Evolution of the modulated electron beam in the inhomogeneous plasma with linear density profile
Evolution of the density profile of the modulated electron beam moving through the plasma with linear density profile is studied via computer simulation. Increase of the beam current and decrease of its velocity results to the substantial inharmonicity of the beam density profile. The deformation of...
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| Zitieren: | Evolution of the modulated electron beam in the inhomogeneous plasma with linear density profile / I.O. Anisimov, O.I. Kelnyk, S.V. Soroka // Вопросы атомной науки и техники. — 2005. — № 1. — С. 125-127. — Бібліогр.: 7 назв. — англ. |
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Anisimov, I.O. Kelnyk, O.I. Soroka, S.V. 2015-03-22T10:30:53Z 2015-03-22T10:30:53Z 2005 Evolution of the modulated electron beam in the inhomogeneous plasma with linear density profile / I.O. Anisimov, O.I. Kelnyk, S.V. Soroka // Вопросы атомной науки и техники. — 2005. — № 1. — С. 125-127. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 52.35.Qz; 52.65.Rr https://nasplib.isofts.kiev.ua/handle/123456789/78893 Evolution of the density profile of the modulated electron beam moving through the plasma with linear density profile is studied via computer simulation. Increase of the beam current and decrease of its velocity results to the substantial inharmonicity of the beam density profile. The deformation of this profile depends on the beam velocity direction. В роботі досліджується еволюція профілю густини модульованого електронного пучка під час його руху крізь неоднорідну плазму з лінійним профілем. Показано, що зі збільшенням густини струму пучка та часу взаємодії пучка із плазмою профіль пучка стає істотно несинусоідальним. Також показано, що напрямок руху пучка впливає на характер деформації його початкового профілю. В работе исследуется эволюция профиля плотности модулированного электронного пучка во время его движения через неоднородную плазму с линейным профилем. Показано, что при увеличении плотности тока пучка и времени взаимодействия пучка с плазмой профиль пучка становится существенно несинусоидальным. Также показано, что направление движение пучка влияет на характер деформации его начального профиля. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma electronics Evolution of the modulated electron beam in the inhomogeneous plasma with linear density profile Еволюція модульованого електронного пучка в неоднорідній плазмі з лінійним профілем Эволюция модулированного электронного пучка в неоднородной плазме с линейным профилем Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Evolution of the modulated electron beam in the inhomogeneous plasma with linear density profile |
| spellingShingle |
Evolution of the modulated electron beam in the inhomogeneous plasma with linear density profile Anisimov, I.O. Kelnyk, O.I. Soroka, S.V. Plasma electronics |
| title_short |
Evolution of the modulated electron beam in the inhomogeneous plasma with linear density profile |
| title_full |
Evolution of the modulated electron beam in the inhomogeneous plasma with linear density profile |
| title_fullStr |
Evolution of the modulated electron beam in the inhomogeneous plasma with linear density profile |
| title_full_unstemmed |
Evolution of the modulated electron beam in the inhomogeneous plasma with linear density profile |
| title_sort |
evolution of the modulated electron beam in the inhomogeneous plasma with linear density profile |
| author |
Anisimov, I.O. Kelnyk, O.I. Soroka, S.V. |
| author_facet |
Anisimov, I.O. Kelnyk, O.I. Soroka, S.V. |
| topic |
Plasma electronics |
| topic_facet |
Plasma electronics |
| publishDate |
2005 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Еволюція модульованого електронного пучка в неоднорідній плазмі з лінійним профілем Эволюция модулированного электронного пучка в неоднородной плазме с линейным профилем |
| description |
Evolution of the density profile of the modulated electron beam moving through the plasma with linear density profile is studied via computer simulation. Increase of the beam current and decrease of its velocity results to the substantial inharmonicity of the beam density profile. The deformation of this profile depends on the beam velocity direction.
В роботі досліджується еволюція профілю густини модульованого електронного пучка під час його руху крізь неоднорідну плазму з лінійним профілем. Показано, що зі збільшенням густини струму пучка та часу взаємодії пучка із плазмою профіль пучка стає істотно несинусоідальним. Також показано, що напрямок руху пучка впливає на характер деформації його початкового профілю.
