель Силина) плотности тепловой энергии плазмы. Уменьшение уровня поглощения высокочастотного
поля соответствует замедлению выгорания ВЧ-поля в образовавшихся кавернах плотности плазмы и уширению спектра
ВЧ-мод. При этом функция распределения ионов по скоростям в моделях Захарова и Силина по форме приближается к
нормальному распределению.
ДИНАМІКА ІОНІВ І ГЕНЕРАЦІЯ ІОННОГО ЗВУКУ ПРИ РОЗВИТКУ МОДУЛЯЦІЙНОЇ НЕСТІЙКОСТІ
ІНТЕНСИВНИХ ЛЕНГМЮРІВСЬКИХ ХВИЛЬ В ПЛАЗМІ
А.Г. Загородній, О.В. Кірічок, В.М. Куклін, О.В. Приймак
Аналізується розвиток 1D-параметричних нестійкостей інтенсивних довгохвильових ленгмюрівських хвиль у
термінах так званих гібридних моделей, коли електрони описуються як рідина, а іони описуються частинками.
Розглядаються випадки, коли середня енергія поля менше (гібридна модель Захарова) і більше (гібридна модель Силіна)
теплової енергії плазми. Зменшення поглинання високочастотного поля відповідає уповільненню вигорання ВЧ-поля в
утворених кавернах щільності плазми і уширенню спектра ВЧ-мод. При цьому функція розподілу іонів за швидкостями
в моделях Захарова та Силіна за формою наближається до нормального розподілу.
Introduction
1. Statement of the problem and the initial conditions
2. The results of numerical simulation
Conclusions
AcknowledgEments
References
ДИНАМИКА ИОНОВ И ГЕНЕРАЦИЯ ИОННОГО ЗВУКА ПРИ РАЗВИТИИ МОДУЛЯЦИОННОЙ НЕУСТОЙЧИВОСТИ ИНТЕНСИВНЫХ ЛЕНГМЮРОВСКИХ ВОЛН В ПЛАЗМЕ
ДИНАМІКА ІОНІВ І ГЕНЕРАЦІЯ ІОННОГО ЗВУКУ ПРИ РОЗВИТКУ МОДУЛЯЦІЙНОЇ НЕСТІЙКОСТІ ІНТЕНСИВНИХ ЛЕНГМЮРІВСЬКИХ ХВИЛЬ В ПЛАЗМІ
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| id | nasplib_isofts_kiev_ua-123456789-112220 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:58:34Z |
| publishDate | 2015 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Kirichok, A.V. Kuklin, V.M. Pryimak, A.V. Zagorodny, A.G. 2017-01-18T19:45:22Z 2017-01-18T19:45:22Z 2015 Ion kinetics and ion sound generation under the development of modulation instability of an intense Langmuir wave in a plasma / A.V. Kirichok, V.M. Kuklin, A.V. Pryimak, A.G. Zagorodny // Вопросы атомной науки и техники. — 2015. — № 4. — С. 258-263. — Бібліогр.: 25 назв. — англ. 1562-6016 PACS: 52.35.-g, 52.65.-y https://nasplib.isofts.kiev.ua/handle/123456789/112220 The development of one-dimensional parametric instabilities of intense long-wave plasma waves is considered in terms of the so-called hybrid models, when electrons are treated as a fluid and ions are regarded as particles. The analysis is performed for both cases when the average plasma field energy is lower (Zakharov's hybrid model − ZHM) or greater (Silin's hybrid model − SHM) than the plasma thermal energy. Reduced absorption of the high-frequency (HF) field leads to the retardation of the HF field burnout within plasma density cavities and to the broadening of the HF spectrum. At the same time, the ion velocity distribution tends to the normal distribution in both ZHM and SHM. Аналізується розвиток 1D-параметричних нестійкостей інтенсивних довгохвильових ленгмюрівських хвиль у термінах так званих гібридних моделей, коли електрони описуються як рідина, а іони описуються частинками. Розглядаються випадки, коли середня енергія поля менше (гібридна модель Захарова) і більше (гібридна модель Силіна) теплової енергії плазми. Зменшення поглинання високочастотного поля відповідає уповільненню вигорання ВЧ-поля в утворених кавернах щільності плазми і уширенню спектра ВЧ-мод. При цьому функція розподілу іонів за швидкостями в моделях Захарова та Силіна за формою наближається до нормального розподілу. Анализируется развитие 1D-параметрических неустойчивостей интенсивных длинноволновых ленгмюровских волн в рамках так называемых гибридных моделей, когда электроны описываются как жидкость, а ионы описываются частицами. Рассматриваются случаи, когда средняя плотность энергии поля меньше (гибридная модель Захарова) и больше (гибридная модель Силина) плотности тепловой энергии плазмы. Уменьшение уровня поглощения высокочастотного поля соответствует замедлению выгорания ВЧ-поля в образовавшихся кавернах плотности плазмы и уширению спектра ВЧ-мод. При этом функция распределения ионов по скоростям в моделях Захарова и Силина по форме приближается к нормальному распределению. This paper was partially supported by the grant of the State Fund for Fundamental Research (project No. Φ 58/175-2014). The authors thank Prof. V.I. Karas' for helpful comments. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Динаміка іонів і генерація іонного звуку при розвитку модуляційної нестійкості інтенсивних ленгмюрівських хвиль в плазмі Ion kinetics and ion sound generation under the development of modulation instability of an intense Langmuir wave in a plasma Динаміка іонів і генерація іонного звуку при розвитку модуляційної нестійкості інтенсивних Ленгмюрівських хвиль в плазмі Динамика ионов и генерация ионного звука при развитии модуляционной неустойчивости интенсивных Ленгмюровских волн в плазме Article published earlier |
| spellingShingle | Ion kinetics and ion sound generation under the development of modulation instability of an intense Langmuir wave in a plasma Kirichok, A.V. Kuklin, V.M. Pryimak, A.V. Zagorodny, A.G. Динаміка іонів і генерація іонного звуку при розвитку модуляційної нестійкості інтенсивних ленгмюрівських хвиль в плазмі |
| title | Ion kinetics and ion sound generation under the development of modulation instability of an intense Langmuir wave in a plasma |
| title_alt | Динаміка іонів і генерація іонного звуку при розвитку модуляційної нестійкості інтенсивних Ленгмюрівських хвиль в плазмі Динамика ионов и генерация ионного звука при развитии модуляционной неустойчивости интенсивных Ленгмюровских волн в плазме |
| title_full | Ion kinetics and ion sound generation under the development of modulation instability of an intense Langmuir wave in a plasma |
| title_fullStr | Ion kinetics and ion sound generation under the development of modulation instability of an intense Langmuir wave in a plasma |
| title_full_unstemmed | Ion kinetics and ion sound generation under the development of modulation instability of an intense Langmuir wave in a plasma |
| title_short | Ion kinetics and ion sound generation under the development of modulation instability of an intense Langmuir wave in a plasma |
| title_sort | ion kinetics and ion sound generation under the development of modulation instability of an intense langmuir wave in a plasma |
| topic | Динаміка іонів і генерація іонного звуку при розвитку модуляційної нестійкості інтенсивних ленгмюрівських хвиль в плазмі |
| topic_facet | Динаміка іонів і генерація іонного звуку при розвитку модуляційної нестійкості інтенсивних ленгмюрівських хвиль в плазмі |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/112220 |
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