Numerical simulation of the beam-plasma turbulence spectrum evolution for weak beams
The results of the numerical simulation of weak non-relativistic monochromatic beam interaction with plasma are introduced. The modified PDP1 package for one-dimensional plasma systems simulation was used. Evolution of the phase portrait and electric field distribution during beam-plasma turbulence...
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irk-123456789-1109892017-01-08T03:03:11Z Numerical simulation of the beam-plasma turbulence spectrum evolution for weak beams Anisimov, I.O. Siversky, T.V. Нелинейные процессы The results of the numerical simulation of weak non-relativistic monochromatic beam interaction with plasma are introduced. The modified PDP1 package for one-dimensional plasma systems simulation was used. Evolution of the phase portrait and electric field distribution during beam-plasma turbulence was investigated. Plasma oscillations spectra were obtained. Their temporal and spatial evolution was studied. 2003 Article Numerical simulation of the beam-plasma turbulence spectrum evolution for weak beams / I.O. Anisimov, T.V. Siversky // Вопросы атомной науки и техники. — 2003. — № 4. — С. 81-84. — Бібліогр.: 11 назв. — англ. 1562-6016 PACS: 52.35.Mw http://dspace.nbuv.gov.ua/handle/123456789/110989 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Нелинейные процессы Нелинейные процессы |
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Нелинейные процессы Нелинейные процессы Anisimov, I.O. Siversky, T.V. Numerical simulation of the beam-plasma turbulence spectrum evolution for weak beams Вопросы атомной науки и техники |
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The results of the numerical simulation of weak non-relativistic monochromatic beam interaction with plasma are introduced. The modified PDP1 package for one-dimensional plasma systems simulation was used. Evolution of the phase portrait and electric field distribution during beam-plasma turbulence was investigated. Plasma oscillations spectra were obtained. Their temporal and spatial evolution was studied. |
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Article |
| author |
Anisimov, I.O. Siversky, T.V. |
| author_facet |
Anisimov, I.O. Siversky, T.V. |
| author_sort |
Anisimov, I.O. |
| title |
Numerical simulation of the beam-plasma turbulence spectrum evolution for weak beams |
| title_short |
Numerical simulation of the beam-plasma turbulence spectrum evolution for weak beams |
| title_full |
Numerical simulation of the beam-plasma turbulence spectrum evolution for weak beams |
| title_fullStr |
Numerical simulation of the beam-plasma turbulence spectrum evolution for weak beams |
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Numerical simulation of the beam-plasma turbulence spectrum evolution for weak beams |
| title_sort |
numerical simulation of the beam-plasma turbulence spectrum evolution for weak beams |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2003 |
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Нелинейные процессы |
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http://dspace.nbuv.gov.ua/handle/123456789/110989 |
| citation_txt |
Numerical simulation of the beam-plasma turbulence spectrum evolution for weak beams / I.O. Anisimov, T.V. Siversky // Вопросы атомной науки и техники. — 2003. — № 4. — С. 81-84. — Бібліогр.: 11 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT anisimovio numericalsimulationofthebeamplasmaturbulencespectrumevolutionforweakbeams AT siverskytv numericalsimulationofthebeamplasmaturbulencespectrumevolutionforweakbeams |
| first_indexed |
2025-07-08T01:28:34Z |
| last_indexed |
2025-07-08T01:28:34Z |
| _version_ |
1837040261260115968 |
| fulltext |
NUMERICAL SIMULATION OF THE BEAM-PLASMA
TURBULENCE SPECTRUM EVOLUTION FOR WEAK BEAMS
I.O.Anisimov, T.V.Siversky
Taras Shevchenko National University of Kyiv, Radio Physics Faculty
Kyiv, Ukraine, ioa@univ.kiev.ua
The results of the numerical simulation of weak non-relativistic monochromatic beam interaction with plasma
are introduced. The modified PDP1 package for one-dimensional plasma systems simulation was used. Evolution of
the phase portrait and electric field distribution during beam-plasma turbulence was investigated. Plasma oscilla-
tions spectra were obtained. Their temporal and spatial evolution was studied.
