Simulation of the Relativistic Dynamics of Charged Particles within the Electrostatic Periodic Field of Perfect Crystalline Undulator

The mathematical model of the passing of relativistic positrons within the interplanar space of positively charged crystalline structures composed of charged ellipsoids was received in this paper. The model includes the numerical-analytical models of both the electrostatic field potential of the structures and the electric intensity of the field as well as the numerical model of the relativistic positrons' dynamics in the field. The model of the field was received by the superposition principle. The case of the positrons passing through the long channel composed of charged ellipsoids, the centers of which are located in the nodal points of a three-dimensional lattice with a cubic unit cell, is considered. It was found the trajectories of positrons are close to sinusoidal on average for long intervals of time when the positrons move within the interplanar space of considered structures

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