Principal possibilities of Kumakhov lenses

New optics widely uses the possibility of controlling x rays during their transmission through systems of bent hollow glass capillaries. One of the main elements of new optics are concentrating devices which got the name `Kumakhov lenses.' Different types of Kumakhov lenses can be used for solving various problems: focusing radiation onto a small spot, forming quasiparallel beams, filtering radiation, reducing or increasing x-ray images, etc. The possibility of controlling x rays is based on the phenomenon of total external reflection which takes place only at grazing incidence angles. But Kumakhov lenses have large angular aperture because they operate on multiple reflections. In this work we investigate the properties of Kumakhov lenses operating on multiple reflections as well as more simple capillary systems which can also focus x rays but operate mainly on single reflections. The latter systems are capillary structures which have straight hollow mutually parallel channels.