Formation of electrons’ and ions’ flows in the background plasma at the initial stage of the beam-plasma instability
Formation of the flow of the background plasma electrons moving to the electron beam injector at the initial stage of the beam-plasma instability development in the region of maximum HF electric field intensity is demonstrated via 1D computer simulation. Effect is caused by the plasma density profil...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2012
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| Назва видання: | Вопросы атомной науки и техники |
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| Цитувати: | Formation of electrons’ and ions’ flows in the background plasma at the initial stage of the beam-plasma instability / D.M. Tanygina, I.O. Anisimov, S.M. Levitsky // Вопросы атомной науки и техники. — 2012. — № 6. — С. 149-151. — Бібліогр.: 9 назв. — англ. |
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irk-123456789-1092232016-11-22T03:03:44Z Formation of electrons’ and ions’ flows in the background plasma at the initial stage of the beam-plasma instability Tanygina, D.M. Anisimov, I.O. Levitsky, S.M. Плазменная электроника Formation of the flow of the background plasma electrons moving to the electron beam injector at the initial stage of the beam-plasma instability development in the region of maximum HF electric field intensity is demonstrated via 1D computer simulation. Effect is caused by the plasma density profile deformation due to the pressure of the inhomogeneous HF electric field. С помощью компьютерного моделирования показано, что на начальной стадии развития плазменно- пучковой неустойчивости в области, где достигается максимум интенсивности высокочастотного электрического поля, формируется поток электронов фоновой плазмы, направленный навстречу электронному пучку. Возникновение этого потока связано с начальным этапом деформации профиля концентрации плазмы под воздействием давления неоднородного ВЧ-электрического поля. Шляхом комп'ютерного моделювання показано, що на початковій стадії розвитку плазмово-пучкової нестійкості в області, де досягається максимум інтенсивності високочастотного електричного поля, формується потік електронів фонової плазми, спрямований назустріч електронному пучку. Виникнення цього потоку пов’язане із початковим етапом деформації профілю концентрації плазми під дією тиску неоднорідного ВЧ-електричного поля. 2012 Article Formation of electrons’ and ions’ flows in the background plasma at the initial stage of the beam-plasma instability / D.M. Tanygina, I.O. Anisimov, S.M. Levitsky // Вопросы атомной науки и техники. — 2012. — № 6. — С. 149-151. — Бібліогр.: 9 назв. — англ. 1562-6016 PACS: 52.35.Mj, 52.35.Mw, 52.65.Rr http://dspace.nbuv.gov.ua/handle/123456789/109223 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| topic |
Плазменная электроника Плазменная электроника |
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Плазменная электроника Плазменная электроника Tanygina, D.M. Anisimov, I.O. Levitsky, S.M. Formation of electrons’ and ions’ flows in the background plasma at the initial stage of the beam-plasma instability Вопросы атомной науки и техники |
| description |
Formation of the flow of the background plasma electrons moving to the electron beam injector at the initial stage of the beam-plasma instability development in the region of maximum HF electric field intensity is demonstrated via 1D computer simulation. Effect is caused by the plasma density profile deformation due to the pressure of the inhomogeneous HF electric field. |
| format |
Article |
| author |
Tanygina, D.M. Anisimov, I.O. Levitsky, S.M. |
| author_facet |
Tanygina, D.M. Anisimov, I.O. Levitsky, S.M. |
| author_sort |
Tanygina, D.M. |
| title |
Formation of electrons’ and ions’ flows in the background plasma at the initial stage of the beam-plasma instability |
| title_short |
Formation of electrons’ and ions’ flows in the background plasma at the initial stage of the beam-plasma instability |
| title_full |
Formation of electrons’ and ions’ flows in the background plasma at the initial stage of the beam-plasma instability |
| title_fullStr |
Formation of electrons’ and ions’ flows in the background plasma at the initial stage of the beam-plasma instability |
| title_full_unstemmed |
Formation of electrons’ and ions’ flows in the background plasma at the initial stage of the beam-plasma instability |
| title_sort |
formation of electrons’ and ions’ flows in the background plasma at the initial stage of the beam-plasma instability |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2012 |
| topic_facet |
Плазменная электроника |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/109223 |
| citation_txt |
Formation of electrons’ and ions’ flows in the background plasma at the initial stage of the beam-plasma instability / D.M. Tanygina, I.O. Anisimov, S.M. Levitsky // Вопросы атомной науки и техники. — 2012. — № 6. — С. 149-151. — Бібліогр.: 9 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2012. №6(82) 149
FORMATION OF ELECTRONS’ AND IONS’ FLOWS
IN THE BACKGROUND PLASMA AT THE INITIAL STAGE
OF THE BEAM-PLASMA INSTABILITY
D.M. Tanygina, I.O. Anisimov, S.M. Levitsky
Taras Shevchenko Kiev National University, Kiev, Ukraine
1E-mail: d.m.velykanets@gmail.com
Formation of the flow of the background plasma electrons moving to the electron beam injector at the initial
stage of the beam-plasma instability development in the region of maximum HF electric field intensity is
demonstrated via 1D computer simulation. Effect is caused by the plasma density profile deformation due to the
pressure of the inhomogeneous HF electric field.
