Diocotron instability in non-neutral plasmas with a stationary point in the rotation frequency profile

A new analytical solution to the problem of the l=1 diocotron mode instability in a hollow density non-neutral plasma column with finite lenght is presented. The starting point of the analysis is the paper of Finn [J. M. Finn, D. del-Castillo-Negrete, and 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." (C) 2005 American Institute of Physics.