Particle diffusion in a wave with randomly jumping phase
Microwave radiation with random phase jumps attracts attention because of its ability to penetrate into the overdense plasma. Along with this the wave with jumping phase is involved into the resonance interaction with more particles than a regular wave, and can be used to accelerate and heat them. T...
Збережено в:
| Дата: | 2015 |
|---|---|
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2015
|
| Назва видання: | Вопросы атомной науки и техники |
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/82089 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Particle diffusion in a wave with randomly jumping phase / V.I. Zasenko, А.G. Zagorodny, O.M. Chernyak // Вопросы атомной науки и техники. — 2015. — № 1. — С. 62-64. — Бібліогр.: 2 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-82089 |
|---|---|
| record_format |
dspace |
| spelling |
nasplib_isofts_kiev_ua-123456789-820892025-02-09T17:30:05Z Particle diffusion in a wave with randomly jumping phase Диффузия частиц в волне со случайно прыгающей фазой Дифузія частинoк у хвилі з випадковими стрибками фази Zasenko, V.I. Zagorodny, A.G. Chernyak, O.M. Фундаментальная физика плазмы Microwave radiation with random phase jumps attracts attention because of its ability to penetrate into the overdense plasma. Along with this the wave with jumping phase is involved into the resonance interaction with more particles than a regular wave, and can be used to accelerate and heat them. The evolution of statistical characteristics of particle ensemble in a wave is calculated numerically for two types of phase jumps, namely, when they are formed in the region of wave interaction with the particles, and when the wave with already generated phase jumps is launched into the interaction region. It is shown that the intensity of heating depends substantially on the type of phase jumps. Интерес к микроволновому излучению со случайными прыжками фазы обусловлен его способностью проникать в плазму с закритической плотностью. Кроме того, волна с прыжками фазы вступает в резонансное взаимодействие с бо́льшим количеством частиц, чем регулярная волна, и может быть использована для их ускорения и нагрева. Методом численного моделирования рассчитана эволюция статистических характеристик ансамбля частиц в поле волны для двух типов прыжков фазы, а именно: когда они образуются в области взаимодействия волны с частицами и когда волна с уже сгенерированными прыжками фазы вводится в область взаимодействия. Показано, что интенсивность нагрева частиц существенно зависит от типа прыжков фазы. Інтерес до мікрохвильового випромінення з випадковими стрибками фази обумовлений його здатністю проникати в плазму із закритичною густиною. Крім того, хвиля зі стрибками фази вступає в резонансну взаємодію з більшою кількістю частинок, ніж регулярна хвиля, і може застосовуватись для їхнього прискорення та нагрівання. Методом числового моделювання розраховано еволюцію статистичних характеристик ансамблю частинок у полі хвилі для двох типів стрибків фази, а саме: коли вони утворюються в області взаємодії хвилі з частинками і коли хвиля із вже згенерованими стрибками фази вводиться в область взаємодії. Показано, що інтенсивність нагрівання частинок істотно залежить від типу стрибків фази. This work is partly supported by the Program on Plasma Physics, Controlled Fusion and Plasma Technology of the National Academy of Sciences of Ukraine. 2015 Article Particle diffusion in a wave with randomly jumping phase / V.I. Zasenko, А.G. Zagorodny, O.M. Chernyak // Вопросы атомной науки и техники. — 2015. — № 1. — С. 62-64. — Бібліогр.: 2 назв. — англ. 1562-6016 PACS: 52.65.Cc https://nasplib.isofts.kiev.ua/handle/123456789/82089 en Вопросы атомной науки и техники application/pdf Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Фундаментальная физика плазмы Фундаментальная физика плазмы |
| spellingShingle |
Фундаментальная физика плазмы Фундаментальная физика плазмы Zasenko, V.I. Zagorodny, A.G. Chernyak, O.M. Particle diffusion in a wave with randomly jumping phase Вопросы атомной науки и техники |
| description |
