According to classical linearized resistive magnetohydrodynamics theory, pressuredriven modes are unstable in the reversed-field pinch (RFP) due to unfavorable magnetic field line curvature. The result is based on the assumption of an adiabatic energy equation where anisotropic thermal conduction effects are ignored as compared to convection and compression. In this thesis the effects of heat conduction in the energy equation have been studied. We have examined these effects on the linear stability of pressure-driven resistive modes using boundary value theory (Δ´ ) and a novel initial-value full resistive MHD code employing the Generalized Weighted Residual Method (GWRM). In the Δ´ method, a shooting technique is employed by integrating from the resistive layer to boundaries. The GWRM method, on the other hand, is a time-spectral Galerkin method in which the fully linearized MHD equations are solved. For detailed computations, efficiency requires the temporal and spatial domains to be divided into subdomains. For this purpose, a number of challenging test cases including linearized ideal MHD equations are treated. Numerical and analytical investigations of equilibria reveal that thermal conduction effects are not stabilizing for reactor relevant values of Lundquist number, S0, and normalized pressure, βθ, for tearing-stable plasmas. These studies show that growth rate scales as  γ~_ S0−1/5 , which is weaker than for the adiabatic case, γ~_ S0−1/3. A numerical study of optimized confinement for an advanced RFP scenario including ohmic heating and heat conduction, is also part of this thesis. The fully nonlinear resistive MHD code DEBSP has been employed. We have identified, using both Δ´ and GWRM methods, that the observed crash of the high confinement is caused by resistive, pressure-driven modes. / <p>QC 20130503</p>

La stabilité des modes magnéto-hydrodynamiques dans les plasmas de tokamaks est modifiée par la présence de particules rapides. Dans un tokamak tel qu'ITER ces particules rapides peuvent être soit les particules alpha créées par les réactions de fusion, soit les ions et électrons accélérés par les dispositifs de chauffage additionnel et de génération de courant. Les modes appelés fishbones électroniques correspondent à la déstabilisation du mode de kink interne due à la résonance avec le lent mouvement de précession toroidale des électrons rapides. Ces modes sont fréquemment observés dans les plasmas des tokamaks actuels en présence de chauffage par onde cyclotronique électronique (ECRH) ou de génération de courant par onde hybride basse (LHCD). La stabilité de ces modes est particulièrement sensible aux détails de la fonction de distribution électronique et du facteur de sécurité, ce qui fait des fishbones électroniques un excellent candidat pour tester la théorie linéaire des instabilités liées aux particules rapides. Dans le tokamak Tore Supra, des fishbones électroniques sont couramment observés lors de décharges où l'utilisation de l'onde hybride basse crée une importante queue de particules rapides dans la fonction de distribution électronique. Bien que ces modes soit clairement liés à la présence de particules rapides, la fréquence observée de ces modes est plus basse que celle prévue par la théorie. En effet, si on estime l'énergie des électrons résonants en faisant correspondre la fréquence du mode avec la fréquence de précession toroidale des électrons faiblement piégés, on obtient une valeur comparable à celle des électrons thermiques. L'objet principal de cette thèse est l'analyse linéaire de la stabilité des fishbones électroniques. La relation de dispersion de ces modes est dérivée et la forme obtenue prend en compte, dans la condition de résonance, la contribution du mouvement parallèle des particules passantes. Cette relation de dispersion est implémentée dans le code MIKE qui est ensuite testé avec succès en utilisant des fonctions de distributions analytiques. En le couplant au code Fokker-Planck relativiste LUKE et à la plate-forme de simulation intégrée CRONOS, MIKE peut estimer la stabilité des fishbones électroniques en utilisant les données reconstruites de l'expérience. En utilisant des fonctions de distributions et des équilibres analytiques dans le code MIKE nous montrons que les électrons faiblement piégés ou faiblement passants peuvent déstabiliser le mode de kink interne en résonant avec lui. Si l'on s'éloigne de la frontière entre électrons passants et piégés, les effets résonants s'affaiblissent. Cependant les électrons passants conservent une influence déstabilisante alors que les électrons piégées tendent à stabiliser le mode. D'autres simulations avec MIKE, utilisant cette fois des distributions complètes similaires à celles obtenues en présence de chauffage de type ECRH, montrent que l'interaction avec les électrons faiblement passants peut entraîner une déstabilisation du mode à une fréquence relativement basse ce qui pourrait permettre d'expliquer les observations sur le tokamak Tore Supra.

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.

