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”.