Pattern Formation by Synchronization in Pure Electron Plasmas and 2D Vortex Dynamics

Magnetized, pure electron plasmas trapped in Penning-Malmberg traps can be modeled (in the drift approximation) by two-dimensional Euler equations of ideal fluids. The plasma density in this approximation is analogous to vorticity, while the radial electric field potential to the stream function of the fluid velocity field. For instance, electron plasma cylinder aligned with the magnetic field is analogous to a circular vortex patch solution of an ideal fluid. We shall show that by starting in such a circular equilibrium, applying a weak external oscillating potential of appropriate symmetry, and slowly varying the frequency of these oscillations, one can excite and control m-fold symmetric interface (vortex) waves in two dimensions (V-states, discovered by Deem and Zabusky nearly 20 years ago. The phenomenon is due to continuos nonlinear resonance in the system as the excited plasma (vortex) boundary preserves its functional form despite the drive, but self-adjusts the aspect ratio to synchronize with the driving potential oscillations. A similar approach can be used in controlling interface dynamics subject to global constraints in many other fields of physics