Chaotic decayes in resonators filled with rare plasma
The results of processes theoretical and experimental investigation of the broadband chaotic HF oscillations in the electrodynamics structure with rare plasma are presented. They are based on the nonlinear decay of HF wave into new HF and LF ones. The natural waves which may take part in this intera...
Saved in:
| Published in: | Вопросы атомной науки и техники |
|---|---|
| Date: | 2008 |
| Main Authors: | , , , , , , |
| Format: | Article |
| Language: | English |
| Published: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2008
|
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/110682 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Chaotic decayes in resonators filled with rare plasma / A.N. Antonov, V.A. Buts, I.K. Kovalchuk, O.F. Kovpik, E.A. Kornilov, V.G. Svichensky, D.V. Tarasov // Вопросы атомной науки и техники. — 2008. — № 4. — С. 245-249. — Бібліогр.: 6 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859628333264797696 |
|---|---|
| author | Antonov, A.N. Buts, V.A. Kovalchuk, I.K. KovpikKovpik, O.F. Kornilov, E.A. Svichensky, V.G. Tarasov, D.V. |
| author_facet | Antonov, A.N. Buts, V.A. Kovalchuk, I.K. KovpikKovpik, O.F. Kornilov, E.A. Svichensky, V.G. Tarasov, D.V. |
| citation_txt | Chaotic decayes in resonators filled with rare plasma / A.N. Antonov, V.A. Buts, I.K. Kovalchuk, O.F. Kovpik, E.A. Kornilov, V.G. Svichensky, D.V. Tarasov // Вопросы атомной науки и техники. — 2008. — № 4. — С. 245-249. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | The results of processes theoretical and experimental investigation of the broadband chaotic HF oscillations in the electrodynamics structure with rare plasma are presented. They are based on the nonlinear decay of HF wave into new HF and LF ones. The natural waves which may take part in this interaction are defined. There is a good agreement between theoretical and experimental results.
Викладені результати теоретичного та експериментального дослідження процесів формування широкосмугових НВЧ-коливань в електродинамічній структурі з рідкою плазмою. Вони ґрунтуються на нелінійному розпаді ВЧ-хвилі на нову ВЧ- та НЧ-хвилі. Визначені власні моди, що можуть приймати участь в такій взаємодії. Між результатами теоретичних та експериментальних досліджень існує добра якісна відповідність.
Изложены результаты теоретического и экспериментального исследования процессов формирования широкополосных СВЧ-колебаний в электродинамической структуре с разреженной плазмой. Они основаны на нелинейном распаде ВЧ-волны на новую ВЧ- и НЧ-волны. Определены собственные моды, которые могут принимать участие в таком взаимодействии. Между результатами теоретических и экспериментальных исследований имеется хорошее качественное соответствие.
|
| first_indexed | 2025-11-29T13:09:19Z |
| format | Article |
| fulltext |
CHAOTIC DECAYES IN RESONATORS FILLED WITH RARE PLASMA
A.N. Antonov, V.A. Buts, I.K. Kovalchuk, O.F. Kovpik, E.A. Kornilov, V.G. Svichensky, D.V. Tarasov
National Science Center “Kharkov Institute of Physics and Technology”, Kharkov, Ukraine
E-mail: vbuts@kipt.kharkov.ua
The results of processes theoretical and experimental investigation of the broadband chaotic HF oscillations in
the electrodynamics structure with rare plasma are presented. They are based on the nonlinear decay of HF wave
into new HF and LF ones. The natural waves which may take part in this interaction are defined. There is a good
agreement between theoretical and experimental results.
PACS:52.40. Mj
1. INTRODUCTION
___________________________________________________________
ВОПРОСЫ АТОМНОЙ НАУКИ И ТЕХНИКИ. 2008. № 4.
