It is shown numerically, both for the two-dimensional Navier-Stokes equations and for two-dimensional magnetohydrodynamics, that the long-time asymptotic state in a forced inverse-cascade situation is one in which the spectrum is completely dominated by its own fundamental. The growth continues until the fundamental is dissipatively limited by its own dissipation rate. An algebraic model is proposed for the dynamics of such a final state.

The subject of this thesis is an analysis of results from pseudospectral simulation of the Strauss equations of reduced three-dimensional magnetohydrodynamics. We have solved these equations in a rigid cylinder of square cross section, a cylinder with perfectly conducting side walls, and periodic ends. We assume that the uniform-density magnetofluid which fills the cylinder is resistive, but inviscid. Situations which we are considering are in several essential ways similar to a tokamak-like plasma; an external magnetic field is imposed, and the plasma carries a net current which produces a poloidal magnetic field of sufficient strength to induce current disruptions. These disruptions are characterized by helical "m = 1, n = 1" current filaments which wrap themselves around the magnetic axis. An ordered, helical velocity field grows out of the broad-band, low amplitude noise with which we initialize the velocity field. Kinetic energy peaks near the time the helical current filament disappears, and the current column broadens and is flattens itself out. We find that this is a nonlinear, turbulent phenomenon, in which many Fourier modes participate. By raising the Lundquist number used in the simulation, we are able to generate situations in which multiple disruptions are induced. When an external electric field is imposed on the plasma, the initial disruption, from a quiescent, state, is found to be very similar to those observed in the undriven runs. After the lobed "m = 1, n = 1" stream function pattern develops, however, a quasi-steady state with flow is maintained for tens of Alfven transit times. If viscous damping is included in the driven problem, the steady state may be avoided, and additional disruptions produced in a time less than a large-scale resistive decay time.

Renormalization group theory is applied to incompressible three-dimension Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term.;Renormalization group theory is also applied to a model Alfven wave turbulence equation. In particular, the effect of small unresolvable subgrid scales on the large scales is computed. It is found that the removal of the subgrid scales leads to a renormalized response function. (i) This response function can be calculated analytically via the difference renormalization group technique. Strong absorption can occur around the Alfven frequency for sharply peaked subgrid frequency spectra. (ii) With the {dollar}\epsilon{dollar} - expansion renormalization group approach, the Lorenzian wavenumber spectrum of Chen and Mahajan can be recovered for finite {dollar}\epsilon{dollar}, but the nonlinear coupling constant still remains small, fully justifying the neglect of higher order nonlinearities introduced by the renormalization group procedure.

The constrained decimation scheme (CDS) is applied to a turbulence model. The CDS is a statistical turbulence theory formulated in 1985 by Robert Kraichnan; it seeks to correctly describe the statistical behavior of a system using only a small sample of the actual dynamics. The full set of dynamical quantities is partitioned into groups, within each of which the statistical properties must be uniform. Each statistical symmetry group is then decimated down to a small sample set of explicit dynamics. The statistical effects of the implicit dynamics outside the sample set are modelled by stochastic forces.;These forces are not totally random; they must satisfy statistical constraints in the following way: Full-system statistical moments are calculated by interpolation among sample-set moments; the stochastic forces are adjusted by an iterative process until decimated-system moments match these calculated full-system moments. Formally, the entire infinite heirarchy of moments describing the system statistics should be constrained. In practice, a small number of low-order moment constraints are enforced; these moments are chosen on the basis of physical insights and known properties of the system.;The system studied in this work is the Betchov model--a large set of coupled, quadratically nonlinear ordinary differential equations with random coupling coefficients. This turbulence model was originally devised to study another statistical theory, the direct interaction approximation (DIA). By design of the Betchov system, the DIA solution for statistical autocorrelation is easy to obtain numerically. This permits comparison of CDS results with DIA results for Betchov systems too large to be solved in full.;The Betchov system is decimated and solved under two sets of statistical constraints. Under the first set, basic statistical properties of the full Betchov system are reproduced for modest decimation strengths (ratios of full-system size to decimated-system size); however, problems arise at stronger decimation. These problems are solved by the second set of constraints. The second constraint set is intimately related to the DIA; that relationship is shown, and results from the CDS under those constraints are shown to approach the DIA results as the decimation strength increases.

