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Self-Consistent Treatment of Equilibrium Space Charge Effects in the l=2 Stellatron

A cyclic accelerator, the stellatron has been proposed to accelerate large electron currents in a magnetic field focusing configuration consisting of the combination of an ordinary weak focusing betatron field, a toroidal field, and a stellarator field. Early treatments of space charge effects in the stellatron employed the ad hoc assumption of a circular beam of arbitrary, unspecified radius. In the present work we obtain an equilibrium distribution function for the l=2 stellatron, analogous to the K-V distribution function, which produces an elliptical beam of constant density, the major and minor radii and orientation of which are specified by the beam current and emittance, and by the externally applied fields. Single particle stability criteria and single particle tunes in the self-consistent fields are also given.