2D electrostatic simulation of the modulated electron beam interaction with inhomogeneous plasma
Electrostatic plasma simulation code for 2D rectangular geometry is presented. Main distinguishing feature of the code is its orientation on the beam-plasma interaction. The code and its graphical interface were developed using MATLAB programming language. Simulation results of inhomogeneous plasm...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2006 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2006
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| Цитувати: | 2D electrostatic simulation of the modulated electron beam interaction with inhomogeneous plasma / I.O. Anisimov, T.Eu. Litoshenko // Вопросы атомной науки и техники. — 2006. — № 6. — С. 175-177. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859841904859938816 |
|---|---|
| author | Anisimov, I.O. Litoshenko, T.Eu. |
| author_facet | Anisimov, I.O. Litoshenko, T.Eu. |
| citation_txt | 2D electrostatic simulation of the modulated electron beam interaction with inhomogeneous plasma / I.O. Anisimov, T.Eu. Litoshenko // Вопросы атомной науки и техники. — 2006. — № 6. — С. 175-177. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | Electrostatic plasma simulation code for 2D rectangular geometry is presented. Main distinguishing feature of the
code is its orientation on the beam-plasma interaction. The code and its graphical interface were developed using
MATLAB programming language. Simulation results of inhomogeneous plasma interaction with modulated electron
beams of different width are compared. In case of wide beam the front of Langmuir waves generated in point of local
plasma resonance is planar and in case of thin beam (or ribbon beam) the front has approximately half-circular form.
|
| first_indexed | 2025-12-07T15:37:00Z |
| format | Article |
| fulltext |
Problems of Atomic Science and Technology. 2006, 6. Series: Plasma Physics (12), p. 175-177 175
2D ELECTROSTATIC SIMULATION OF THE MODULATED ELECTRON
BEAM INTERACTION WITH INHOMOGENEOUS PLASMA
I.O. Anisimov, T.Eu. Litoshenko
Taras Shevchenko Kyiv National University, Radio Physics Faculty, Kyiv, Ukraine,
e-mail: ioa@univ.kiev.ua
Electrostatic plasma simulation code for 2D rectangular geometry is presented. Main distinguishing feature of the
code is its orientation on the beam-plasma interaction. The code and its graphical interface were developed using
MATLAB programming language. Simulation results of inhomogeneous plasma interaction with modulated electron
beams of different width are compared. In case of wide beam the front of Langmuir waves generated in point of local
plasma resonance is planar and in case of thin beam (or ribbon beam) the front has approximately half-circular form.
PACS: 52.65.-y
1. INTRODUCTION
Beam-plasma interaction is the object of scientific
interest for many years. Deeper understanding of this
phenomenon would cause a progress in a large number of
applications from space weather prediction to plasma
electronic devices construction.
Interaction of inhomogeneous plasma with modulated
electron beams in 1D geometry is studied both theoreti-
cally and via numerical simulation (see, e.g., [1-2]). In
fact, this model with the beam of infinite transversal
length corresponds to plasma with the strong magnetic
field parallel to the density gradient. But for real beams of
finite radius the radial component of electric field appears
causing the electrons’ and ions’ radial motion. 1D models
do not describe this effect.
The report presents electrostatic simulation of the
modulated electron beam interaction with inhomogeneous
plasma in 2D plane geometry. The simulation was per-
formed using large particles’ method. Large particles in-
teract electrostatically and can move in two dimensions
freely or driven by external forces. The code gives possi-
bility of charged particles’ beam injection into inhomoge-
neous plasma.
2. ALGORITHM AND COMPUTER CODE
Particle in cell (PIC) algorithm [2] lies in the base of
presented code. This algorithm considers plasma as a set
of charged particles that consists of large number of ele-
mentary particles. The big particles interact with each
other not directly but through a grid – an object that ap-
pears after breaking a simulating volume on the set of
cells. FFT method was used for difference Poisson’s
equation solving [3].
The above described algorithm is coded using the lan-
guage for technical computing MATLAB. The core of the
code is a cycle in which the operations of particles’
charge weighting, electrical field calculation and particles
coordinates and velocities updating are consequently re-
peated.
Modular architecture is laid in the basis of the devel-
oped code. The main routines such as routine of Poisson’s
equation for electrical field solving, particles’ charges
weighting routine and others are independent building
blocks of the program.
The other distinguishing feature of the presented code
is a presence of graphical interface which makes the code
operation easier for a user. The interface includes a num-
ber of dialogues for putting simulation parameters into the
code and graphical window for system state visualization
during a simulation.
