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It is shown that plasma-based optics can be used to guide and focus highlydivergent laser-generated ion beams. A hollow cylinder is considered, whichinitially contains a hot electron population. Plasma streaming toward thecylinder axis maintains a focusing electrostatic field due to the positiveradial pressure gradient. The cylinder works as thick lens, whose parametersare obtained from similarity theory for freely expanding plasma in cylindricalgeometry. Because the lens parameters are energy dependent, the lens focuses aselected energy range of ions and works as a monochromator. Because thefocusing is due to the quasineutral part of the expanding plasma, the lensparameters depend on the hot electron temperature $T_e$ only, and not theirdensity

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