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R. M. Feshchenko

Publications and source records attributed to R. M. Feshchenko.

9 recordsLinked to original sources
arXiv2021

A theory of reflective X-ray multilayer structures with graded period and its applications

In this paper a theory of reflective X-ray multilayer structures with a graded (slowly varying) period based on the coupled waves method and quasi-classical asymptotic expansions is reported. A number of exact solutions of the coupled wave equations is obtained and analyzed demonstrating suitability of this method for the description of the reflective properties of the graded multilayers. The developed theory is then used as a basis for the solution of the inverse problem, i.e. designing multilayer structures with a pre-specified reflectivity dependence on the wavelength or grazing angle. A number numerical experiments is conducted to demonstrate the capabilities of the proposed method in designing reflective multilayer coatings with an arbitrary shape of the reflectivity curve. The problem of maximization of the integral reflectivity is considered and a second order differential equation, which solutions correspond to multilayer structures with the maximal reflectivity, is derived. Finally, an upper limit on the integral reflectivity achievable with a graded multilayer is estimated.

physics.optics↗
arXiv2021

Exact transparent boundary condition for the multidimensional Schrödinger equation in hyperrectangular computational domain

In this paper an exact transparent boundary condition (TBC) for the multidimensional Schrödinger equation in a hyperrectangular computational domain is proposed. It is derived as a generalization of exact transparent boundary conditions for 2D and 3D equations reported before. A new exact fully discrete (i.e. derived directly from the finite-difference scheme used) 1D transparent boundary condition is also proposed. Several numerical experiments using an improved unconditionally stable numerical implementation in the 3D space demonstrate propagation of Gaussian wave packets in free space and penetration of a particle through a 3D spherically asymmetrical barrier. The application of the multidimensional transparent boundary condition to the dynamics of the 2D system of two non-interacting particles is considered. The proposed boundary condition is simple, robust and can be useful in the field of computational quantum mechanics, when an exact solution of the multidimensional Schrödinger equation (including multi-particle problems) is required.

math-ph↗
arXiv2020

On inverse problem with phase retrieval for an inclined line in the parabolic approximation

The inverse problem of amplitude reconstruction on an inclined line based on the values of amplitude or its module as recorded on semi-infinite line orthogonal to the beam propagation direction is considered within the framework of 2D parabolic equation. It is demonstrated that this inverse problem, in case when the complex image plane amplitude is known, can be reduced to a singular Cauchy type integral equation. The existence of its solutions requires that certain conditions be met but if a solution exists it is necessary unique. The obtained integral equation is then approximated piece-wisely and the resulting linear algebraic system is solved numerically while applying necessary regularization procedures to enhance the stability of its solutions. Finally, an iterative method of phase retrieval is developed and a set of numerical experiments is performed.

math.NA↗
arXiv2019

Numerical simulation of Ni-like Xe plasma dynamics and laser gain in a low inductivity capillary discharge

X-ray lasers based on transitions in highly charged \textit{Ni}-like ions generating in the "water window" wavelength range can be pumped by compact laboratory discharge sources. This makes them promising candidates for use as compact coherent X-ray sources in laboratory applications including biological imaging and investigations of carbon containing materials. In this paper, the results of numerical simulations of the plasma dynamics and kinetics in an X-ray laser based on transitions in \textit{Ni}-like xenon ions are reported. The laser active medium is created by an extended low-inductive high current Z-discharge capable of producing two successive electrical pulses. The non-equilibrium multi-charged ion plasma dynamics is studied numerically using a non-stationary 1D two-temperature radiation-MHD model, which describes plasma hydrodynamics, non-stationary ionization, transfer of the continuum and line radiation as well as processes in the pumping electrical circuit. The ionic energy level populations are calculated in the quasi-stationary approximation. The simulation results allowed determination of the electrical and energy pumping parameters necessary to obtain a weak signal gain for the working transitions of the order of $g^+\sim1$ $\mbox{cm}^{-1}$. It was demonstrated that plasma with the electronic temperature of more than 400 eV and the density of more than $10^{19}$ $\mbox{cm}^{-3}$ can be created by a low inductive two step discharge with peak current exceeding 200 kA.

physics.plasm-ph↗
arXiv2016

Influence of the electron beam emittance on the polarization of a laser--electron X-ray generator

In this paper we analyze the polarization of the X-ray radiation coming from laser--electron X-ray generator (LEXG). We obtain general relations connecting the polarization state of outgoing X-ray radiation to the polarization state of laser beam as well as to the parameters of electron beam. We demonstrate that finite electron beam emittance causes a partial depolarization of initially fully polarized X-ray radiation even when the laser beam is fully polarized. We demonstrate with a number of numerical experiments that finite electron beam emittance can in some cases fundamentally alter the polarization state of X-ray radiation as compared to the polarization state of X-ray radiation scattered by electron beam with a zero emittance. Possible applications of polarized LEXG's radiation are discussed.

physics.acc-ph↗
arXiv2016

Exact transparent boundary conditions for the parabolic wave equations with linear and quadratic potentials

In this paper exact 1D transparent boundary conditions (TBC) for the 2D parabolic wave equation with a linear or a quadratic dependence of the dielectric permittivity on the transversal coordinate are reported. Unlike the previously derived TBCs they contain only elementary functions. The obtained boundary conditions can be used to numerically solve the 2D parabolic equation describing the propagation of light in weakly bent optical waveguides and fibers including waveguides with variable curvature. They also are useful when solving the equivalent 1D Schrödinger equation with a potential depending linearly or quadratically on the coordinate. The prospects and problems of discretization of the derived transparent boundary conditions are discussed.

physics.class-ph↗
arXiv2008

Stimulated Radiation Cooling

In this paper the Stimulated radiation cooling (SRC) of ion beams and methods of formation of the broadband laser beams with given spectral distribution are discussed.

physics.acc-ph↗
arXiv2004

Energy losses and efficiency of laser - electron X-ray generator for medical applications

A source of medical x-rays based on a 50 Mev storage ring and a quasi-continues picosecond laser is considered. It is shown that such generator produces useful X-ray flux with higher average power and higher efficiency than that of conventional X-ray tubes. The main energy losses are related to coherent synchrotron radiation. Taking this into account the required parameters of the storage ring and injector are determined.

physics.acc-ph↗