l = 1 Diocotron Instability of Single Charged Plasmas in a Cylindrical Penning Trap with Central Conductor

摘要

The linear stability analysis of the l = 1 diocotron perturbations in a single charged plasma confined in a cylindrical Penning trap is critically revisited. Particular attention is devoted to the instability due to the presence of 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 t~(1/2)) is extended to the case of a cylindrical Penning trap with an additional coaxial inner conductor, and 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). The analytical results are compared with the numerical solution of the linearized two-dimensional drift Poisson equations.