A fundamental requirement for the successful operation of a tokamak is the maintenance of a toroidal electric current within the tokamak plasma itself. Maintaining this internal plasma current can be a very difficult technological problem. In this work, a well-known but non-standard method for maintaining the tokamak current called the bootstrap effect is discussed. The bootstrap effect occurs when a fusion plasma is near thermonuclear conditions, and allows the tokamak to greatly amplify its electric current.;Because the bootstrap effect amplifies but does not create a plasma current, it has long been argued that a completely bootstrapped tokamak is not possible. That is, it has been argued that some fraction of the tokamak current must be created externally and injected into the plasma for a bootstrap amplification to occur. This injection of current is not desirable, however, since current-drive schemes are difficult to implement and are only marginally efficient.;An important but largely unexplored implification of the bootstrap effect is that the effect, by itself, creates hollow (outwardly peaked) tokamak current profiles. Hollow tokamak current profiles are known to lead to tearing modes, which are resistive (non-ideal) magnetohydrodynamic (MHD) plasma instabilities. Although usually characterized as harmful for plasma confinement, it turns out that tearing modes may actually be beneficial for the tokamak bootstrap effect.;In this work, a new theoretical approach based on a helicity conserving mean-field Ohm's law is used to examine the interaction between the bootstrap effect and tearing modes. Magnetic helicity is a topological quantity which is conserved even in turbulent plasma. Computer simulation results of the mean-field Ohm's law are presented which suggest that a completely bootstrapped tokamak may indeed be possible. In a completely bootstrapped tokamak, the tokamak self-maintains its electric current by amplifying an intrinsic internal plasma current due to the tearing modes.

The interaction of a high intensity laser beam with a plasma is generally susceptible to the filamentation instability due to nonuniformities in the laser profile. In ponderomotive filamentation high intensity spots in the beam expell plasma by ponderomotive force, lowering the local density, causing even more light to be focused into the already high intensity region. The result--the beam is broken up into a filamentary structure.;Several optical smoothing techniques have been proposed to eliminate this problem. In the Random Phase Plates (RPS) approach, the beam is split into a very fine scale, time-stationary interference pattern. The irregularities in this pattern are small enough that thermal diffusion is then responsible for smoothing the illumination. In the Induced Spatial Incoherence (ISI) approach the beam is broken up into a larger scale but non-time-stationary interference pattern. In this dissertation we propose that the photons in an ISI beam resonantly interact with the sound waves in the wake of the beam. Such a resonant interaction induces diffusion in the velocity space of the photons. The diffusion will tend to spread the distribution of photons, thus if the diffusion time is much shorter than the e-folding time of the filamentation instability, the instability will be suppressed.;Using a wave-kinetic description of laser-plasma interactions we have applied quasilinear theory to model the resonant interaction of the photons in an ISI beam with the beam's wake field. We have derived an analytic expression for the transverse diffusion coefficient. The quasilinear hypothesis was tested numerically and shown to yield an underestimate of the diffusion rate. By comparing the quasilinear diffusion rate, {dollar}\gamma\sb{lcub}D{rcub}{dollar}, with the maximum growth rate for the ponderomotive filamentation of a uniform beam, {dollar}\gamma\sb{lcub}f\sb{lcub}max{rcub}{rcub}{dollar}, we have derived a worst case criterion for stability against ponderomotive filamentation: {dollar}{dollar}{lcub}\gamma\sb{lcub}f\sb{lcub}max{rcub}{rcub}\over \gamma\sb D{rcub} \sim .5 {lcub}\tilde f\sp5/\tilde D\sp5\over \vert \tilde E\vert\sp2 \tilde\omega\sbsp{lcub}0{rcub}{lcub}2{rcub}\tilde N\sp6{rcub}\ll 1.{dollar}{dollar}The tildaed quantities are scaled to the following fusion relevant reference values; laser intensity: {dollar}\vert E\vert\sp2{dollar} = 10{dollar}\sp{lcub}15{rcub}\vert\tilde E\vert{dollar} Watts cm,{dollar}\sp{lcub}-2{rcub}{dollar} focal length: {dollar}f = 30\tilde f{dollar}m, width of each ISI echelon: {dollar}D = .75\tilde D{dollar} cm, laser carrier frequency: {dollar}\omega\sb{lcub}0{rcub} = 7.5 \times 10\sp{lcub}15{rcub}\tilde\omega\sb0{dollar} s{dollar}\sp{lcub}-1{rcub}{dollar}, and the number of ISI echelons: {dollar}N = 20\tilde N{dollar}.