Серия: Плазменная электроника и новые методы ускорения (6), с.245-249. 245
)
The opportunity of spectra management of HF gen-
erators represents significant scientific and practical in-
terest. It is necessary to notice that conventional way for
creating such generators with wide noise spectra is very
difficult technical problem. We offer to use features of
dynamics of the charged particles and electromagnetic
fields at enough large intensity for formation of radiation
with the desire spectral characteristics. Such approach
allows to divide the process of generation of radiation
from the process of formation of its spectrum. Mecha-
nisms of widen spectra of excited radiation can be chaotic
dynamics of particles, and also chaotic dynamics of non-
linear interaction of waves. The basic attention below we
will pay on using of decaying processes with chaotic
dynamics. For realization of decay processes it is neces-
sary to have special dispersion of plasma electrodynamics
structure. This dispersion should be as decay dispersion.
Two cases of occurrence of chaotic dynamics are consid-
ered at nonlinear interaction of waves below. In first three
waves take part in nonlinear process, in the second cas-
cade of waves participate in disintegration process. Be-
sides dispersion properties of cylindrical waveguide
which partially filled by plasma, and results of experi-
mental researches are presented in this work, in which the
features of chaotic disintegrations are also investigated
and which demonstrate an opportunity of generation of
broadband noise signals.
2. NUMERICAL INVESTIGATION OF THREE-
WAVE PROCESS OF STOCHASTIC DECAY
The works [1,2] are devoted to research of occur-
rence of dynamic chaos at nonlinear interaction of three
waves in conditions of the modified disintegration. Ana-
lytical criterion of occurrence of chaos was fined there,
and the results of numerical modeling were represented
there too. The numerical results have confirmed analyti-
cal criterion of occurrence of chaos. The received reali-
zations can be characterized as irregular. The spectra
and the correlation functions, and also main of Lyapu-
nov index were determined for them. At fulfillment of
stochastic criterion the spectra were wide, and the corre-
lation functions quickly fell down, the main Lyapunov
index had a positive real part. It confirms chaotic cha-
racter of three-wave process of the modified
disintegration. At break down of this criterion (reduc-
tion of initial amplitude of a pumping wave) the spectra
were narrowed, and the time of correlation was in-
creased. It qualitatively coincides with experimental
results which are stated below.
3. CHAOS AT CASCADE WAVES
INTERACTION
Above we have observed interacting triplets of
waves. However in electrodynamics structure observed
by us which represents the cylindrical resonator filled
by rare plasma, a great number of triplets can take part
in the interacting. The elementary dispersion diagram of
interacting waves is presented in Fig.1. It is possible to
say, that the scheme of interacting transverse electro-
magnetic waves with Langmuir waves of plasma is rep-
resented in this figure. From this scheme follows, that it
is possible the cascade of decaying waves. Really, if
initially the high-frequency transverse wave is excited,
it can interact with the return transverse high-frequency
electromagnetic wave and with the plasma wave. The
high-frequency wave excited at such process, in turn,
can decay on the same high-frequency and on Lang-
muir. This process can contain a significant amount of
stages (see Fig.2). In order to describe it let's present, as
well as earlier, the electric field of the transverse elec-
tromagnetic waves in the form of:
( ) (0 0exp ,nE A i n t i k n kω ω⎡ ⎤= + Δ − + Δ⎣ ⎦∑
r r
(1)
where 0 0,kω
r
− the minimal frequency and wave vector of
one of eigen transverse waves of the resonator; ωΔ − the
distance between eigen transverse waves of the resonator;
nA complex amplitudes of eigen transverse waves.
Let us consider, that distance between eigen trans-
verse modes is equal to low-frequency plasma waves:
ωΔ = Ω . These (Langmuir) waves have equal frequency,
but different wave vectors. The electric field of Langmuir
waves can be presented in the following form:
( 0,exp .l n l lE B i t i k n k )⎡ ⎤= Ω − + Δ⎣ ⎦∑
r r (2)
The equations which present evolution of complex am-
plitudes of the transverse and plasma waves, can be pre-
sented in the following set of equations:
* *0 1
10 1 0 00 0 0 21 2 1
*2
11 1 1 32 3 2 1, 1 1 1
* *0 1
1 1 0 2 2 1 1
, ,
, ,
, ,
n
n n n n
n
n n n
A A
V A B V A B V A B
t t
AA
V A B V A B V A B
t t
B BB
W A A W A A W A A
t t t
− − − −
* .−
∂ ∂
= = +
∂ ∂
∂∂
= + =
∂ ∂
∂ ∂∂
= = =
∂ ∂ ∂
(3)
While getting (3) we supposed the following satis-
fied requirement of synchronism 1 ,n nω ω −− = Ω
1n nk k k− l− = Δ
r r r
(the law of conservation of energy and
momentum) for all three waves participating in interacting.
