Strong fields. Some features of dynamics of particles and waves
Some most significant results, which were got at research of wave - particle type interaction and of wave - wave type interaction are briefly reported. Коротко викладені деякі найбільш важливі результаты, які були здобуті при дослідженні процесу взаємодії типу хвиля-частинка та типу хвиля-хвиля. Кра...
Saved in:
| Published in: | Вопросы атомной науки и техники |
|---|---|
| Date: | 2008 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2008
|
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/110793 |
| 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: | Strong fields. Some features of dynamics of particles and waves / V.A. Buts // Вопросы атомной науки и техники. — 2008. — № 6. — С. 126-128. — Бібліогр.: 17назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860218958524710912 |
|---|---|
| author | Buts, V.A. |
| author_facet | Buts, V.A. |
| citation_txt | Strong fields. Some features of dynamics of particles and waves / V.A. Buts // Вопросы атомной науки и техники. — 2008. — № 6. — С. 126-128. — Бібліогр.: 17назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | Some most significant results, which were got at research of wave - particle type interaction and of wave - wave type interaction are briefly reported.
Коротко викладені деякі найбільш важливі результаты, які були здобуті при дослідженні процесу взаємодії типу хвиля-частинка та типу хвиля-хвиля.
Кратко изложены некоторые наиболее важные результаты, полученные при исследовании взаимодействий типа волна-частица и типа волна-волна.
|
| first_indexed | 2025-12-07T18:17:20Z |
| format | Article |
| fulltext |
STRONG FIELDS.
SOME FEATURES OF DYNAMICS OF PARTICLES AND WAVES
V.A. Buts
National Science Center “Kharkov Institute of Physics and Technology”,
61108, Kharkov,Ukraine, e-mail: vbuts@kipt.kharkov.ua
Some most significant results, which were got at research of wave - particle type interaction and of wave - wave
type interaction are briefly reported.
PACS: 52.20.-j; 52.35.Ra; 52.35.Py
1. RESULTS CONNECTED
WITH TRANSITIONS TO DYNAMIC CHAOS
AT WAVE - PARTICLE TYPE INTERACTION
In our previous works (see, for example, [1-3]) the
simple enough analytical conditions for occurrence of
dynamic chaos for all known types of resonant interaction
of a wave - particle type were formulated. The reason of
occurrence of dynamic chaos was overlapping of
nonlinear resonances. It seemed, what exactly this
scenario of transition to chaos should cover all possible
physical situations. Really, the interaction of an
electromagnetic wave with the charged particle can be
described by the following Hamiltonian:
( ) ( )0 1, , ,H H q p H q p t= +r r r r
. Here ( )0 ,H q pr r
- integrable
part of Hamiltonian; ( ) ( )1 1, , , ,H q p t H q p t T= +r r r r
- periodic
perturbation. It is well known, that short-cut equations
describing influence of such perturbation in singular
theory of perturbation, is habitually reduced to researches
of a mathematical pendulum. Therefore, it seems that the
received results cover all possible processes of a wave-
particle type interaction. Using these criteria, the
numerous results were received, from which we shall note
only one - opportunity of unlimited acceleration of the
charged particles by an electromagnetic wave in vacuum
at overlapping of cyclotron resonances. The importance
of this result is caused by that fact, that up to it only one
mechanism of unlimited acceleration of the charged
particles was known - it is a mechanism of an
autoresonance (Davidovsky - Kolomensky - Lebedev
mechanism). It is necessary, however, to emphasize, that
the rate of unlimited stochastic acceleration is lower, than
at the autoresonance and the quality of the accelerated
ensemble of particles is much worse. Now it was
revealed by us, that for the description of nonrelativistic
particles the short-cut equations are not equation of a
mathematical pendulum, but system of the equations,
which are topology equivalent to Duffing oscillator.
Duffing oscillator, in contrast to a mathematical
pendulum, has two free parameters. This facts are lead to
the result that at change of amplitude of a wave, in which
the particle is, its phase portrait (phase portrait of Duffing
oscillator) can qualitatively changed. Presence of such
qualitative change of a phase portrait is a reason of
chaotic dynamics appearing. As an example of such
scenario of transition to chaotic dynamics we have
considered a task about movement of the charged particle
in a constant magnetic field and in a field of an
electromagnetic wave. It had shown that in nonrelativistic
case this scenario is realized. In more details with these
results it is possible to familiarize in [4].