Microwave radiation with random phase jumps attracts attention because of its ability to penetrate into the overdense plasma. Along with this the wave with jumping phase is involved into the resonance interaction with more particles than a regular wave, and can be used to accelerate and heat them. The evolution of statistical characteristics of particle ensemble in a wave is calculated numerically for two types of phase jumps, namely, when they are formed in the region of wave interaction with the particles, and when the wave with already generated phase jumps is launched into the interaction region. It is shown that the intensity of heating depends substantially on the type of phase jumps. |
| format |
Article |
| author |
Zasenko, V.I. Zagorodny, A.G. Chernyak, O.M. |
| author_facet |
Zasenko, V.I. Zagorodny, A.G. Chernyak, O.M. |
| author_sort |
Zasenko, V.I. |
| title |
Particle diffusion in a wave with randomly jumping phase |
| title_short |
Particle diffusion in a wave with randomly jumping phase |
| title_full |
Particle diffusion in a wave with randomly jumping phase |
| title_fullStr |
Particle diffusion in a wave with randomly jumping phase |
| title_full_unstemmed |
Particle diffusion in a wave with randomly jumping phase |
| title_sort |
particle diffusion in a wave with randomly jumping phase |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2015 |
| topic_facet |
Фундаментальная физика плазмы |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/82089 |
| citation_txt |
Particle diffusion in a wave with randomly jumping phase / V.I. Zasenko, А.G. Zagorodny, O.M. Chernyak // Вопросы атомной науки и техники. — 2015. — № 1. — С. 62-64. — Бібліогр.: 2 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT zasenkovi particlediffusioninawavewithrandomlyjumpingphase AT zagorodnyag particlediffusioninawavewithrandomlyjumpingphase AT chernyakom particlediffusioninawavewithrandomlyjumpingphase AT zasenkovi diffuziâčasticvvolnesoslučajnoprygaûŝejfazoj AT zagorodnyag diffuziâčasticvvolnesoslučajnoprygaûŝejfazoj AT chernyakom diffuziâčasticvvolnesoslučajnoprygaûŝejfazoj AT zasenkovi difuzíâčastinokuhvilízvipadkovimistribkamifazi AT zagorodnyag difuzíâčastinokuhvilízvipadkovimistribkamifazi AT chernyakom difuzíâčastinokuhvilízvipadkovimistribkamifazi |
| first_indexed |
2025-11-28T18:23:37Z |
| last_indexed |
2025-11-28T18:23:37Z |
| _version_ |
1850059494826967040 |
| fulltext |
BASIC PLASMA PHYSICS
ISSN 1562-6016. ВАНТ. 2015. №1(95)
62 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2015, № 1. Series: Plasma Physics (21), p. 62-64.
PARTICLE DIFFUSION IN A WAVE WITH RANDOMLY JUMPING
PHASE
V.I. Zasenko, А.G. Zagorodny, O.M. Chernyak
Bogolyubov Institute for Theoretical Physics, Kyiv, Ukraine
Microwave radiation with random phase jumps attracts attention because of its ability to penetrate into the
overdense plasma. Along with this the wave with jumping phase is involved into the resonance interaction with
more particles than a regular wave, and can be used to accelerate and heat them. The evolution of statistical
characteristics of particle ensemble in a wave is calculated numerically for two types of phase jumps, namely, when
they are formed in the region of wave interaction with the particles, and when the wave with already generated
phase jumps is launched into the interaction region. It is shown that the intensity of heating depends substantially on
the type of phase jumps.
PACS: 52.65.Cc
INTRODUCTION
Microwave radiation with phase jumps was observed
in experiments, and it is of considerable interest because
of the ability to penetrate overdense plasma. It can be
used to heat plasmas, in particular in discharges that are
considered as promising sources of light radiation of the
solar spectrum [1, 2]. On the other hand, sudden
changes of a wave phase may occur due to nonlinear
effects in plasma. They will influence the diffusion of
particles in coordinate and velocity space.
Direct numerical simulation is used to study the
behaviour of particles in a wave with random phase
jumps. Two types of jumps are considered. First, when
the phase jumps occur just in the plasma medium where
the wave interacts with the particles. Then the frequency
of jumps in a coordinate system moving with a particle
does not depend on its velocity (uniform phase jumps).
Second, when the wave with already jumping phase is
launched into the plasma. Then frequency of jumps in
the moving coordinate system decreases as particle
velocity approaches wave phase velocity (slowing phase
jumps) by analogy with the Doppler effect.
