Deformation of the plasma concentration profile due field of the modulated electron beam: numerical simulation
Deformation of the concentration profile of the weakly inhomogeneous plasma due to the modulated electron beam was studied via computer simulation using big-particles-in-cells method. At the first stages the electric field increase in the local plasma resonance region was observed. It resulted to th...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2003
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| Цитувати: | Deformation of the plasma concentration profile due field of the modulated electron beam: numerical simulation / I.O. Anisimov, O.I. Kelnyk, T.V. Siversky, C.V. Soroka // Вопросы атомной науки и техники. — 2003. — № 4. — С. 91-93. — Бібліогр.: 10 назв. — англ. |
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irk-123456789-1109862017-01-08T03:03:36Z Deformation of the plasma concentration profile due field of the modulated electron beam: numerical simulation Anisimov, I.O. Kelnyk, O.I. Siversky, T.V. Soroka, C.V. Нелинейные процессы Deformation of the concentration profile of the weakly inhomogeneous plasma due to the modulated electron beam was studied via computer simulation using big-particles-in-cells method. At the first stages the electric field increase in the local plasma resonance region was observed. It resulted to the density cavity formation. For the isothermic plasma the density cavity transformed into the plasma concentration jump. For plasma with the hot electrons ion-acoustic turbulence was observed at the late time points. 2003 Article Deformation of the plasma concentration profile due field of the modulated electron beam: numerical simulation / I.O. Anisimov, O.I. Kelnyk, T.V. Siversky, C.V. Soroka // Вопросы атомной науки и техники. — 2003. — № 4. — С. 91-93. — Бібліогр.: 10 назв. — англ. 1562-6016 PACS: 52.35.Mw http://dspace.nbuv.gov.ua/handle/123456789/110986 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. Kelnyk, O.I. Siversky, T.V. Soroka, C.V. Deformation of the plasma concentration profile due field of the modulated electron beam: numerical simulation Вопросы атомной науки и техники |
| description |
Deformation of the concentration profile of the weakly inhomogeneous plasma due to the modulated electron beam was studied via computer simulation using big-particles-in-cells method. At the first stages the electric field increase in the local plasma resonance region was observed. It resulted to the density cavity formation. For the isothermic plasma the density cavity transformed into the plasma concentration jump. For plasma with the hot electrons ion-acoustic turbulence was observed at the late time points. |
| format |
Article |
| author |
Anisimov, I.O. Kelnyk, O.I. Siversky, T.V. Soroka, C.V. |
| author_facet |
Anisimov, I.O. Kelnyk, O.I. Siversky, T.V. Soroka, C.V. |
| author_sort |
Anisimov, I.O. |
| title |
Deformation of the plasma concentration profile due field of the modulated electron beam: numerical simulation |
| title_short |
Deformation of the plasma concentration profile due field of the modulated electron beam: numerical simulation |
| title_full |
Deformation of the plasma concentration profile due field of the modulated electron beam: numerical simulation |
| title_fullStr |
Deformation of the plasma concentration profile due field of the modulated electron beam: numerical simulation |
| title_full_unstemmed |
Deformation of the plasma concentration profile due field of the modulated electron beam: numerical simulation |
| title_sort |
deformation of the plasma concentration profile due field of the modulated electron beam: numerical simulation |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2003 |
| topic_facet |
Нелинейные процессы |
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http://dspace.nbuv.gov.ua/handle/123456789/110986 |
| citation_txt |
Deformation of the plasma concentration profile due field of the modulated electron beam: numerical simulation / I.O. Anisimov, O.I. Kelnyk, T.V. Siversky, C.V. Soroka // Вопросы атомной науки и техники. — 2003. — № 4. — С. 91-93. — Бібліогр.: 10 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-07-08T01:28:20Z |
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2025-07-08T01:28:20Z |
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1837040246102949888 |
| fulltext |
DEFORMATION OF THE PLASMA CONCENTRATION PROFILE DUE
FIELD OF THE MODULATED ELECTRON BEAM: NUMERICAL SIMU-
LATION
I.O. Anisimov, O.I. Kelnyk, T.V. Siversky, C.V. Soroka
Taras Shevchenko National University of Kyiv, Radio Physics Faculty, Kyiv, Ukraine, ioa@u-
niv.kiev.ua
Deformation of the concentration profile of the weakly inhomogeneous plasma due to the modulated elec-
tron beam was studied via computer simulation using big-particles-in-cells method. At the first stages the
electric field increase in the local plasma resonance region was observed. It resulted to the density cavity for-
mation. For the isothermic plasma the density cavity transformed into the plasma concentration jump. For
plasma with the hot electrons ion-acoustic turbulence was observed at the late time points.
