The effect of the relativistic transformation law of angles on laser ranging of satellites moving in circular orbits equipped with a single retroreflector

It is shown that due to the relativistic transformation law of angles, a laser pulse reflected from a moving retroreflector propagates not strictly back, but at a small angle to the direction of the laser station. For this reason, the ray located on the periphery of a pulse reaches the receiving telescope of the laser station instead of the central ray of a pulse. As a result, the flux of electromagnetic energy received by the laser station is certainly less than the flux of energy in the vicinity of the central ray. The energy flux attenuation coefficient is assessed on the basis of numerical analysis. It is shown that if the receiving telescope is separated from the laser station in order to be mobile and is moving along the Earth’s surface so that the center of each spot formed by a pulse of the reflected light hits the telescope, then the electromagnetic energy flux during laser probing of the satellite will be higher by more than 100 times in comparison with the energy flux received by the stationary telescope of the laser station. From our study it follows that the maximum speed of motion of the centers of spots on the Earth’s surface does not exceed 8 km/h.     

Mathematical modeling of laser sublimation cutting

The mathematical modeling of the laser cutting of steel plates is considered here by implementing the model proposed by Niziev and Nesterov, as formulated in [1]. The 3D-cutting front is described, according to this model, by a highly nonlinear partial differential equation. A number of simplifying assumptions can be formulated, however, so that this complex equation can be handled more easily. This enables us to concentrate on the physics of the model, rather than having to struggle with its mathematical manipulations. This simple model confirms in a capturing way the conjecture originally launched in [1] that cutting speed can be increased with a factor of about 1.5 to 2 by switching over from circular to radial polarization. As a further consequence, the model predicts that a similar improvement is also found regarding the plate thickness at a constant cutting speed.     

Mathematical modeling of the intracavity Q-switched Nd-glass laser

The temporal characteristics of the Q-switched Nd-glass laser have been numerically investigated. A mathematical model describing the dynamic emission and different physical processes has been adapted. This model allows the investigation of the nonlinear saturable absorber effects on the mode characteristics of the Nd-glass laser, and studying the affects of the laser input parameters on the output laser pulse characteristics.Numerical solutions of a nonlinear rate equation system predict the generation of nanosecond pulses of Q-switched Nd-glass laser. The solutions estimate the laser density and the relative population inversion of the Nd-glass laser rod and saturable absorber for different emission regimes. The estimated results of the laser output pulse characteristics are in a good agreement with the other calculated and experimental results.     

Mathematical modeling of laser ablation in liquids with application to laser ultrasonics

The use of laser ablation as a means of generating ultrasonic waves in liquid metals is studied in this paper. A mathematical model for predicting the onset of ablation is developed, as is a model of the ablation process based on steady state, one-dimensional gas dynamics in which the vapor phase is treated as an ideal gas. The results of this model are then used in a quasi-two-dimensional model of laser ablation that accounts for the spatial distribution of intensity in the laser beam. Model predictions are compared with experiments conducted on liquid mercury and excellent agreement is obtained. Based on these results, a simplified model is developed that shows excellent agreement with both the theory and the experiments.     

Mathematical modeling of localized melting around graphite nodules during laser surface hardening of austempered ductile iron

An attempt has been made to mathematically predict the optimum conditions of laser surface hardening (LSH) of austempered ductile iron (ADI) that can ensure a predominantly martensitic microstructure and preclude partial/complete dissolution of graphite nodules in the laser hardened zone during laser irradiation. The exercise involves prediction of the thermal profile (using the Ashby and Easterling model), and consequently, the carbon diffusion profile around the graphite nodules at different depths from the surface for the given conditions of LSH. Microstructural investigations have been carried out by optical and scanning electron microscopy to study the morphology, shape and width of the partially/completely melted graphite nodules as a function of the LSH parameters. Finally, the predicted maximum width of the melted zone around the graphite nodules is compared with the relevant experimental data to validate the proposed model.     

