Dynamics of the modulated electron beam in the inhomogeneous plasma barrier: kinetic effects
Evolution of the modulated electron beam moving through the inhomogeneous plasma barrier with parameters corresponding to experimental conditions [1-2] is studied via computer simulation using PIC method. Electrons’ energy distribution function of the initially density modulated electron beam moving...
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| Zitieren: | Dynamics of the modulated electron beam in the inhomogeneous plasma barrier: kinetic effects / I.O. Anisimov, M.J. Soloviova // Вопросы атомной науки и техники. — 2008. — № 6. — С. 129-131. — Бібліогр.: 11 назв. — англ. |
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Anisimov, I.O. Soloviova, M.J. 2017-01-06T11:47:12Z 2017-01-06T11:47:12Z 2008 Dynamics of the modulated electron beam in the inhomogeneous plasma barrier: kinetic effects / I.O. Anisimov, M.J. Soloviova // Вопросы атомной науки и техники. — 2008. — № 6. — С. 129-131. — Бібліогр.: 11 назв. — англ. 1562-6016 PACS: 52.35.-g, 52.65.Rr, 52.35.Mw https://nasplib.isofts.kiev.ua/handle/123456789/110771 Evolution of the modulated electron beam moving through the inhomogeneous plasma barrier with parameters corresponding to experimental conditions [1-2] is studied via computer simulation using PIC method. Electrons’ energy distribution function of the initially density modulated electron beam moving through the barrier with Gaussian plasma density profile is studied. Initial-boundary problem is solved, and results obtained are compared with results of experiments and previous simulations. Досліджено еволюцію модульованого електронного пучка в плазмовому бар’єрі шляхом комп’ютерного моделювання методом крупних частинок. Розглядається неоднорідний плазмовий бар’єр, що відповідає умовам лабораторного експерименту. Вивчається функція розподілу електронів пучка за швидкостями. Отримані результати розв’язку початково-гранично задачі порівнюються з результатами експериментів та висновками попередніх моделювань. Исследуется эволюция модулированного электронного пучка в плазменном барьере с помощью компьютерного моделирования методом крупных частиц. Рассматривается неоднородный плазменный барьер, соответствующий условиям лабораторного эксперимента. Изучается функция распределения электронов пучка по скоростям. Полученные результаты решения начально-граничной задачи сравниваются с результатами экспериментов и выводами предыдущих моделирований. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma electronics Dynamics of the modulated electron beam in the inhomogeneous plasma barrier: kinetic effects Динаміка модульованого електронного пучка в неоднорідному плазмовому бар’єрі: кінетичні ефекти Динамика модулированного электронного пучка в неоднородном плазменном барьере: кинетические эффекты Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Dynamics of the modulated electron beam in the inhomogeneous plasma barrier: kinetic effects |
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Dynamics of the modulated electron beam in the inhomogeneous plasma barrier: kinetic effects Anisimov, I.O. Soloviova, M.J. Plasma electronics |
| title_short |
Dynamics of the modulated electron beam in the inhomogeneous plasma barrier: kinetic effects |
| title_full |
Dynamics of the modulated electron beam in the inhomogeneous plasma barrier: kinetic effects |
| title_fullStr |
Dynamics of the modulated electron beam in the inhomogeneous plasma barrier: kinetic effects |
| title_full_unstemmed |
Dynamics of the modulated electron beam in the inhomogeneous plasma barrier: kinetic effects |
| title_sort |
dynamics of the modulated electron beam in the inhomogeneous plasma barrier: kinetic effects |
| author |
Anisimov, I.O. Soloviova, M.J. |
| author_facet |
Anisimov, I.O. Soloviova, M.J. |
| topic |
Plasma electronics |
| topic_facet |
Plasma electronics |
| publishDate |
2008 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Динаміка модульованого електронного пучка в неоднорідному плазмовому бар’єрі: кінетичні ефекти Динамика модулированного электронного пучка в неоднородном плазменном барьере: кинетические эффекты |
| description |
Evolution of the modulated electron beam moving through the inhomogeneous plasma barrier with parameters corresponding to experimental conditions [1-2] is studied via computer simulation using PIC method. Electrons’ energy distribution function of the initially density modulated electron beam moving through the barrier with Gaussian plasma density profile is studied. Initial-boundary problem is solved, and results obtained are compared with results of experiments and previous simulations.
