Complex Gaussianity of Long-Distance Random Wave Processes

The development of the Beamlet laser has involved extensive and detailed modeling of laser performance and beam propagation to: (1) predict the performance limits of the laser, (2) select system configurations with higher performance, (3) analyze experiments and provide guidance for subsequent laser shots, and (4) design optical components and establish component manufacturing specifications. In contrast to modeling efforts of previous laser systems such as Nova, those for Beamlet include as much measured optical characterization data as possible. This article concentrates on modeling of beam propagation in the Beamlet laser system, including the frequency converter, and compares modeling predictions with experimental results for several Beamlet shots. It briefly describes the workstation-based propagation and frequency conversion codes used to accomplish modeling of the Beamlet.

Scintillation model of laser beam propagation in satellite-to-ground bidirectional atmospheric channels

This paper presents a new statistical damage constitutive model using symmetric normal distribution. The broken rock microbody obeyed symmetric normal distribution and the equivalent strain principle in damage mechanics. The uniaxial compression tests of samples subjected to dry-wet cycles were performed. The damage model was established using the equivalent strain principle and symmetric normal distribution. The damage variable was defined by the elastic modulus under various dry-wet cycles. Parameters of the damage constitutive model were identified using MATLAB software, and the proposed model is verified to be in good agreement with uniaxial compression test results. Fracturing of the rock microbody is well described by symmetric normal distribution, and the proposed statistical damage constitutive model has good adaptability to the uniaxial compression stress-strain curve.

Ponderomotive effects that arise when an intense plane pumping wave acts on low-concentration electron and plasma bunches are theoretically studied within the framework of a one-dimensional model. Using the Lagrange variables, an electron (plasma) bunch under the action of a pumping field can be represented as a gas comprising macroparticles with ponderomotive and Coulomb interactions. The ponderomotive force at small interparticle distances is attractive, that is, directed oppositely to the Coulomb force; it cannot, however, completely balance the latter. The constructed model is used to study superradiance, which arises when an intense pumping wave acts on an extended electron bunch. Radiation is then scattered in the form of narrow pulses whose amplitude is proportional to the total number of particles in the bunch. In addition, we describe acceleration of a neutral plasma layer, narrow on the wavelength scale, in the field of an intense wave and radiation field-induced partial contraction of an electron bunch with an incompletely compensated charge.

Is shown, that the field of a wave by a scattered rough surface, has the spatial distribution similar to a field of a diffraction wave on an aperture, conterminous under the form and the size with illuminated area. A maximal intensity in diffractive orders form speckle pattern. Dependence of a time spectrum of intensity fluctuations, of scattered radiation by a moving surface from size of a roughness is received. With use of dynamic speckles experimental measurement of base lengths and a root-mean-square roughness on these lengths is lead. Results of experiment have confirmed the offered model of a scattering and have shown an opportunity of simultaneous definition of ensembles of statistical parameters of a roughness.

The pattern of calculation of amplitudes of a series of processes in the field of an intensive laser wave, in which two fermions p; p and two real photons k 1 ; k 2 participate, is considered. In relation to one-photon processes, these processes are of the second order on α if the wave intensity ξ 1 (i.e., actually absorption from the wave only one quantum). Otherwise, they are competing and essentially nonlinear. Onephoton processes have a number of the important physical applications. For example, γe and γγ colliders work on their basis. Some of these processes calculated in [1] in Diagonal Spin Basis (see [2] in this issue). Two-photons back Compton-effect in intensive laser wave occurs together with one-photon process and thus influences the formation of spectr and polarisation of photon beam. The amplitudes of two-photon annihilation of a fermion pair in an intensive laser wave are applicable for calculating of induced decay of orthopositronium into two photons. And in this approach there is no necessity to assume the relative momentum equal to zero. In DSB the calculation is conducted at the level of reaction amplitudes. It essentially simplifies both the calculation and the form of obtained results; those combinations of amplitudes which describe the spin effects are easy to calculate. And these effects are especially essential in nonlinear processes. The calculations are conducted in covariant form. Besides compactness, this provides independence of the frames of reference and energy modes. The masses of fermions are taken into account precisely and are not assumed equal each other (heavy leptons, modes of various decays). The process under consideration is described by 2 5 amplitudes. Because of parity conservation, we need to calculate 16 amplitudes (in our approach, they are described by 8 formulas). Therefore, here we can present only the pattern of calculation. The necessary formulas are cited in accordance with monograph [3] with the indication paragraph number,where §40 “An electron in the field of the plane electromagnetic wave”; §89 “An annihilation of a positronium”; §101 “Radiation of a photon by an electron in the field of an intensive electromagnetic wave”. Unlike [3], we assume γ 5 iγ 0 γ 1 γ 2 γ 3 (opposite sign) and elementary charge e 0. Process Laser e e γ 1 γ 2 described by amplitude