PACS: 52.35.Mw
1. INTRODUCTION
Deformation of the plasma concentration profile due
to the field of the incident electromagnetic wave was of-
ten discussed (see, e.g., [1-2]). For the obliquely inci-
dent p-polarized waves of the moderate power the con-
centration profile deformation occurs mainly in the local
plasma resonance region (LPRR). It has a form of the
quasi-periodical generation of the density cavities [1] or
formation of the sharp concentration jump [2]. Similar
effects were predicted in [3] for the field excited by
modulated electron beam moving through the inhomo-
geneous plasma. This problem was studied in [4-5] us-
ing numerical solution of the non-linear equations set
for the electric field and plasma concentration. For this
case problem was solved in the given beam current’ ap-
proximation.
Deformation of the inhomogeneous plasma profile
due to the field of the modulated electron beam is treat-
ed in this work. Numerical simulation was carried out
using the big-particles-in-cells method [6-7] (i.e. self-
consistent approximation) for one-dimensional model.
2. NUMERICAL SIMULATION METHOD
AND PARAMETERS SELECTION
The program used for simulation is the modification
of the PDP1 code [4], but it has some additional re-
source. It gives the possibility to introduce modulation
of the electron beam velocity or density and inhomo-
geneity of the initial plasma concentration profile.
In our simulation the beam density was modulated
sinusoidally with the depth of 100%. The beam current
and velocity v0 as well as the characteristic inhomogene-
ity length L were selected so that the charge density pro-
file in LPRR did not differ strongly from the sinusoidal
shape (fig.1).
After the beam passage through LPRR significant
deformation of the electron bunches’ profile did not oc-
cur. This result justifies the validity of the given current
approximation for this problem that was used in [4-5].
Initial concentration profile was linear. Concentra-
tion varied from 0.5пс to 1.5пс (пс is the critical electron
concentration for the beam modulation frequency). Thus
LPRR was placed in the middle of the simulation re-
gion. Mass of the plasma ions was selected so that char-
acteristic time of the ion concentration profile deforma-
tion did not exceed the time of simulation (a few hun-
dreds periods of Langmuir oscillations). Ions of hydro-
gen satisfy this condition.
a
b
Fig.1. Space distribution of the beam electrons’ con-
centration in the steady-state regime for L=2.5m, ω/2π
=1.3⋅108Hz, |v0|=7⋅107m/s, Те=25eV: a – v0>0;
b – v0<0
Both cases of the beam velocity sign (v0>0 – beam
moving into the dense plasma and v0<0 – beam moving
from the dense plasma) were studied. Simulation was
carried out for isothermic plasma (Те=Ті) and plasma
with hot electrons (Те>>Ті).
3. FIELD EXCITATION AT THE INITIAL
TIME POINTS
At the initial time points after the injection start the
space periodicity and motion direction of the electric
field wave are similar to the current wave of electron
beam (Fig.2).
However after some time periods of modulation the
space period of electric field starts decreasing while its
magnitude in the LPRR gradually increases. Field spa-
tial distribution is symmetrical relatively to the LPRR
for these time points. The field magnitude in LPRR in-
creases during some units or some tens of the modula-
tion periods. The increase time is directly proportional
to the plasma inhomogeneity length and inversely pro-
portional to the thermal velocity of the plasma electrons.
The field increase can be non-monotonic (in agreement
with the calculation [8]).
Later the spatial field distribution is modified. Peri-
odic oscillations in supercritical plasma disappear. In
the subcritical plasma Langmuir wave is formed moving
Fig.2. Time evolution of the electric field spatial distri-
bution at the initial time points after the injection start
(v0>0, f⋅t1≈6; t1<t2<t3)
out from the dense plasma. Oscillations in the LPRR
have now the phase velocity directed antiparallelly to
the beam velocity (Fig.3).
