Interaction of the modulated electron beam with plasma: kinetic effects
Evolution of the velocity distribution functions of plasma and beam electrons during modulated electron beam propagation in homogeneous and inhomogeneous plasma was studied numerically. Velocity distribution function of plasma electrons at the late time moments strongly differs from initially Maxwel...
Gespeichert in:
| Datum: | 2007 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2007
|
| Schriftenreihe: | Вопросы атомной науки и техники |
| Schlagworte: | |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/110530 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Interaction of the modulated electron beam with plasma: kinetic effects / I.O. Anisimov, M.J. Kiyanchuk, S.V. Soroka, D.M. Velykanets // Вопросы атомной науки и техники. — 2007. — № 1. — С. 113-115. — Бібліогр.: 5 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-110530 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1105302017-01-05T03:04:15Z Interaction of the modulated electron beam with plasma: kinetic effects Anisimov, I.O. Kiyanchuk, M.J. Soroka, S.V. Velykanets, D.M. Plasma electronics Evolution of the velocity distribution functions of plasma and beam electrons during modulated electron beam propagation in homogeneous and inhomogeneous plasma was studied numerically. Velocity distribution function of plasma electrons at the late time moments strongly differs from initially Maxwellian one. In the regions of strong electric field plasma electrons’ bunches are formed. Comparison of distribution functions of beam electrons for modulated and non-modulated beams shows that deep initial modulation suppresses resonant instability development. In the inhomogeneous plasma acceleration of electrons in the plasma resonance point can be observed. Числовими методами досліджена еволюція функції розподілу електронів плазми та пучка за швидкостями при поширенні модульованого електронного пучка в однорідній і неоднорідній плазмі. Функція розподілу для електронів плазми в пізні моменти часу суттєво відрізняється від початкової максвеллівської. В областях сильного електричного поля утворюються згустки електронів плазми. Порівняння функцій розподілу електронів пучка для модульованих і немодульованих пучків показує, що глибока початкова модуляція придушує розвиток резонансної нестійкості. В неоднорідній плазмі може спостерігатися прискорення електронів у точці локального плазмового резонансу. Численно исследована эволюция функции распределения электронов плазмы и пучка по скоростям при распространении модулированного электронного пучка в однородной и неоднородной плазме. Функция распределения для электронов плазмы в поздние моменты времени существенно отличается от начальной максвелловской. В областях сильного электрического поля образуются сгустки электронов плазмы. Сравнение функций распределения электронов пучка для модулированных и немодулированных пучков показывает, что глубокая начальная модуляция подавляет развитие резонансной неустойчивости. В неоднородной плазме может наблюдаться ускорение электронов в точке локального плазменного резонанса. 2007 Article Interaction of the modulated electron beam with plasma: kinetic effects / I.O. Anisimov, M.J. Kiyanchuk, S.V. Soroka, D.M. Velykanets // Вопросы атомной науки и техники. — 2007. — № 1. — С. 113-115. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 52.35.-g http://dspace.nbuv.gov.ua/handle/123456789/110530 en Вопросы атомной науки и техники 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 |
Plasma electronics Plasma electronics |
| spellingShingle |
Plasma electronics Plasma electronics Anisimov, I.O. Kiyanchuk, M.J. Soroka, S.V. Velykanets, D.M. Interaction of the modulated electron beam with plasma: kinetic effects Вопросы атомной науки и техники |
| description |
Evolution of the velocity distribution functions of plasma and beam electrons during modulated electron beam propagation in homogeneous and inhomogeneous plasma was studied numerically. Velocity distribution function of plasma electrons at the late time moments strongly differs from initially Maxwellian one. In the regions of strong electric field plasma electrons’ bunches are formed. Comparison of distribution functions of beam electrons for modulated and non-modulated beams shows that deep initial modulation suppresses resonant instability development. In the inhomogeneous plasma acceleration of electrons in the plasma resonance point can be observed. |
| format |
Article |
| author |
Anisimov, I.O. Kiyanchuk, M.J. Soroka, S.V. Velykanets, D.M. |
| author_facet |
Anisimov, I.O. Kiyanchuk, M.J. Soroka, S.V. Velykanets, D.M. |
| author_sort |
Anisimov, I.O. |
| title |
Interaction of the modulated electron beam with plasma: kinetic effects |
| title_short |
Interaction of the modulated electron beam with plasma: kinetic effects |
| title_full |
