When a fast charged particle enters a single crystal, the plane wave function of the free particle is rearranged into a superposition of the localized wave functions, associated with bound transversal motion in channeling states. Transition of a free particle into the channeling state of bound transversal motion can be accompanied with quasi-characteristic electromagnetic radiation. This type of radiation, emitted when a particle enters the crystal, amends the known radiation, associated with transitions between discrete levels of transversal motion, generated in the depth of the single crystal.  Comparison of intensities of the two types of radiation is the objective of this note. 

The behavior of acoustic waves in a rarefied high-temperature plasma is studied, as an example of which the plasma of the solar corona is considered. The effects of thermal conductivity and heating/radiation losses are taken into account, and data on the temperature distribution of radiation intensity are used. An analytical representation in the form of interpolation by cubic splines is constructed for the radiation function. In the gas dynamics approximation, the dispersion relation for acoustic waves is obtained, from which the frequency, phase velocity and damping coefficient are found. In general, the superiority in dispersion and in damping of the thermal conductivity effect is shown. Heating and radiation losses manifest themselves at large wavelengths.

The paper considers the neutron and hard X-ray (HXR) generation by plasma focus chambers operating as part of the ING-102Э subkilojoule neutron generator with a storage capacity of 4.4 μF and an amplitude of the discharge current through the chamber electrodes in the range from 100 to 200 kA. T19-L316 type chamber was used. which ensures the neutron yield with an energy of 2.5 MeV at a level of 10⁵–10⁷ neutrons/pulse. Measurement of the neutron level yield and HXR of the T19-L316 chamber was carried out, the presence of operating modes with the generation of HXR without neutron radiation with deuterium filling of the chamber is shown. The neutron pulses duration of the T19-L316chamber was determined, and the dependence of the duration on the neutron yield level and on the composition of the working gas in the PF chamber was studied. The PF chamber operation in the regime wihout neutrons was experimentally confirmed when the chamber volume was filled with hydrogen, and a comparison was made of the level of the HXR yield when working with hydrogen, deuterium, and deuterium with an admixture of argon. Also, a T19-L316chamber design for neutron generation with a 100-fold reduced HXR yield, implemented is proposed.

The paper describes a technique for representing solutions of a nonlinear partial differential equation – the Burgers equation – in the form of an infinite trigonometric series from a spatial variable. The coefficients of the series are the desired functions of time. The procedure for obtaining an infinite system of ordinary differential equations, the solutions of which set the desired coefficients of the series, is described. Due to the specific properties of the solutions of the considered infinite systems of ordinary differential equations, the theorems on multiple frequencies are proved and the convergence of an infinite trigonometric series in some neighborhood of the point t = 0 and for all values of the independent variable x is investigated. With the help of finite sums, concrete approximate solutions of the Burgers equation are constructed. In particular, it is established that the solution has large values of derivatives in the spatial variable at a finite time under given smooth initial conditions. Which, nevertheless, does not lead to the occurrence of unreasonable oscillations or to the destruction of the solution.

The mathematical model is considered for describing the propagation of pulses in a nonlinear optical medium, which is described by the generalized Triki-Biswas equation. The Cauchy problem for the nonlinear partial differential equation under study is not solved by the method of inverse scattering transformation, therefore, a transition is made to the traveling wave variable. The resulting ordinary differential equation is considered as a system of two equations for the real and imaginary parts of the original equation. After a series of transformations related to finding the first integrals of the equations under consideration, the system of equations is transformed to a nonlinear ordinary differential equation of the first order, the solution of which cannot be expressed in a general form using elementary functions. The method of transformation of the dependent and independent variables is applied, with the help of which the solution of the considered differential equation is written using the Jacobi elliptic functions in an implicit form. We study the question of the existence of degenerate solutions depending on the values of the parameters of the original differential equation. A degenerate case is presented when the solution has the form of a solitary wave and is written in an implicit form. The solutions found in the form of periodic and solitary waves are illustrated for various values of the parameters of the model under study.