
ntroduction
In the early eighties, M.A. Kumakhov proposed a new kind of optics based on the total external reflection of x-rays from smooth surfaces. X-rays incident on the interior of the tubes at small angles (lesser than the critical angle for total external reflection) are guided down the tubes by total external reflection. Since then the technology to control x-rays using systematic arrangements of glass polycapillaries has developed rapidly. Depending on the specific arrangement and application, x-ray beams can be focused or divergent beams made quasi-parallel.
Lenses for visible light are made of a transparent material with an index of refraction substantially different from 1. Such a material does not exist for x-rays. Therefore, only optics based on diffraction and interference effects, such as multilayer mirrors, zone and phase plates, are available (1)
However these optics are generally small in size and must be designed for a particular incident angle and energy, thus restricting their apllicability for braodband divergent radiation. Grazing incidence optics depend on the phenomenon of total external reflection, but are restricted in their use because of their very small angular aperture, large size, or large focal length (2) . Total external reflection also allows x-rays to be transmitted through single straight or tapered hollow glass tubes in a manner analogous to visible light fiber optics (3) .
Recently, a new type of x-ray optic, based on an assembly of a large number of hollow capillary tubes brought together to form a "Kumakhov lens," was invented in Moscow (4) .

Graph of the output intensity of a 3rd generation capillary. optic versus position of the source in the focal plane.
References(1) J.H. Underwood and D.T. Attwood, Phys. Today, 34, p. 44, (1984).
(2) F. Jentzch, Phys. Z. 30, p. 1268 (1929).
(3) D.J. Thiel, E.A. Stern, D.H. Bilderbeck, A.Lewis, Physica B, 158, p. 314 (1989).
(4) V.A. Arkd'ev, A. I. Kolomitsev, M.A. Kumakhov, I. Yu. Ponomarev, I.A. Khodeev, Yu. P. Chertov and I.M. Shakparonov, Sov. Phys. Usp. 32 (3), p. 271, March 1989.
(5) M.A. Kumakhov, Nuclear Instruments and Methods, B48 p. 283 (1990).
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