Compressional diocotron instability in a non-neutral plasma with a stationary point in the rotation frequency profile

An analytical solution to the problem of the l = 1 diocotron mode instability in a hollow density non-neutral plasma column with finite length is presented. The starting point of the analysis is the paper of Finn et al. [J. M. Finn, D. del-Castillo-Negrete, D. C. Barnes, Phys. Plasmas 6, 3744 (1999)], where the instability mechanism involves compression of the plasma in the direction parallel to the magnetic field, with conservation of its line-integrated density. In the limit of small curvature of the plasma end-fronts, the method presented here provides both eigenvalue and eigenfunction for the unstable l = 1 "extreme mode".