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.

The interaction of ultrashort laser pulses with materials is the subject of much modern research due to their ability to reach terawatt peak powers. Novel methods for temporally structuring femtosecond pulses have led to a new regime of burst mode ablation. The combination of burst mode operation with laser filamentation has been used to generate stitched filaments which form long-lasting plasma channels and can lead to increased laser ablation upon material interaction. In this work, laser ablation theory is discussed and compares the ablation effects of single, smoothly varying nanosecond pulses to a nanosecond envelope containing a GHz burst of femtosecond pulses. To directly compare the ablation efficiency by bursts of femtosecond pulses, a high-power nanosecond laser is used to ablate silicon and aluminum samples with energies comparable to the envelope energies of a burst of 32 hundred-femtosecond pulses each separated by 400 ps, as well as a bursts of 16 pulses separated by 400 or 800 ps. This experiment showed clear superiority of femtosecond burst mode over traditional nanosecond pulses at ablation at high fluences, with efficiencies forty times higher in aluminum and fourteen times higher in silicon. For the first time ever, burst mode operation was outfitted on a filamentation laser for outdoor propagation, and ablation measurements were measured after 250 meters of propagation. Single femtosecond pulses were compared to bursts of 8 pulses separated by 400 ps, and ablation craters were found only for burst modes at the highest energy during periods of low turbulence. The lack of ablation under other conditions suggests that turbulence plays a pivotal role in burst mode ablation efficacy during outdoor propagation and gives cause for further experiments at a distance.

Laser filaments are beneficial in long range outdoor applications. An intense ultrashort pulse will propagate nonlinearly through air and experience a balance of self-focusing and defocusing effects to generate a filament consisting of a plasma channel and high-intensity light beam over a long range of propagation. Filaments can propagate several times the Rayleigh distance, allowing the projection of high energy densities in a small spot size over kilometer scale distances. However, filaments are limited by clamped values of their intensity, plasma electron density, plasma lifetime, and spot size. We have previously demonstrated the "stitching" of filaments to extend the plasma lifetime. This was accomplished via our burst mode optical pulse system (BMOPS), which produces a 13 ns burst of pulses separated by an interval shorter than the plasma lifetime at the 10 Hz laser repetition rate, resulting in a higher average power than a single pulse. Stitching temporally separates and precisely spatially overlaps pulses to produce a filament with a lifetime many times that of a filament formed by a single pulse. This enhanced lifetime can improve the performance of many filamentation applications. We have recently implemented BMOPS into MU-HELF, our mobile ultrafast laser sitting on a 1 km range. Here, we present initial results of stitching and spatial confinement of burst mode energy over a 250 m range through turbulent conditions.

A wide range of laboratory and naturally occurring plasmas are frequently attributed a fluid description and as such, demonstrate turbulent flows. We will investigate a variety of forms which may be taken by the correlation functions of these turbulent flows. The most commonly discussed isotropic symmetry is not generally applicable since most systems of interest have been shown to be strongly anisotropic. This thesis will develop an axi-symmetric description from which the magnetic helicity may be extracted together with its spectrum. This description will be compared to the form taken by axi-symmetric, helical Navier Stokes turbulence which will also be derived here. The microscales for this geometry will be tabulated and for completeness, the Von Karman Howarth equations will be derived.

The development of anisotropy in an initially isotropic spectrum is studied numerically for two-dimensional magnetohydrodynamic (MHD) turbulence. The anisotropy develops due to the combined effects of an externally imposed dc magnetic field and viscous and resistive dissipation at high wave numbers. The effect is most pronounced at high mechanical and magnetic Reynolds numbers. The anisotropy is greater at the higher wave numbers.;The statistical structure of two-dimensional MHD turbulence is also considered. It is shown that the three known rugged invariants of the isotropic case reduce to two for the anisotropic case. Randomness and ergodicity are also briefly discussed.