Image-Charge Method for Contour Dynamics in Systems with Cylindrical Boundaries

Abstract

In the paper, the classic contour dynamics method for the study of inviscid two-dimensional flow in an infinite domain is extended to systems with a circular boundary. A suitable use of the image-charge technique allows one to express the velocity on the contour of each vortex in terms of line integrals on the contours. Results are presented in the framework of the dynamics of non-neutral plasmas in a Penning trap (the problem is isomorphic to the classic fluid-dynamics problem for a Euler fluid), showing the high accuracy attainable with the method.