## Linear and nonlinear waves in space plasmas.

##### Abstract

The work presented in this thesis is about a study of some linear and nonlinear
plasma waves.
Firstly, a kinetic-theoretical approach is used to study ion Bernstein
waves in an electron-proton plasma with a kappa velocity distribution. The
effects of the parameter kappa on the dispersion relation of ion Bernstein
waves are discussed in detail, considering various values of the ratio of the
ion plasma frequency to the ion cyclotron frequency, ωpi/ωci, allowing application
of the results to various space environments.
For a fixed value of ωpi/ωci, we have found that the dispersion relation
depends significantly on the parameter kappa of the ions, κi, but is independent
of the electron kappa. Over all cyclotron harmonics, the dispersion
curves are shifted to higher wavenumbers (k) if κi is reduced. When the
value of ωpi/ωci is increased, the fall-off of the wave frequency, ω, at large k
is smaller for lower κi, and curves are shifted towards larger wavenumbers.
For large values of ωpi/ωci, the ion Bernstein wave dispersion curves
within and above the lower hybrid frequency band exhibit coupling for the
Maxwellian case, unlike the kappa case. We have suggested that this result
may be a useful diagnostic for determining whether the ion velocity
distribution possesses a power law tail.
Considering parameter values that have been observed in the Earth’s
plasma sheet boundary layer, and neighbouring environments, it has been
found that the dispersion curves of ion Bernstein waves are typical of those
obtained for the case of a high-density plasma immersed in a weak magnetic
field.
Secondly, a fluid model is used to study linear and nonlinear ion acoustic
waves supported by a two-adiabatic-ion plasma in which both ion species are
positively and singly charged. This plasma model supports the propagation
of two modes with different phase speeds. By normalising variables with
respect to the characteristics of the hotter ion species, the thermal effects of
the cooler ion species and the electrons on the two modes are discussed in
detail.
The main thrust has been to study arbitrary amplitude ion acoustic solitons
and double layers, using the fully nonlinear Sagdeev potential theory,
but we have also considered linear theory and the KdV theory as a useful
background.
The thermal effects of the cooler ion species and the electrons on the
soliton existence domain and on the soliton/double layer speed, amplitude,
and maximum profile steepness are discussed in detail. While some of the
results are consistent with the results that are in the literature, there are
many new results which have not been reported previously.
These include the existence of a novel stopband in the existence domain
of fast solitons. By a stopband, we mean a range of Mach numbers between
two passbands of an existence domain over which solitary wave propagation
does not occur. The presence of a stopband is dependent on the ion-ion
mass ratio and the hotter ion to electron temperature ratio, and it exists
only when the thermal effects of the cooler ion species are small.