Electron vortex orbits and merger

Abstract

Pure electron plasma columns are contained inside hollow conducting cylinders in an axial magnetic field. In the 2D E×B drift approximation, an electron column is a vortex evolving in (r,θ) according to the Euler equation. First the center-of-mass orbits of two vortices sufficiently well-separated to be stable to merger are characterized. Equilibria are observed in which the vortices orbit about the center of the cylinder, with either oscillations about stable equilibria or exponential divergence away from unstable equilibria. The equilibrium positions, oscillation frequencies, and instability rates for these spatially extended vortices agree well with the predictions of point vortex theory, apparently because surface waves and shape distortions do not couple significantly to the center-of-mass motion. Next, the merger of two vortices with unequal radii is quantified. Merger is accompanied by the formation of filamentary arms, and results ultimately in an axisymmetric central core surrounded by a lower density halo. The self-energy of the merged core is found to be roughly the sum of the self-energy of the merging vortices. The fraction of the total circulation entrained into the core varies from 70% to 90% as the ratio of the initial vortex radii is varied from 1:1 to 2:1. The point-like vortex dynamics and the circulation loss with merger are both consistent with the ‘‘punctuated Hamiltonian’’ models of decaying turbulence.