PACS: 52.35.Mw
1. INTRODUCTION
The accurate analytical model of beam-plasma sys-
tems was build only for initial and boundary problems
[1,2]. It does not correspond with the real experiment
conditions [3]. For this reason a lot of numerical emula-
tions of such systems were done. There are two basic
approaches in simulation of kinetic processes in plasma.
The first one is based on Vlasov-Poisson set of equa-
tions [4]. The second one directly uses charged particle
motion equation and Poisson equation. Such approach is
used, for instance, in the PDP1 program package. The
modified version of this package was used in our re-
search.
Most of the researchers took an interest in quasi-lin-
ear regime of beam relaxation (see, e.g., [4]), or strong
relativistic monochromatic beams’ interaction with plas-
ma [5]. But there are some problems in plasma electron-
ics (such as plasma barriers’ transillumination for elec-
tromagnetic waves by means of electron beams [6])
where weak beams are used. Therefore we concern
weak non-relativistic beams in beam-plasma instability
investigations. In particular, information about spatial
and temporal evolution of the beam-plasma turbulence
spectra in such systems is presented.
2. MODIFIED PDP1 PACKAGE
As was mentioned above, one of the widely used
methods for computer simulation of the beam-plasma
systems is the big-particles-in-cells method [7]. It is
used, e.g., in the well-known package PDP1 [8], which
can simulate initial-boundary problem for one-dimen-
sional model.
We have created the modified package PDP1 [9]
that has some advantages in comparison with the origi-
nal version. Some main features of the modified pro-
gram are listed below.
Program is realized for 32-bit Windows operation
systems (Windows 95/98/NT/2000/XP). There are no
implicit limitations on the big particles’ number. This
number is specified for each type of particles separately
and limited only by the size of computer memory.
Program gives the possibility to save the intermedi-
ate results of simulation in the text files or binary files.
Spatial distribution of the electric field and potential,
charge density, current density, phase trajectory of sin-
gle particle, particles’ coordinates and velocities can be
saved. It helps to obtain, e.g., frequency spectrum of os-
cillations at various coordinates.
More comfortable way for assignment of the number
of real particles in one big particle is developed. In our
program this numbers can vary for each type of parti-
cles. It gives the possibility to assign a small beam elec-
trons’ concentration in comparison with bulk plasma
electrons’ concentration.
3. SIMULATION PARAMETERS SELEC-
TION
It was already noted that initial-boundary problem
was considered in our simulation (beam starts injecting
at the initial moment from the left side of the system).
Plasma was initially homogenous and isothermic. Plas-
ma particles are reflected by the walls. The electron
beam was monoenergetic (without initial modulation).
The beam current was selected so that the transition pro-
cesses due to the beam forefront were negligible [10].
The plasma quasineutrality violation caused by the
beam was insignificant.
The values of the simulated system basic parameters
(which fulfill above-listed conditions) are:
L/λD = 103, where L is the system length, λD is
Debye length;
Vb/Vt = 8, where Vb is the beam velocity, Vt is the
thermal velocity of the plasma electrons;
nb/n ∼ 10-4 – 10-2, where nb is the beam electrons’
concentration, n is the plasma electrons’ concentration.
The number of big particles was about 105 for every
type of particles. The number of cells in the system was
103.
Selected parameters correspond to moderate turbu-
lence regime (τc/τNL ≡ Ω/γ = 8.6; W/nT = 1.6⋅10-2) [4].
4. QUALITATIVE DESCRIPTION OF THE
BEAM-PLASMA INSTABILITY
EVOLUTION
At the beginning of the injection of relatively weak
beam (nb/n = 7.8⋅10-5) slight modulation appears (fig.1).
Fig.1. Linear stage of the beam-plasma instability evo-
lution: phase plane (ωpt = 165, nb/n = 7.8⋅10- 5)
Oscillation increment does not depend on time and co-
ordinate at this case. Later the front tipping over appears
on the beam phase plane (fig.2). At the same time elec-
tric field magnitude oscillates in space (fig.3). This ef-
fect corresponds with spatial (stationary) problem solu-
tion [1].
