plasma confined in a cylindrical Penning trap is critically revisited. Particular attention is devoted to the insta-
bility due to the presence of one or more stationary points in the radial profile of the azimuthal rotation fre-
quency. The asymptotic analysis of Smith and Rosenbluth for the case of a single-bounded plasma column
(algebraic instability proportional to t 1/2) is generalized in a few respects. In particular, the existence of unper-
turbed density profiles that give rise to l = 1 algebraic instabilities growing with time proportionally to t 1
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 alge-
braically 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 a 4/3 for a
0. The theoretical results are compared with the numerical solution of the linearized two-dimensional drift Poisson
equations. © 2002 MAIK “Nauka/Interperiodica”.