Dynamics of a relativistic particle in the field of a Gaussian laser pulse in 3+1 dimensions

The investigation examines the behavior of a relativistic particle in the field of a Gaussian laser pulse in 3+1 dimensions through an approach based on the method of coupled parameters within Lobachevsky geometry. The dynamics of an electron in a modulated laser pulse (in terms of amplitude, phase, and polarization) are analyzed, and the optimal conditions for phase synchronization of particle acceleration in an intense laser field of 1022 W/cm2 are determined. The role of a constant homogeneous magnetic field in stabilizing trajectories and enhancing the directed radiation of particles, including polarization and synchrotron effects, is investigated. Special attention is given to the spectral characteristics of radiation and the angular distribution of power, paving the way for the development of efficient radiation sources in high-energy physics and laser technologies.