A single species cylindrical plasma (electrons only, ions only,...) can be confined by a uniform axial magnetic field. Such a cylindrical electron plasma (or ion plasma) rotates about its axis so that the inward v x B force balances the outward force of space charge repulsion. When the particle density is uniform (independent of radius) the plasma rotates as a rigid body, but when the density depends on radius the angular velocity also depends on radius and the flow is sheared.
Mixing of two-dimensional disturbances in such a plasma occurs because of the sheared flow as illustrated in the figures above. The first shows an initial quadrupole(m=2) perturbation in density [white-red... represents an increase in density whereas black-blue... represents a decrease in density]. Subsequent frames show the effect of differential rotation of the sheared flow. The blobs are eventually stretched into very fine filaments. It can be shown that in such single species plasmas the density is proportional to the vorticity, hence such plasmas are useful in experimental study of vortex dynamics. The above figures were obtained by numerical computation with the self-consistent electric fields (including those due to perturbations) included[1]. Viscosity was neglected.
The electric field at the edge of the plasma (e.g. the charge induced on a nearby electrode) is expected to show an oscillatory behavior as blobs of increased density and decreased density pass by alternately because of rotation. As the blobs stretch and wrap around, because of differential rotation the magnitude of the oscillating field at the edge of the plasma decays. The quadrupole moment of charge decays. This is a dissipationless decay due to phase mixing and is similar, mathematically, to Landau damping of Langmuir waves in a plasma. It has previously been observed experimentally in rotating pure electron plasmas [2].
[1] David A. Bachman and Roy W. Gould, Landau-like Damping in Rotating Pure Electron Plasmas", IEEE Transactions on Plasma Science, Vol. 24, No. 1, Part 2, pp 14-15, (1996).
[2] N. S. Pillai and R. W. Gould, "Damping and Trapping in 2D Inviscid Fluids", Phys. Rev. Lett. 73, pp 2849-2852, (1994).
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