PACS: 52.35.Mj, 52.35.Mw, 52.65.Rr
INTRODUCTION
Interaction of electron beams with plasma is an
important problem of plasma physics. Most analytical
studies of the beam-plasma instability paid the primary
attention to instability mechanisms at the linear stage of
the beam-plasma interaction [1]. Non-linear effects play
an essential role in the beam-plasma interaction [2, 3].
These effects mainly demonstrate themselves in the
electron beam [4]. Background plasma nonlinearities
were also studied. These nonlinearities were observed in
numerous experiments. Among the plasma
nonlinearities one can mention, for instance, modular
instability of the Langmuir waves, exited in plasma by
the electron beam, and the following deformation of
plasma density profile with the consequent collapse of
cavities [5]. Kinetic effects, which accompany the
development of beam-plasma instability, for instance,
plateau formation on beam-plasma systems’ distribution
function [6], were also studied. However, kinetic effects
in the background plasma, which take place during the
development of beam-plasma instability, are not entirely
studied till now.
Beam-plasma interaction can result to the formation
of plasma electrons’ flows. In [7] this effect was
observed when deformation of plasma density profile
started.
The aim of the present work is to study the
formation of the background plasma charged particles’
(both electrons and ions) flows at the initial stage of the
beam-plasma instability via computer simulation. We
consider the initial stage as the time period during
which the significant deformation of ions’ density
profile is not observed; in other words, redistribution of
plasma density doesn't lead to reverse influence on the
HF-field distribution in plasma.
1. MODEL DESCRIPTION
AND SIMULATION PARAMETERS
To study the formation of the plasma particles’
flows, 1D computer simulation using modified package
PDP1 [8] was carried out. In 1D space plasma was
located between two conductive walls. At the initial
time point injection of the monoenergetic electron beam
into plasma started from the left wall (injector) of the
simulation space, i.e. the initial-boundary problem was
solved. Beam electrons were absorbed by the right wall
(collector). Velocity distribution function of plasma
electrons was initially maxwellian. Simulation was
carried out for several beams’ current densities
(jb=1.5 mA/cm2, 2.4 mA/cm2, 5 mA/cm2, 10 mA/cm2)
for the beam velocity Vb=3⋅109 cm/s and three different
beams’ velocities (Vb=1⋅109 cm/s, 3⋅109 cm/s,
5⋅109 cm/s) for the current density 2.4 mA/cm2. Other
simulation parameters: plasma density – ne,i=2⋅109 cm–3
(corresponding electron plasma period – Tp=2,49 ns);
distance between injector and collector – L=50 cm;
thermal velocities of plasma electrons and ions –
VTe=2⋅108 cm/s and VTi=1⋅106 cm/s, respectively.
2. RESULTS AND DISCUSSION
We will discuss the simulation results for the beam
current density 2.4 mA/cm2 and velocity Vb=3⋅109 cm/s,
which are typical for the whole array of the data
obtained.
Fig. 1, a-b presents instantaneous space distributions
of plasma electrons’ and ions’ averaged velocities,
correspondingly, for the time point t=60Tp. These
distributions were obtained via averaging over plasma
period the velocities of particles located in the small
space interval Δх.
At the initial stage of the beam-plasma instability
plasma electrons are accelerated primarily in the
direction of injector. At the same time, plasma ions are
accelerated both to injector and to collector (see
Fig. 1,a-b).
Fig. 2 demonstrates space distributions of plasma
electrons’ averaged velocities, moving only to the right
(Fig. 2,a) and only to the left (see Fig. 2,b). Plasma
electrons’ averaged velocities distribution, presented on
Fig. 1,a, is the sum of the distributions presented on
Fig. 2.
To find out the cause of the plasma electrons’ flow
formation (see Fig. 1,a), we considered an instantaneous
space distribution of electric field, exited by the electron
beam, averaged over the plasma period, for the time
point t=60Tp (Fig. 3,a). This distribution corresponds to
the slow (in the time scale of plasma period) component
of averaged electric field. Area of the negative field is
located near the injector, while the positive field area
with the larger strength value is located near the
collector (see Fig. 3,a). Under the influence of negative
field, plasma electrons are accelerated to the collector,
then they appear in the area of larger positive field, and
finally they start to move to the beams’ injector.
150 ISSN 1562-6016. ВАНТ. 2012. №6(82)
Otherwise, negative field accelerates ions to the
injector, and positive field – to the collector. Thus,
electrons of the background plasma are accelerated to
the injector, while ions are accelerated both to injector,
and (primarily) to the collector. The proposed
mechanism of the electron flow formation is confirmed
by the quasi-stationary potential distribution (see
Fig. 3,b).
a b
Fig. 1. Instantaneous space distributions of plasma electrons (a) and ions (b) velocity, averaged over the plasma
period, for the time point t=60Tp
a b
Fig. 2. Instantaneous space distributions of plasma electrons moving only to the right (a) and only to the left (b),
for the time point t=60Tp
a b
Fig. 3. Instantaneous space distribution of the electric field averaged over the plasma period for the time point
t=60Tp (a); –instantaneous space distribution of averaged potential for the time point t=60Tp (b)
We can also mention that oscillations in this
potential well just correspond to plasma electrons’ flows
to the left and to the right, presented on Fig. 2,a-b.
