This study uses the Magnetohydrodynamics (MHD) method to simulate unsteady two-dimensional transport variables in argon (Ar) plasma, under low pressure, high density, and weak ionization between two infinite planar electrodes suddenly biased by a negative voltage. Plasma has been widely used in materials processing, thin film manufacturing, light source, nuclear fusion, and etching, etc. Properties of plasmas are also becoming important area for research in physics, chemistry, photonics, aerospace, engineering science and technology. Studying transport processes of plasmas therefore is important. This research consider by electric fields and magnetic fields, viscous, momentum exchange collisions between electrons ions and neutral particles. The computed results in this work quantitatively show density, velocity, electric potential, temperature, magnetic field, viscosity, thermal conductivity of the electrons ions and neutral particles across the sheath to the surfaces suddenly biased by a DC negative voltage. And increase of the boundary layer and sheath thickness. We can compare the theory and the simulation to know the behavior of the plasma near a surface.

The effect of an imposed magnetic field on the thermal convection between rigid plates heated from below under the influence of gravity is numerically simulated in a computational domain with periodic horizontal extent. The numerical technique is based on solenoidal basis functions satisfying the boundary conditions for both velocity and induced magnetic field. The expansion bases for the thermal field are also constructed to satisfy the boundary conditions. The governing partial differential equations are reduced to a system of ordinary differential equations governing the time evolution of the expansion coefficients under Galerkin projection onto the subspace spanned by the dual bases. In the process, the pressure term in the momentum equation is eliminated. The system validated in the linear regime is then used for some numerical experiments in the nonlinear regime.

Thesis (M.Sc.-Res.)--University of Wollongong, 2009. / Typescript. Includes bibliographical references: leaf 91-95.

The Magnetorotational Instability (MRI) is believed to be the primary mechanism for angular momentum transfer in astrophysical accretion disks. This instability, which exists in ionized disks in the presence of weak magnetic fields, can either transfer angular momentum directly, or give rise to anomalous viscosity via non-linear turbulence. While many previous analytical treatments are concerned with the local theory of the MRI, when the length scale of rotation shear is comparable to the length scale of the most unstable modes, a global analysis is necessary. In this dissertation we investigate the global theory of the linear MRI. In particular, we show how rotation shear can localize global modes and how the global growth rates can differ signicantly from the local approximation in certain cases. Changes in the equilibrium density are considered. In addition, the effects of Hall Magnetohydrodynamics on the MRI are studied in both the local and global cases. / text

While the process that converts implosion into explosion in core collapse supernovae is poorly understood, their observed asphericity provides new constraints on the physics of these events. Since pulsars are rotating and magnetized neutron stars, there is no doubt that rotation and magnetic fields are inherent to the exploding engine. We have shown that magnetic field amplification is an inevitable by-product of the differential rotation that accompanies core-collapse. We performed 1D core-collapse simulations of rotating iron cores with various rotational profiles and velocities. We found that differential rotation was a generic feature of rotating iron core collapse. As a result, the magnetorotational instability (MRI) generates magnetic fields of order 10¹⁵⁻¹⁷ G in a few tens of milliseconds where the negative shear is the strongest. Although magnetic fields of order 10¹⁵⁻¹⁷ G are very strong, they are not strong enough to modify the equation of state of degenerate electron gas near the proto-neutron star. The corresponding MHD luminosity available is ~10⁵² erg s⁻¹, which can modify the explosion dynamics if the power is sustained for a fraction of a second. When rotational effects are included, we found that there is a critical iron core rotation rate that gives the most rapidly rotating proto-neutron star, faster than which the rotational velocity of the proto-neutron star decreases due to centrifugal support. This non-monotonic behavior of post-collapse core rotation suggests that the progenitor of the most rapidly rotating proto-neutron star is not the most rapidly rotating iron core, but that those iron cores with nearly the critical initial rotation rate may produce the maximum proto-neutron star rotation, the strongest magnetic fields, and the most robust supernova explosions. Even small rotation may induce non-axisymmetric instabilities, which drive magneto-acoustic flux in to the mantle, transporting enegy out of the proto-neutron star to the region near the stalled shock. Further implications for rotation and magnetic fields, pulsars and magnetars, and jet formation mechanisms are discussed. / text

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The work in this thesis focuses primarily on equilibrium and stability properties of collisionless current sheet models, in particular of the force-free Harris sheet model. A detailed investigation is carried out into the properties of the distribution function found by Harrison and Neukirch (Physical Review Letters 102, 135003, 2009) for the force-free Harris sheet, which is so far the only known nonlinear force-free Vlasov-Maxwell equilibrium. Exact conditions on the parameters of the distribution function are found, which show when it can be single or multi-peaked in two of the velocity space directions. This is important because it may have implications for the stability of the equilibrium. One major aim of this thesis is to find new force-free equilibrium distribution functions. By using a new method which is different from that of Harrison and Neukirch, it is possible to find a complete family of distribution functions for the force-free Harris sheet, which includes the Harrison and Neukirch distribution function (Physical Review Letters 102, 135003, 2009). Each member of this family has a different dependence on the particle energy, although the dependence on the canonical momenta remains the same. Three detailed analytical examples are presented. Other possibilities for finding further collisionless force-free equilibrium distribution functions have been explored, but were unsuccessful. The first linear stability analysis of the Harrison and Neukirch equilibrium distribution function is then carried out, concentrating on macroscopic instabilities, and considering two-dimensional perturbations only. The analysis is based on the technique of integration over unperturbed orbits. Similarly to the Harris sheet case (Nuovo Cimento, 23:115, 1962), this is only possible by using approximations to the exact orbits, which are unknown. Furthermore, the approximations for the Harris sheet case cannot be used for the force-free Harris sheet, and so new techniques have to be developed in order to make analytical progress. Full analytical expressions for the perturbed current density are derived but, for the sake of simplicity, only the long wavelength limit is investigated. The dependence of the stability on various equilibrium parameters is investigated.

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