Іgnition of the beam-plasma discharge in the initially neitral gas
Initial stage of the beam-plasma discharge was studied via computer simulation for 2D electrostatic model. Stripped non-relativistic electron beam was injected into initially non-ionized helium. At the first stage transversal expansion of the beam was observed caused by its space charge. At the sa...
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irk-123456789-1473602019-02-15T01:23:42Z Іgnition of the beam-plasma discharge in the initially neitral gas Dadyka, D.I. Anisimov, I.O. Плазменно-пучковый разряд, газовый разряд и плазмохимия Initial stage of the beam-plasma discharge was studied via computer simulation for 2D electrostatic model. Stripped non-relativistic electron beam was injected into initially non-ionized helium. At the first stage transversal expansion of the beam was observed caused by its space charge. At the same time helium ionization via electron impact took place. Later beam focusing has been developed due to the space charge of the ions. Development of the beam-plasma instability as well as the background plasma heating was observed at the last stage of the simulation. За допомогою комп'ютерного моделювання для двовимірної електростатичної моделі досліджена початкова стадія плазмово-пучкового розряду. Стрічкоподібний електронний пучок інжектувався в первісно нейтральний гелій. На першому етапі спостерігалося поперечне розбухання пучка, зумовлене його об'ємним зарядом. В той же час відбувалася іонізація гелію електронним ударом. Потім спостерігалося фокусування пучка завдяки об'ємному заряду іонів. На останній стадії моделювання розвивалася плазмово-пучкова нестійкість і відбувався розігрів фонової плазми. С помощью компьютерного моделирования для двухмерной электростатической модели исследована начальная стадия плазменно-пучкового разряда. Ленточный электронный пучок инжектировался в первоначально нейтральный гелий. На первом этапе наблюдалось поперечное разбухание пучка, обусловленное его объемным зарядом. В то же время происходила ионизация гелия электронным ударом. Затем наблюдалась фокусировка пучка благодаря объемному заряду ионов. На последней стадии моделирования развивалась плазменно-пучковая неустойчивость и происходил разогрев фоновой плазмы. 2018 Article Іgnition of the beam-plasma discharge in the initially neitral gas / D.I. Dadyka, I.O. Anisimov // Вопросы атомной науки и техники. — 2018. — № 4. — С. 204-207. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 52.35 Fp, 52.40 Mj, 52.65 Rr, 52.80 Tn http://dspace.nbuv.gov.ua/handle/123456789/147360 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Плазменно-пучковый разряд, газовый разряд и плазмохимия Плазменно-пучковый разряд, газовый разряд и плазмохимия |
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Плазменно-пучковый разряд, газовый разряд и плазмохимия Плазменно-пучковый разряд, газовый разряд и плазмохимия Dadyka, D.I. Anisimov, I.O. Іgnition of the beam-plasma discharge in the initially neitral gas Вопросы атомной науки и техники |
| description |
Initial stage of the beam-plasma discharge was studied via computer simulation for 2D electrostatic model.
Stripped non-relativistic electron beam was injected into initially non-ionized helium. At the first stage transversal
expansion of the beam was observed caused by its space charge. At the same time helium ionization via electron
impact took place. Later beam focusing has been developed due to the space charge of the ions. Development of the
beam-plasma instability as well as the background plasma heating was observed at the last stage of the simulation. |
| format |
Article |
| author |
Dadyka, D.I. Anisimov, I.O. |
| author_facet |
Dadyka, D.I. Anisimov, I.O. |
| author_sort |
Dadyka, D.I. |
| title |
Іgnition of the beam-plasma discharge in the initially neitral gas |
| title_short |
Іgnition of the beam-plasma discharge in the initially neitral gas |
| title_full |
Іgnition of the beam-plasma discharge in the initially neitral gas |
| title_fullStr |
Іgnition of the beam-plasma discharge in the initially neitral gas |
| title_full_unstemmed |
Іgnition of the beam-plasma discharge in the initially neitral gas |
| title_sort |
іgnition of the beam-plasma discharge in the initially neitral gas |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2018 |
| topic_facet |
Плазменно-пучковый разряд, газовый разряд и плазмохимия |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147360 |
| citation_txt |
Іgnition of the beam-plasma discharge in the initially neitral gas / D.I. Dadyka, I.O. Anisimov // Вопросы атомной науки и техники. — 2018. — № 4. — С. 204-207. — Бібліогр.: 8 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT dadykadi ígnitionofthebeamplasmadischargeintheinitiallyneitralgas AT anisimovio ígnitionofthebeamplasmadischargeintheinitiallyneitralgas |
| first_indexed |
2025-07-11T02:17:29Z |
| last_indexed |
2025-07-11T02:17:29Z |
| _version_ |
1837315405584007168 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2018. №4(116) 204
IGNITION OF THE BEAM-PLASMA DISCHARGE
IN THE INITIALLY NEITRAL GAS
D.I. Dadyka, I.O. Anisimov
Taras Shevchenko National University of Kyiv,
Faculty of Radio Physics, Electronics and Computer Systems, Kyiv, Ukraine
E-mail: d.dadyka@gmail.com
Initial stage of the beam-plasma discharge was studied via computer simulation for 2D electrostatic model.
