Electron columns confined magnetically in vacuum evolve in ( r , θ ) as N ∼10 9 field-aligned rods of charge, or point vortices. Neglecting discreteness, the column evolves as would vorticity in an inviscid, incompressible fluid, governed by the Euler equations. The macroscopic flow dynamics is readily imaged, including effects such as surface waves and inviscid damping, two vortex merger, and gradient-driven vortex motion. Turbulent initial states are observed to relax to “vortex crystal” meta-equlibria, due to vortex “cooling” from entropic mixing of background vorticity; and characteristics of this process are predicted by theory. The microscopic discreteness gives rise to point-vortex diffusion, which is strongly affected by the overall flow shear. Macroscopically and microscopically, the vortex dynamics depends critically on whether the vortex is prograde or retrograde with respect to the flow shear.

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Vortex dynamics of 2D electron plasmas

Recent experiments have characterized trapped-particle modes on a non-neutral plasma column [A. A. Kabantsev, C. F. Driscoll, T. J. Hilsabeck, T. M. O’Neil, and J. H. Yu, Phys. Rev. Lett. 87, 225002 (2001)], and in this paper we present a theoretical model of the modes. Theoretical predictions for the mode frequency, damping rate, and eigenmode structure are compared to experimental observation. The modes are excited on a non-neutral plasma column in which classes of trapped and passing particles have been created by the application of a potential barrier. The column resides in a Malmberg–Penning trap, and the barrier is created by applying a voltage to an azimuthally symmetric section of the wall near the axial mid-point of the column. Low energy particles near the edge of the column (where the barrier is strong) are trapped in one end or the other, while high energy particles near the center of the column transit the entire length. The modes have azimuthal variation l=1,2,…, and odd z-symmetry. The trap...

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Trapped-particle diocotron modes

Jupiter-style Jet Stability

Image-charge method for contour dynamics in systems with cylindrical boundaries

The linear stability analysis of the l=1 diocotron perturbations in a low density single charged plasma confined in a cylindrical Penning trap is critically revisited. Particular attention is devoted to the instability due to the presence of one or more stationary points in the radial profile of the azimuthal rotation frequency. The asymptotic analysis of Smith and Rosenbluth for the case of a single-bounded plasma column (algebraic instability proportional to t1/2) is generalized in a few respects. In particular, the existence of unperturbed density profiles that give rise to l=1 algebraic instabilities growing with time proportionally to t1−1/m, m≥ 3 being the order of a stationary point in the rotation frequency profile, and even proportionally to t, is pointed out. It is also shown that smoothing the density jumps of a multistep density profile can convert algebraically growing perturbations into exponentially decaying modes. The relevant damping rates are computed. The asymptotic analysis (t → ∞) of the fundamental diocotron perturbations is then generalized to the case of a cylindrical Penning trap with an additional coaxial inner conductor. It is shown that the algebraic instability found in the case of a single-bounded plasma column becomes exponential at longer times. The relevant linear growth rate is computed by a suitable inverse Laplace transform (contour integral in the complex plane). In the particular case of an uncharged inner conductor of radius a, the growth rate is shown to scale as a4/3 for a → 0. The theoretical results are compared with the numerical solution of the linearized two-dimensional drift Poisson equations.

L = 1 diocotron instability of single charged plasmas

Diocotron modes are discussed for a finite length nonneutral plasma column under the assumption of bounce averaged E×B drift dynamics and small Debye length. In this regime, which is common to experiments, Debye shielding forces the mode potential to be constant along field lines within the plasma (i.e., ∂δφ/∂z=0). One can think of the plasma as a collection of magnetic-field aligned rods that undergo E×B drift across the field and adjust their length so as to maintain the condition ∂δφ/∂z=0 inside the plasma. Using the Green function (for a region bounded by a conducting cylinder) to relate the perturbed charge density and the perturbed potential, imposing the constraint ∂δφ/∂z=0, and discretizing yields a matrix eigenvalue problem. The mode eigenvector δNl,ω(rj)≡∫dz δnl,ω(rj,z) is the lth azimuthal Fourier component of the z-integrated density perturbation, and the frequency ω is the eigenvalue. The solutions include the full continuum and discrete stable and unstable diocotron modes. Finite column leng...

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T. M. O’Neil

Papers

Finite length diocotron modes