Formation of hollow ion beams of various shapes using multipole magnets

This study describes a novel and simple beam-focusing method for the formation of a charged-particle beam with a hollow transverse intensity distribution using the nonlinear focusing force of multipole magnets in a beam transport line. The dynamic behavior of the beam focused by multipole magnets is theoretically investigated to predict the phase-space shape and spatial profile of the hollow beam. It is shown numerically and experimentally that the hollow beam has a steep peak at the peripheral edge and high contrast between the edge peak intensity and the intensity near the beam center. Depending on the order and strength of the applied nonlinear multipole field, the cross-sectional shape of the hollow beam can be diversely transformed, e.g., into an ellipse, a rounded rectangle, a rhombus for octupole focusing, or a triangle for sextupole focusing. The present beam-formation method, applicable to various charged-particle beams of different parameters such as the particle species, kinetic energy, and time structure, enables the shaping of the transverse profile that can never be realized through conventional linear beam optics.