Stripped non-relativistic electron beam was injected into initially non-ionized helium. At the first stage transversal
expansion of the beam was observed caused by its space charge. At the same time helium ionization via electron
impact took place. Later beam focusing has been developed due to the space charge of the ions. Development of the
beam-plasma instability as well as the background plasma heating was observed at the last stage of the simulation.
PACS: 52.35 Fp, 52.40 Mj, 52.65 Rr, 52.80 Tn
INTRODUCTION
Study of the beam-plasma discharge (BPD) is inter-
esting for construction of the powerful sources of dense
plasma, interpretation of results of an active experi-
ments in the ionosphere plasma, etc.
Mechanism of the BPD development is based on the
beam-plasma instability (BPI). BPI moves to the for-
mation of a high-frequency electromagnetic field that
accelerates electrons of the background plasma. Forced
oscillations of these electrons are destructed due to the
collisions with heavy particles (i.e. neutral atoms and
ions). Collisions lead to the heating of the electron gas.
Finally the heated electrons result to the intense ioniza-
tion of the neutral component, i.e. BPD ignition [1].
The leading role of BPI in the background plasma
heating was demonstrated in our previous modelling [2].
However, initially ionized medium with a relatively
high ionization level was considered, that corresponds
to the late stages of the BPD development. In this paper,
we attempted to investigate the development of BPD in
an initially non-ionized gas via computer simulation
using PIC method [3].
1. COMPUTER SIMULATION OF THE BPD
Analytic study of BPD in the real geometry is ex-
tremely complex, so computer simulation is often used,
including the large particles in cell methods [3]. All the
results outlined below are obtained by the original PLS
package [4]. Electrostatic non-relativistic model was
used. Elementary interactions (elastic collisions between
electrons and neutral molecules, excitation and ioniza-
tion of neutral molecules and dissociative recombina-
tion) were described using Monte Carlo method. The
coefficient of dissociative recombination for helium was
βd=2.3 cm3/s. The neutral gas was considered to be ho-
mogeneous and its density was constant in time.
2. PROPAGATION OF ELECTRON BEAM
IN THE VACUUM
First the motion of electron beam in a vacuum was
studied. It is well known that such motion is accompa-
nied by the formation of the space charge. Virtual cath-
ode appears for the beam current exceeding some criti-
cal value. It leads to the reflection of a part of the elec-
trons back to the injector and to the limitation of the
output current [5, 6].
Let us evaluate the critical current for a two-
dimensional model of motion of the stripped beam in a
rectangular volume bounded by conducting grounded
planes (Fig. 1). Beam moves along x-axis, y=0 is the
plane of symmetry.
Fig 1. Geometry of the considered model
Infinite longitudinal magnetic field is considered to
suppress the transversal motion of electrons.
Consider the electron beam as a uniform plane layer
of charge density ρ and width a. Then the potential dis-
tribution along plane y=0 can be found from the follow-
ing equations and boundary conditions:
(1)
Taking into account that , where is the beam
current density, and is the beam electrons` velocity,
from (1) one can obtain:
. (2)
Then equality of the initial kinetic energy of the
electrons and the maximal potential ener-
gy max and expressing the velocity via the
accelerating voltage move to the formula for the critical
current density:
. (3)
Inhomogeneous spatial distribution of electrons
should be taken into account for more accurate consid-
eration.
mailto:d.dadyka@gmail.com
ISSN 1562-6016. ВАНТ. 2018. №4(116) 205
For the model shown in Fig. 1, simulation was per-
formed, and the critical current was estimated. Fig. 2
shows the distributions of potential (a) and beam elec-
trons density (2). The critical current obtained from the
simulation was twice lower then analytical estimation. It
can be explained by a doubling of the initial beam elec-
trons` density in the centre of the beam (x=L/2). While
the beam current significantly exceeds the critical value,
the virtual cathode is formed near the injector. Reflec-
tion of the significant part of the electrons back to injec-
tor takes place. Reflection of electrons occurs from the
vicinity of the middle beam plane, where the maximum
of the potential is placed. So the cavity is formed in the
beam (see Fig. 2,c).