The spatial distribution of the quasi-stationary
electric field allows to explain the formation of
particles’ flows in the background plasma (at least, at
the qualitative level). Thereby, the electron beam, which
is decelerated by the exited HF-electric field, indirectly
transfers its impulse exactly to plasma ions.The quasi-
stationary electric field formation is a result of plasma
electrical neutrality perturbation owing to the plasma
electrons’ extrusion from the area of intensive HF
electric field (ponderomotive force) [10]. Instantaneous
spatial distribution of HF electric fields’ intensity,
averaged over the plasma period, for the time point
t=60Tp is presented on Fig. 4,a. Present mechanism is a
first stage of background plasma striction nonlinearity
development under the influence of inhomogeneous HF
electric field, exited by the electron beam. At the next
stage quasi-stationary electric field results to
redistribution of the plasma ions’ density, so quasi-
neutrality perturbation is compensated. As it is clear
from Fig. 4,a, HF electric fields’ intensity gradient is
larger from the side of collector comparing to its’
gradient from the side of injector. Thus, the magnitude
of corresponding electric field has to be larger, which is
in good accordance with Fig. 4,a.
Fig. 4,b demonstrates an instantaneous spatial
distribution of the striction electric field intensity,
averaged over the plasma period, for the time point
t=60Tp. This field is related with the HF electric fields’
intensity gradient by the expression:
2
24
str
p
e dE E
dxm
=
ω
,
where 2p pTω = π is the electron plasma frequency,
2E is the HF electric field intensity, averaged over the
ISSN 1562-6016. ВАНТ. 2012. №6(82) 151
plasma period. Comparison of Figs. 3,a and 4,b
demonstrates that exactly the striction field makes the
main contribution to the quasi-stationary electric field.
So asymmetry of the HF field intensity distribution
results to the formation of the background plasma
electrons’ flow directed to the electron beam injector.
a b
Fig. 4. Instantaneous spatial distribution of HF electric fields’ intensity, averaged over plasma period for the time
point t=60Tp (а);– instantaneous spatial distribution of striction field, caused by the gradient of HF electric fields’
intensity for the time point t=60Tp (b)
CONCLUSIONS
1. At the initial stages of the beam-plasma instability
the flow of plasma electrons appears in the area of the
intensive HF electric field. This flow is formed as the
sum of two opposite flows, which appear due to the
plasma electrons’ oscillations in the potential well. The
result flow is directed to the beams’ injector (oppositely
to the direction of the beam motion). In the same region
the flows of plasma ions appear with both directions.
Moreover, the ions’ flow, directed along the electron
beams’ propagation direction, is more intensive.
2. The cause of plasma particles’ flows formation is
the quasi-stationary electric field, which change its’
direction in space. Area of the negative field is located
near the injector, while region of positive field is located
further from the injector, and its’ absolute value is
larger.
3. Calculation shows that the cause of quasi-
stationary electric field formation is plasma electrons’
extrusion from the region of intensive HF electric field.
Peculiarities of the quasi-stationary field space
distribution are defined by the distribution of HF field
intensity.
4. The results obtained are valid for the beams with
the transversal length that is large in the scale of the
inversed spatial increment of the beam-plasma
instability.
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Article received 20.09.12
ФОРМИРОВАНИЕ ПОТОКОВ ЭЛЕКТРОНОВ И ИОНОВ В ФОНОВОЙ ПЛАЗМЕ НА НАЧАЛЬНОЙ
СТАДИИ РАЗВИТИЯ ПУЧКОВО-ПЛАЗМЕННОЙ НЕУСТОЙЧИВОСТИ
Д.М. Таныгина, И.О. Анисимов, С.М. Левитский
С помощью компьютерного моделирования показано, что на начальной стадии развития плазменно-
пучковой неустойчивости в области, где достигается максимум интенсивности высокочастотного
электрического поля, формируется поток электронов фоновой плазмы, направленный навстречу
электронному пучку. Возникновение этого потока связано с начальным этапом деформации профиля
концентрации плазмы под воздействием давления неоднородного ВЧ-электрического поля.
ФОРМУВАННЯ ПОТОКІВ ЕЛЕКТРОНІВ ТА ІОНІВ У ФОНОВІЙ ПЛАЗМІ НА ПОЧАТКОВІЙ
СТАДІЇ РОЗВИТКУ ПУЧКОВО-ПЛАЗМОВОЇ НЕСТІЙКОСТІ
Д.М. Танигіна, І.О. Анісімов, С.М. Левитський
Шляхом комп'ютерного моделювання показано, що на початковій стадії розвитку плазмово-пучкової
нестійкості в області, де досягається максимум інтенсивності високочастотного електричного поля,
формується потік електронів фонової плазми, спрямований назустріч електронному пучку. Виникнення
цього потоку пов’язане із початковим етапом деформації профілю концентрації плазми під дією тиску
неоднорідного ВЧ-електричного поля.
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