Scattering effects in passive foil focusing of ion beams

A stack of thin, closely spaced conducting foils has been investigated by Lund et al. [Phys. Rev. ST Accel. Beams 16, 044202 (2013)] as a passive focusing lens for intense ion beams. The foils mitigate space-charge defocusing forces to enable the beam self-magnetic field to focus. In this study, we analyze possible degradation of focusing due to scattering of beam ions resulting from finite foil thickness using an envelope model and numerical simulations with the particle-in-cell code WARP. Ranges of kinetic energy where scattering effects are sufficient to destroy passive focusing are quantified. The scheme may be utilized to focus protons produced in intense laser-solid accelerator schemes. As an example, the spot size of an initially collimated 30 MeV proton beam with initial rms radius $200\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$, perveance $Q=1.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$, and initial transverse emittance ${ϵ}_{x,\mathrm{rms}}=0.87\text{ }\text{ }\mathrm{mm}\text{ }\mathrm{mrad}$ propagating through a stack of $6.4\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ thick foils, spaced $100\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ apart, gives a $127.5\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ spot with scattering and a $81.0\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$ spot without scattering, illustrating the importance of including scattering effects.