A.F. Kryachko, V.M. Lihachov, M.E. Neveykin

Research of questions of diffraction of electromagnetic waves on cylindrical bodies of difficult cross section causes considerable interest and remains actual. It is caused by that the full and effective solution of this task in case of any configuration of a disseminating body isn't received. Various methods its solutions, applicable changes in this or that range of the wave extent of object of research are proposed: low-frequency, resonant and high-frequency. Now it is possible to allocate two main approaches of the solution of the specified problem. In the first approach the border of a cylindrical body with edges is considered as a uniform, difficult contour with surface breaks. The main idea of the second approach is representation of a cylindrical body as some compound object formed by "sewing together" of some key elements. Thus each of these elements is a separate side of a body. As such elements those lenses for whom the strict solution of a problem of diffraction is known can act. At such approach receiving a scattered field on bodies with edges is closely connected with a problem of diffraction on N bodies. As a result, the resultant field disseminated by such body can be presented in the form of superposition of the fields disseminated by each side of a body. In article approach to creation of a short-wave asymptotics for problems of diffraction in cases when the beam method is inapplicable is considered. It can be problems of dispersion on various rough bodies, such as bodies with edges and lines of a rupture of curvature, for example, cylinders of difficult cross section. Previously it is required to find the solution of a problem of diffraction for cases when the site of a contour represents a piece of a straight line and a site of an arch of a convex or concave curve. For a contour being a piece of a straight line, we will use results of the solution of a problem of diffraction of a flat wave on half-plane. The asymptotics of area density of current on a curvilinear site of a contour is as jump of a normal derivative on border of an asymptotics of a field. Expression for diffraction current can be presented in the form of the sum of final number composed, caused by wave of geometrical optics, normal waves and some rest. It is possible to apply asymptotic decomposition to calculation of the rest on the parameter connected with the specified distance. The field asymptotics everywhere can be found from Green's formula on the basis of expression for an asymptotics of the corresponding current. The beam field in angular area with the bent sides when performing conditions of applicability of a short-wave asymptotics, is based on calculation of integral of Sommerfeld. Then depending on that, the surface convex or concave is, the decision, fair in an edge vicinity, is sewed in case of a convex curve with superposition of waves of sliding and in case of a concave curve - with superposition of waves of whispering gallery. The method of receiving an asymptotics consists in the following: the scattered field is looked for in the form of the sum of a fields of geometrical optics and diffraction fields. The resultant scattered field represents superposition of the falling, reflected, diffraction field, and also water sliding and whispering gallery. On the basis of the considered mathematical model disseminating properties of a considered body are estimated. Nature of change of the directional pattern and diameter of the return dispersion is for this purpose studied.