ω
k
246
Fig.1. The dispersion diagram of interacting waves
a
b
a
a
b
a a
Fig.2. The diagram of decay
From system (3), and from Fig.1 and diagram 2 we
can see, that the first equation presents dynamics of the
lowest-frequency transverse electromagnetic wave. This
wave does not decay on other waves. The last equation
for amplitudes of the transverse electromagnetic waves
presents dynamics of the highest-frequency transverse
electromagnetic wave. This wave decays. The inflow of
energy to it occurs only when the phase of the low-
frequency wave with which it interreacts changes the
sign. For the further analysis of the set of equations (3)
it is convenient to transfer to real variables amplitude
and the phase:
1 ,k
k k k k
1 .kA a e B b eϕ= = ψ
k
(4)
The interaction matrix elements also W are not
arbitrary. We shall consider, that all the diagonal ele-
ments of this matrix are equal, as well as nondiagonal
elements ; . In order to de-
fine the specific value of these elements of a matrix, it is
necessary to take into account the law of conservation
of energies and momenta. From these laws it follows
; . Except the law of conser-
vation of energies and momentums it is possible to get
the following integral:
ikV
iiV V−= ,ikV V W i k+= = ≠
1iiV = − 1 ,ikV W i= = ≠
2 ,ka const=∑ (5)
which expresses the law of conservation the number of
high-frequency quantums.
Using all these laws, it is finally possible to get the
following set of equations for the description of dynam-
ics of the real amplitudes and the real phases ia ,i iϕ ψ :
( )
( )
( )
(
where 0,1,....n N= ; 1, ...m N≡ ;
1 2
0, 0,
1, 0 1,
n o n N
n n
δ δ
N
= =⎧ ⎧
= =⎨ ⎨≠ ≠⎩ ⎩
.
Fig.3 is the characteristic dependence of amplitude
of the third wave on the time; the phase plane for the
second wave is in Fig.4, the correlation function is in
Fig.4, the characteristic spectra is in Fig.5. From time
dependences, from the spectrums and the behavior of
the correlation function it is seen that the dynamics of
interacting waves is chaotic for all considered cases.
Fig.3. Time evolution of the amplitude of the third wave
Fig.4. The projection of the phase space of the second
wave to the plane 2 2a ϕ
0 125 250 375 500 625 750 875 1 103×
3 10 4−×
3.2 10 4−×
3.4 10 4−×
3.6 10 4−×
3.8 10 4−×
4 10 4−×
Rl
l
Fig.5. The correlation function for a3
)
( )
( )
1 1 1 1
2 1 1
1 1 1 1
1 1
1 1
1
2 1
1
1 1
1
2 cos
cos ,
cos ,
2 sin
sin ,
sin ,
n n n n n n
n n n n n
n m m m m m
n n
n n n
n
n n
n n n
n
m m
m m m m
m
a a b
a b
b a a
a b
a
a b
a
a a
b
δ ϕ ϕ ψ
δ ϕ ϕ ψ
ϕ ϕ ψ
ϕ δ ϕ ϕ ψ
δ ϕ ϕ
ψ ϕ ϕ ψ
− − − −
+ +
− − − −
− −
− −
−
+
−
− −
−
= − − + +
+ − −
= − −
= − − + +
+ −
= − −
&
&
&
&
4. THE DISPERSION EQUATIONS OF THE
MAGNETIZED PLASMA IN THE A METAL
SHEATH
1
1
n
ψ
−
−
(6)
Let's observe the cylindrical ideally conducting wa-
veguide of radius b partially filled with plasma with
plasma frequency pω . The plasma is presented as the
cylinder of radius , coaxial with the waveguide. All
system is placed in the constant magnetic field guided
along the axis of system. There can be both fast and
slow waves. The last ones are observed in [3] in details.