This paper considers density evolution for low-density parity-check (LDPC) and multi-edge type LDPC (MET-LDPC) codes over the binary input additive white Gaussian noise channel. We first analyze three single-parameter Gaussian approximations for density evolution and discuss their accuracy under several conditions, namely, at low rates, with punctured and degree-one variable nodes. We observe that the assumption of symmetric Gaussian distribution for the density-evolution messages is not accurate in the early decoding iterations, particularly at low rates and with punctured variable nodes. Thus, single-parameter Gaussian approximation methods produce very poor results in these cases. Based on these observations, we then introduce a new density evolution approximation algorithm for LDPC and MET-LDPC codes. Our method is a combination of full density evolution and a single-parameter Gaussian approximation, where we assume a symmetric Gaussian distribution only after density-evolution messages closely follow a symmetric Gaussian distribution. Our method significantly improves the accuracy of the code threshold estimation. Additionally, the proposed method significantly reduces the computational time of evaluating the code threshold compared with full density evolution thereby making it more suitable for code design.

Gaussian beam is an important complex geometrical optical technology for modeling seismic wave propagation and diffraction in the subsurface with complex geological structure. Current methods for Gaussian beam modeling rely on the dynamic ray tracing and the evanescent wave tracking. However, the dynamic ray tracing method is based on the paraxial ray approximation and the evanescent wave tracking method cannot describe strongly evanescent fields. This leads to inaccuracy of the computed wave fields in the region with a strong inhomogeneous medium. To address this problem, we compute Gaussian beam wave fields using the complex phase by directly solving the complex eikonal equation. In this method, the fast marching method, which is widely used for phase calculation, is combined with Gauss–Newton optimization algorithm to obtain the complex phase at the regular grid points. The main theoretical challenge in combination of this method with Gaussian beam modeling is to address the irregular boundary near the curved central ray. To cope with this challenge, we present the non-uniform finite difference operator and a modified fast marching method. The numerical results confirm the proposed approach.

The chapter presents a new scalar model of optical beam propagation in nonlinear media, as it is developed in [1, 2, 3, 4]. The model addresses narrow beams and stresses on nonlinearly induced diffraction, an effect of medium inhomogeneity introduced by the spatial variation of the nonlinear polarization. Strarting from the vector nonparaxial model of beam propagation in nonlinear media, it is shown that not the vectorial nature of the carrier wave field, but a scalar effect which comes out from the (div/E)-term in the wave equation and has the meaning of nonlinear diffraction, controls predominating over the nonparaxiality, the balance between diffraction and nonlinearity in the formation of the spatial solitons. The conclusion is based on analytical and numerical solutiuons of the nonlinear equations for the beam envelopes and on analysis of the wave power conservation laws derived. Both third (Kerr-type)- and second- order nonlinearities are treated as well as both planar waveguides and bulk media are covered. Single beam propagation and beam interaction and coupling are described. New solitary-wave solutions are presented.

In this chapter we will consider a charged particle interaction with a strong EM wave in the presence of a uniform magnetic field along the wave propagation direction when the resonant effect of the wave on the particle rotational motion in the static magnetic field is possible. In vacuum, as a result of the interaction of a charged particle with a monochromatic EM wave and uniform magnetic field the resonance created at the initial moment for the free-particle velocity automatically holds throughout the interaction process due to the equal Doppler shifts of the Larmor and wave frequencies in the field. This phenomenon is known as “Autoresonance”. This property of cyclotron resonance in vacuum makes possible the creation of a generator of coherent radioemission by an electron beam, namely a cyclotron resonance maser (CRM). From the point of view of quantum theory the relativistic nonequidistant Landau levels of the particle in the wave field become equidistant in the autoresonance due to the quantum recoil at the absorption/emission of photons by the particle. In addition, the dynamic Stark effect of the wave electric field on the transverse bound states of the particle does not violate the equidistance of Landau levels in the autoresonance. Then the inverse process, that is, multiphoton resonant excitation of Landau levels by strong EM wave and, consequently, the particle acceleration in vacuum due to cyclotron resonance, in principle, is possible. In a medium with arbitrary refractive properties (dielectric or plasma) because of the different Doppler shifts of the Larmor and wave frequencies in the interaction process the autoresonance is violated. However, the threshold (by the wave intensity) phenomenon of electron hysteresis in a medium due to the nonlinear cyclotron resonance in the field of strong monochromatic EM wave takes place. In contrast to autoresonance, the nonlinear cyclotron resonance in a medium proceeds with a large enough resonant width. This so-called phenomenon of electron hysteresis leads to a significant acceleration of particles, especially in the plasmalike media where the superstrong laser fields of relativistic intensities can be applied. The use of dielectriclike (gaseous) media makes it possible to realize cyclotron resonance in the optical domain (with laser radiation) due to an arbitrarily small Doppler shift of a wave frequency close to the Cherenkov cone, in contrast to the vacuum case where the cyclotron resonance for the existing maximal powerful static magnetic fields is possible only in the radio-frequency domain.

