The inviscid damping of an asymmetric perturbation on a two-dimensional circular vortex is examined theoretically, and with an electron plasma experiment. In the experiment, an elliptical perturbation is created by an external impulse. After the impulse, the ellipticity ͑quadrupole moment͒ of the vortex exhibits an early stage of exponential decay. The measured decay rate is in good agreement with theory, in which the perturbation is governed by the linearized Euler equations. Often, the exponential decay of ellipticity is slow compared to a vortex rotation period, due to the excitation of a quasimode. A quasimode is a vorticity perturbation that behaves like a single azimuthally propagating wave, which is weakly damped by a resonant interaction with corotating fluid. Analytically, the quasimode appears as a wave packet of undamped continuum modes, with a sharply peaked frequency spectrum, and it decays through interference as the modes disperse. When the exponential decay rate of ellipticity is comparable to the vortex rotation frequency, the vorticity perturbation does not resemble a quasimode; rather, it is rapidly dominated by spiral filaments. Over longer times, linear theory predicts algebraic decay of ellipticity; however, nonlinear oscillations of ellipticity emerge in the experiment before a transition to algebraic decay would occur.

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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.

We apply "rotating wall" electric fields to spin up a non-neutral plasma in a Penning-Malmberg trap, resulting in steady-state confinement (weeks) of up to 10 9 Mg 1 ions. The resulting ion columns can be near global thermal equilibrium, with near-uniform temperature and rotation frequency. The equilibrated plasma E 3 B rotation rate f E is observed to be somewhat less than the drive frequency f w , with slip Df ϵ f w 2 f E depending on temperature as Df~T 1͞2 for 0.05 & T & 5 eV. Dynamic measurements of applied torque versus slip frequency show plasma spin up and compression for Df. 0 and plasma slowing and expansion for Df , 0. By gradually increasing f w , density compression up to 20% of the Brillouin density limit has been achieved. Heating resonances and hysteresis in plasma parameters are also observed.