Interaction of the modulated electron beam with plasma: kinetic effects |
| title_fullStr |
Interaction of the modulated electron beam with plasma: kinetic effects |
| title_full_unstemmed |
Interaction of the modulated electron beam with plasma: kinetic effects |
| title_sort |
interaction of the modulated electron beam with plasma: kinetic effects |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2007 |
| topic_facet |
Plasma electronics |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/110530 |
| citation_txt |
Interaction of the modulated electron beam with plasma: kinetic effects / I.O. Anisimov, M.J. Kiyanchuk, S.V. Soroka, D.M. Velykanets // Вопросы атомной науки и техники. — 2007. — № 1. — С. 113-115. — Бібліогр.: 5 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT anisimovio interactionofthemodulatedelectronbeamwithplasmakineticeffects AT kiyanchukmj interactionofthemodulatedelectronbeamwithplasmakineticeffects AT sorokasv interactionofthemodulatedelectronbeamwithplasmakineticeffects AT velykanetsdm interactionofthemodulatedelectronbeamwithplasmakineticeffects |
| first_indexed |
2025-07-08T00:42:39Z |
| last_indexed |
2025-07-08T00:42:39Z |
| _version_ |
1837037372280143872 |
| fulltext |
Problems of Atomic Science and Technology. 2007, 1. Series: Plasma Physics (13), p. 113-115 113
INTERACTION OF THE MODULATED ELECTRON BEAM
WITH PLASMA: KINETIC EFFECTS
I.O. Anisimov, M.J. Kiyanchuk, S.V. Soroka, D.M. Velykanets’
Taras Shevchenko Kyiv National University, Radio Physics Faculty, Kyiv, Ukraine,
e-mail: ioa@univ.kiev.ua
Evolution of the velocity distribution functions of plasma and beam electrons during modulated electron beam
propagation in homogeneous and inhomogeneous plasma was studied numerically. Velocity distribution function of
plasma electrons at the late time moments strongly differs from initially Maxwellian one. In the regions of strong elec-
tric field plasma electrons’ bunches are formed. Comparison of distribution functions of beam electrons for modulated
and non-modulated beams shows that deep initial modulation suppresses resonant instability development. In the inho-
mogeneous plasma acceleration of electrons in the plasma resonance point can be observed.
PACS: 52.35.-g
1. INTRODUCTION
Problems of the modulated electron beam interaction
with homogeneous and inhomogeneous plasma are of
interest in various branches of plasma electronics such as
electron beams’ using as emitters of the electromagnetic
waves in ionosphere, transillumination of the plasma bar-
riers for electromagnetic waves using electron beams etc.
In our previous works [1,2] interaction of modulated
electron beams with plasma was studied via computer
simulation using modified package PDP1. Discussion of
kinetic effects during the interaction of the modulated
electron beam with homogeneous and inhomogeneous
plasma is presented in this report.
2. MODIFICATION OF THE VELOCITY
DISTRIBUTION FUNCTIONS DURING
MODULATED ELECTRON BEAM
PROPAGATION IN HOMOGENEOUS
PLASMA
Simulation was carried out via particle-in-cell method
using modified program package PDP1. 1D model was
treated. Initially homogeneous background plasma layer
was located between two plane conductive electrodes.
Electron beam was injected from left electrode and moved
to right one. The plasma particles were absorbed by elec-
trodes.
Plasma was formed by hydrogen ions, and it was
completely ionized. Simulation parameters corresponded
approximately to the conditions of laboratory experiment
[3]. The beam density was modulated harmonically with
the initial depth 0.3. Simulation was carried out during the
time interval of 5·10-8 s that contained approximately 200
electron plasma periods or 5 ion plasma periods. During
this time electron beam reached the opposite electrode,
and approximately stationary processes were settled.
Possibility to save coordinates and velocities of large
particles was used to obtain the velocity distribution func-
tion.
Fig. 1 presents velocity distribution functions of
plasma electrons for different time moments (a,b) and
space-time distribution of electric field (c). The darker
areas correspond to the larger number of particles and
field strength. Velocity distribution functions of plasma
electrons at the late moments of time strongly differ
from initially Maxwellian one (compare Fig. 1 a,b). In the
regions of strong electric field plasma electrons’ bunches
are formed (Fig. 1b). One can see that regions of plasma
electrons’ bunch formation coincide with maximums of
electric field (for t=4.5·10-9 s – 0.06-0.08m, 0.11-0.12m,
0.19–0.2m). After the start of injection maximum of the
a
b
c
Fig. 1. Velocity distribution functions of plasma elec-
trons for different time moments ( a) t=2.5·10 -9;
b) t=4.5·10 -9) and electric field strength (c)
mailto:ioa@univ.kiev.ua
114
electric field moves to the injector, and energy exchange
between the electric field and the beam electrons occurs.