Some general approaches to studying the magnetized
a
plasma in a metal housing, are studied in [4]. Getting
the dispersion equation in a general case is a rather dif-
ficult task. Besides such equation will be rather com-
plex. In paper [5] the attention was paid to finding the
real solutions in the field of parameters where the trans-
verse wave numbers are complex. In [6] dispersion
properties and structure of the fields of axially asym-
metrical waves are studied when plasma completely fills
a metal sheath.
247
First of all we are interested in fast modes which can
participate in the processes of nonlinear decay. We shall
restrict our consideration to the axially symmetrical
oscillations near the upper hybrid resonance which is of
interest to specific experimental requirements. The dis-
persion equation in this case is:
00 01
1 2 2
10 11
01 00
1 2 1
11 10
2
00 01
1 1 2 2 2 12
10 11
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( )
( ) ( )
p
a a
y y f
a a
a a
y y f
a a
a a
f y f y f f
a a
κ κ
κ κ
ω κ κ
ω
⎛ ⎞Δ ⎛ Δ ⎞
− − −⎜ ⎟ ⎜ ⎟Δ Δ⎝ ⎠⎝ ⎠
⎛ ⎞⎛ Δ ⎞ Δ
− − − =⎜ ⎟⎜ ⎟Δ Δ⎝ ⎠ ⎝ ⎠
Δ ⎡ Δ ⎤
= − +⎢ ⎥Δ Δ⎣ ⎦
,−
(7)
where ω − the excited frequency in the sys-
tem , 2 2 2 , /zk k k cκ ω= − = zk − the longitudinal wave
number, ω − the oscillation frequency
( ) (1,2 1,2 0 1,2 0 1,2( ) / ( )y k J k a kJ k a=
( ) ( ) ( ) ( )
)
( )ik i k i kr N r J b J r N bκ κ κ κΔ = − ( )iJ x , −
Bessel and Neumann's functions -th order accord-
ingly, − the wave numbers, presenting the transverse
structure of the field in plasma which look like
( )iN x
i
1,2k
2 2 2 2 2
1,2
2 2 2 2
2 2
2 2 2 2 2 2 2 2 2
2 2
(1 / )
( )
2
4 (
,
2
z p
p h z
p h z h z
k k k
k k
k k k k
ω ω
ω ω
ω ω
ω ω ω ω
ω ω
⎡ ⎤= − − − −⎣ ⎦
+
− ±
Δ
Δ + +
±
Δ
)
2
(8)
where 2 2 2
e pω ω ω ωΔ = − − , eω − electron cyclotron
frequency, pω − electron plasma frequency
2 2 2 2 2 2 2
1,2 ( ) 4 ( )e z ef sign k k kω κ ω ω ω= Δ Δ + +m 2 2
z k
, h
.
As it is seen from (8) the squares of the transverse
wave numbers can be both negative and positive.
Depending on their signs the dispersion equations will
have absolutely different shape and structure of the
solutions. The expressions (8) have been simplified and
analyzed for the fields of frequencies near upper hybrid
resonance
1,2k
2 2 2ω ω ωΔ << 2 2
h; ω ω
2
. It is also sup-
posed, that 2
pω ω<< . In the fields and
one of the numbers is close to vacuum
( ) and does not depend on the applied magnetic
field. The second one, on the contrary, is defined by the
2 0ωΔ >
2 0ωΔ < 1,2k
1,2k κ≈
hω . For , at . For
, at , and
2 0ωΔ > 2 0ωΔ → 1k κ≈ 2
2k → −∞
2 0ωΔ < 2| | 0 2
1k →∞ωΔ → 2k κ≈ . As it is
seen from the given above relationships, in our case it is
possible to put into operation two dimensionless small
parameters: 2 2/ 1pω ω << and . The char-
acter of solutions of the dispersion equations essentially
depends on the relationship between them. Accomplish-
ing both requirements
2 2/ hω ωΔ < 1<
2 2 2/ 2/p eω ω ω< Δ ω the wave
numbers are close to vacuum value ( ), and solu-
tions of the dispersion equation (7) in this case are close
to modes of the empty circular guide. Otherwise the
influence of the plasma is essential.
