Relativistic cold fluid radial equilibrium of an annular nonneutral plasma

The relativistic radial equilibrium of a nonneutral plasma confined in a cylindrical trap is considered for the general case in which a coaxial inner charged conductor is present. Both rigid and sheared modes of plasma rotation in crossed self-consistent electric and magnetic fields are analyzed. It is found that relativistic effects can limit the outer radius of an annular nonneutral plasma column for the fast sheared rotational mode. For the particular case of a uniform plasma density, the outer radius cannot exceed √3ric/|Ω| if the inner radius of the plasma column ri is smaller than 3c/|Ω|, where Ω is the cyclotron frequency. On the contrary, radially unlimited equilibria are found when ri > 3c/|Ω|. The Brillouin density limit is also analyzed and a class of sheared equilibria is found where the limit valid for the case of rigid rotation can be overcome.