Generation of a hollow ion beam: Calculation of the rotation frequency required to accommodate symmetry constraint

A hollow intense heavy ion beam with an annular focal spot has many important applications. The Gesellschaft für Schwerionenforschung, Darmstadt is planning to develop a radio frequency wobbler that will rotate the beam at extremely high frequencies and thus create an annular (ring shaped) focal spot. In this paper, we present an analytical model that determines the minimum rotation frequency of the wobbler in order to achieve a high degree of irradiation symmetry (an asymmetry of a few percent) of the target. Estimates for a typical heavy ion imploded target are also presented.