Fig.3. Space-time course electric field in LPRR (v0>0, f
⋅t1≈67; t1<t2<t3<t4)
In this case condition of the weak plasma inhomogene-
ity k0L>>v0
3/cvTe
2 (where k0=ω/c, v0 and vTe are the
beam velocity and thermal velocity of the plasma elec-
trons respectively, L is the inhomogeneity size) is not
satisfied. Therefore the simulation results do not de-
pend sufficiently from the sign of the beam velocity [9-
10].
At the late time points deformation of the ion con-
centration profile predicted in [3-5] was observed in
the LPRR.
4. DEFORMATION OF THE
CONCENTRATION PROFILE OF
ISOTHERMIC PLASMA
Firstly the short-wave perturbation (in the scale of
the LPRR width) appears. Instantaneous ion and elec-
tron concentration profiles strongly differ on this stage
(Fig.4a). Later the density cavity is formed in this re-
gion (Fig.4b). Sometimes local maximum of the plas-
ma concentration is observed in the center of the cavity
(Fig.5).
In the isothermic plasma (Те=Ті) at the late times
points the density cavity is transformed. Its left border
is smoothed (Fig.6a). At the same time its right border
becomes like a step. It results to the cavity transforma-
tion into the plasma concentration jump (Fig.6b). This
result agrees qualitatively with the calculation [2]. This
calculation was carried out for the plasma concentra-
tion profile deformation due to the HF electric field
(stationary case).
This concentration profile lasted out for the long pe-
riod (the time of about some hundreds of the modulation
periods). It indicates the balance between the plasma
thermal pressure and the HF electric field excited in the
LPRR by the modulated electron beam.
After the interval of about a thousand of the modula-
tion periods the concentration profile is smoothened due
to the diffusion. It results to the decrease of the concen-
tration jump.
The case of the beam moving from the dense plasma
was also examined. It does not differ significantly from
the previous case (as well as the linear stage of the pro-
cess).
а
б
Fig.4: a – deformation of the ion concentration profile
(f⋅t1≈65); b – formation of the density cavity (f⋅t1≈120).
ne, ni is concentration of electron and ion respectively.
L=1m, Те=6eV
Fig.5. Local maximum in the center of the cavity (f⋅t1≈
110)
a
b
Fig.6. L=2.5m, Те=25eV: a – transformation of cavity (f
⋅t1≈143); b – forming of concentration jump (f⋅t1≈195)
a
b
Fig. 7 a – excitation of ion-acoustic wave (f⋅t1≈235),
b – motion of ion-acoustic wave (t4>t3>t2>t1)
Fig.8. Plasma concentration profile for the late time
points (f⋅t1≈1650)
5. DEFORMATION OF THE
CONCENTRATION PROFILE OF PLASMA
WITH HOT ELECTRONS
When the electron plasma temperature is consider-
ably larger relatively to the ion temperature (plasma
with hot electrons) the ion-acoustic type’ perturbations
propagated from the cavity are observed (Fig.7). This
effect was predicted in [4] for the weakly non-linear
regime. Velocity of these ion perturbations measured
from the computer simulation was near to the ion-acous-
tic wave’ velocity calculated for the simulation parame-
ters. Electron concentration profile almost accurately re-
peats the ion concentration profile (Fig.7).
After the period of about two thousands of the mod-
ulation periods the ion concentration profile becomes
strongly indented in the wide region around the local
plasma resonance point (Fig.8). This result may be ex-
plained by the ion-acoustic turbulence excitation.
6. CONCLUSION
1. Interaction of the modulated electron beam with
the inhomogeneous plasma has been studied by means
of computer simulation using big-particles-in-cells
method.
2. The field in the local plasma resonance region ex-
cited by the modulated electron beam results to the de-
formation of the plasma concentration profile in this re-
gion. At the initial time points the density cavity is
formed on the spot of LPRR.
3. Character of the plasma concentration profile on
the spot of LPRR at the late time points depends strong-
ly upon the relation of the temperatures of plasma elec-
trons and ions. In the isothermic plasma (Те=Ті) the den-
sity cavity is transformed into the plasma concentration
jump. In the plasma with hot electrons the ion concen-
tration profile becomes strongly indented in the wide re-
gion around the spot of LPRR due to the ion-acoustic
turbulence excitation.
4. Quasi-periodical generation of the density cavities
in the LPRR that was obtained in [2] due to homoge-
neous external HF field was not observed in this simula-
tion.
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PACS: 52.35.Mw
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