<p> Geometric integrators yield high-fidelity numerical results by retaining conservation laws in the time advance. A particularly powerful class of geometric integrators is symplectic integrators, which are widely used in orbital mechanics and accelerator physics. An important application presently lacking symplectic integrators is the guiding center motion of magnetized particles represented by non-canonical coordinates. Because guiding center trajectories are foundational to many simulations of magnetically confined plasmas, geometric guiding center algorithms have high potential for impact. The motivation is compounded by the need to simulate long-pulse fusion devices, including ITER, and opportunities in high performance computing, including the use of petascale resources and beyond. </p><p> This dissertation uses a systematic procedure for constructing geometric integrators &mdash; known as variational integration &mdash; to deliver new algorithms for guiding center trajectories and other plasma-relevant dynamical systems. These variational integrators are non-trivial because the Lagrangians of interest are degenerate - the Euler-Lagrange equations are first-order differential equations and the Legendre transform is not invertible. The first contribution of this dissertation is that variational integrators for degenerate Lagrangian systems are typically <i>multistep methods.</i> Multistep methods admit parasitic mode instabilities that can ruin the numerical results. These instabilities motivate the second major contribution: degenerate variational integrators. By replicating the degeneracy of the continuous system, degenerate variational integrators avoid parasitic mode instabilities. The new methods are therefore robust geometric integrators for degenerate Lagrangian systems. </p><p> These developments in variational integration theory culminate in one-step degenerate variational integrators for non-canonical magnetic field line flow and guiding center dynamics. The guiding center integrator assumes coordinates such that one component of the magnetic field is zero; it is shown how to construct such coordinates for nested magnetic surface configurations. Additionally, collisional drag effects are incorporated in the variational guiding center algorithm for the first time, allowing simulation of energetic particle thermalization. Advantages relative to existing canonical-symplectic and non-geometric algorithms are numerically demonstrated. All algorithms have been implemented as part of a modern, parallel, ODE-solving library, suitable for use in high-performance simulations.</p>

Because the universe is primarily composed of plasma, the interaction of plasmas and magnetic fields is of great importance for astrophysics. In this dissertation, we investigate three magnetic instabilities and examine their possible effects on astrophysical objects. First, we model solar coronal structures as Double Beltrami states, which are the lowest energy equilibria of Hall magnetohydrodynamics. We find that these states can undergo a catastrophe with characteristics similar to those of a solar eruption, such as a flare or coronal mass ejection. We then investigate magnetic reconnection and particle acceleration in moderately magnetized relativistic pair plasmas with three-dimensional particle-in-cell simulations of a kinetic-scale current sheet. We find that in three dimensions the tearing instability produces a network of interconnected and interacting magnetic flux ropes. In its nonlinear evolution, the current sheet evolves toward a three-dimensional, disordered state in which the resulting flux rope segments contain magnetic substructure on kinetic scales and sites of temporally and spatially intermittent dissipation. We find that reconnection produces significant particle acceleration, primarily due to the electric field in the X-line regions between flux ropes; the resulting particle energy spectrum can extend to high Lorentz factors. We find that the highest energy particles are moderately beamed within. / text

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Studies of emission corresponding to the second (3w0) and three-halves (3/2w0) harmonics are reported from laser produced plasmas. These plasmas were produced by means of a neodymium laser with an irradiance up to 2.10¹⁶ W/cm-2, in pulses of nominally 100ps duration. The spectral resolution of these harmonics from a range of targets has enabled various theories tobe verified and the location of the interaction identified. Acomputer code has been used to account for refraction of the emerging radiation in the plasma density profile. The expansion velocity and temporal variation of this profile has also been taken into account. Temporal resolution of the 2Wo and 3/2-Wo spectra has shown both harmonics to occur in pulses of less than the instrumental resolution limit which was ~10ps. This result gives some indication of the timescale for growth and saturation of parametrically excited instabilities.

The instabilities which occur in the interaction of CO2 laser radiation with a dense plasma have been studied. A TEA CO2 laser provided pulses of up to 30 joules of energy with a duration of 50 nanoseconds. By focussing the radiation on to a plane target a focal spot of about 180 micrometers diameter was formed with a irradiance of 10 to 10 W cm. The scattered radiation was collected by a laser focussing lens and analysed with a grating spectrometer. Linear relationships have been found between the incident irradiance and the back scattered energies. This is in contrast to the results of other workers who have found quadratic relations at high irradiance. The back scattered energies were of the order compared with the incident energy. The spectrum of shows a displacement to longer wavelength which is attributed to stimulated Brillouin scattering, there being an ion acoustic wave which is driven by the laser radiation. A similar displacement occurs in the 2 W spectrum and is attributed to the scattering of plasmons from the ion acoustic wave. The measured displacement is in agreement with a theory due to Silin. Fine structure also exists in the 2W spectrum, a shoulder being found on the red side of the line and this may result from a non-Maxwellian electron temperature distribution. There is also a satellite which is displaced towards longer wavelengths by about 0.1 micrometers from the precise value of 2W Explanations of this feature are offered. The self-generated magnetic field has been measured and its effect on the interactions have been examined. The plasma temperature has been determined by X-ray measurements and compared with the values estimated from the scattered spectrum.