Fig.2. Front tipping over in the beam phase plane (ω
pt = 255, nb/n = 7.8⋅10- 5)
Fig.3. Electric field spatial distribution at the begin-
ning of the nonlinear stage of beam-plasma instability
(ωpt = 1128, nb/n = 7.8⋅10- 5)
a
b
Fig.4. Beam phase plane (a) and electric field spa-
tial distribution (b) at the turbulence stage of the
beam-plasma instability (ωpt = 1612, nb/n = 7.8⋅
10- 5)
Fig.5. Plasma transillumination for electron beam (ω
pt = 7876, nb/n = 7.8⋅10- 5)
Fig.6. Beam phase plane at the turbulence stage of
the beam-plasma instability (ωpt = 828, nb/n = 7.8⋅
10-4)
Fig.7. Bulk plasma electrons’ acceleration by the
beam electrons (ωpt = 164, nb/n = 6.9⋅10-3)
For the next moments the beam electrons’ motion
becomes more chaotic (fig.4a). Depth of the electric
field modulation decreases (fig.4b). Fig.4b demonstrates
lack of the full trapping of beam electrons by the wave.
One can see on the phase plane both trajectories of finite
motion (corresponding to the electrons trapped by the
wave) and trajectories of infinite motion (corresponding
to the drift particles). Chaotic motion of electrons is
caused by trajectories’ instability near the separatrix be-
tween those trajectories types [11]. Later chaotic region
of beam’s phase plane moves towards the injector. At
the late stage (ωt ∼ 8⋅103) transillumination of plasma
for beam near injector can be observed, so the beam
electrons’ motion becomes less chaotic (fig.5).
Increasing of the electron beam current leads to the
faster transition from regular dynamics to chaotic one.
So the distance between injector and chaotic region de-
creases (fig.6). Sufficiently dense beam (nb/n ≥ 10-2)
could lead to the well-known [10] effect of bulk plasma
electrons acceleration (fig.7). Very dense beams cause
an appreciable quasineutrality violation, so the virtual
cathode could appear.
5. BEAM-PLASMA TURBULENCE SPEC-
TRA
Oscillation spectra as a function of distance from in-
jector were obtained by processing of simulation results.
Time interval used by the Fourier transform was almost
a thousand Langmuir periods long. It starts from the
moment when the oscillations’ magnitude maximum
stops moving towards the injector. Spectra of electric
field and current density were almost identical. Oscilla-
tion spectrum is concentrated at the narrow band near
the plasma frequency (∆ω/ω~0.03 at the level 0.1 of
maximal magnitude). This effect can be easily ex-
plained: plasma acts as a high-Q resonator, so it sup-
presses all oscillations except the eigenmodes. Detailed
Fig.8. Spatial distribution of the beam-plasma insta-
bility spectrum at the interval from ωpt = 1128 to ω
pt = 5640 (nb/n = 7.8⋅10- 5)
а
b
Fig.9. Time evolution of the spatial distribution of the
beam-plasma instability spectrum (nb/n = 7.8⋅10- 5): a
– time interval from ωpt = 1128 to ωpt = 2256; b –
time interval from ωpt = 4512 to ωpt = 5640
analysis shows that the spectrum maximum is not sharp
but has a complex indented shape. It was no significant
widening of the spectrum along the system. Gradual de-
crease of the spectral intensity and increase of the
peaks’ number were observed instead (fig.8).
Note that the shape of the obtained spectrum qualita-
tively corresponds with the radiation spectra of the
beam-plasma discharge (for relatively weak currents)
[3].
Time evolution of the spectrum was also investigat-
ed. The whole time interval was divided on four equal
parts. The spectrum was found to be essentially non-sta-
tionary. At the first time interval it has the sharp peak
near the injector that expands and decreases at some dis-
tance from it (fig.9a). At other time intervals spectrum
comes down and expands, it becomes more homoge-
nous along the system (fig.9b).
6. Conclusion
Numerical simulation using the big-particles-in-cells
method gives the possibility to study the spatial and
temporal evolution of the beam-plasma system in case
of weak non-relativistic electron beams.
Simulation results contradict the analytical theory of
the nonlinear stage of the beam-plasma instability [1,2]:
stationary oscillations were not observed even for the
weak beam. For any beam current the moderate turbu-
lence regime [4] appeared at some distance from injec-
tor.
