2D3V electromagnetic particle-in-cell simulations of plasmas having kappa velocity distributions.
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Date
2018
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Abstract
It is now well established that the kappa distribution is a more appropriate kinetic model
for space plasmas than the Maxwellian distribution. In particular it possesses a power-law
tail, frequently observed in space plasmas. The research presented in this thesis outlines
the development of a two-dimensional electromagnetic particle-in-cell (PIC) simulation code,
designed to run on general purpose graphics processing units (GPGPUs), and presents results
from simulations of waves and instabilities obtained using it. While PIC simulations
are not new, the majority have focussed on the old paradigm of initial particle loadings with
a Maxwellian velocity distribution, or one of its variants. Distinguishing this research from
previous PIC simulations is the use of the kappa distribution for the initial particle loading.
To achieve this, a fast and e cient algorithm for generating multi-dimensional kappa
distributed deviates was developed.
The code is rst applied to the study of waves in an electron-ion plasma, in a stable equilibrium
con guration with a constant background magnetic eld. Both species are modelled by
isotropic (a) kappa and (b) Maxwellian velocity distributions. In each case, spectral analysis
of the eld
uctuations is performed, allowing mode identi cation. For parallel propagation,
the maximum
uctuation intensities follow the dispersion relations for the L and R modes,
respectively, while those at perpendicular propagation follow the dispersion relations for the
X, O and electromagnetic electron and ion Bernstein waves. The variation of wave intensity
for the oblique angles is also investigated. For the kappa case, this yields new and important
information presently unavailable by analysis alone. The e ects of the kappa distribution on
wave intensity, as well as its e ect on the dispersion relations of the modes is discussed in
detail.
The second application is to the simulation of the electron temperature anisotropy driven
whistler instability in an electron-ion plasma, where the electron species is modelled by the (a)
bi-kappa and (b) bi-Maxwellian velocity distribution. For parallel propagation, the maximum
eld
uctuation intensities agree well with the dispersion relation for the whistler instability
in a kappa plasma. While most of the wave intensity is in the parallel whistler mode, the
oblique modes also contribute signi cantly to the overall
uctuation spectrum, but their
intensities vary with angle of propagation relative to the magnetic eld. The dependence of
the growth rate on the index e of the electron kappa distribution is discussed in detail and
compared with the well known Maxwellian results. Saturation of the instability via pitch
angle scattering, reducing the electron temperature anisotropy, is observed.
Description
Doctoral Degree. University of KwaZulu-Natal, Durban.