In this thesis, the two-dimensional initial and boundary value problems invol-ving convection and diffusion terms are solved using the boundary element method (BEM). The fundamental solution of steady magnetohydrodynamic (MHD) flow equations in the original coupled form which are convection-diffusion type is established in order to apply the BEM directly to these coupled equations with the most general form of wall conductivities. Thus, the solutions of MHD flow in rectangular ducts and in infinite regions with mixed boundary conditions are obtained for high values of Hartmann number, M. For the solution of transient convection-diffusion type equations the dual reciprocity boundary element method (DRBEM) in space is combined with the differential quadrature method (DQM) in time. The DRBEM is applied with the fundamental solution of Laplace equation treating all the other terms in the equation as nonhomogeneity. The use of DQM eliminates the need of iteration and very small time increments since it is unconditionally stable. Applications include unsteady MHD duct flow and elastodynamic problems. The transient Navier-Stokes equations which are nonlinear in nature are also solved with the DRBEM in space - DQM in time procedure iteratively in terms of stream function and vorticity. The procedure is applied to the lid-driven cavity flow for moderate values of Reynolds number. The natural convection cavity flow problem is also solved for high values of Rayleigh number when the energy equation is added.

An almost universal instability in high pressure plasmas is the Neoclassical Tearing Mode (NTM). NTMs are driven by local perturbations in the current density and result in magnetic island like deformations of the magnetic topology. They can be stabilized by compensating the current perturbations with local electron cyclotron resonance heating (ECRH) or with non-inductive current drive (ECCD). The modified Rutherford equation describes the nonlinear evolution of tearing modes as determined by various contributions to the local current density pertubation. An extensive investigation of the two terms representing the stabilizing effects from ECRH and ECCD have been made resulting in accurate description of both terms. The results of this model can now be compared to the experimental observations. For this purpose, an extensive data set exists from the past experiments on tearing mode stabilization by ECRH and ECCD on TEXTOR. The properly benchmarked model can then be used to predict the effectiveness of ECRH and ECCD for NTM stabilization on International Thermonuclear Experimental Reactor (ITER). In addition, a number of predictions on the effects of ECRH and ECCD on the growth of the NTM have been made on the basis of crude approximations to the ECRH and ECCD tems in the modified Rutherford equation. These predictions can now be checked against the more accurate expressions obtained.

In this thesis, the two-dimensional initial and boundary value problems governed by unsteady partial differential equations are solved by making use of boundary element techniques. The boundary element method (BEM) with time-dependent fundamental solution is presented as an efficient procedure for the solution of diffusion, wave and convection-diffusion equations. It interpenetrates the equations in such a way that the boundary solution is advanced to all time levels, simultaneously. The solution at a required interior point can then be obtained by using the computed boundary solution. Then, the coupled system of nonlinear reaction-diffusion equations and the magnetohydrodynamic (MHD) flow equations in a duct are solved by using the time-domain BEM. The numerical approach is based on the iteration between the equations of the system. The advantage of time-domain BEM are still made use of utilizing large time increments. Mainly, MHD flow equations in a duct having variable wall conductivities are solved successfully for large values of Hartmann number. Variable conductivity on the walls produces coupled boundary conditions which causes difficulties in numerical treatment of the problem by the usual BEM. Thus, a new time-domain BEM approach is derived in order to solve these equations as a whole despite the coupled boundary conditions, which is one of the main contributions of this thesis. Further, the full MHD equations in stream function-vorticity-magnetic induction-current density form are solved. The dual reciprocity boundary element method (DRBEM), producing only boundary integrals, is used due to the nonlinear convection terms in the equations. In addition, the missing boundary conditions for vorticity and current density are derived with the help of coordinate functions in DRBEM. The resulting ordinary differential equations are discretized in time by using unconditionally stable Gear&#039 / s scheme so that large time increments can be used. The Navier-Stokes equations are solved in a square cavity up to Reynolds number 2000. Then, the solution of full MHD flow in a lid-driven cavity and a backward facing step is obtained for different values of Reynolds, magnetic Reynolds and Hartmann numbers. The solution procedure is quite efficient to capture the well known characteristics of MHD flow.