In fact the analytical theory does not take into ac-
count plasma modification due to the energy taken from
the beam. This effect results to the non-stationarity of
the beam-plasma interaction in the model examined.
Analysis of oscillation spectra spatial distribution at
late stage of the beam-plasma turbulence shows that in
case of weak beam the oscillation frequencies are con-
centrated in relatively narrow band near the electron
Langmuir frequency. It is no significant widening of the
spectrum along the system. At the same time there is a
smooth changing of spectrum. It becomes more homo-
geneous along the system.
Obtained spectrum of beam-plasma turbulence qual-
itatively corresponds with the experimental data.
Note that one-dimensional simulation cannot repro-
duce all the possible effects observed in experiments.
E.g., we could not observe the effect of plasma extru-
sion from the electron beam volume caused by high-fre-
quency pressure of electric field [3]. Also the excitation
of “oblique” waves (with respect to beam direction) is
impossible for this model. At least two-dimensional
model must be used to simulate such effects.
REFERENCES
1. A.N.Kondratenko, V.M.Kuklin. Fundamentals of
plasma electronics. Moscow: Energoatomizdat,
1988, 320 p. (in Russian).
2. E.V.Mishin, Yu.Ya.Ruzhyn, V.A.Telegin. Electron
beams and ionospheric plasma interaction.
Leningrad: Gidrometeoizdat, 1989, 264 p. (in Rus-
sian).
3. L.Yu.Kochmaryov, A.I.Chmil', E.G.Shustin. Struc-
tures and mechanism of HF oscillations generation
in beam-plasma discharge // Fizika Plazmy, 1995,
v. 21, №3, p. 257 - 266 (in Russian).
4. Yu.S.Sigov, V.D.Levchenko. Coherent phenomena
in relaxation of the diffuse electron beams in open
plasma systems // Fizika Plazmy, 1997, v. 23, №4,
p. 325-342 (in Russian).
5. A.A.Rukhadze, L.S.Bogdankevich, S.E.Rosinsky,
V.G.Rukhlin. Physics of the strong relativistic
electron beams. Moscow: Atomizdat, 1980, 168 p.
(in Russian).
6. I.O.Anisimov, S.M.Levitsky, A.V.Opanasenko,
L.I.Romanyuk. Experimental observation of the
plasma wave barrier transillumination using elec-
tron beam // Zhurn. Tekhn. Fiz., 1991, v. 3, №61, p.
59 - 63 (in Russian).
7. Ch.K.Birdsall, A.B.Langdon. Plasma Physics via
Computer Simulation. McGraw-Hill Book Compa-
ny, 1985.
8. J.P.Verboncoeur, M.V.Alves, V.Vahedi and
Ch.K.Birdsall. Simultaneous Potential and Circuit
Solution for 1D bounded Plasma Particle Simula-
tion Codes // J. Comp. Physics. 1993, №104, p. 321
- 328.
9. I.O.Anisimov, I.A.Blazhko, T.V.Siversky. Modi-
fied PDP1 package for beam-plasma systems simu-
lation // Proc. 2nd Int. Young Scientists Conf. on
Applied Physics. T. Shevchenko National Universi-
ty of Kyiv, Faculty of Radiophysics, 2002, p.6-7.
10. G.V.Lizunov, O.V.Podladchikova. On the problem
of bursty generation of Langmuir waves by “mo-
noenergetic” electron beam // Ukr. Fiz. Zhurn.,
1998, v. 43, p. 182 - 187 (in Ukrainian).
11. G.M.Zaslavsky, R.Z.Sagdeev. Introduction to non-
linear physics: from pendulum to turbulence and
chaos. Moscow: "Nauka", 1988, 368 p. (in Rus-
sian).
I.O.Anisimov, T.V.Siversky
Taras Shevchenko National University of Kyiv, Radio Physics Faculty
Kyiv, Ukraine, ioa@univ.kiev.ua
PACS: 52.35.Mw
Fig.5. Plasma transillumination for electron beam (pt = 7876, nb/n = 7.810‑5)
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