On the relativistic cold fluid radial equilibrium of a nonneutral plasma

It is shown that relativistic effects strongly modify the equilibrium of nonneutral plasmas even if the linear velocity of plasma rotation in crossed electric and magnetic fields is small as compared to the speed of light. The change is especially pronounced for the fast rigid-rotor equilibrium, when the frequency of the azimuthal rotation is close to the cyclotron frequency, and the radial density profile becomes approximately parabolic rather than stepwise as predicted by the non-relativistic theory. It is argued that such effects could be detected in experiments similar to those performed by Theiss et al. [A.J. Theiss, R.A. Mahaffey, A.W. Trivelpiece, Phys. Rev. Lett. 35 (1975) 1436]. The relativistic modification of the Brillouin density limit is also addressed.