Досліджено еволюцію модульованого електронного пучка в плазмовому бар’єрі шляхом комп’ютерного моделювання методом крупних частинок. Розглядається неоднорідний плазмовий бар’єр, що відповідає умовам лабораторного експерименту. Вивчається функція розподілу електронів пучка за швидкостями. Отримані результати розв’язку початково-гранично задачі порівнюються з результатами експериментів та висновками попередніх моделювань.
Исследуется эволюция модулированного электронного пучка в плазменном барьере с помощью компьютерного моделирования методом крупных частиц. Рассматривается неоднородный плазменный барьер, соответствующий условиям лабораторного эксперимента. Изучается функция распределения электронов пучка по скоростям. Полученные результаты решения начально-граничной задачи сравниваются с результатами экспериментов и выводами предыдущих моделирований.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/110771 |
| citation_txt |
Dynamics of the modulated electron beam in the inhomogeneous plasma barrier: kinetic effects / I.O. Anisimov, M.J. Soloviova // Вопросы атомной науки и техники. — 2008. — № 6. — С. 129-131. — Бібліогр.: 11 назв. — англ. |
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2025-11-26T16:26:47Z |
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| fulltext |
DYNAMICS OF THE MODULATED ELECTRON BEAM
IN THE INHOMOGENEOUS PLASMA BARRIER:
KINETIC EFFECTS
I.O. Anisimov, M.J. Soloviova
Taras Shevchenko National University of Kyiv, Radio Physics Faculty,
64 Volodymyrs'ka St., 01033, Kyiv, Ukraine,
E-mail: ioa@univ.kiev.ua
Evolution of the modulated electron beam moving through the inhomogeneous plasma barrier with parameters
corresponding to experimental conditions [1-2] is studied via computer simulation using PIC method. Electrons’ energy
distribution function of the initially density modulated electron beam moving through the barrier with Gaussian plasma
density profile is studied. Initial-boundary problem is solved, and results obtained are compared with results of
experiments and previous simulations.
PACS: 52.35.-g, 52.65.Rr, 52.35.Mw
1. INTRODUCTION
Study of dynamics of electron beam in plasma was
started as far back as 1930-th by Langmuir. The last
works devoted to this problem use computer simulation
[3-4] as well as laboratory experiments [5]. But in the
most cases only non-modulated beams were treated.
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2008. № 6. 129
Series: Plasma Physics (14), p. 129-131.
Evolution of the modulated electron beam in super-
critical plasma barrier was studied experimentally in
[1-2]. In our previous works [6-9] evolution of the
modulated electron beam in plasma for the initial-
boundary problem was investigated via computer
simulation using PIC method. But homogeneous plasma
barrier in [6-8] doesn’t correspond to the experimental
one that is close to Gaussian shape [1-2]. The first
simulation results for such barriers were presented in [9].
In this paper electrons’ energy distribution function of the
initially density modulated electron beam moving through
the barrier with Gaussian plasma density profile is
studied. Initial-boundary problem is solved, and results
obtained are compared with results of experiments and
previous simulations.
2. MODEL DESCRIPTION,
SIMULATION METHOD AND PARAMETERS
Warm isotropic collisionless plasma with initial Gaus-
sian density profile is studied. Simulation is carried out
via particle-in-cell method using modified program pack-
age PDP1 [10].
1D region between two electrodes is simulated.
Interelectrode space is filled with fully ionized hydrogen
plasma. Initial plasma density profile is obtained by the
approximation of experimental axial plasma density
profile [1-2] by Gaussian function. So initial electron and
ion plasma density is set as
2
0
0( ) exp
2m
x xn x n n
⎡ ⎤−⎛ ⎞= + −⎢ ⎥⎜ ⎟Δ⎝ ⎠⎢ ⎥⎣ ⎦
, (1)
where n0 is the plasma density for x→∞, n0 + nm is the
peak plasma density inside the barrier at x=x0, and Δ is
half-width of the plasma density profile. Simulation
parameters are presented in the Table.
