I report experimental and numerical studies of microparticle motion in a dusty plasma. These microparticles are negatively charged and are levitated in a plasma consisting of electrons, ions and neutral gas atoms. The microparticles repel each other, and are confined by the electric fields in the plasma. The neutral gas damps the microparticle motion, and also exerts random forces on them. I investigate and characterize microparticle motion. In order to do this, I study velocity distributions of microparticles and correlations of their motion. To perform such a study, I develop new experimental and analysis techniques. My thesis consists of four separate projects. In the first project, the battle between deterministic and random motion of microparticles is investigated. Two particle velocity distributions and correlations have previously studied only in theory. I performed an experiment with a very simple one dimensional (1D) system of two microparticles in a plasma. My study of velocity correlations involves just two microparticles which is the simplest system that allows interactions. A study of such a simple system provides insight into the motions of the microparticles. It allowed for the experimental measurement of two-particle distributions and correlations. For such a system, it is shown that the motion of the microparticles is dominated by deterministic or oscillatory effects. In the second project, two experiments with just two microparticles are performed to isolate the effects of ion wakes. The two experiments differ in the alignment of the two microparticles: they are aligned either perpendicular or parallel to the ion flow. To have different alignments, the sheath is shaped differently in the two experiments. I demonstrate that microparticle motion is more correlated when they are aligned along the ion flow, rather than perpendicular to the ion flow. In the third project, I develop a model with some key assumptions to compare with the experiments in the first two projects. My model includes all significant forces: gravity, electrical forces due to curved sheath and interparticle interaction, and gas forces. The model does not agree with both the experiments. In the last project, I study the non-Gaussian statistics by analyzing data for microparticle motion from an experiment performed under microgranity conditions. Microparticle motion is studied in a very thin region of microparticles in a three dimensional dust cloud. The microparticle velocity distributions exhibit non-Gaussian characteristics.

<p>Plasma-based particle acceleration holds the promise to make the applications that revolve around accelerators more affordable. The central unifying theme of this dissertation is the modeling of certain non-linear and relativistic phenomena in plasma dynamics to devise mechanisms that benefit plasma-accelerators. Plasma acceleration presented here has two distinct flavors depending upon the accelerated particle mass which dictates the acceleration structure velocity and potential. The first deals with ion acceleration, where acceleration structure velocities are a significant fraction of the speed of light, with major applications in medicine. The second focusses on the acceleration of electrons and positrons for light-sources and colliders where the acceleration structures are wakefields with phase-velocities near the speed of light.</p> <p>The increasing Lorentz factor of the laser-driven electron quiver momentum forms the basis of Relativistically Induced Transparency Acceleration (RITA) scheme of ion acceleration. Lighter ions are accelerated by reflecting off a propagating acceleration structure, referred to as a snowplow, formed by the compression of ponderomotively driven critical layer electrons excited in front of a high intensity laser pulse in a fixed-ion plasma. Its velocity is controlled by tailoring the laser pulse rise-time and rising density gradient scale-length. We analytically model its induced transparency driven propagation with a 1-D model based on the linearized dispersion relation. The model is shown to be in good agreement with the weakly non-linear simulations. As the density compression rises into the strongly non-linear regime, the scaling law predictions remain accurate but the model does not exactly predict the RITA velocity or the accelerated ion-energy. Multi-dimensional plasma effects modify the laser radial envelope by self-focussing in the rising density gradient which can be integrated into our model and filamentation which is mitigated by a matched laser focal spot-size. We show that the critical layer motion in RITA compares favorably to the bulk-plasma motion driven by radiation pressure or collision-less shocks.</p> <p>Non-linear mixing of the laser, incident on and reflected off the propagating critical layer modulates its envelope affecting the acceleration structure velocity and potential, in the process setting up a feedback loop. For long pulses the envelope distortion grows with time, disrupting the accelerated ion-beam spectral shape. We model the Chirp Induced Transparency Acceleration (ChITA) mechanism that over- comes this effect by introducing decoherence through a frequency chirp in the laser. </p> <p>In a rising density gradient, the non-linearity of electron trajectories leads to the phase-mixing self-injection of electrons into high phase-velocity plasma wakefields. The onset of trapping depends upon the wake amplitude and the density gradient scale-length. This self-injection mechanism is also applicable to controlling the spuriously accelerated electrons that affect the beam-quality. </p> <p>Non-linear ion dynamics behind a train of asymmetric electron-wake excites a cylindrical ion-soliton similar to the solution of the cylindrical Korteweg-de Vries (cKdV) equation. This non-linear ion-wake establishes an upper limit on the repetition rate of the future plasma colliders. The soliton is excited at the non-linear electron wake radius due to the time-asymmetry of its radial fields. In a non-equilibrium wake heated plasma the radial electron temperature gradient drives the soliton. Its radially outwards propagation leaves behind a partially-filled ion-wake channel. </p> <p>We show positron-beam driven wakefield acceleration in the ion-wake channel. Optimal positron-wakefield acceleration with linear focussing fields is shown to require a matched hollow-plasma channel of a radius that depends upon the beam properties. </p> / Dissertation