The results of a study of non-thermal Carbon and Fluorine plasmas in an electromagnetic acceleration device are presented, the plasmas being created by ablation from the surface of a solid dielectric. The dielectric is close to a steady discharge through which ablated material, on entry, is heated and accelerated, and it is concluded that the high level of radiative power loss, which consists mainly of optically thick resonance line radiation, is in part responsible for the uniformity and stability of the plasma plume. Plasma velocities around 1-2 x 10⁶ cm/s. are attained. In addition to conventional electrical and spectroscopic diagnostic methods, several new spectroscopic techniques are described, providing greater accuracy in the measurement of particle temperatures and densities in non-thermal, non-hydrogenic plasmas. In order to make these methods possible, as well as allowing estimates of the radiation losses, a model describing the papulation distribution among the bound ionic states was constructed and solved for a wide range of plasma conditions. From these results new values of collisional-radiative ionization and recombination coefficients are obtained, which are in broad agreement with experimental values. A model was developed which described the rate of ablation from the solid and which formed part of a larger numerical scheme for calculating the temperature, density and velocity of the plasma plume. This model gives results which are in good agreement with the observations and is used to predict the plasma behaviour under different operating conditions and with different dielectric materials. The extension of certain parts of this work to other situations is also discussed, in particular, laser heating of plasmas, problems of ablation in high-temperature plasma containment devices, and as a source for selective excitation spectroscopy. The possibility of using the device as a soft X-ray laser is also investigated.

An investigation into wave interactions between self-excited ionization waves - striations - in the positive column of a direct current argon discharge is described. Since such self-excited ionization waves are determined by the ionization processes in the discharge, they are inherently nonlinear and a variety of nonlinear effects may be observed. After reviewing the theory and experimental observations for small amplitude linear ionization waves in gas discharges, experimental data obtained from an argon discharge, 5 cm in diameter, 110 cms in length, run at gas pressures between 0.1-1.5 torr and discharge currents of 20-250mA, are presented. Linear interactions between large amplitude self-excited waves of the same frequency, and nonlinear mode coupling between waves of different frequencies and wave numbers are reported and the characteristics of each wave type are described. In order to interpret some of the phenomena observed for the self-excited waves, experiments where an external alternating voltage was applied across the discharge were performed. Following a general discussion of wave modulation the wave-wave mode coupling is interpreted as due to nonlinear interactions which may arise during the initial nonlinear growth of ionization waves. A physical model for the nonlinear behaviour is described. By including a nonlinear term in the basic theory of striations expressions are derived which account for the mode-coupling and support the physical interpretation. Theoretical techniques previously used to describe the nonlinear behaviour of water waves are outlined, and then applied to ionization waves to predict further nonlinear effects which could not be obtained from the modified linear theory. Finally, a general overall view of two-wave interactions between ionization waves in a discharge is presented using, as an example, the results from a neon discharge. The experimental observations are related to the linear and nonlinear growth of the waves.

The high pressure plasma produced by an r.f. induction plasma torch has been investigated in a pulsed magnetic field using spectroscopy, high speed photography, inductive probes and a diamagnetic loop. Radiation and temperature of the plasma have been measured under various conditions of the torch and various intensities of the pulsed field. In most cases Joule-heating has been found the main mechanism of energy transfer to the plasma. From the decay of temperature in the plasma afterglow a value of radiative recombination in dense argon plasma has been found. Various properties of the torch in the absence of a pulsed magnetic field have also been investigated. These investigations cover gas breakdown at the torch initiation, measurements of the r.f. magnetic field in the plasma and the plasma instabilities. The measurements of the r.f. magnetic field provide information leading to estimates of plasma conductivity, electrical parameters and efficiency of the torch. The study of plasma instabilities reveals their sources and helps to suppress the acoustic noise from the torch.

<p> The self-regulation of cosmic ray (CR) transport in the interstellar and intracluster media has long been viewed through the lenses of linear and quasilinear kinetic plasma physics. Such theories are believed to capture the essence of CR behavior in the pres- ence of self-generated turbulence, forming the basis for the so-called &ldquo;self-confinement paradigm,&rdquo; which has been proposed to explain the isotropic propagation of CRs in the interstellar medium. However, the coupled nonlinear equations that describe the time-dependent system of CRs and electromagnetic fields are analytically intractable in the general case. Thus, obtaining analytical solutions has always relied on simplify- ing assumptions that remove potentially critical details arising from the nonlinearities of the problem. </p><p> We utilize the Particle-in-Cell (PIC) numerical method to study the time- dependent nonlinear behavior of the gyroresonant streaming instabilities, self- consistently following the combined evolution of particle distributions and self- generated wave spectra in one-dimensional periodic and aperiodic simulations. In the periodic case, we demonstrate that the early growth of instability conforms to the predictions from linear physics, but that the behavior can vary depending on the properties of the initial CR distribution. We emphasize that the nonlinear stages of instability depend strongly on the initial anisotropy of CRs. We derive estimates for the wave amplitudes at saturation and the time scales for relaxation of the CR distribution. In the aperiodic case, we show that the expansion of CRs from small injection regions naturally induces highly anisotropic CR distributions. Pitch-angle diffusion of CRs is then limited by the predominantly right-handed circularly polarized self-generated turbulence, allowing bulk CR drift velocities of ?0.5c. We compare against a set of analytical solutions to the CR expansion problem and find that they do not accurately predict the time-dependent properties of the CR population. We briefly study the wave damping processes of nonlinear Landau iii damping and ion-neutral friction in order to assess the viability of performing damped CR streaming simulations in the future with the PIC method. </p><p>