Collisionless relaxation in beam-plasma systems

Abstract

This thesis reports the results from the theoretical investigations, both numerical and analytical, of collisionless relaxation phenomena in beam-plasma systems. Many results of this work can also be applied to other lossless systems of plasma physics, beam physics and astrophysics.Di erent aspects of the physics of collisionless relaxation and its modeling are addressed. A new theoretical framework, named Coupled Moment Equations (CME), is derived and used in numerical and analytical studies of the relaxation of second order moments such as beam size and emittance oscillations. This technique extends the well-known envelope equation formalism, and it can be applied to general systems with nonlinear forces. It is based on a systematic moment expansion of the Vlasov equation. In contrast to the envelope equation, which is derived assuming constant rms beam emittance, the CME model allows the emittance to vary through coupling to higher order moments. The CME model is implemented in slab geometry in the absence of return currents. The CME simulation yields rms beam sizes, velocity spreads and emittances that are in good agreement with particle-in-cell (PIC) simulations for a wide range of system parameters.The mechanism of relaxation is also considered within the framework of the CME system. It is discovered that the rapid relaxation or beam size oscillations can be attributed to a resonant coupling between di erent modes of the system. A simple analytical estimate of the relaxation time is developed.The nal state of the system reached after the relaxation is complete is investigated. New and accurate analytical results for the second order moments in the phase-mixed 2 state are obtained. Unlike previous results, these connect the nal values of the second order moments with the initial beam mismatch. These analytical estimates are in good agreement with the CME model and PIC simulations. Predictions for the nal density and temperature are developed that show main important features of the spatial dependence of the pro les. Di erent aspect of the nal coarse-grained state such as its non-thermal nature, the appearance of 'hot' regions on the periphery and the core-halo character of the density are investigated.Professor Jonathan S. Wurtele Dissertation Committee Chair iii To my grandmothers, whose di erent lives were always an inspiration...