Experiments on vortex dynamics in pure electron plasmas

Abstract

Magnetically confined columns of electrons are excellent experimental manifestations of two-dimensional (2-D) vortices in an inviscid fluid. Surface charge perturbations on the electron column (diocotron modes) are equivalent to surface ripples on extended vortices; and unstable diocotron modes on hollow electron columns are examples of the Kelvin–Helmholtz instability. Experiments demonstrate that the stable and unstable modes are distinct and may coexist, having different frequencies and radial eigenfunctions. For azimuthal mode number l=1, an exponentially unstable mode is observed on hollow columns, in apparent contradiction to 2-D fluid theory. For l=2, a similar unstable mode is observed, consistent with fluid theory. These diocotron instabilities on hollow columns saturate with the formation of smaller vortex structures, and radial transport is determined by the nonlinear interaction of these secondary vortices. The vortex pairing instability has been observed for isolated, well-controlled vortices, and the instability is found to depend critically on the vortex separation distance.

On the energy of elliptical vortices

“…Perturbed vortices such as ͑1͒ can be realized experimentally by manipulating columns of magnetically confined electron plasmas. 4 Once the external perturbation is switched off or is reduced to a low level, Eq. ͑1͒ defines a disturbed smooth vortex, and self-induction then leads to a nonelliptical rearrangement of the vorticity.…”

Dynamics of vorticity defects in shear

“…Some recent experimental work using nonneutral plasmas as a laboratory analogue of inviscid two-dimensional fluid mechanics (Driscoll & Fine 1990) may be relevant. Experiments with this system (Pillai & Gould 1994) have shown that stable disturbances have an initial exponential decay which is then followed by a protracted algebraic decay.…”

Vortex Dynamics and Shear-Layer Instability in High-Intensity Cyclotrons

“…In the Euler case, the vorticity plays the role of the density n, and the stream function plays the role of the electrostatic potential φ. This isomorphism has been highlighted in a different context [18,19]. A major difference is that in [18,19], the plasma is surrounded by a cylindrical conductor, whereas in our model Poisson's equation is solved with free space boundary conditions.…”

“…This isomorphism has been highlighted in a different context [18,19]. A major difference is that in [18,19], the plasma is surrounded by a cylindrical conductor, whereas in our model Poisson's equation is solved with free space boundary conditions. Some of the phenomena we discuss in this letter occur in elongated beams that would be hard to create in the experiments described in [18,19] and have not been studied in that context.…”

“…A major difference is that in [18,19], the plasma is surrounded by a cylindrical conductor, whereas in our model Poisson's equation is solved with free space boundary conditions. Some of the phenomena we discuss in this letter occur in elongated beams that would be hard to create in the experiments described in [18,19] and have not been studied in that context. The isomorphism between our model and the Euler equations allows us to study the beam dynamics by relying on the rich fluid dynamics literature and on available numerical solvers.…”