2. RESULTS CONNECTED WITH LASER
ACCELERATION
At acceleration of electron by laser radiation the
accelerated particles oscillate in a laser field. At that the
intensive radiations arise. This radiation, as well as the
radiation in cyclic accelerators, can limit energy, which
can get accelerated particles. The restrictions on the
maximal energy can be received by equating accelerating
forces to forces of radiating friction. So, for example, in
work [5], considering acceleration of electrons by a field
of laser radiation, the authors have equated force of
radiating friction to accelerating forces (forces of high-
frequency pressure). They have found, that in a field of
laser radiation the electrons can not get energy large, than
200 MeV ( ~ 1 kλ µ ). At that, as force of high-frequency
pressure and force of radiating friction both are
proportional to 2ε ( /e E mcε ω= Ч - parameter of wave
force), this result does not depend from intensity of a laser
field. In this sense he is universal.
In works [6,7] had shown, that the forces of friction,
including forces of radiating friction, can promote
transfers of energy from an external laser field to
accelerated particles. Besides is shown, that the restriction
on the maximal size of energy in 200 Mev, which can get
particles in a field of laser radiation, generally is absent.
The condition that the forces of friction will promote
transfers of energy from a wave to a particle there will be
an inequality: 1Iγ >Ч , where the value
zI p constγ= − = represents integral. At large intensity
of a laser field 1ε > > this condition is always carried
out. At performance of a inverse inequality 1Iγ <Ч the
forces of friction brake particles. The reason of such
influence of friction forces at laser acceleration is that
fact, that the forces of friction shift a phase between of a
wave and particle at interaction. This shift can promote to
acceleration. Despite of fact that the accelerated particles
lose their energy on radiation, this shift lead to
compensation of these losses and to additional
acceleration of particles. It is necessary to note, that the
losses of energy on radiation at laser acceleration are not
such catastrofical as it takes place, for example, in
126 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2008. № 6.
Series: Plasma Physics (14), p. 126-128.
synchrotron. Really, the particles, moving with
acceleration, lose a part of the energy on radiation. And,
the more energy has particle, the more energy she loss at
radiation. So, if relativistic electron is moving along
circular orbit, radius of which is unchanged (for example,
at moving in magnetic field of cyclic acceleration). Then
the expression for power of radiation one can represent
as: ( ) 2 2 42 / 3W e c K γ= Ч Ч Ч Ч . Here γ - relativistic factor;
K - curvature of orbit.
From this formula it is visible, that the losses grow as
the fourth degree of energy of a particle. This fact limits
opportunities of cyclic accelerators of electrons. In the
case, considered by us (laser acceleration) radius of
curvature of electrons trajectory grows proportionally to
square of electron energy ( 2~ 1/K γ ). That is why the
power of radiation does not vary with growth of energy
and the problem connected with growth of radiating
losses does not arise. By one of the perspective schemas
of acceleration, which allow to accelerate the charged
particles in vacuum is the scheme of the inverted laser on
free electrons (IFEL). Such scheme of acceleration is
widely discussed in the scientific literature (see, for
example, [8-9]). She has many important features, from
which we shall note only one - the acceleration occurs in
vacuum and by cross electromagnetic waves. Earlier was
shown by us [10], that in the real schemes FEL and IFEL,
as a result of presence in real laser fields large number
selfmodes, the stochastic instability practically always
develops. Such instability essentially limits efficiency of
use of these schemes. It had seemed that at use one mode
laser we shall can avoid development of this instability.
However, as shown in our last researches [11, 12], at
increase of amplitude of accelerating laser radiation the
stochastic instability develops and in this case.
3. DYNAMIC CHAOS IN LINEAR
AND IN QUANTUM SYSTEMS
Now in an obvious kind is formulated paradigm that
the evolutionary operator describing dynamics of system
with a regime of dynamic chaos should have two
unconditional properties: 1. To be stretching; 2. To be
nonlinear. Certainly, these two features are necessary for
realization of dynamic chaos. However, it is necessary to
give some explanation concerning the second (nonlinear)
property. Really, for example, it is known, that the
equations of the quantum mechanics and Maxwell
equations are the linear equations. However at transition
from the quantum equations of movement to the classical
equations of movement, and also at transition from the
Maxwell equation to the equations of geometrical optics
we get systems of the nonlinear equations. Such equations
can describe regimes with dynamic chaos. Thus, now we
are know at least two examples when in linear systems at
the certain meanings of their parameters (which allow to
pass to classical description) the regimes with dynamic
chaos are possible. In work [13] is shown, that this
situation is considerably more widespread, that the
regimes with dynamic chaos is internally inherent for
huge number of linear systems. In this work the results of
the analysis of this feature for the quantum systems are
given. On the basis of the Schrödinger equation the
elementary quantum systems, in which the regimes with
dynamic chaos is possible, are considered. Such system,
first of all, is the three-level system. The conditions of
occurrence of dynamic chaos in such system are
determined. The necessary amplitudes of perturbation
potential for realization of a regime with dynamic chaos
are found. The characteristic times of diffuse of quantum
system in space of energy are determined. The possible
applications of the received results are discussed. In more
details with these results it is possible to get acquainted in
[14].