Electron beam is injected into plasma barrier from the
left electrode. It moves to the right one. Electrodes absorb
both plasma and beam particles. Initially electron beam is
density-modulated:
0( ) (1 cos )t m tρ = ρ + ω , (2)
where m is the modulation depth.
Modulation frequency was selected in the range
ωp(n0)<ω<ωp(n0+nm), where ωp(n) is electron plasma
frequency corresponding to the plasma density n. Two
local plasma resonance regions are located inside the
barrier at the modulation frequency.
The simulation was carried out during the time
interval of approximately 200 electron plasma periods or
5 ion plasma periods. During this time electron beam
reached the opposite electrode, and quasi-stationary
regime was settled.
Simulation parameters
n0 5.5·1010 cm-3
nm 2.04·1011 cm-3
x0 10 cm
Δ 3.87 cm
Simulation region length 20 cm
Plasma electrons' thermal velocity 6⋅107 cm/s
Plasma ions' thermal velocity 2,33⋅106 cm/s
Beam electrons velocity 2⋅109 cm/s
Electron beam modulation
frequency 2.77 GHz
Electron beam modulation depth 0.01 – 0.3 with
the step 0.01
Simulation time step 10-13 s
a
b
c
d e
f
Fig. 1 Velocity distribution functions of beam electrons for weak-modulated (m=0.05 – a, b, c) and strong-modulated
(m=0.28 – d, e, f) electron beam at the time points: t=10 -8s (a, d), t=2·10 -8s (b, e), t=4·10 -8s (c, f)
3. SIMULATION RESULTS
Fig. 1 presents velocity distribution functions of beam
electrons for weakly modulated (m=0.05) and strongly
modulated (m=0.28) electron beam for various time
moments. In x-v plane these figures present phase
portraits of the electron beam. For the first time points
these distribution functions are similar to sinusoids. In
comparison with the case of homogeneous barrier [7]
these sinusoids are more smeared. This fact can be
explained by excitation of quazi-continuous spectrum at
the frequencies ωp(z) in the electron beam during it’s
propagation inside the barrier.
3.1 SMALL INITIAL MODULATION
DEPTH OF THE BEAM
All dependencies discussed in this section correspond to
the initial modulation depth m=0.05. The width of the beam
electrons’ velocity distribution function slightly decreases at
the late stage of the simulation in comparison with the case of
non-modulated beam. Two time intervals with characteristic
behavior of the velocity distribution function can be marked
out from Fig. 1,a-c: (i) t = 9−30 ns - one can see gradual beam
electrons’ velocity smearing in the direction of energy
decrease in the space region of plasma density recession; (ii)
t = 35−45 ns - beam electrons’ velocity spread decreases. This
fact can be connected with electric field strength reduction
caused by deformation of the ion density profile (Fig. 2). This
deformation is characterized by strong irregularity. This effect
can be explained by l-s decay of the resonant mode that results
in ion-acoustic waves’ excitation [6-8].
3.2 LARGE INITIAL MODULATION
DEPTH OF THE BEAM
130
All dependencies discussed in this section correspond
to the initial modulation depth m=0.28. Deep initial beam
modulation leads to the noticeable suppressing of the
resonant instability development [11] just as in the case of
homogeneous barriers [7]. This effect is connected with
beam electrons’ trapping by non-resonant mode (at the
modulation frequency) [6-8].
Fig. 2 Deformation of the ion concentration profile for
initial modulation depth m=0.05
For the case of large initial beam modulation depths
behavior of the velocity distribution function differs from
one described in section 3.1 (Fig. 1, d-f).
