Abstract
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.
Highlights
Charged particle beams tend to radially expand under space-charge forces and thermal forces if no applied focusing fields constrain their transverse dynamics [1,2]
Foil stacks can be used for transverse focusing of laser-produced proton beams [10] where intense space-charge has been limiting applications [11]
An idealized analytical envelope theory was previously developed by Lund et al [6] and agrees with particle-in-cell simulations. This guided an ongoing campaign of experiments, described in Ref. [12] designed to study the mitigation of the defocusing self-electric field of proton beams
Summary
Charged particle beams tend to radially expand under space-charge forces and thermal forces if no applied focusing fields constrain their transverse dynamics [1,2]. Passive focusing schemes have been investigated which employ material structures to reduce self-fields These include: Metallic conic guide tubes for electron focusing [3] and ion focusing [4], and stacks of thin foils for electron focusing [5]. Foil stacks can be used for transverse focusing of laser-produced proton beams [10] where intense space-charge has been limiting applications [11]. An idealized analytical envelope theory was previously developed by Lund et al [6] and agrees with particle-in-cell simulations This guided an ongoing campaign of experiments, described in Ref. Good agreement between the envelope theory and numerical model is found
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