No abstract

No 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.

Vortex-in-cell simulations that numerically integrate the 2D Euler equations are compared directly to experiments on magnetized electron columns ͓K. S. Fine, A. C. Cass, W. G. Flynn, and C. F. Driscoll, ''Relaxation of 2D turbulence to vortex crystals,'' Phys. Rev. Lett. 75, 3277 ͑1995͔͒, where turbulent flows relax to metastable vortex crystals. A vortex crystal is a lattice of intense small diameter vortices that rotates rigidly in a lower vorticity background. The simulations and experiments relax at the same rates to vortex crystals with similar vorticity distributions. The relaxation is caused by mixing of the background by the intense vortices: the relaxation rate is peaked when the background circulation is 0.2-0.4 times the total circulation. Close quantitative agreement between experiment and simulation provides strong evidence that vortex crystals can be explained without incorporating physics beyond 2D Euler theory, despite small differences between a magnetized electron column and an ideal 2D fluid.

Transport of magnetically confined pure electron plasmas to global thermal equilibrium has recently been observed. In equilibrium, the ExB and diamagnetic drifts calculated from the measured temperature and density profiles combine to give rigid rotation (i.e., ive) -cor), as expected. However, the density profile relaxes towards equilibrium up to 5000 times faster than predicted by Boltzmann transport theory: Over a decade range of magnetic field, the density equilibration time is always less than predicted, and scales as B i rather than as B 4 .