В работе исследуется эволюция профиля плотности модулированного электронного пучка во время его движения через неоднородную плазму с линейным профилем. Показано, что при увеличении плотности тока пучка и времени взаимодействия пучка с плазмой профиль пучка становится существенно несинусоидальным. Также показано, что направление движение пучка влияет на характер деформации его начального профиля.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/78893 |
| citation_txt |
Evolution of the modulated electron beam in the inhomogeneous plasma with linear density profile / I.O. Anisimov, O.I. Kelnyk, S.V. Soroka // Вопросы атомной науки и техники. — 2005. — № 1. — С. 125-127. — Бібліогр.: 7 назв. — англ. |
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2025-11-26T00:08:09Z |
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2025-11-26T00:08:09Z |
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| fulltext |
EVOLUTION OF THE MODULATED ELECTRON BEAM IN THE
INHOMOGENEOUS PLASMA WITH LINEAR DENSITY PROFILE
I.O. Anisimov, O.I. Kelnyk, S.V. Soroka
Taras Shevchenko National University of Kyiv, Radio Physics Faculty, 64 Volodymyrs’ka St.,
01033, Kyiv, Ukraine, soroka@univ.kiev.ua
Evolution of the density profile of the modulated electron beam moving through the plasma with linear density
profile is studied via computer simulation. Increase of the beam current and decrease of its velocity results to the
substantial inharmonicity of the beam density profile. The deformation of this profile depends on the beam velocity
direction.
PACS: 52.35.Qz; 52.65.Rr
1. INTRODUCTION
Transformation of the beam modes into the Langmuir
waves takes place mainly in the local plasma resonance
region (LPRR) of the inhomogeneous plasma [1-3].
Maximum of electric field amplitude excited by the
modulated electron beam is also localized in LPRR. This
maximum results to the deformation of the plasma density
profile (see, e.g., [4]). Analytic calculations [1-3] were
carried out for harmonic current of the beam. But during
the beam motion through plasma beam-plasma instability
occurs. It results to the density and velocity modulation of
the beam. In the nonlinear stage of the beam-plasma
instability the overtaking of the particles occur, and the
alternative current of the beam becomes substantially
inharmonic [5].
In the beam-plasma amplifiers the input and output
signals must have the same frequency. The nonlinear
stage of the beam-plasma instability results to the
appearance of higher harmonics in the output signal. This
effect is undesirable.
The problem of the beam-plasma instability evolution
in the inhomogeneous plasma was previously discussed in
[6-7]. In this work evolution of the density modulated
electron beam moving in the inhomogeneous plasma is
studied. The conditions of harmonicity of the beam
current in the LPRR are found.
Computer simulation using the modified package
PDP1 [8] was carried out. In this package plasma forms
the plane layer between two electrodes. Stationary plasma
density changed linearly from 1⋅1014m-3 near the left
electrode to 3⋅1014m-3 near the right electrode. LPRR was
in the middle of the simulation region. The cases of beam
injection from left and right electrode were treated.
2. THE BEAM MOVING INTO DENSE
PLASMA
Spatial dependencies of the beam electrons’ density
and velocity as well as the beam current spectrum in
LPRR are plotted on Fig.1 for V=7⋅107m/s, jm=1A/m2.
The beam density profile remains quasi-harmonic in the
whole simulation region, but the alternative current
amplitude decreases slowly. The amplitude of the second
harmonic is about 5% from the amplitude of the first one
(Fig.1c). Velocity modulation appears in the initially
monokinetic beam. The bunches with higher density have
smaller velocities (Fig.1b). It results to the steepening of
the trailing front of the bunch.
These effects can be simply interpreted qualitatively.
The beam moves initially in the subcritical plasma, where
ε>0, so the electrons in the bunch repulse one another. It
results to the bunch swelling and decrease of the density
in its center.
a
b
c
Fig.1. Profile of the beam electron density (a), its
phase trajectory (b) and beam current spectrum in
LPRR (c) for V=7⋅107m/s, jm=1A/m2
Fig.2 demonstrates the simulation results for V=7⋅
107m/s, j=5A/m2. The beam electrons’ density profile near
LPRR (z=1m) becomes substantially inharmonic for this
case. All the processes described above also take place.
But for the forth bunch the wave in the phase space has
almost overturned (Fig.2b). It results to the increase of its
amplitude and significant profile deformation (Fig.1a).
Problems of Atomic Science and Technology. 2005. № 1. Series: Plasma Physics (10). P. 125-127 125
Harmonics up to the forth one appear in the spectrum
(Fig.2c).
a
b
c
Fig.2. Profile of the beam electron density (a), its
phase trajectory (b) and beam current spectrum in
LPRR (c) for V=7⋅107m/s, jm=5A/m2
a
b
c
Fig.3. Profile of the beam electron density (a), its
phase trajectory (b) and beam current spectrum in
LPRR (c) for V=3⋅107m/s, jm=3A/m2
Simulation results for V=3⋅107m/s, j=3A/m2 are
plotted on Fig.3. Here the time of the beam-plasma
interaction is increased. Consequently the particles’
overtaking (Fig.3b) and bunch front overturn occurred
before the beam reached LPRR. Due to the overturn the
beam density profile has a form of separate narrow peaks
of the large magnitude (Fig.3a). The harmonics of the
downshifted frequency appear in the spectrum
additionally to the higher harmonics of the modulation
frequency (Fig.3c). The spectral lines are widened, and
the spectrum becomes continuos.
