Finite Beta Equilibria of Relativistic Electron Beams in Toroidal Geometry

Vlasov equilibria of axisymmetric toroidal plasma pinches are obtained by a perturbation expansion with the inverse aspect ratio, $r_p\mathrm{/R}$ , as the small parameter ($r_p$ and $R$ are the minor and major toroid radii). The particle distribution function is a delta function in the two constants of motion, the canonical azimuthal angular momentum and the total energy. The equilibria studied include a plasma pinch contained within a conducting toroidal vessel and a plasma ring such as might be formed by transverse injection into a mirror field.