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Parametric Excitation Of Counter-Propagating Surface Waves By A Normal Electric Field

Yu.A. Akimov¤ and N.A. Azarenkov¤
¤Karazin Kharkiv National University, 31 Kurchatov av., 61108 Kharkiv, Ukraine
Abstract. This report presents a study of the nonresonant parametric excitation of counter-propagating surface waves by a
uniform in space and variable in time electric pump field, perpendicular to a planar plasma-dielectric interface. The criterion
of the wave excitation has been derived and analyzed. Expressions for the growth rates in the linear stage of instability are
obtained, and the threshold amplitudes of the external electric field above which the parametric instability can occur are found.
It is analyzed also the spectrum of excited waves.
Keywords: Surface waves, parametric instability, nonresonant excitation
PACS: 52.35.Mw, 52.40.Db
Intensive research on surface wave (SWs) parametric instability in bounded plasma-like mediums date from the 1970s
– 1980s. They were connected with the necessity to solve a problem of energy input to working volumes of plasma
installations, including controlled fusion ones. Therefore, the main attention in these research was focused on the
parametric excitation of SWs owing to the induced scattering of electromagnetic waves incident from a dielectric or
vacuum area on a semibounded plasma. More recently, these research have found the continuation in the study of SWs
excited under irradiation of solid targets by intense, ultrashort laser pulses.
Other research direction on SW parametric instability is connected with their excitation by an external homogeneous
electric pump field. Influence of the pump field lying on the boundary plane is full enough studied, while research
on SW excitation in isotropic plasma installations with a high frequency electric field, oriented perpendicularly to
the medium interface, are represented much more poorly. Our research, is devoted to the analysis of a nonresonant
parametric instability of two counter-propagating SWs in a cold isotropic plasma, which is immersed in a normal to
the medium interface high frequency electric field.
We consider a semibounded homogeneous dissipative isotropic plasma bounded by a dielectric. Let the z-axis is
directed along the wave propagation direction, while the x-axis is perpendicular to the plasma-dielectric interface. The
plasma occupies the half-space x > 0, whereas the dielectric occupies the x < 0 region. In the considered structure, the
wavenumber kz and frequency.

This condition imposes a restriction on a minimum value of the pump field amplitude, above which the SW excitation
is possible, jE0jth. Under smaller amplitudes of the pump field, the SW damping dominates over the growth of their
amplitudes due to the parametric instability and results in a decreasing of both the SW amplitudes in time. At excess
by the pump field of the threshold value (22), a simultaneous growth of both the SW amplitudes appears. This growth
is characterized by the nonlinear rate
gNL =
a2jE0j2¡Dw2¡g : (23)
Thus, an increase in the pump field amplitude, jE0j, as well as a decrease of the linear damping rate, g , leads to an
increase of the nonlinear growth rate, gNL. At that, a maximum of the growth rate is reached at a resonant excitation of
the SWs (Dw = 0) [2], when two counter-propagating SWs are excited with the frequencies w =w0=2.
The numerical analysis (fig. 1) shows that the threshold value (22) decreases, as the frequency w0 increases or the
mismatch frequency, Dw, decreases. Thus, the considered pump field can excite a spectrum of the SWs (fig. 1). A
width of this spectrum, Dw+(E0)¡Dw¡(E0), is determined by the values Dw§(E0), at which jE0jcr = jE0j and the
nonlinear growth rate gNL vanishes.
According to the results shown in fig. 1, an increase in the frequency and amplitude of the pump field leads to
an increase of the excited SW spectrum width, while the half-frequency of pump field, w0=2, does not come close
to a maximum value of the SW frequency, wmax = wpe=
1+ed, above which the SW existence is impossible
[1]. It explains behavior of the curve in fig. 1 corresponding to w0=wpe = 1:0. At that value of the parameter
w0=wpe, the half-frequency of pump field, w0=2, exceeds the maximum SW frequency, wmax, (in the presented
calculations wmax ¼ 0:457 wpe). As a result, the excitation of SWs with frequencies above the half-frequency of
pump field, w >w0=2, becomes impossible. Further increase of w0 results in a decreasing of the SW spectrum, while
w0=2+Dw¡(E0) does not reach the value wmax, when the excitation of any SWs becomes impossible.
1. A. N. Kondratenko, Plasma Waveguides, Atomizdat, Moscow, 1976.
2. J. Weiland and H. Wilhelmsson, Coherent Nonlinear Interaction of Waves in Plasmas, Pergamon, Oxford, 1976.

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