In the absence of the longitudinal magnetic field the
beam expansion due to electrostatic forces and its re-
flection from the space charge area take place (Fig. 3).
a
b
c
Fig. 2. Potential (a) and density (b) distributions along x direction at the middle plane of the beam for beam current
close to critical value (U = 5 kV, J = 300 A/m2, a = 2 cm) and beam electrons' spatial distribution (c)
for current that is significantly larger than critical value (Ua = 1 kV, J = 1 kA/m2, a = 2 cm, L=H=5 cm)
a b c
Fig. 3. Spatial distributions of the beam electrons’ density for the initial current density 102A/m2 (a), 3·102A/m2 (b)
and 103 A/m2 (с). Beam width a=2 cm, Ua =5 kV
3. PROPAGATION OF ELECTRON BEAM
IN THE GAS
The beam dynamics in the gas was studied by simu-
lation for system with parameters listed in Table. The
simulation results are shown on Figs. 4, 5.
Simulation parameters
Gas pressure р = 0.1 Torr
Gas temperature T = 0.025 eV
Beam width d = 1 cm
Camera length L = 25 cm
Camera height H = 25 cm
Beam acceleration voltage U = 5 kV
Beam current density J = 103 A/m2
Electron beam motion in a gas is accompanied by the
scattering of electrons due to the elastic collisions and gas
ionization. The electrons appeared due to the ionization
are accelerated (mainly in the transverse direction) by the
space charge field. Its potential is of the order of the ac-
celerating voltage for the overcritical beam current.
Beam electrons collide with neutral atoms resulting to
the formation of plasma with very high electrons tem-
perature (up to 1 keV) in the camera (see Fig. 5,g).
Over time, ions appeared due to the electron impact
ionization compensate the spatial charge of the beam. It
leads to beam focusing (see Fig. 4). At this moment, the
effective energy transfer from the beam to the plasma
electrons ceases and plasma electron temperature gradu-
ally decreases Fig. 4,b,e,g. At this stage, it is often pos-
sible to observe transverse waves along the beam that
violate the transverse symmetry of the system. The field
of such waves is not very ample and practically doesn't
heat up the background plasma.
At a later stage of the discharge, the density of plas-
ma formed by ionization becomes sufficient for the de-
velopment of an BPI.
For the development of BPI period of plasma oscil-
lations must be substantially less than transit time of the
beam electrons and the average time between electron-
neutrals collisions). The development of BPI forms an
effective mechanism for energy transfer from the beam
to the background plasma. Consequently, the tempera-
ture of the electrons grows again (see Fig. 5,i). This
effect gives rise to the increase of the ionization velocity
(vicinity of the point A, Fig. 6).
Note that temporal evolution of the electron beam
behaviour in the initially neutral gas described above
qualitatively agrees with the results of the laboratory
experiment [8].
ISSN 1562-6016. ВАНТ. 2018. №4(116) 206
a b c
d e f
Fig. 4. Spatial distributions of the beam electrons’ density (a, b, c) and ions’ density (d, e, f)
for time points t=7·10-10s (a, d), t=1.4·10-8 s (b, e) та t=2.8·10-8 s (c, f)
a b c
d e f
g h i
Fig. 5. Spatial distributions of electric potential (a, b, c), beam electrons` density (d, e, f)
and electron temperature of the background plasma (g, h, i) for time points t=2.56·10-8 s (a, d, g),
t=7.85·10-8 s (b, e, h) and t=2.67·10-7 s (a, d, g)
ISSN 1562-6016. ВАНТ. 2018. №4(116) 207
Fig. 6. Time course of the average ion density
Over time, the BPI development area shifts further
from the injector to the right wall of the camera, which
leads to the BPI suppression. The reason for this phe-
nomenon is likely to be the significant plasma density
gradient along the beam due to ionisation inhomogeneity.
It looks as if the BPD development can be accompanied
by quasiperiodic excitation and suppression of BPI.
