EVOLUTION OF THE MODULATED ELECTRON BEAM IN SUPERCRITICAL PLASMA: SIMULATION OF INITIAL-BOUNDARY PROBLEM
Kiyanchuk M.J., Anisimov I.O.
Taras Shevchenko National University of Kyiv, Radio Physics Faculty
The problem of the modulated electron beam evolution in plasma is 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 barriers for electromagnetic waves using
electron beams  etc.
Study of the polarization beam-plasma instability at single frequency demonstrated its saturation
due to the beam electrons’ trapping by the potential electric wave . But for non-resonant
instability these results can be changed strongly due to the concurrence with the resonant mode (i.e.,
the mode in synchronism with the beam). If the initial modulation depth is not too large the beam
electrons can be trapped by the resonant mode, and further increase of the non-resonant mode can
be suppressed. This effect results to the linear dependence of the peak signal amplitude on its initial
Simulation in previous works  was carried out for the initial problem. But real experiments
 correspond to the initial-boundary problem. Computer simulation results for such kind of
the problem is given in this report.
2. Simulation method and parameters
Simulation was carried out via particle-in-cell method using modified program package PDP1
[6-7]. This package allows to define the initial modulation depth and to save intermediate modelling
results. One-dimensional model was treated. Initially homogeneous background plasma layer
is located between two plane conductive electrodes. Electron beam is injected from left electrode
and moves to right one. Simulation parameters (table 1) correspond approximately to the conditions
of experiment . The beam density was modulated harmonically with the depth over the
range of 0.05÷0.4.
Table 1. Simulation parameters
Plasma density 1011 cm-3
Simulation region length 20 cm
Plasma electrons’ thermal velocity 6 107 cm/s
Plasma ions’ thermal velocity 2,33 106 cm/s
Beam velocity 2 109 cm/s
Beam modulation frequency 2,6 GHz
3. Simulation results
Space-time distributions of ion and electron densities as well as electron beam density and
electric field strength were obtained. All the presented plots correspond to the modulation depth
Fig. 1 presents the space-time distributions of the electron beam density (a, b). Incidence of
lines corresponds to the beam velocity. During injection the beam density was modulated by the
signal frequency that is some smaller than ωр. During further propagation of the beam the resonant
instability develops from the noise level. As its increment exceeds signal’s increment, so in some
stage resonant instability traps beam electrons and cause modification of the modulation period.
Evolution of the modulated electron beam moving through the supercritical plasma was
studied in this work via computer simulation using PIC method. Results obtained correspond
qualitatively to the experimental data. It was shown that concurrence between the resonant mode
and the signal mode leads to the suppression of the non-resonant mode, as it was proposed in  on
the basis of simulation results of initial problem with periodic boundary conditions.
In contrast to previous simulation  it is obtained that the resonance instability occurs in
the broad frequency band. This fact adjusts with experiment. Frequency band expansion (for the
resonant instability) can be explained by the processes of l-s decay of the initial Langmuir wave.
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