This thesis presents an analytical and computational approach to modelling partially ionised, spatially-inhomogeneous and recombining plasmas. The specific contextfor this study is astrophysical plasmas, the early Universe in particular. Two models are investigated in detail: a magnetohydrodynamic (MHD) plasma model to simulatepartially ionised plasmas; and a fully electromagnetic/kinetic model, used to study recombining plasmas. The first section further develops an existing computational model of a partially ionised plasma as a mixture of two cospatial fluids: an MHD plasma and a neutral gas. In order to model the interaction between the plasma and neutral gas populations ab initio, a collisional momentum exchange term was added to the momentum equation of each fluid. The model was used to investigate the combined response to different wave modes driven in the plasma or the neutral gas. The momentum coupling between theplasma and the neutral gas leads to complex interactions between the two populations. In particular, the propagation of plasma waves induces waves in the neutral gas byvirtue of the collisional momentum exchange between the velocity fields of each fluid. This means that the normal wave modes of each independent fluid are modified toproduce a combined, hybrid response, with the intriguing possibility that neutral gas can not only respond indirectly to magnetic fluctuations but also generate them via sound waves. This model is used to examine an existing observational method known as the ‘Chandrasekhar-Fermi method’ (CF53) for the diagnosis of magnetic fields in astrophysical plasmas. CF53 is commonly applied to objects such as nebulae and molecular clouds which are partially-ionised plasmas. It assumes that the gas motion canbe used to infer the magnetic field strength, given coupling between Alfv´en waves in the plasma and the thermal motion of the neutral gas. Computational results show that this method may need to be refined, and that certain assumptions made should be re-evaluated. This is consistent with reports in the literature of CF53 under- orover-estimating the magnetic fields in objects such as molecular clouds.The second part of this thesis concentrates on the non-equilibrium evolution of magnetic field structures at the onset of the large-scale recombination of an inhomogeneouslyionised plasma, such as the Universe was during the epoch of recombination. The conduction currents sustaining the magnetic structure will be removed as the charges comprising them combine into neutrals. The effect that a decaying magnetic flux has on the acceleration of remaining charged particles via the transient induced electric field is considered. Since the residual charged-particle number density is small as a result of decoupling, the magnetic and electric fields can be considered essentially to be imposed, neglecting for now the feedback from any minority accelerated population. The electromagnetic treatment of this phase transition can produce energetic electrons scattered throughout the Universe. Such particles could have a significant effecton cosmic evolution in several ways: (i) their presence could influence the overall physics of the recombination era; and (ii) a population of energetic particles mightlend a Coulomb contribution to localized gravitational collapse. This is confirmed by a numerical simulation in which a magnetic domain is modelled as a uniform field region produced by a thin surrounding current sheet. The imposed decay of the current sheet simulates the formation of neutrals characteristic of the decoupling era, and the induced electric field accompanying the magnetic collapseis able to accelerate ambient stationary electrons (that is, electrons not participating in the current sheet) to energies of up to order 10keV. This is consistent with theoretical predictions.
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Cosmic magnetism: The plasma physics of the recombining universe