Linear Longitudinal Oscillations in Collisionless Plasma Diodes with Thin Sheaths. Part 2. Application to an Extended Pierce-Type Problem.

摘要

This paper constitutes Part II of a study proposing an integral-equation approach to linear longitudinal oscillations in collisionless plasma diodes with thin sheaths. The method was formally developed in Part I and is comprehensive in that it handles the combined initial-value and external-perturbation problem, thus including the eigenmode problem as a special case, and allows for explicit and simultaneous inclusion of three basic constituents of bounded plasma systems, namely the plasma itself, the boundaries, and the external circuit. The present restriction to one-dimensional diode geometry is not inherent to the integral-equation approach as such and is likely to become dispensable at a later stage of development of the theory. In this paper, the method developed in Part I is employed to solve an extended Pierce-type problem involving a non-trivial external circuit. The author's goal is to demonstrate the applicability and handling of the method, and to show the in numerical detail that the external circuit, an essential part of any bounded plasma system, may crucially influence the overall dynamic and stability behavior.