CONCLUSIONS
Critical current for the beam motion in vacuum ob-
tained from the simulation is in a good agreement with
analytic estimation. It confirms the correctness of PLS
operation.
The initial stage of the electron beam motion in a
gas is accompanied by ionization of gas and beam fo-
cusing due to compensation of beam space charge by
ions fild. The virtual cathode disappears and beam cur-
rent that can flow in the system is much larger than the
critical current in vacuum.
The ionization of the neutral gas by an electron
beam leads to the gradual accumulation of plasma, that
starts to interact with the beam through the BPI devel-
opment.
In addition to the transverse beam density oscilla-
tions inherent to BPI longitudinal oscillations of the
beam are observed. They violate the system symmetry
with respect to the central plane.
The BPI development substantially enhances the
transfer of energy from electron beam to plasma. Elastic
electron-neutral collisions lead to significant back-
ground plasma heating and an increase of the velocity of
the gas ionization. At this stage, impact ionization by an
electron beam practically does not affect the overall
plasma density dynamics.
Significant gradient of the plasma density along the
beam affects the BPI development and can suppress the BPI.
REFERENCES
1. E.V. Mishin, Yu.Ya. Ruzhin, V.A. Telegin. Interac-
tion of Electron Fluxes with Ionospheric Plasma.
M.: “Edition of Hydromereorology”, 1989.
2. D.I. Dadyka, I.O. Anisimov. 2d simulation of the
initial stage of the beam-plasma discharge // Prob-
lems of Atomic Science and Technology. Series
“Plasma Physics”. 2015, № 1, p. 149-151.
3. C.K. Birdsall, A.B. Langdon. Plasma Physics via
Computer Simulation / McGraw-Hill book company.
1985. 5. D.I. D.
4. D.I. Dadyka, I.O. Anisimov. PLS: A new parallel
gpu accelerated package for plasma simulations //
Proc. Intern. Seminar Actual problems of plasma
physics, Kharkov, Jan. 16, 2018.
5. R. Miller. Introduction to physics of high-current
beams of charged particles. M.: “Mir”, 1984.
6. A.G. Lymar, L.A. Bondarenco, A.M. Yegorov. Nu-
merical investigation of the possibility of ions accel-
eration by virtual cathode // Problems of Atomic Sci-
ence and Technology. Series “Nuclear Physics In-
vestigations”. 2012, № 3, p. 155-158.
7. V.A. Tutyk. Study of the beam-plasma discharge
mode during the operation of electron gun using the
gas discharge // Problems of Atomic Science and
Technology. Series “Plasma Electronics and New
Methods of Acceleration”. 2008, № 4, p. 184-188.
8. V.P. Popovich, I.F Kharchenko, E.G. Shustin.
Beam-plasma discharge without magnetic field //
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p. 649-651.
Article received 02.07.2018
ЗАЖИГАНИЕ ПЛАЗМЕННО-ПУЧКОВОГО РАЗРЯДА В ИЗНАЧАЛЬНО НЕИОНИЗИРОВАННОМ ГАЗЕ
Д.И. Дадыка, И.А. Анисимов
С помощью компьютерного моделирования для двухмерной электростатической модели исследована
начальная стадия плазменно-пучкового разряда. Ленточный электронный пучок инжектировался в первона-
чально нейтральный гелий. На первом этапе наблюдалось поперечное разбухание пучка, обусловленное его
объемным зарядом. В то же время происходила ионизация гелия электронным ударом. Затем наблюдалась
фокусировка пучка благодаря объемному заряду ионов. На последней стадии моделирования развивалась
плазменно-пучковая неустойчивость и происходил разогрев фоновой плазмы.
ЗАПАЛЮВАННЯ ПЛАЗМОВО-ПУЧКОВОГО РОЗРЯДУ В ПОЧАТКОВО НЕІОНІЗОВАНОМУ ГАЗІ
Д.І. Дадика, І.О. Анісімов
За допомогою комп'ютерного моделювання для двовимірної електростатичної моделі досліджена почат-
кова стадія плазмово-пучкового розряду. Стрічкоподібний електронний пучок інжектувався в первісно ней-
тральний гелій. На першому етапі спостерігалося поперечне розбухання пучка, зумовлене його об'ємним
зарядом. В той же час відбувалася іонізація гелію електронним ударом. Потім спостерігалося фокусування
пучка завдяки об'ємному заряду іонів. На останній стадії моделювання розвивалася плазмово-пучкова не-
стійкість і відбувався розігрів фонової плазми.
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