Relativistic positrons dynamics in the electrostatic field of perfect periodic positively charged structures

In this paper, the channeling effect is considered, which consists in the ability of charged particles to penetrate relatively large distances into the interior of the crystal, in which particles move in the interplanar space and are affected by an electrostatic field created by ions of the crystal lattice. Interest in this effect arises due to the fact that channeling is accompanied by directed electromagnetic radiation. This was facilitated, on the one hand, by the versatility and complexity of the problem from a theoretical point of view and, on the other hand, by the practical possibility of using such radiation, the parameters of which can vary in a wide range by changing the parameters of the crystal structure in many fields of science and technology. In the work, the electrostatic field inside an arbitrary periodic structure is considered and a mathematical model is constructed that describes the main characteristics of the field in the ellipsoidal approximation: the scalar potential of the electric field and its intensity. The paper also provides all the necessary mathematical relationships.