Large amplitude ℓ=1 coherent structures in non-neutral plasmas confined in a cylindrical trap

The computation of ℓ = 1 coherent structures in non-neutral plasmas with arbitrary density profiles and for large displacements of the plasma from the symmetry axis of a confining cylindrical trap is described. As the structures are displaced from the axis, they revolve about the symmetry axis with a frequency that typically increases with displacement. The plasma also is distorted into an approximately elliptical shape. The frequency shifts and the eccentricities as a function of displacement, plasma size, and the shape of the density profile are both computed numerically and calculated analytically. The results are shown to be consistent with data of Fine, Driscoll, and Malmberg [Phys. Rev. Lett. 63, 2232 (1989)] which are measured for relatively large, constant-density (waterbag) plasmas (R/a = 0.38–0.71) and modest off-axis displacements (D/a<0.3). Here R is the radius of the plasma at half of peak density when centered, D is the off-axis displacement, and a is the radius of the cylinder.