Observations of relativistic beam focusing by a passive plasma lens have demonstrated a reduction in focusing strength due to plasma return current. A 50 MeV beam was propagated through a 1-3 cm long plasma with density around 10 14 cm 23. Beam size was measured as a function of propagation distance. For a ratio of collisionless plasma skin depth to beam spot size k p s r 0.33, no significant reduction in focusing was observed. Reduced focusing was measured for k p s r 1.1, where a significant fraction of the inductively driven return current in the plasma flows within the beam. The observations are in good agreement with an envelope equation model and with particle-in-cell simulations.

The stability of non-neutral plasma equilibria subjected to external, azimuthal-asymmetric potentials is studied. The system exhibits a wide range of complex, symmetry-dependent, bifurcation phenomena.

A magnetic trap for simultaneous confinement of neutral atoms and a non-neutral plasma AIP Conf. Stability of highly asymmetric non-neutral plasmasA pure electron plasma held in a Malmberg-Penning trap deforms into an ellipse when subjected to a stationary, lϭ2 voltage perturbation on the trap wall. At first, the plasma's ellipticity is proportional to the strength of the perturbation, but once the perturbation increases beyond a critical value, the plasma equilibrium bifurcates into two stable off-axis equilibria and an unstable saddle. At the bifurcation point, the lϭ1 diocotron frequency dips to near zero. The diocotron orbits become very elliptical just below the bifurcation, and, after the bifurcation, split into three classes delimited by a separatrix: two classes surrounding the individual new equilibria, and one class surrounding both equilibria. The mode frequencies slow near the separatrix, and the trajectories themselves slow near the saddle at the origin. Interaction with the elliptical mode causes the diocotron mode to spontaneously and reversibly jump across the separatrix.

We consider the problem of extending the solution of a particular two-dimensional Poisson equation to a larger domain. This problem is related to the problem of putting a non-neutral plasma into equilibrium by applying a suitable wall potential, and to similar problems in two-dimensional fluid dynamics. While one cannot always find an exact solution, one can always find an approximate solution if the plasma has no holes.

Pure electron plasmas are usually confined within cylindrically symmetric Penning-Malmberg traps. When azimuthally asymmetric potentials are imposed on the trap walls, the plasmas deform into asymmetric shapes. Such deformed plasmas have been observed experimentally, and are long lived. This paper analyzes the equilibria of these plasmas. Wall potentials can be found which place many asymmetric, flat-top plasmas into exact equilibrium; virtually any flat-top plasma can be placed into approximate equilibrium.