1,2k κ≈
The dispersion equation (7) can be converted at
2 0ωΔ < 2| |ω 0Δ → . Bessel's functions of zero and the
first order from argument in this case can be
exchanged by their asymptotic approximation. The equ-
ation (7) in this case will look like:
1k a →∞
2 22 2
2 2
2 2 2
2 2 2 20 2 01 002
3
1 2 11 10
2 20 2 00 012
3 3
1 2 10 11
2 200 01
3
10 11
( )
4| | | |
( )
( )
( )
( )
( )
( ) ,
p pz
z
z z
z
k k
ctg k k a
k
J k ak
k k k k
J k a
J k ak
k k
k J k a
k k
ω ω π
ω ω
ε
κ
κ ε
κ
ε
⎛ ⎞+ ⎜ ⎟+ − ×
⎜ ⎟Δ Δ⎝ ⎠
⎡ ⎤⎛ ⎞Δ Δ
× + − + =⎢ ⎥⎜ ⎟Δ Δ⎢ ⎥⎝ ⎠⎣ ⎦
⎡ ⎛ ⎞Δ Δ
= +⎢ ⎜ ⎟Δ Δ⎢ ⎝ ⎠⎣
⎤Δ Δ
− + ⎥Δ Δ ⎦
−
(9)
where 2 2
3 1 /pε ω ω= − .
As it is seen, in the case when and 2 0ωΔ <
2| |ω 0Δ → at fixed zk the dispersion equation for the
fast waves has the infinite number of solutions which
are condensed near to the upper hybrid frequency
2
h e
2
pω ω ω= + . The dispersion curves are placed in the
narrow frequency band between eω and hω .
The dispersion equation (7) was solved numerically.
The character of the dispersion curves is presented in
Fig.6; 6а and 7. As it is seen, in the field of frequencies
eω ω< the dispersion of the waveguide partially filled
with plasma is similar to the dispersion of the empty
cylindrical waveguide. While approaching the electron
cyclotron frequency the dispersion curves correspond-
ing the empty waveguide become deformed. They enter
the frequency band between electron cyclotron and up-
per hybrid where they are located parallely to horizontal
axis that is shown in Fig.6 in details. Besides in this
field of frequencies there is the infinite number of
branches which do not go beyond. I.e. their cut-off fre-
quencies are in the field of between eω and hω .
Thus, it coincides with the made above inference,
received due to the analytical analysis, that in the field
of the parameters 2 2 2/ 2/p eω ω ω> Δ ω the dispersion is
defined by the properties of plasma. In the field of fre-
quencies hω ω> the dispersion of the observed wave-
guide filled with plasma is close to the dispersion of the
empty one. The analytical analysis and the numerical
calculations show that accomplishing the requirement
2 2 2/ 2/p eω ω ω ω<Δ we get . 1 2k k κ≈ ≈
Fig.6. The dispersion of cylindrical waveguide partially
filled with plasma. Wide gray curves correspond to dis-
persion of empty waveguide, and black ones correspond
to waveguide filled with plasma. The region pointed by
dashed rectangle is presented in Fig.6,a
Рис.6а. The dispersion of cylindrical waveguide
partially filled with plasma. This figure corresponds
to dashed rectangle in Fig.6
Fig.7. The dispersion of cylindrical waveguide partially
filled with magnetoactive plasma near upper hybrid
resonance frequency. Horizontal line in upper part of
figure corresponds to this frequency
I.e. the structure of the field corresponding this field
of frequencies in plasma is close to the structure of the
field in vacuum. As it was noted above in the frequency
band e hω ω ω≤ ≤ 2
1k →∞ , and , that specifies
fast oscillating in transverse direction structure of the
field in plasma.
2k κ≈
In paper [6] the dispersion of the metal waveguide
completely filled with the plasma placed in finite mag-
netic field for axially asymmetrical modes was studied.
Its specific features are qualitatively close to the struc-
ture observed in the present report.