Mathematical modeling of CO2 TEA laser

Five and six-temperature models for the CO₂–N₂–He system are used to describe the process of the dynamic emission in the TEA CO₂ laser. All physical constants and relaxation rates related to these models are examined to estimate the output pulse parameters as a function of the input parameters. The two pumping processes implemented; empirical function and differential equation show a good agreement with the experimental data.     

Mathematical modeling of laser induced heating and melting in solids

An analytical method for treating the problem of laser heating and melting is developed in this paper. The analytical method has been applied to aluminum, titanium, copper, silver and fused quartz and the time needed to melt and vaporize and the effects of laser power density on the melt depth for four metals are also obtained. In addition, the depth profile and time evolution of the temperature of aluminum before melting and after melting are given, in which a discontinuity in the temperature gradient is obviously observed due to the latent heat of fusion and the increment in thermal conductivity in solid phase. Additionally, the calculated melt depth evolution of fused quartz induced by 10.6 μm laser irradiation is in good agreement with the experimental results.     

Mathematical modeling of hybrid CO2 laser

A Teller–Landau six-temperature model describing the dynamic emission of single-mode TEA CO₂ laser has been adapted. This model has been also used to describe the mechanism of obtaining relatively high-power output pulses from hybrid TE-TEA or CW-TEA CO₂ laser consisting of high- and low-pressure sections. The suggested mathematical model allows to investigate the mechanism which limits the TEA oscillation to single longitudinal mode (SLM) due to the narrow gain bandwidth of low-pressure section, and also to study the effect of the laser input parameters on the smooth output laser pulse parameters. In addition, numerical solutions of non-linear rate equation system of the suggested model are quantitatively discussed. The solutions describe the radiation field intensity, the population inversion, and the energy transfer processes. The calculated values of maximum peak power, total energy in pulse, pulse width, etc. are in a very good agreement with the observed experimental values.     

Double-slit interference of a relativistic vortex laser

The interference of a relativistic vortex laser is investigated for the case when a linearly polarized Laguerre–Gaussian pulse impinges on a double-slit solid target. Three-dimensional particle-in-cell simulation results show that the interference fringes of high-order harmonics are twisted, similar to that of the fundamental vortex laser. The twisting order of the interference pattern is determined by the order of the vortex high-order harmonics, which can be explained by the classic double-slit interference models. The usual double-slit interference has been extended to the regime of relativistic intensity,which may have potential applications for measuring the topological charge of vortex high-order harmonics.     

Observation of laser satellites in a plasma produced by a femtosecond laser pulse

Laser satellites are detected in the emission spectra of magnesium and aluminum plasmas produced by femtosecond laser pulses. This is made possible by the realization of picosecond time resolution in a high-luminosity x-ray spectrograph with a spherically curved mica crystal. The temporal characteristics of these newly recorded spectral lines show unequivocally that they are formed as a result of nonlinear processes. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 7, 454–459 (10 October 1997)     

Numerical modeling of the thermal lensing effect in a grazing-incidence laser

The numerical modeling of thermal lensing effect is investigated in a grazing-incidence laser. The deformation of the bounce face is introduced into the modeling for the first time, and the Gaussian distribution of the pump light and the anisotropic heat conduction are considered. The results indicate that the proportion of the deformation on the bounce face to the thermal lensing effect is as high as 80% for small grazing-incident angle of 5°. The thermal lensing effect sensitively depends on the pump power, grazing-incident angle and the pump distribution in a grazing-incidence bounce geometry laser.     

Mathematical modeling of a satellite communications network

A dynamic multiple-access protocol with notification of clashes is proposed for operation with a satellite communications network. Mathematical modeling is used to find some basic probabilistic and temporal characteristics of the network: the throughput, the wait time, etc. It thus becomes possible to determine the region of initial parameter values in which this protocol is more effective than the ALOHA network protocol.V. D. Kuznetsov Siberian Physicotechnical Institute, Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 120–127, September, 1992.     

