Self fields and particle oscillation frequencies in a rotating electron sheet beam loaded with positive ions

An approximate analytical treatment is presented for the electric and magnetic self fields of a long rotating sheet beam between coaxial conductors. By suitable choice of the conductor radii and/or by apply ing a voltage between the conductors it is possible to shift the potential minimum to the major radius of the beam; the condition for this is derived. Expressions for the equilibrium fields and gradients and for the particle oscillation frequencies in various geometries are presented.