<p>Conventional one-point turbulence closures have beenextended with an additional transported scalar for modeling ofmagnetohydrodynamic (MHD) turbulence. The new scalar, α ,captures the length scale anisotropy and tendency towardstwo-dimensionality, which is characteristic feature of MHDturbulence, and allows accurate modeling of the Jouledissipation of turbulence. The concept has been used for both afull Reynolds stress closure, and a three-equation<i>K-ε -α</i>model. An exact transport equation forαwas derived from the governing equations. All terms inthe equation require modeling, however. The proposed modeltransport equation for α includes terms for magneticdissipation, nonlinear energy transfer, and effects of meanshear and strain. Modeling of the magnetic and strain-relatedterms was based on rapid distortion analysis of the linearizedequations, while modeling of nonlinear effects isphenomenological in nature. For homogeneous turbulence, themodel was compared with linear theory, direct numericalsimulations and experiments. For turbulence subjected to astrong magnetic field, the model reproduces the energy andlength scale evolution predicted by linear theory. Whennonlinear effects are of importance, it predicts energy decayand length scale evolution in agreement with experiments. Theeddy viscosity and Reynolds stress versions of the modelcoincide with the respective conventional models in the absenceof a magnetic field. The objective of this project has been todevelop efficient MHD turbulence models for engineeringapplications, especially for modeling of continuous steelcasting. The novel MHD turbulence models appear to benumerically robust, and they have been implemented in acommercial flow solver, together with electromagnetic equationsfor the Lorentz forces in the mean momentum equations.</p><p><b>Keywords:</b>Turbulence model, magnetohydrodynamics, MHD,magnetohydrodynamic turbulence, computational fluid dynamics,continuous casting, dimensionality, Reynolds stresses, eddyviscosity</p>

<p>The Reversed-Field Pinch (RFP) is one of the major alternatives for realizing energy production from thermonuclear fusion. Compared to alternative configurations (such as the tokamak and the stellarator) it has some advantages that suggest that an RFP reactor may be more economic. However, the conventional RFP is flawed with anomalously large energy and particle transport (which leads to unacceptably low energy confinement) due to a phenomenon called the "RFP dynam".</p><p>The dynamo is driven by the gradient in the plasma current in the plasma core, and it has been shown that flattening of the plasma current profile quenches the dynamo and increases confinement. Various forms of current profile control schemes have been developed and tested in both numerical simulations and experiments.</p><p>In this thesis an automatic current profile control routine has been developed for the three-dimensional, non-linear resistive magnetohydrodynamic computer code DEBSP. The routine utilizes active feedback of the dynamo associated fluctuating electric field, and is optimized for replacing it with an externally supplied field while maintaining field reversal. By introducing a semi-automatic feedback scheme, the number of free parameters is reduced, making a parameter scan feasible. A scaling study was performed and scaling laws for the confinement of the advanced RFP (an RFP with enhanced confinement due to current profile control) have been obtained.</p><p>The conclusions from this research project are that energy confinement is enhanced substantially in the advanced RFP and that poloidal beta values are possible beyond the previous theoretical limit beta β_Θ < ½. Scalings toward the reactor regime indicate strongly enhanced confinement as compared to conventional RFP scenarios, but the question of reactor viability remains open.</p>

In this thesis the effect of the Hall term in the generalised Ohm's law on Alfvén (shear) and fast wave propagation and dissipation in the ion cyclotron frequency range is investigated. The damping of an initially Gaussian field perturbation in a uniform Hall MHD plasma is treated analytically. Subsequently a 2D Lagrangian remap code (Lare2d) is used to study the damping and phase mixing of initially Gaussian field perturbations and a harmonic series of boundary-driven perturbations in a uniform field (in the presence of a transverse equilibrium density gradient). The same code is then used to study a range of initially shear and fast-wave perturbations in the vicinity of a magnetic X-type null point. The magnetic energy associated with an initially Gaussian field perturbation in a uniform resistive plasma is shown to decay algebraically at a rate that is unaffected by the Hall term to leading order in kδ where k is wavenumber and δ is ion skin depth. A similar decay law applies to whistler perturbations in the limit kδ>>>1. We demonstrate that in both geometries considered, the inclusion of the Hall term reduces the effectiveness of phase-mixing in plasma heating. The reduction in the damping rate in the uniform field (non-uniform density) cases, arising from dispersive effects, tends to zero in both the weak and strong phase mixing limits. In the Hall MHD X-point case, minimal reductions are seen for initially shear wave pulses, suggesting that little or no phase-mixing takes place. Nonlinear fast wave pulses which interact with the initial X-point destabilise the local field sufficiently to generate multiple null pairs; subsequent oscillatory current sheet behaviour appears unaffected by earlier differences between the MHD and Hall MHD cases.

We present a novel new method for modelling magnetized molecular cloud cores using submillimetre linear polarization maps from thermal dust emission. Our PolCat modelling software builds a three-dimensional core model via the use of consecutive parametrized coordinate transformations, and produces simulated polarization maps to fit to observational datasets. We utilize the Ferret evolutionary optimizer to search the parameter space to simultaneously minimize chi-squared for the intensity and polarization position angle maps separately. We have applied PolCat to multiple test problems and several datasets from the SCUPOL Legacy Catalogue. We find that PolCat is able to distinguish between maps of twisted and non-twisted field geometries and identify twist symmetry. Preliminary fits to several datasets show that the best potential field geometries to our sample cores contain field twists. Further research using a larger number of maps is required to determine if twisted fields are commonplace in cores.