Effects of longitudinal space charge in beams for heavy-ion fusion

A new analytic model is presented that accurately estimates the radially averaged axial component of the space-charge field of an axisymmetric heavy ion beam in a cylindrical beam pipe. The model recovers details of the field near the beam ends that are overlooked by simpler models, and the results compare well with exact solutions of Poissonʹs equation. Field values are shown for several simple beam profiles and are compared with values obtained from simpler models. The model has been implemented in the fluid-envelope code CIRCE and used to study longitudinal confinement in beams with a variety of axial profiles. The effects of errors in the longitudinal control fields are presented.