1. MODEL
We consider the motion of an ensemble of
noninteracting particles in a field of the wave
0 0cos( ( )),E t k x tω ϕ− + (1)
where Е is the amplitude of the wave, 0ω and 0k are
the frequency and the wave number, t and x are time and
coordinate, ( )tϕ is the phase of the wave, which varies
with time by random jumps. A unique set of random
phase jumps is prescribed to each particle from an
ensemble.
Two types of phase jumps are considered. First type
is characterized by constant probability p of a phase
jump in the end of each period. In simulation we take
р=0.2; the value of a phase jump is distributed with
equal probability within the interval (0, 2π).
Second type of phase jumps is characterized by
variable in time probability p(t). It decreases as particle
velocity averaged over fast oscillations ( )v t< >
approaches phase velocity of the wave ( )p t =
0 01 ( ( ) / )p k v t ω− < > .
2. RESULTS OF SIMULATION
The results of simulation are shown in Figs. 1-6.
Statistical characteristics of the ensemble of particles
undergoing a wave field with random phase jumps were
obtained from calculations of trajectories of
104 particles. In all plots length is normalized
to 0(2 / )kπ and time to 0(2 / )π ω . The magnitude of
the electric field in this calculation corresponds to the
amplitude of velocity oscillation of trapped particles
which makes 0.141 of the wave phase velocity. And for
the initial velocity of particles we took value 0.85. Note
that particles with such initial velocity are not trapped
by harmonic wave without phase variation, i.e. they
would be non-resonant for regular wave.
If a wave phase is jumping then particles come into
resonance interaction in a wider range of initial velocity.
Eventually their bounce averaged velocity tends to
phase velocity of a wave for both types of phase jumps.
Thus particles with an initial velocity less than the phase
velocity are accelerated, and for our initial condition
particle averaged velocity increases from 0.85 to 1. The
mechanism of this acceleration is similar to the
stochastic Fermi acceleration. Along with acceleration
stochastic heating of particles occurs, its measure is
velocity dispersion. Note, that the growth of dispersion
with time for the first type of phase jumps, which
probability remain constant, is significantly greater then
for the second type of phase jumps, which probability
drops in accordance with the Doppler effect.
Bounce averaged velocities of ten arbitrary particles
in a wave with phase jumps of the first and second types
are shown in Figs. 1, 2. If the frequency of phase jumps
is slowed down according to the Doppler effect (second
type of jumps, Fig. 2) then particles wandering occurs
mainly in a constricted region of phase space.
Consequently coordinate and velocity dispersion is less
than for the first type of jumps (see Fig. 1). Also for the
second type of jumps is noticeable a fraction of
particles, individual velocity of which tends to phase
velocity of the wave.
ISSN 1562-6016. ВАНТ. 2015. №1(95) 63
Such behaviour of individual particles corresponds to
spreading of the velocity distribution function shown in
Figs. 3, 4 for three instants in time equal to 200, 103 and
104 periods. In a wave with constant probability of
jumps the velocity distribution function is considerably
expanded (see Fig. 3) that means that intensive heating
process continues throughout the simulation time. In
contrast with that for the second type of phase jumps the
distribution function of particle velocity, after the initial
expansion, almost keeps its shape (see Fig. 4).
Fig. 1. Ten trajectories in velocity space for uniform
jumps of phase (first type of phase jumps)
Fig. 2. Ten trajectories in velocity space for slowing
jumps of phase (second type of phase jumps)
Fig. 3. Distribution function in velocity space for
uniform jumps of phase
In process of expansion of velocity distribution
function for both types of phase jumps more particles
leave the velocity interval of resonant interaction than
get into it from a non-resonant region.
.
Fig. 4. Distribution function in velocity space for
slowing jumps of phase
Fig. 5. Distribution function in coordinate space for
uniform jumps of phase
Fig. 6. Distribution function in coordinate space for
slowing jumps of phase (space scale is smaller in
compare with Fig. 5
The evolution of the particle distribution functions in
coordinate space is given in Figs. 5, 6, where its shape is
shown for three instants in time. Note that the spatial
scales on these two figures for two types of phase jumps
are very different. Spreading of the coordinate
distribution function for the first type of phase jumps
(see Fig. 5) are even more apparent than spreading of
the corresponding velocity distribution function (see
Fig. 3). In Fig. 6 we can see the peak of the coordinate
distribution function for the second type of phase jumps
at t = 100, it keeps the memory of the initial conditions,
when all the particles were at one point of the phase
space. It dissipates with time, however in overall this
distribution function retain its shape much better than its
counterpart given in Fig. 5.
