## Linear and nonlinear electron-acoustic waves in plasmas with two electron components.

##### Abstract

Measurements of broadband electrostatic wave emIssons in conjunction
with particle distributions in the earth's magnetosphere, have provided motivation
for a number of studies of waves in plasmas with two electron
components. One such wave-the electron-acoustic wave-arises when the
two electron components have widely disparate temperatures (Watanabe &
Taniuti 1977), and has a characteristic frequency that lies between the ion
and electron plasma frequencies. Because of this broadband nature and because
it is predominantly electrostatic, it provides a likely candidate for the
explanation of the electrostatic component of "cusp auroral hiss" observed
in the dayside polar cusp at between 2 and 4 earth radii as well as the broadband
electrostatic noise (BEN) observed in the dayside polar regions and in
the geomagnetic tail. The electron-acoustic wave and its properties provide
the subjects for much of the investigation undertaken in this thesis.
The thesis is divided into two parts. Part I is concerned with certain
aspects of the linear theory of the electron-acoustic wave and is based on
a kinetic description of the plasma. The dispersion relation for plane electrostatic
waves obtained via linearisation of the Vlasov-Poisson system is
studied in detail using analytical and numerical/geometrical techniques, and
conditions under which the electron-acoustic wave arises are expounded.
This work represents an extension of earlier works on Langmuir waves (Dell,
Gledhill & Hellberg 1987) and the electron-acoustic wave (Gary & Tokar
1985). The effects of electron drifts and magnetization are investigated. These
result, respectively, in a destabilization of the electron-acoustic wave and a
modification of the dispersive properties. In this plasma configuration the
model more closely replicates the conditions to be found in the terrestrial
polar regions. We extend the parameter regimes considered in earlier works
(Tokar &Gary 1984) and in addition, identify another electron sound branch
related to the electron-cyclotron wave/instability.
Effects of ion-beam destabilization of the electron-acoustic wave are also
investigated briefly with a view to explaining BEN in the geomagnetic tail
and also to provide a comparison with the electron-driven instability.
In part II the nonlinear electron-acoustic wave is studied by employing
a warm hydrodynamic model of the plasma components. We first consider
weak nonlinearity and employ the asymptotic reductive perturbation technique
of Washimi &Taniuti (1966) to render the hydrodynamical equations
in the form of simpler evolutionary equations describing weakly-nonlinear
electron-acoustic waves. These equations admit solitary-wave or soliton solutions
which are studied in detail.
Wherever possible we have justified our small amplitude results with full
numerical integration of the original hydrodynamical equations. In so doing
we extended the range of validity of our results to arbitrary wave amplitudes
and also find some interesting features not directly predicted by the small
amplitude wave equations. In this respect we were able to determine the important
role played by the cool- to-hot electron temperature ratio for soliton
existence. This important effect is in accordance with linear theory where
the electron temperature ratio is found to be critical for electron-acoustic
wave existence.
The effects of magnetization on electron-acoustic soliton propagation is
examined. We found that the magnetized electron-acoustic solitons are governed
by a Korteweg-de Vries-Zakharov-Kusnetsov equation. In addition,
it is shown that in very strong magnetic fields ion magnetization can become
important yielding significant changes in the soliton characteristics.
Multi-dimensional electron-acoustic solitons, which have greater stability
than their plane counterparts, are also briefly discussed.
Employing a weakly-relativistic hydrodynamic model of the plasma, the
effect of a cool, relativistic electron beam on such soliton parameters as
width, amplitude and speed is studied in detail. Both small- and large amplitude
solitons are considered. The arbitrary-amplitude theory of Baboolal
et al. (1988) is generalised to include relativistic streaming as well
as relativistic thermal effects. The importance of the cool electron (beam)to-
hot electron temperature in conjunction with the beam speed is pointed
out.
Finally, we derive a modified Korteweg-de Vries (mKdV) equation in an
attempt to establish whether electron-acoustic double layers are admitted
by our fluid model. Although double layers formally appear as stationary
solutions to the mKdV equation, the parameter values required are prohibitive.
This is borne out by the full fluid theory where no double layer
solutions are found.