Thus in metallic cylindrical waveguide partially
filled with magnetized plasma in the region of frequen-
cies close to upper hybrid resonance the infinite number
of modes exists. We are interested in nonlinear proc-
esses of wave decay by the following scheme:
HF→HF+LF. One of the natural mode can be used as
pump mode, which decays on new HF, localized lower
then upper hybrid resonance and other one of the LF
plasma modes. Large set of natural oscillations in con-
sidered system can be used for realization of cascade
decay processes.
5. EXPERIMENTAL RESULTS
The experimental setup is multimode resonator
which is laced into longitudinal magnetic field. To ex-
cite field in resonator the magnetron generator is used.
The resonator is excited at frequency 2.77 GHz. When
these experiments were carried out it was revealed that
pulse duration of exciting HF oscillations is more longer
then duration of magnetron pulse.
When introduced power is 20% more then threshold
one, corresponding to decay process beginning the elec-
trons with energy of hundreds of KeV appear. In some
microseconds after pulse ending the pulses of HF radia-
tion start appearing. The oscillations with frequencies
1.3; 2.68; 3.75; 5 GHz were registered in them with
bandwidth 10 MHz. The temporal interval between
pulses may vary in limits 0…30 µs.
The appearance of pulses was random on time and
amplitude. When magnetic field value on half resonator
length is decreased on 25% the regularity of repeated
pulses appearance was increased.
When repeated pulses were appeared the pulses of
plasma luminescence and X-ray radiation appeared too,
conditioned by the slowing-down of accelerated electrons
with tens – hundreds keV on neutral molecules of gas.
The spectrum of low frequency oscillations in cavity
was defined experimentally versus introducing power.
The signal oscillograms from resonator are presented in
Fig.8-10 for three values of introduced power 17, 58
and 167 kW. It is seen that when introduced power is
increased the kind of registered signal in resonator be-
comes less regular. In Fig.11 the experimental depend-
ence of bandwidth versus introduced power is pre-
sented. Growth of bandwidth of spectrum and kind of
oscillograms point out that when amplitude of pumping
wave increases the processes in resonator, partially
filled by magnetoactive plasma became chaotic. Analo-
gous dynamics was observed at numerical simulation of
process of three wave decay.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.E+00 2.E-07 4.E-07 6.E-07 8.E-07 1.E-06
T, s
A, orb.
units
Fig.8. Signal LF oscillogram in cavity at introduced
power 17 kW
248
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.E+00 2.E-07 4.E-07 6.E-07 8.E-07 1.E-06
T, s
A, orb.
units
249
Fig.9. Signal LF oscillogram in cavity at introduced
power 58 kW
0
0.2
0.4
0.6
0.8
1
0.E+00 2.E-07 4.E-07 6.E-07 8.E-07 1.E-06
T, s
A, orb.
units
Fig.10. Signal LF oscillogram in cavity at introduced
power 167 kW
0
50
100
150
200
250
300
350
400
0 50 100 150 200
P, kW
S, MHz
Fig.11. Bandwidth of spectrum versus introducing power
CONCLUSIONS
In this article the results of theoretical and experimen-
tal investigations on exciting of wideband noise oscilla-
tions in cylindrical resonator partially filled by plasma are
presented. This process is basing on the modified decay
of high frequency wave in this system into new high fre-
quency and low frequency ones. Briefly results of nu-
merical simulation of such decay have been stated. The
possibility of the chaos development in many wave cas-
cade regime has been shown. The dispersion properties of
natural axial symmetric modes of cylindrical resonator
partially filled by magnetoactive plasma were investi-
gated. Those of them which may take part in chaotic
decay processes are pointed out. The results of experi-
mental investigations which qualitatively agree with
theoretical conclusion are presented.
The results presented in [2] and in this article show a
good agreement of theoretical views about chaotic de-
cay and experimental data. It is necessary to note that
obviously in [2] and in present work the process of cha-
otic decay was first investigated experimentally. We
note that in experiment the conditions for chaotization
of interaction are satisfied not only for wave-wave proc-
esses, but for the wave-particle processes too. This be-
comes obvious that simultaneously with stochastic de-
cay stochastic heating of plasma particles takes place.
For our goals this process is harmful. It can be removed
by introducing nonuniformity of magnetic field.