Cyclone–anticyclone asymmetry in spontaneous gravity wave radiation from a co-rotating vortex pair is investigated in an $f$-plane shallow water system. The far field of gravity waves is derived analytically by analogy with the theory of aeroacoustic sound wave radiation (Lighthill theory). In the derived form, the Earth’s rotation affects not only the propagation of gravity waves but also their source. While the results correspond to the theory of vortex sound in the limit of $f\rightarrow 0$, there is an asymmetry in gravity wave radiation between cyclone pairs and anticyclone pairs for finite values of $f$. Anticyclone pairs radiate gravity waves more intensely than cyclone pairs due to the effect of the Earth’s rotation. In addition, there is a local maximum of intensity of gravity waves from anticyclone pairs at an intermediate $f$. To verify the analytical solution, a numerical simulation is also performed with a newly developed spectral method in an unbounded domain. The novelty of this method is the absence of wave reflection at the boundary due to a conformal mapping and a pseudo-hyperviscosity that acts like a sponge layer in the far field of waves. The numerical results are in excellent agreement with the analytical results even for finite values of $f$ for both cyclone pairs and anticyclone pairs.

Currently, Industry 4.0 creates new opportunities for analyzing data on production processes and extracting knowledge from them. With the Internet of Things, data is continuously collected from machine sensors to analyze machine health. Thanks to artificial intelligence methods and discrete simulation, it is possible to process data and dynamically adjust the operating conditions of the production line to the expected time of failure-free operation of the machine or reliable work of an employee. Recently, machine learning techniques have been used to automatically adapt the production line to changes in a given production environment. The paper presents various methods of modeling actions, i.e., forecasting the failure-free operation time of a machine or the error-free working time of an employee. The possible actions the agent can perform, the possible prediction techniques that can be selected are presented. The time between failures is described by a log-normal distribution. The asymmetric lognormal distribution is much more flexible for practical modeling compared to the “perfectly” symmetric normal distribution. In practice, the asymmetric lognormal distribution, strongly shifted to the left, can be used to describe the decreasing time between failures due to human error, as well as the time between failures of a machine in the third phase of its life cycle, which decreases as the machine ages and its components wear out. The parameters of the distribution are estimated using the maximum-likelihood approach, theempirical moments approach, the renewal-theory approach, the empirical distribution function and the method based on coefficient of variation. Numerical examples of predicting failure-free operation times described by the log-normal distribution are presented. The results are compared assuming that failure-free times are described by exponential, normal and Weibull distributions. The results are also compared with an example of the simplest learning method.

When waves propagate through a complex medium like the turbulent atmosphere the wave field becomes incoherent and the wave intensity forms a complex speckle pattern. In this paper we study a speckle memory effect in the frequency domain and some of its consequences. This effect means that certain properties of the speckle pattern produced by wave transmission through a randomly scattering medium is preserved when shifting the frequency of the illumination. The speckle memory effect is characterized via a detailed novel analysis of the fourth-order moment of the random paraxial Green’s function at four different frequencies. We arrive at a precise characterization of the frequency memory effect and what governs the strength of the memory. As an application we quantify the statistical stability of time-reversal wave refocusing through a randomly scattering medium in the paraxial or beam regime. Time reversal refers to the situation when a transmitted wave field is recorded on a time-reversal mirror then time reversed and sent back into the complex medium. The re-emitted wave field then refocuses at the original source point. We compute the mean of the refocused wave and identify a novel quantitative description of its variance in terms of the radius of the time-reversal mirror, the size of its elements, the source bandwidth, and the statistics of the random medium fluctuations.

Development of a full scale remote steerable ECRH mm-wave launching system test set-up for ITER

Plano-concave optical microresonators (PCMRs) are optical microcavities formed of one planar and one concave mirror separated by a spacer. PCMRs illuminated by Gaussian laser beams are used as sensors and filters in fields including quantum electrodynamics, temperature sensing, and photoacoustic imaging. To predict characteristics such as the sensitivity of PCMRs, a model of Gaussian beam propagation through PCMRs based on the ABCD matrix method was developed. To validate the model, interferometer transfer functions (ITFs) calculated for a range of PCMRs and beams were compared to experimental measurements. A good agreement was observed, suggesting the model is valid. It could therefore constitute a useful tool for designing and evaluating PCMR systems in various fields. The computer code implementing the model has been made available online.