It is necessary to tell, that the phenomenon of
quantum chaos for a long time is intensively studied (see,
for example, [15]). At that, however, all authors are
emphasize, that the quantum chaos is not true chaos, that
in quantum chaos those quantum systems are studied,
which parameters allow semiclassical description and
which in a classical limit have a regimes with dynamic
chaos. Many authors for this reason take the name of
quantum chaos in inverted commas. In this work were
studied true quantum systems. The parameters of these
quantum systems were such, that they did not allow
semiclassical consideration. For this reason it is possible
to name a set of these phenomena as true quantum chaos.
4. DYNAMICAL CHAOS AT WAVE-WAVE
TYPE INTERACTION
The second fundamental process in plasma and in
plasma-beam systems is the process of wave-wave
interaction. We earlier had found simple analytical
conditions, at which performance dynamics of such
processes became chaotic (see, for example, [16]). The
proof that the process of the modified decaying always is
chaotic was one of main results. The received theoretical
results have allowed to give enough con-vincing
interpretation to many processes proceeding at plasma-
beams instability [17]. In particular, the processes of
stabilization and breakdown of intense oscillation in
plasma-beam systems have received an explanation. The
decaying processes with stochastic dynamics can be used
for controlling of spectra form of radiation that is exited
by traditional highly effective generators (for example,
magnetrons). However, there was left a question, under
what conditions such process can be realized in
experiments? What intensity of a field is necessary for
this purpose? The analysis shows, for example, that the
decay of cross waves on a cross wave and on Langmuir
wave in unlimited plasma does not result in development
of local instability [16]. In this case for development of
such instability is necessary very large intensity of
electromagnetic fields. The theoretical models, used in
these analyses (models with weak nonlinearity) at such
intensity are cease to be true. In our researches was
shown, that for realization of stochastic decay the
electrodynamics systems, in which the distance between
own modes is enough small, can be used. Such system, in
127
particular, can serve round metal waveguide filled by
some media, which have anisotropy characteristics. Such
media can play role of the element, which provides
nonlinear interaction. An example of such media can be
magnetoactive plasma, ferrite or ferroelectric.
REFERENCES
1. V.A. Buts, A.N. Lebedev, V.I. Kurilko. The Theory
of Coherent Radiation by Intense Electron Beams.
Berlin: “Springer”. 2006, p. 263.
2. V.А. Balakirev, V.A. Buts, А.P.Tolstoluzhskii and
Yu.A. Turkin. Randomization of motion of a beam of
phased oscillators // Sov. Phys. JETP. 1983, v. 57,
N4, p. 741-746.
3. V.А. Balakirev, V.A. Buts, А.P.Tolstoluzhskii and
Yu.A. Turlin. Charged-particle dynamics in the field
of two electromagnetic waves // Sov. Phys. JETP.
1989, v. 68, N 4, p. 710-717.
4. V.A. Buts, A.P. Tolstoluzhsky. Nonrelativistic particles
dynamics at cyclotron resonances // Problems of
Atomic Science and Technology. Series “Plasma
Physics” (14). 2008, N 6, p.117-119 (herein).
5. N.B. Baranov, М.О. Scalli, B.Ya. Zeldovich.
Acceleration of charged particles by laser beams //
JETP. 1994, v. 105, issue 3, p. 469–486.
6. V.A. Buts. Peculiarities of particles and field
dynamics at critical intensity of electromagnetic
waves (part 1) // Problems of Atomic Science and
Technology Series “Plasma Physics” (10). 2005, N
1, p.119-121.
7. V.A. Buts, V.V. Kuzmin. Dynamics of particles in
fields of large intensity // Progress of Modern
Radioelectronics. 2005, N 11, p. 5-20.