It is also necessary to note the peculiarities of the
dispersive properties of the electrodynamics structures
with rare plasma. In spite of low plasma density the
system dispersion essentially changes due to the reso-
nance interaction of waves with plasma particles. In
particular, the large number of the additional eigen
modes arises, which can be used for chaotization of de-
cay processes.
REFERENCES
1. V.A. Buts, I.K. Kovalchuk, E.A. Kornilov, D.V. Tarasov.
Stabilization beam instability as a result of development
of local instability at interaction of type a wave-wave //
Physics of plasma. 2006, v.32, №6, p.1-10.
2. V.A. Buts, I.K. Kovalchuk, E.A.Kornilov, D.V. Ta-
rasov. Dynamical chaos rise in the system of large
number of nonlinear coupled oscillators // Voprosy
atomnoy nauki i tekhniki. 2007, №3(2), p.260-264
(in Russian).
3 A.N. Kondrtenko. Plazmenniye volnovody. M.: “At-
omizdat”, 1976, 232 p. (in Russian).
4 Entsiklopediya nizkotemperaturnoy plazmy.
M.: “Nauka”, 2000, v.4, part X, p.132-151 (in Rus-
sian).
5 I.N. Onishchenko, G.V. Sotnikov. Dispersiya plazmen-
nikh voln v konechnom magnitnom pole // Phizika
plazmy. 1992, v.18, №3, p.335-345 (in Russian).
6. G.I. Zaginaylov, V.I. Shcherbinin, K. Shunemann. Ne-
kotoriye osobennosty dispersionnikh svoystv volno-
vodov, zapolnennikh plazmoy v magnitnom pole //
Phizika plazmy. 2005, v.31, №7, p.647-751 (in Rusian).
Статья поступила в редакцию 31.05.2008 г.
ХАОТИЧЕСКИЕ РАСПАДЫ В РЕЗОНАТОРАХ С РАЗРЕЖЕННОЙ ПЛАЗМОЙ
А.Н. Антонов, В.А. Буц, И.К. Ковальчук, О.Ф. Ковпик, Е.А. Корнилов, В.Г. Свиченский, Д.В. Тарасов
Изложены результаты теоретического и экспериментального исследования процессов формирования
широкополосных СВЧ-колебаний в электродинамической структуре с разреженной плазмой. Они основаны на
нелинейном распаде ВЧ-волны на новую ВЧ- и НЧ-волны. Определены собственные моды, которые могут принимать
участие в таком взаимодействии. Между результатами теоретических и экспериментальных исследований имеется
хорошее качественное соответствие.
ХАОТИЧНІ РОЗПАДИ В РЕЗОНАТОРАХ З РІДКОЮ ПЛАЗМОЮ
А.М. Антонов, В.О. Буц, І.К. Ковальчук, О.Ф. Ковпик, Є.О. Корнілов, В.Г. Свіченський, Д.В. Тарасов
Викладені результати теоретичного та експериментального дослідження процесів формування широкосмугових НВЧ-
коливань в електродинамічній структурі з рідкою плазмою. Вони ґрунтуються на нелінійному розпаді ВЧ-хвилі на нову
ВЧ- та НЧ-хвилі. Визначені власні моди, що можуть приймати участь в такій взаємодії. Між результатами теоретичних та
експериментальних досліджень існує добра якісна відповідність.
