The local limiting theorem for probability distribution density of random values of an additive quadratic functional over the trajectories of the complex-valued Ornstein-Uhlenbeck process is proved. The additive functional support is extended unlimitedly. A guaranteed estimate of the asymptotic formula derived is given.

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The results of experimental studies and modeling calculations for controlling the transverse dimensions of an electron beam formed by a magnetron gun with a secondary emission cathode are presented. In the gun, the secondary emission process is launched by a voltage pulse with an amplitude of up to 15 kV supplied to its anode. The dependence of the radial dimensions of the electron beam on the amplitude and gradient of the magnetic field in the transport channel is investigated. It is shown that the obtained experimental results are consistent with the simulation results. The possibility of adjusting the beam diameter by varying the configuration of the magnetic field is established. The experimental results presented indicate the possibility of realizing irradiation of the outer surface of cylindrical samples placed in the region of the gradient magnetic field.

The results of the study on the formation of electron beams by the magnetron gun at various configurations of the magnetic field in the beam transport channel are presented. A technique for modeling the processes of formation of electron flows and control of the distribution of beams by collimation is presented. Numerical simulation of the dynamics of electron beams in the magnetic field of the gun for its various configurations has been carried out. Experimental data on the transportation and collimation of electron beams are presented. The possibility of stable formation of an electron beam in the axial direction during its transportation is shown. Imprints of the collimated electron beam were obtained on metal targets. The possibility of controlling the beam diameter by varying the magnetic field is shown. Comparison of the results of numerical modeling and experimental data on the motion and collimation of the tubular electron flow is carried out.