Focusing of laser-generated ion beams by a plasma cylinder: Similarity theory and the thick lens formula

It is shown that plasma-based optics can be used to guide and focus highly divergent laser-generated ion beams. A hollow cylinder is considered, which initially contains a hot electron population. Plasma streaming toward the cylinder axis maintains a focusing electrostatic field due to the positive radial pressure gradient. The cylinder works as a thick lens, whose parameters are obtained from similarity theory for freely expanding plasma in cylindrical geometry. Because the lens parameters are energy dependent, the lens focuses a selected energy range of ions and works as a monochromator. Because the focusing is due to the quasineutral part of the expanding plasma, the lens parameters depend on the hot electron temperature T_e only, and not their density.