|
| id | nasplib_isofts_kiev_ua-123456789-110682 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-11-29T13:09:19Z |
| publishDate | 2008 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Antonov, A.N. Buts, V.A. Kovalchuk, I.K. KovpikKovpik, O.F. Kornilov, E.A. Svichensky, V.G. Tarasov, D.V. 2017-01-06T07:48:27Z 2017-01-06T07:48:27Z 2008 Chaotic decayes in resonators filled with rare plasma / A.N. Antonov, V.A. Buts, I.K. Kovalchuk, O.F. Kovpik, E.A. Kornilov, V.G. Svichensky, D.V. Tarasov // Вопросы атомной науки и техники. — 2008. — № 4. — С. 245-249. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS:52.40. Mj https://nasplib.isofts.kiev.ua/handle/123456789/110682 The results of processes theoretical and experimental investigation of the broadband chaotic HF oscillations in the electrodynamics structure with rare plasma are presented. They are based on the nonlinear decay of HF wave into new HF and LF ones. The natural waves which may take part in this interaction are defined. There is a good agreement between theoretical and experimental results. Викладені результати теоретичного та експериментального дослідження процесів формування широкосмугових НВЧ-коливань в електродинамічній структурі з рідкою плазмою. Вони ґрунтуються на нелінійному розпаді ВЧ-хвилі на нову ВЧ- та НЧ-хвилі. Визначені власні моди, що можуть приймати участь в такій взаємодії. Між результатами теоретичних та експериментальних досліджень існує добра якісна відповідність. Изложены результаты теоретического и экспериментального исследования процессов формирования широкополосных СВЧ-колебаний в электродинамической структуре с разреженной плазмой. Они основаны на нелинейном распаде ВЧ-волны на новую ВЧ- и НЧ-волны. Определены собственные моды, которые могут принимать участие в таком взаимодействии. Между результатами теоретических и экспериментальных исследований имеется хорошее качественное соответствие. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Нелинейные процессы в плазменных средах Chaotic decayes in resonators filled with rare plasma Хаотичні розпади в резонаторах з рідкою плазмою Хаотические распады в резонаторах с разреженной плазмой Article published earlier |
| spellingShingle | Chaotic decayes in resonators filled with rare plasma Antonov, A.N. Buts, V.A. Kovalchuk, I.K. KovpikKovpik, O.F. Kornilov, E.A. Svichensky, V.G. Tarasov, D.V. Нелинейные процессы в плазменных средах |
| title | Chaotic decayes in resonators filled with rare plasma |
| title_alt | Хаотичні розпади в резонаторах з рідкою плазмою Хаотические распады в резонаторах с разреженной плазмой |
| title_full | Chaotic decayes in resonators filled with rare plasma |
| title_fullStr | Chaotic decayes in resonators filled with rare plasma |
| title_full_unstemmed | Chaotic decayes in resonators filled with rare plasma |
| title_short | Chaotic decayes in resonators filled with rare plasma |
| title_sort | chaotic decayes in resonators filled with rare plasma |
| topic | Нелинейные процессы в плазменных средах |
| topic_facet | Нелинейные процессы в плазменных средах |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110682 |
| work_keys_str_mv | AT antonovan chaoticdecayesinresonatorsfilledwithrareplasma AT butsva chaoticdecayesinresonatorsfilledwithrareplasma AT kovalchukik chaoticdecayesinresonatorsfilledwithrareplasma AT kovpikkovpikof chaoticdecayesinresonatorsfilledwithrareplasma AT kornilovea chaoticdecayesinresonatorsfilledwithrareplasma AT svichenskyvg chaoticdecayesinresonatorsfilledwithrareplasma AT tarasovdv chaoticdecayesinresonatorsfilledwithrareplasma AT antonovan haotičnírozpadivrezonatorahzrídkoûplazmoû AT butsva haotičnírozpadivrezonatorahzrídkoûplazmoû AT kovalchukik haotičnírozpadivrezonatorahzrídkoûplazmoû AT kovpikkovpikof haotičnírozpadivrezonatorahzrídkoûplazmoû AT kornilovea haotičnírozpadivrezonatorahzrídkoûplazmoû AT svichenskyvg haotičnírozpadivrezonatorahzrídkoûplazmoû AT tarasovdv haotičnírozpadivrezonatorahzrídkoûplazmoû AT antonovan haotičeskieraspadyvrezonatorahsrazrežennoiplazmoi AT butsva haotičeskieraspadyvrezonatorahsrazrežennoiplazmoi AT kovalchukik haotičeskieraspadyvrezonatorahsrazrežennoiplazmoi AT kovpikkovpikof haotičeskieraspadyvrezonatorahsrazrežennoiplazmoi AT kornilovea haotičeskieraspadyvrezonatorahsrazrežennoiplazmoi AT svichenskyvg haotičeskieraspadyvrezonatorahsrazrežennoiplazmoi AT tarasovdv haotičeskieraspadyvrezonatorahsrazrežennoiplazmoi |