Canonical Operator on Connected Manifolds as an Asymptotic Solution to the Problem of Critical Reflection of a Cylindrical Wave from an Inhomogeneous Plasma Layer

Based on the Maslov canonical operator method, an asymptotic solution is constructed for the model problem of a wave incident on a parabolic plasma layer emitted by a point source located outside the plasma layer. The solution takes into consideration both the formation of focal structures of various types in an inhomogeneous layer and the translucency effects of the layer for different parts of the spatial wave spectrum. The effects of layer translucency (partial reflection of waves passing through the layer and partial seepage of waves reflected by the layer) are presented as the interaction of individual solution modes corresponding to various submanifolds of the Lagrangian manifold of the problem. The interaction of modes is taken into consideration by matching the measure density on various submanifolds, which provides an asymptotic representation of the solution for all its components uniform in terms of proximity to the conditions of critical reflection (formulas for the main terms of the asymptotics are presented).