With the advent of massively parallel processor machines, thermal lattice Boltzmann equation (TLBE) techniques offer an attractive way of handling turbulence simulations. TLBE is new form of DNS (direct numerical simulation method)--with the important advantages of being ideal for multi-parallel processors as well as being able to handle complicated geometries. Since there are many kinetic models that will reproduce the macroscopic nonlinear (compressible) transport equations, TLBE chooses that subset which can be readily solved on a discrete spatial lattice. The lattice geometry must be so chosen that the discrete phase representation of TLBE will not taint the rotational symmetric continuum equations. For 2D compressible flows, linear stability analyses described in this work indicates that the hexagonal lattice is optimum.;In nearly all lattice Boltzmann literature, the linearized Boltzmann collision operator has been taken to be the simple single-time Krook relaxation collision operator. This scalar collision operator is sufficient to recover the nonlinear transport equations under Chapmann-Enskog expansions. However, all previous LBE have suffered from the problem of density dependent transport coefficients. Even though this poses no problem for incompressible flows, it is critical and must be handled for compressible fluid simulations. The other deficiency of conventional TLBE scheme with single relaxation operator is that it only allows for fixed Prandtl number flow simulations.;In this work, to simulate flows with arbitrary Prandtl number, a matrix collision operator is introduced. With the inclusion of additional free parameter in the off-diagonal components, the scheme is now extended to a multi-relaxation process. This allows generalizations on relaxation parameters to produce density independent transport coefficients. Explicit solutions of TLBE are presented for 2D free decaying turbulence.

A method for simulating a turbulent binary fluid flow system based on the Lattice Boltzmann Method (LBM) is presented. The fluid equations up to the Navier-Stokes transport level are derived for this two fluid system, and results from numerical simulations using this method are shown. Finally, grid resolution is performed in a single fluid (LBM) simulation which determines the largest valid mesh size for a simulation that seeks to resolve physical structures of all scales.

Using electron beam evaporation for the production of polycrystalline silicon (pc-Si) thin-film solar cells is an attractive alternative to PECVD deposition. Due to its faster deposition rate, using evaporation technology could significantly reduce module production costs. Other advantages are lower running costs, and the fact that no toxic gases are involved. However, currently no on-shelf equipment is available, and research in this field often relies on in-house designed systems. These can have various problems with reliability, deposition uniformity, and due to their custom design require frequent maintenance. In this work, a newly purchased electron beam evaporation system was upgraded and redesigned to be capable of depositing amorphous Si diodes for the fabrication of pc-Si thin-film solar cells. The main goal of the upgrade was to provide a safe and reliable tool which allows for the deposition of high purity semiconductor material. Reliable and safe operation was accomplished by designing the entire electrical supply circuit and incorporating various safety interlocks. Source cross-contamination issues were addressed by installing a specially designed shroud (source housing). To provide uniform substrate temperatures up to 600??C, a heater was specially designed, fabricated, installed and tested. Accurate design of all mechanical system components was realised by using 3D product design software (ProEngineer). The new evaporator was commissioned, which included testing and calibration of all the system components required for depositing on substrate sizes of up to 10x10cm2. Over this area a Si film thickness uniformity of +/-2%, performed with a maximum deposition rate of 7nm/s was achieved. Initial experiments using solid phase crystallisation and rapid thermal annealing revealed a sheet resistance uniformity of +/-4% for the Phosphorus and +/-7% for the Boron dopant effusion cell. Experimentation via Raman spectrometry and X-ray diffraction has revealed good crystalline properties, of the crystallised Si films, which is comparable to those of existing evaporation systems. Although the system was upgraded to achieve deposition pressures below 3x10-7 mbar, experiments have shown that this quality of vacuum may not be necessary for the fabrication of low impurity films. The system is now ready for further research in the field of thin-film photovoltaics, and the first functioning devices have been fabricated.

This thesis deals with a systematic procedure for the derivation of exact expression for the frequency equation of composite beams undergoing forced vibration with damping. The governing differential equations of motion of the composite beam are derived analytically for bending and shear deformation. The basic equations of Timoshenko beam theory and assumption of maximum rate of dissipation are employed. The principle involved is that of vibration energy dissipation due to damping as a result of deformation of materials in sandwich beam. The boundary conditions for displacements and forces for the cantilever beam are imposed and the frequency equation is obtained. The expressions for the amplitude of displacements are also derived in explicit analytical form. Numerical results of the displacement amplitude in cantilever sandwich beam varying with damping coefficient are evaluated.