Numerical simulation of the excitation and evolution of coherent vortices in hollow magnetized electron columns

We apply a finite-element code to study the excitation and nonlinear evolution of two-dimensional (2D) vortices in a hollow electron column using 2D guiding center equations. The pertubation (wilh m =2) of the hollow column results in an instability (diocotron or Kelvin-IIelmholtz instability) that evolves towards the formation of vortices (two vortices for the m = 2 perturbation). The subsequent evolution shows the nonlinear evolution of two vortices interacting to coalesce (cascading to lower azimuthal mode number), with a simultaneous radial transport toward the center of the column.