First‐order optimization of multiple magnetic lens systems for transport and focusing of annular ion beams

A standard matrix method for tracing rays through an ion optical system is extended to include a recently discovered [W. Z. Liu and F. D. Bechetti, Rev. Sci. Instrum. 60, 1228 (1989)] defocusing solenoidal lens. The results of the matrix approach are shown to correspond with results obtained by numerical integration of particle trajectories through real coil configurations. First‐order radial miss distances due to radial divergence of the beam, chromatic aberration of the lens system, and physical extent of the source are compared for one and two lens systems using the matrix formulation. It is demonstrated that a two lens system in a focusing‐defocusing arrangement can simultaneously correct to first order for chromatic aberration and beam divergence, producing a better focus for thin annular beams with significant energy spread and divergence. A new calculation of the focal length for the negative solenoidal lens is also included.