64 ISSN 1562-6016. ВАНТ. 2015. №1(95)
CONCLUSIONS
Experimental observations show that intense wave in
a plasma is characterized by a certain irregularity, which
can be considered as random phase jumps. We drawn
attention to strong dependence of the resonant particles
behaviour on the way in which phase jumps occur. If
phase jumps are formed during the interaction of the
wave with particles, a probability of jumps in the
coordinate system moving with the particle does not
depend on its velocity. If the wave with phase jumps
was generated earlier and then was launched into the
interaction region, a probability of jumps in the moving
coordinate system depends on particle velocity.
Simulation shows that due to jumps of a wave phase
particles within a wider range of initial velocity, than it
would be for harmonic waves without phase variation,
are involved in the resonant interaction. In particular,
particles with an initial velocity less than the phase
velocity of the wave are accelerated. If the jumping
phases are formed during acceleration, frequency of
jumps in the coordinate system moving with the particle
does not depend on velocity. Because of this, expansion
of the particle distribution function in velocity and
coordinate space continues permanently, respectively
the dispersion of velocity is increased, and particles are
heated.
If particles interact with a wave whose phase change
is already formed they do not so much affected by
jumps of phase while their velocities approach to phase
velocity of the wave, and field for them looks similar to
the field of harmonic waves without phase jumps.
Consequently their acceleration is not accompanied by a
significant increase of dispersion.
ACKNOWLEDGEMENTS
This work is partly supported by the Program on
Plasma Physics, Controlled Fusion and Plasma
Technology of the National Academy of Sciences of
Ukraine.
REFERENCES
1. V.I. Karas’, V.D. Levchenko. Penetration of micro-
wave with a stochastic jumping phase into overdense
plasmas and electron collisionles heating by it //
Problems of Atomic Science and Technology. Series
“Plasma Electronics and New Acceleration Methods”.
2003, № 4(3), p. 133-136.
2. A.F. Alisov, A.M. Artamoshkin, et al. Low-press-ure
discharge induced by microwave radiation with a
stochastically jumping phase // Plasma Physics Reports.
2010, v. 36, № 8, p. 736-749.
Article received 22.10.2014
ДИФФУЗИЯ ЧАСТИЦ В ВОЛНЕ СО СЛУЧАЙНО ПРЫГАЮЩЕЙ ФАЗОЙ
В.И. Засенко, А.Г. Загородний, А.Н. Черняк
Интерес к микроволновому излучению со случайными прыжками фазы обусловлен его способностью
проникать в плазму с закритической плотностью. Кроме того, волна с прыжками фазы вступает в
резонансное взаимодействие с бо́льшим количеством частиц, чем регулярная волна, и может быть
использована для их ускорения и нагрева. Методом численного моделирования рассчитана эволюция
статистических характеристик ансамбля частиц в поле волны для двух типов прыжков фазы, а именно: когда
они образуются в области взаимодействия волны с частицами и когда волна с уже сгенерированными
прыжками фазы вводится в область взаимодействия. Показано, что интенсивность нагрева частиц
существенно зависит от типа прыжков фазы.
ДИФУЗІЯ ЧАСТИНOК У ХВИЛІ З ВИПАДКОВИМИ СТРИБКАМИ ФАЗИ
В.І. Засенко, А.Г. Загородній, О.М. Черняк
Інтерес до мікрохвильового випромінення з випадковими стрибками фази обумовлений його здатністю
проникати в плазму із закритичною густиною. Крім того, хвиля зі стрибками фази вступає в резонансну
взаємодію з більшою кількістю частинок, ніж регулярна хвиля, і може застосовуватись для їхнього
прискорення та нагрівання. Методом числового моделювання розраховано еволюцію статистичних
характеристик ансамблю частинок у полі хвилі для двох типів стрибків фази, а саме: коли вони утворюються
в області взаємодії хвилі з частинками і коли хвиля із вже згенерованими стрибками фази вводиться в
область взаємодії. Показано, що інтенсивність нагрівання частинок істотно залежить від типу стрибків фази.
|