3. THE BEAM MOVING INTO LOW-DENSITY
PLASMA
Spatial dependencies of the beam density and velocity
as well as beam current spectrum in LPRR for V=7⋅
107m/s, j=1A/m2 are given on Fig.4. The processes that
take place are similar to the described above. But now the
beam electron bunches’ density increases gradually, and
bunches converge. During the beam motion the velocity
modulation density initially increases, and somewhat
decreases near the right electrode (Fig.4b). Now the beam
initially moves in the supercritical plasma (ε<0), so the
electrons in the bunch attract to one another. The
forefront of the beam is decelerated, and the trailing front
is accelerated (Fig.4b). When the beam gets the
subcritical plasma, electrons start repulsing, and the
velocity modulation depth decreases. The second
harmonic with the small magnitude appears in the beam
spectrum (Fig.4c). The beam profile remains quasi-
harmonic.
a
b
c
Fig.4. Profile of the beam electron density (a), its
phase trajectory (b) and beam current spectrum in
126
LPRR (c) for V=7⋅107m/s, jm=1A/m2
For V=7⋅107m/s, j=5A/m2 the beam density profile
near LPRR becomes substantially inharmonic (Fig.5a).
The second, third and forth harmonics appear in the
spectrum (Fig.5c). Magnitude of the second harmonic is
about 30% of the magnitude of the first one. The
overtaking of the wave front in the phase space takes
place for the lust bunch (Fig.5a). It results to the strong
increase of the bunch magnitude and deformation of its
profile (Fig.5c).
a
b
c
Fig.5. Profile of the beam electron density (a), its phase
trajectory (b) and beam current spectrum in LPRR (c) for
V=1⋅107m/s, jm=5A/m2
4. CONCLUSIONS
1. Higher harmonics of the significant magnitude
appear in the spectrum of the modulated electron beam
current when the current density is increased or the beam
velocity is decreased.
2. The beam density profile in the LPRR depends
substantially from the beam velocity direction. When the
beam initially moves in the subcritical plasma, bunches
are widened. If it moves initially in the supercritical
plasma, bunches converge.
5. REFERENCES
1. N.S.Erokhin, S.S.Moiseev. Transformation of waves
in inhomogeneous unstable plasma // ZhETF. (65).
1973, №4, p.1431-1447. (In Russian)
2. K.P.Shamrai. Transformation and amplification of
waves in a non-uniform plasma involving
monoenergetic electron beam // J. Plasma Phys. (31).
1984, №2, p.301-311.
3. I.O.Anisimov, O.A.Borisov. Electrical field
excitation in non-uniform plasma by the modulated
electron beam // Physica Scripta (62). 2000, №5,
p.375-380.
4. A.N.Kondratenko. On the possibility to control
beam-plasma instability on the emission stage of this
evolution // UPhZh. (26). 1981, № 4, p. 678-680 (In
Russian).
5. E.V.Mishin, Yu.Ya.Ruzhin. V.A.Telegin. Interaction
electron stream with ionosphere plasma. Moscow:
“Gidrometeoizdat”, 1989. (In Russian).
6. K.Yu.Blioh, On the influence of the plasma
inhomogeneity upon the beam instability
development // Radio physics & radio astronomy (3).
1998. №1, p.49-60. (In Russian)
7. I.O.Anisimov, D.V.Sasyuk, T.V.Siversky. Modified
package PDP1 for beam-plasma systems’ simulation
// Dynamical System Modelling and Stability
Investigation. Thesis of Conf. Reports. Kyiv, 2003,
p.257.
ЭВОЛЮЦИЯ МОДУЛИРОВАННОГО ЭЛЕКТРОННОГО ПУЧКА В
НЕОДНОРОДНОЙ ПЛАЗМЕ С ЛИНЕЙНЫМ ПРОФИЛЕМ
И.А. Анисимов, О.І. Мельник, С.В. Сорока
В работе исследуется эволюция профиля плотности модулированного электронного пучка во время его
движения через неоднородную плазму с линейным профилем. Показано, что при увеличении плотности тока
пучка и времени взаимодействия пучка с плазмой профиль пучка становится существенно несинусоидальным.
Также показано, что направление движение пучка влияет на характер деформации его начального профиля.
ЕВОЛЮЦІЯ МОДУЛЬОВАНОГО ЕЛЕКТРОННОГО ПУЧКА В НЕОДНОРІДНІЙ
ПЛАЗМІ З ЛІНІЙНИМ ПРОФІЛЕМ
І.О. Анісімов, О.І. Kельник, С.В. Сорока
В роботі досліджується еволюція профілю густини модульованого електронного пучка під час його руху
крізь неоднорідну плазму з лінійним профілем. Показано, що зі збільшенням густини струму пучка та часу
взаємодії пучка із плазмою профіль пучка стає істотно несинусоідальним. Також показано, що напрямок руху
пучка впливає на характер деформації його початкового профілю.
127
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