Figs. 2-4 show velocity distribution functions of beam
electrons for modulated and non-modulated electron beam
for different time moments (dark parts correspond to lar-
ger electron densities). In x-v plane these figures present
phase portraits of electron beam. At Fig. 2 a,b one can see
that most part of the beam electrons is decelerated. Ap-
pearance of secondary bunches can be connected with
front reversal in the phase space. Comparison of pictures
for modulated and non-modulated beams shows that suf-
ficiently large initial modulation depth suppresses reso-
nant instability development [4]. From Fig. 4 a,b one can
see that distances between injector and region where
resonant instability becomes significant for modulated
and non-modulated beams are strongly different
(0.04 - 0.05 and 0.02 - 0.25 m).
For the late moments of time the point where resonant
instability becomes significant moves to injector both for
modulated and non-modulated beams (Fig. 2-4). This
effect is connected with the motion of the electric field
maximum to injector (Fig. 1 c).
a b a b
Fig. 2. Velocity distribution functions of beam electrons
for modulated (a) and non-modulated (b), electron beam
at the time moment t=10 -8s
Fig. 3. Velocity distribution functions of beam electrons
for modulated (a) and non-modulated (b), electron beam
at the time moment t=2⋅10 -8s
a b
Fig. 4. Velocity distribution functions of beam elec-
trons for modulated (a) and non-modulated (b), elec-
tron beam at the time moment t=4·10 -8s
N
0
100
200
300
400
500
600
0 100000
0
200000
0
300000
0
400000
0
500000
0
N
a
N
0
100
200
300
400
500
600
0 1000000 2000000 3000000 4000000 5000000
N
b
Fig. 5. The instant distribution functions of the electrons
of the plasma: ) for the moment of time t=0,3 s;
b) for the moment of time t=0,9 s
a
b
Fig. 6. Space-time distribution of the absolute value of
electric field (a) and ion density perturbation (b)
115
3. ELECTRONS’ ACCELERATION IN THE
LOCAL PLASMA RESONANCE REGION
During the study of inhomogeneous plasma dynamics
in the homogeneous pumping electric field the effect of
plasma electrons’ acceleration in local plasma resonance
region was found out [5]. It was shown that electrons ac-
celerated in such a way move in the direction of plasma
density decreasing in the weakly inhomogeneous plasma.
The model studied in this section differs from the pre-
vious one. The difference is that now plasma density
grows linearly from left electrode to the right one. Plasma
resonance point where modulation frequency of the beam
coincides with the local Langmuir frequency is situated in
the center of simulation interval.
The instant distribution functions of the plasma elec-
trons during it’s interaction with modulated electron beam
is shown on Fig. 5 a,b. Space-time distribution of the ab-
solute value of electric field (dark color corresponds in-
tensive field regions) and ion density (dark color corre-
sponds cavities in density profile) is shown on Fig. 6 a,b,
respectively. In the moment of time t=0,5 s the density
cavity is formed.
Fig. 5 a corresponds to the moment of time when the
electric oscillations in LPRR have been already excited
(see Fig. 6 a) but plasma density profile was not yet per-
turbed (see Fig. 6,b). The local peak on the distribution
function can be associated with the electrons accelerated
in LPRR.
Fig.5 b corresponds to the late moment of time when
the density cavity has been already formed in LPRR, and
the electric field in this region has been decreased (see
Fig.6 a,b). So there is no more electron acceleration in
LPRR. Consequently there is no perturbations on the dis-
tribution function.
REFERENCES
1. I.O. Anisimov, O.I. Kelnyk, T.V. Siversky, S.V. So-
roka. Inhomogeneous plasma profile deformation due to
the modulated electron beam: computer simulation via
PIC method // ICPP 2006. Proceedings. Contributed Pa-
pers. Rep. NoC001o.
2. M.J. Kiyanchuk, I.O. Anisimov. Evolution of the mo-
dulated electron beam in supercritical plasma: simulation
of initial-boundary problem. // Ibid. Rep. NoD150p.
3. I.O. Anisimov, O.A. Zubarev, S.M. Levitsky,
O.V. Opanasenko, D.B. Palets, L.I. Romanyuk. Study of
the plasma barriers' transillumination for electromagnetic
waves using electron beams. 1. Existence of the transil-
lumination effect // Ukr. Fiz. Zhurn. 1995, v. 40, 3,
p.198-203 (in Ukrainian).
4. A.K. Berezin, Ja.B. Fajnberg, I.A. Bezjazichniy. Ex-
perimental study of the possibility to control the beam
instability via modulation // Pis'ma v ZhETF. 1968, v. 7,
5, p.156-160 (in Russian).
5. L.M. Kovrizhnykh, O.S. Sakharov. Cavitons’
generation in the plasma resonance region // Fizika
plasmy. 1980, v.6, 1, p.150 – 158 (In Russian).
:
. , . , . , .
.
. .
,
.
.
:
. , . , . , .
.
. -
.
,
. -
.
|