| Summary: | This dissertation documents my mathematical and computational research on plasmas which contain small, charged particulate matter (dust) in the presence of magnetic fields. Phenomena from two limiting cases of dust dominance are considered, these being where the grains are plentiful enough to introduce new collective plasma behaviours and sparse enough such that the grains are effectively passengers in the plasma. The study into the former limit looks at the effect which immobile dust grains have on transversely and obliquely propagating Alfv´enic solitary waves, with application to cometary and planetary magnetospheres. The spatial structure and permissible range of speeds is derived for the transverse wave. For oblique waves the problem is partially solved, with necessary, but not sufficient, restrictions on the wave speed and direction being found. Next is a study where dust is not dominant, looking at the plasma structure near to a conducting wall which has an embedded magnetic dipole oriented perpendicular to the surface, with application to dusty crystal experiments and lunar swirls. A study of electron kinetic behaviour is carried out and a novel way to calculate their density is formulated. Once implemented into a sheath model this reveals that a ring of positive space charge appears in the sheath which is capable of influencing dust grain dynamics and repelling incoming ions.
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