| dc.description.abstract | Explosive instability due to non?linear wave–wave
interaction is one of the most interesting phenomena in
non?linear plasma theory. Since it is widely recognized
that plasma, either in nature or in laboratory, is
bounded in one way or the other, in the present work the
author examines the explosive instabilities of a bounded
plasma and their saturation through the mechanism of a
non?linear frequency shift.
The thesis starts with the description of the
motivation and summary of the work, in the introductory
chapter. In the second chapter, the high?frequency
three?wave non?linear “explosive” interaction of the
surface modes of a semi?infinite beam–plasma system under
no external field is investigated. The conditions that
favour non?linear instability keep the plasma linearly
stable. The beam runs parallel to the surface and the
density of beam (n?) is less than the density of
plasma (n). The explosion time of bulk and surface
waves is determined. A comparative study of the explosion
time of the bulk and surface waves for different cases of
wave propagation reveals some interesting results. If at
least one of the three wave vectors of the surface modes
is parallel to the beam, explosive interaction at the
surface takes place after it has happened in the plasma
bulk, provided the bulk waves propagate almost perpendicular
to the surface and are of short wavelength. On the other
hand, if bulk modes have long wavelength and are
parallel to the surface, the surface modes can explode first.
In the third chapter, the study of the saturation of
explosive instability due to non?linear frequency shift
is taken up. This chapter is devoted to the derivation
of surface and bulk coupling coefficients for four?wave
interaction. For four?wave interaction, only those three
waves creating explosive instabilities (as discussed in
the previous chapter) are taken into consideration along
with the fourth one which is the complex conjugate of any of
those three waves. The non?linear frequency shift for both
the bulk and surface waves is calculated. The frequency
shift is found to be different for different cases of
wave propagation of the bulk as well as surface waves.
Since it is well known that a frequency mismatch in
resonance conditions can stabilize an explosive instability,
this non?linear frequency shift can saturate the explosively
growing amplitudes of the bulk and surface waves. Secondly,
a change in beam density within the limit n? < n can
saturate explosive instabilities for different types of wave
propagation along the plane of the boundary surface. Increasing
the beam density, the parallel waves saturate earlier than
the antiparallel wave (k?? > k?? — where k?? and k??
are the wave vectors of the antiparallel wave lying along
the boundary surface). Within a small variation of beam
density this is followed by the saturation of the antiparallel
wave (k?? < k??). In the concluding chapter,
some of the main results of this thesis are briefly reviewed. | |