Scattering of relativistic electrons by a focused laser pulse

The problem of the motion of a classical relativistic electron in a focused high-intensity laser pulse is solved. A new three-dimensional model of the electromagnetic field, which is an exact solution of Maxwell’s equations, is proposed to describe a stationary laser beam. An extension of the model is proposed. This extension describes a laser pulse of finite duration and is an approximate solution of Maxwell’s equations. The equations for the average motion of an electron in the field of a laser pulse, described by our model, are derived assuming weak spatial and temporal nonuniformities of the field. It is shown that, to a first approximation in the parameters of the nonuniformities, the average (ponderomotive) force acting on a particle is described by the gradient of the ponderomotive potential, but it loses its potential character even in second order. It is found that the three-dimensional ponderomotive potential is asymmetric. The trajectories of relativistic electrons moving in a laser field are obtained and the cross sections for scattering of electrons by a stationary laser beam are calculated. It is shown that reflection of electrons from the laser pulse and the surfing effect are present in the model studied. It is found that for certain impact parameters of the incident electrons the asymmetic ponderomotive potential can manifest itself effectively as an attractive potential. It is also shown that even in the case of a symmetric potential the scattering cross section contains singularities, known as rainbow scattering. The results are applicable for fields characterized by large (compared to 1) values of the dimensionless parameter η² = e ²〈E ²〉/m ²ω² and arbitrary electron energies.     

Mathematical modeling of ruby laser as a pumping source of a “self Q-switched” distributed feedback dye laser

A mathematical model describing the dynamic emission of the ruby laser as a pumping source of a distributed feedback dye laser (DFDL) has been adapted. The suggested model allows the temporal behavior investigation of the ruby laser and the DFDL on mode characteristics and, moreover, investigating the affect of laser input parameters on the output laser pulses in the ruby laser and in the DFDL.The numerical solutions of a coupled nonlinear rate equations system of the adapted model that predict the generation of picoseconds pulses, with neglecting the effect of refractive index variation, are discussed (feedback process is achieved only by optical gain). The model estimates the density of the emitted radiation, energy density of the first excited state, and the output power of the DFDL. The adapted mathematical model is in good agreement with the available experimental data.     

Scattering of a few-cycle laser pulse by a single relativistic electron

The scattering of a single relativistic electron with few-cycle plane wave laser pulse with intensity of about $I=1.38\times 10^{14}\,\text{ W/cm }^{2}$ is theoretically and numerically analyzed in the linear regime, and the radiated energy spectra of electron shows that zeptosecond X-ray pulses can be supported. The influences of the initial carrier-envelope phase offset $\varphi _0$ of the incident few-cycle laser pulses are studied, and the results demonstrate that a single zeptosecond pulse can be produced from scattering by using a single-cycle laser pulse with fixed initial carrier-envelope phase offset $\varphi _0 =\pi /2$ . It is discovered that the influence of the initial carrier-envelope phase $\varphi _0$ on the spectrum of the radiation is apparent for low and high frequency of the spectrum, but there is no influence of the central part of the spectrum.     

Mathematical modeling of the Magnus effect in the geometrical optics approximation

The Magnus effect in multimode fibers with triangular and parabolic refractive index profiles (RIPs) is simulated in the geometrical optics approximation. The calculations confirm the linear relation between the angle of rotation Δ? and the fiber length z. The results of calculations for a spiral path with constant radius are compared with the analytical solution obtained. For a fiber with a parabolic RIP, the value of Δ? obtained in this work is one-half the result obtained in the wave approach.     

Mathematical modeling the formation of a histone octamer

A physical model of the interaction of protein molecules and their ability to form complex biological systems for the in vitro case in a solution of monovalent salt has been developed. Their reactive abilities using the methods of electrostatics based on the example of the step-by-step formation of the histone octamer from the H2A, H2B, H3, and H4 proteins have been studied. To analyze the ability of protein molecules to form compounds the matrix of potential energy of interactions between protein molecules in solutions with different concentrations of monovalent salt has been examined.