In the time interval t = 9−30 ns beam electrons’
velocity smearing is noticeably smaller than for small
initial modulation. Simultaneously in the region of plasma
density decrease electric field strength amplitude is twice
131
Electrons’ ene of the initially
de
plasma
ime points spread of the beam
el
no a
CES
1. I.A. Anisimov, O.V. Opanasenko,
. Kotlyarov, S.M. Levitsky,
olar
ko. Dynamics and
allaqua,
of the
. Soroka,
Inter dula
e
, M.J. Soloviova. Dynamics of the
.
y
Article received 22.09.08.
smaller than for small modulation. Accordingly non-
linear plasma density deformation decreases noticeably.
As a result in the time interval t = 35−45 ns beam
electrons’ velocity distribution function spreads distinctly
more than for small initial modulation depth. But even in
this case at the time point t = 50 ns width of the beam
electrons’ velocity distribution function decreases in
comparison with previous time moments. As in previous
case this result can be connected with the non-linear
deformation of the plasma density profile.
4. CONCLUSIONS
rgy distribution function
nsity modulated electron beam moving through the
barrier with Gaussian plasma density profile was studied.
1. Effect of the suppression of the resonant beam-
instability by the deep initial beam modulation
takes place as in the case of homogeneous barrier. This
leads to smaller spreading of beam electrons’ velocity
distribution function.
2. At the late t
ectrons’ velocity distribution function decreases due to
the deformation of the plasma density profile. This
deformation can be explained by ion-acoustic waves
excitation caused by l-s decay of the resonant mode [6-8].
3. Deformation of the plasma density profile is more
tice ble in the case of small initial modulation depth
and becomes more valuable in the region of plasma
density decrease where resonant mode’s electric field
strength increases distinctly [9].
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S.M. Levitsky,
L.I. Romanyuk. Experimental observation of the plasma
wave barrier transillumination via electron beam // JTPh.
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2. I.O. Anisimov, I.Yu
O.V. Opanasenko, D.B. Palets, L.I. Romanyuk. The
investigation of the transillumination of the plasma
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D.M. Karfidov. Measurements of beam relaxation length
in an electron beam plasma experiment // Brasilian
Journal of Physics. 1997, v. 27, N 4, p. 481-487.
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D.M. Velykanets’. action of the mo ted electron
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beam-plasma turbulence // Ukr. Fiz. Zhurn. 2008, v. 53.
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modulated electron beam in the inhomogeneous plasma
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mputer Simulation. “McGraw-Hill Book Company”. 1985.
11. A.K. Berezin, Ya.B. Fainberg, I.A. Bezjazichniy
Experimental stud of the possibility to control beam
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ДИНАМИКА МОДУЛИРОВАННОГО ЭЛЕКТРОННОГО ПУЧКА
В НЕОДНОРОДНОМ ПЛАЗМЕННОМ БАРЬЕРЕ: КИНЕТИЧЕСКИЕ ЭФФЕКТЫ
И.А. Анисимов, М.И. Соловьёва
Исследуется эволюция модулированного электронного пучка в плазменном барьере с помощью
компьютерного моделирования методом крупных частиц. Рассматривается неоднородный плазменный барьер,
соответствующий условиям лабораторного эксперимента. Изучается функция распределения электронов пучка
по скоростям. Полученные результаты решения начально-граничной задачи сравниваются с результатами
экспериментов и выводами предыдущих моделирований.
ДИНАМІКА МОДУЛЬОВАНОГО ЕЛЕКТРОННОГО ПУЧКА
В НЕОДНОРІДНОМУ ПЛАЗМОВОМУ БАР’ЄРІ: КІНЕТИЧНІ ЕФЕКТИ
І.О. Анісімов, М.Й. Соловйова
Досліджено еволюцію модульованого електронного пучка в плазмовому бар’єрі шляхом комп’ютерного
моделювання методом крупних частинок. Розглядається неоднорідний плазмовий бар’єр, що відповідає умовам
лабораторного експерименту. Вивчається функція розподілу електронів пучка за швидкостями. Отримані
результати розв’язку початково-гранично задачі порівнюються з результатами експериментів та висновками
попередніх моделювань.
http://www.sciencedirect.com/science/journal/02731177
http://www.sciencedirect.com/science/journal/02731177
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