Date of Award

Spring 2011

Project Type


Program or Major


Degree Name

Doctor of Philosophy

First Advisor

Amitava Bhattacharjee


Kinetic plasma behaviors have long been of interest to those studying space and laboratory plasmas. For instance, kinetic plasma instabilities are widely believed to be responsible for the generation of anomalous resistivity in reconnection layers, providing a possible mechanism for fast reconnection. The concept of Landau damping is fundamental to such wave kinetic instabilities in space, and is treated typically within the framework of the collisionless Vlasov equation. It has become clear in recent theoretical and experimental work that weak collisions are a singular perturbation on the collisionless theory, and qualitatively alter the results of the collisionless theory. In particular, it has been demonstrated by C. S. Ng, A. Bhattacharjee, and F. Skiff that the Case-Van Kampen continuous spectrum, which are the underlying eigenmodes of the collisionless system, are completely eliminated and replaced by a discrete spectrum (hereafter referred to as the NBS spectrum). The NBS spectrum includes Landau-damped roots as exact eigenmodes, but is significantly broader, including a larger spectrum of discrete roots. We discuss the implications of these results for two nonlinear applications, the plasma wave echo and the ion acoustic instability, by means of a new Vlasov code that has been modified to include the Lenard-Bernstein collision operator. We show that the existing collisional theories for the echo, which fail to account for the discrete collisional spectrum, come close, but do not quite yield the appropriate collisional damping rates. Of greater practical importance to problems involving dissipation and anomalous transport is the generation of anomalous resistivity due to microinstabilities. As a specific example, we consider the ion acoustic wave. We compare our numerical findings with the anomalous resistivity estimates of A. Galeev and R. Z. Sagdeev for both collisionless and weakly collisional systems. In the regime of applicability of the theoretical estimates, the agreement is good within an order of magnitude.