3. NUMERICAL SIMULATION OF
MODULATED BEAM INTERACTION WITH
INHOMOGENEOUS PLASMA
Simulation of beam-plasma interaction was performed
using electrostatic 2D computer code. The simulated vol-
ume is bounded by two pairs of parallel planes with
Lx=4cm, Ly=1cm. The rectangular grid is introduced in
system with 1024x256 cells. The volume is filled with
plasma which is modeled as a number of large electrons
(Nbig = 106) with temperature Te = 0.5 eV and a mo-
tionless positive background charge. The large particle in
the 2D rectangular geometry is an infinite uniformly
charged rod which moves perpendicularly to its axis. The
linear density of the large particle in the presented simula-
tions is 8·103 elementary particles per meter for beam
electrons and 2.56·106 m-1 for plasma electrons. The
plasma concentration is constant along y coordinate and
changes linearly along x coordinate from 3.2·1015 m-3 on
the left electrode to 9.6·1015 m-3 on the right electrode.
Plasma particles are reflected from the left and right
boundaries and translated into the simulated volume by
adding or subtracting Ly from their y coordinate if they
have crossed bottom or top boundary.
Boundary conditions of the Dirichlet type on the left
and right electrodes and periodic boundary conditions on
the top and bottom electrodes were used for the Poisson’s
equation solving:
0)()0( ==== xLxx φφ , ( ) )(0 yLyy === φφ .
The time step of simulations dt=5·10-11 is two order
less than the period of plasma oscillations Tp=1.1·10-9 s in
the maximal density region at x=Lx (Tp>>dt). The Debye
length Ld and size of cell dx are one order less then the
wave length L of generated Langmuir waves
dx:Ld L=1:2.4:24 at x=0. Number of particles in the De-
bye sphere (Debye cylinder in the 2D geometry) is Nd =
·kb·Te 0/(e2 )=8.5, where =2.56·106m-1– linear density
of the large particles.
Modulated beams of different width were injected into
the volume and their interaction with plasma in the point
of local resonance was investigated.
mailto:ioa@univ.kiev.ua
176
3.1. BEAM-PLASMA INTERACTION IN QUASI 1D
GEOMETRY
In this section results of simulation of inhomogeneous
plasma interaction with modulated beam which width is
equal to Ly are reported. Due to periodicity of boundary
conditions on the top and bottom electrodes the interac-
tion in this case can be thought as quasi one-dimensional.
Beam particles are injected into the plasma with
vx=27vT=8·106m/s, vy=0. Beam density is modulated with
frequency fm=7.5·108 Hz, modulation depth m=1 and
maximal value nb=5·1013 m-3.
Perturbation of plasma electrons density for 5 subse-
quent time moments is shown on Fig.1.
Fig. 1. Planar Langmuir waves generation generated in
quasi 1D beam-plasma interaction
It can be easily observed that Langmuir waves are
generated in the point of local plasma resonance xlpr and
propagate leftwards. Phase velocity of the waves decrease
with plasma density decreasing. Wave front is planar, and
plasma electrons density is roughly constant along x axis.
Fig. 2. Time dependence of plasma electron density
perturbation on the axis of the system for quasi 1D
beam-plasma interaction
Time development of wave process on the axis of the
system (y=0.5 cm) is shown on Fig. 2. Dashed line marks
the point of local plasma resonance calculated theoreti-
cally. From this point waves of plasma density propagate
toward left electrode, and trajectories of their maxima are
shown by white color.
Density of beam electrons is shown on Fig. 3. It
changes from 0 to -6·1013 m-3 due to modulation. It can be
easily observed that the beam becomes “fibrous” during
its motion toward the right electrode.
Fig. 3. Beam density for t = 140 ns. Simulation for quasi
1D interaction
3.2. SIMULATION OF PLASMA INTERACTION
WITH THIN (RIBBON) BEAM
In this section results of simulation of inhomogeneous
plasma interaction with thin modulated beam are reported.
The fact that beam density is not constant along y axis
makes the simulation essentially two-dimensional.
The beam width is Lb=Ly/20=0.05cm, maximal beam
density nb=1·1015m-3, so the total current in the system is
equal for both simulations. Modulation frequency and
depth are also remained unchanged.
Perturbation of plasma electron density at 5 subsequent
time moments during one Langmuir period is shown on Fig.4.
Fig. 4. Spherical (cylindrical) Langmuir waves
generated by thin beam
Intensive oscillations of plasma electrons' density can be
observed in the local plasma resonance point. Oscillations
with the period equal to the beam modulation period propa-
gate in regions of lower plasma density. Wave front has ap-
proximately half-circular form. The explanation of this effect
is that the region of intensive beam-plasma interaction can be
treated as point-like source.
Time development of the plasma density oscillations
on the axis of the system (y=0.5cm) is shown on Fig.5. At
the early stage (t<20 ns) the waves of space charge den-
sity that propagate rightwards are visible. These waves
are caused by non-compensated beam charge.
