Abstract
For a complete set of equilibrium particle densities and temperatures, the corresponding distribution functions including space charge effects are provided through solution of the inverse equilibrium problem. An accompanying orbit theory shows that the projected transverse “rosette” orbit can be analyzed into a circular rotation (drift) and a betatron vortex gyration. In the presence of more general beam density profiles, the betatron vortex gyrations assume an elliptical rather than circular shape.
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