8. T. Marshall. Free electron laser. 1987, М.: “Mir”.
9. M.V. Fedorov. Electron in strong light field. M.:
“Nauka”, 1991, p. 224.
10. V.A. Buts, V.V. Ognivenko. Stochastic instability of
movement of particles in free electron lasers //
Letters to JETP . 1983, v. 38, issue 9, p. 434–436.
11. V.A. Buts, V.V. Kuzmin. Stochastic instability of
movement of particles in schemes of inverce free
electron lasers // Problems of Atomic Science and
Technology. 2006, N 5, p. 3-6.
12. V.A. Buts, V.V. Kuzmin. Acceleration of charged
particles by intense laser radiation // Progress of
modern radioelectronics. 2007, N 6, p. 68-75.
13. V.A. Buts. Chaotic dynamics of linear systems //
Electromagnetic waves and electron systems. 2006,
v. 11, № 11, p.65-70.
14. V.A. Buts. True quantum chaos. Problems of
Atomic Science and Technology. Series “Plasma
Physics” (14). 2008, N 6, p.120-122 (herein).
15. M. Tabor. Chaos and Integrability in Nonlinear
Dynamics. New York, 1988, p.318.
16. V.A. Buts, О.V. Manuilenko, K.N. Stepanov
А.P. Tolstoluzhskii. Chaotic dynamics of charged
particles at wave-particle type interaction and chaotic
dynamics of waves at a weak nonlinear wave-wave
type interaction // Plasma Physics. 1994, v.20, N 9,
p. 794-801.
17. 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, N 6, p. 1–10.
Article received 22.09.08.
СИЛЬНЫЕ ПОЛЯ. НЕКОТОРЫЕ ОСОБЕННОСТИ ДИНАМИКИ ЧАСТИЦ И ВОЛН
В.А. Буц
Кратко изложены некоторые наиболее важные результаты, полученные при исследовании взаимодействий
типа волна-частица и типа волна-волна.
СИЛЬНІ ПОЛЯ. ДЕЯКІ ОСОБЛИВОСТІ ДИНАМИКИ ЧАСТИНОК ТА ХВИЛЬ
В.О. Буц
Коротко викладені деякі найбільш важливі результаты, які були здобуті при дослідженні процесу взаємодії
типу хвиля-частинка та типу хвиля-хвиля.
128
|
| id | nasplib_isofts_kiev_ua-123456789-110793 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:17:20Z |
| publishDate | 2008 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Buts, V.A. 2017-01-06T12:54:22Z 2017-01-06T12:54:22Z 2008 Strong fields. Some features of dynamics of particles and waves / V.A. Buts // Вопросы атомной науки и техники. — 2008. — № 6. — С. 126-128. — Бібліогр.: 17назв. — англ. 1562-6016 PACS: 52.20.-j; 52.35.Ra; 52.35.Py https://nasplib.isofts.kiev.ua/handle/123456789/110793 Some most significant results, which were got at research of wave - particle type interaction and of wave - wave type interaction are briefly reported. Коротко викладені деякі найбільш важливі результаты, які були здобуті при дослідженні процесу взаємодії типу хвиля-частинка та типу хвиля-хвиля. Кратко изложены некоторые наиболее важные результаты, полученные при исследовании взаимодействий типа волна-частица и типа волна-волна. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma electronics Strong fields. Some features of dynamics of particles and waves Сильні поля. Деякі особливості динамики частинок та хвиль Сильные поля. Некоторые особенности динамики частиц и волн Article published earlier |
| spellingShingle | Strong fields. Some features of dynamics of particles and waves Buts, V.A. Plasma electronics |
| title | Strong fields. Some features of dynamics of particles and waves |
| title_alt | Сильні поля. Деякі особливості динамики частинок та хвиль Сильные поля. Некоторые особенности динамики частиц и волн |
| title_full | Strong fields. Some features of dynamics of particles and waves |
| title_fullStr | Strong fields. Some features of dynamics of particles and waves |
| title_full_unstemmed | Strong fields. Some features of dynamics of particles and waves |
| title_short | Strong fields. Some features of dynamics of particles and waves |
| title_sort | strong fields. some features of dynamics of particles and waves |
| topic | Plasma electronics |
| topic_facet | Plasma electronics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110793 |
| work_keys_str_mv | AT butsva strongfieldssomefeaturesofdynamicsofparticlesandwaves AT butsva silʹnípolâdeâkíosoblivostídinamikičastinoktahvilʹ AT butsva silʹnyepolânekotoryeosobennostidinamikičasticivoln |