177
Fig.5. Time dependence of plasma electron density
perturbation on the axis of the system for inhomogeneous
plasma interaction with thin beam
Fig. 6. Spatial distribution of the beam electrons' density
for t = 140 ns
Later charge density waves start interfering with Lan-
muir waves that propagate leftwards. On Fig. 5 this inter-
ference appears as a spatial beating of plasma density that
is predicted theoretically [4-6].
Density of beam electrons is shown on Fig. 6. Non-
compensated beam charge causes beam widening .
4. CONCLUSIONS
Two simulations of modulated electron beam interac-
tion with inhomogeneous plasma interaction for different
beam width were performed. The first simulation deals
with quasi 1D beam-plasma interaction, when the beam
width is equal to the length of the system along y direc-
tion. Langmuir waves propagation from the region of lo-
cal plasma resonance to the regions of lower plasma den-
sity was observed. The “fibrous” beam structure was dis-
covered.
The second simulation deals with essentially 2D
beam-plasma interaction. Beam is thin in comparison with
system length along y direction. Langmuir waves with
quasi half-circular wave front were observed in this case.
The effect of spatial beating between waves of space
charge driven by beam and Langmuir waves generated in
region of beam-plasma resonance was established during
the simulation.
REFERENCES
1.A.N. Kondratenko, V.M. Kuklin. Fundamentals of
plasma electronics. M.: “Energoatomisdat”, 1988 (in
Russian).
2.Yu.S. Sigov. Computational experiment: the bridge
between past and future of plasma physics. M.: “Fis-
matgis”, 2001 (in Russian).
3.William H. Press, Saul A. Teukolsky, Wil-
liam T. Vetterling, Brian P. Flannery. Numerical Reci-
pes in C: The Art of Scientific Computing. Cambridge
University Press, 1992.
4.L.M. Kovrizhnykh, A.S. Sakharov. Cavitons’ genera-
tion in the plasma resonance region // Fizika plazmy.
1980, N 6, p. 150-158. (In Russian).
5.G.J. Morales, Y.C. Lee. Generation of density cavities
and localized electric field in a non-uniform plasma //
Phys. Fluids. 1977, v.20, p. 1135-1147.
6.I.O. Anisimov, O.A. Borisov. Electrical Field Excita-
tion in Non-Uniform Plasma by a Modulated Electron
Beam // Physica Scripta, 62, 2000, 375-380.
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| id | nasplib_isofts_kiev_ua-123456789-82298 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T15:37:00Z |
| publishDate | 2006 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Anisimov, I.O. Litoshenko, T.Eu. 2015-05-27T15:00:53Z 2015-05-27T15:00:53Z 2006 2D electrostatic simulation of the modulated electron beam interaction with inhomogeneous plasma / I.O. Anisimov, T.Eu. Litoshenko // Вопросы атомной науки и техники. — 2006. — № 6. — С. 175-177. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 52.65.-y https://nasplib.isofts.kiev.ua/handle/123456789/82298 Electrostatic plasma simulation code for 2D rectangular geometry is presented. Main distinguishing feature of the code is its orientation on the beam-plasma interaction. The code and its graphical interface were developed using MATLAB programming language. Simulation results of inhomogeneous plasma interaction with modulated electron beams of different width are compared. In case of wide beam the front of Langmuir waves generated in point of local plasma resonance is planar and in case of thin beam (or ribbon beam) the front has approximately half-circular form. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma electronics 2D electrostatic simulation of the modulated electron beam interaction with inhomogeneous plasma Article published earlier |
| spellingShingle | 2D electrostatic simulation of the modulated electron beam interaction with inhomogeneous plasma Anisimov, I.O. Litoshenko, T.Eu. Plasma electronics |
| title | 2D electrostatic simulation of the modulated electron beam interaction with inhomogeneous plasma |
| title_full | 2D electrostatic simulation of the modulated electron beam interaction with inhomogeneous plasma |
| title_fullStr | 2D electrostatic simulation of the modulated electron beam interaction with inhomogeneous plasma |
| title_full_unstemmed | 2D electrostatic simulation of the modulated electron beam interaction with inhomogeneous plasma |
| title_short | 2D electrostatic simulation of the modulated electron beam interaction with inhomogeneous plasma |
| title_sort | 2d electrostatic simulation of the modulated electron beam interaction with inhomogeneous plasma |
| topic | Plasma electronics |
| topic_facet | Plasma electronics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/82298 |
| work_keys_str_mv | AT anisimovio 2delectrostaticsimulationofthemodulatedelectronbeaminteractionwithinhomogeneousplasma AT litoshenkoteu 2delectrostaticsimulationofthemodulatedelectronbeaminteractionwithinhomogeneousplasma |