super-Gaussian Distribution Research Articles

Estimation of Shape Parameter of GGD Function by Negentropy Matching

In this paper we present a novel method for the estimation of the shape parameter of the Generalized Gaussian Distribution (GGD) function for the leptokurtic and Gaussian signals by matching negentropy of GGD function and that of data approximated by some non-polynomial functions. The negentropy of GGD function is monotonic function of its shape parameter for values corresponding to super-Gaussian and Gaussian distribution family. The simulation results have been compared with those obtained by existing methods such as Mallat's method and Kurtosis matching method. It has been found that the proposed method is effective and useful in the cases where we have a few observation samples and distribution is highly spiky.

Calculation of the laser-beam M2 factor by the method of moments

The method is proposed for calculating the M2 factor by using the averaged description of wave beams (the method of moments). The values of M2 are calculated for the super-Gaussian intensity distribution with phase distortions caused by the electron and thermal self-focusing and spherical aberration.

Enhanced electron–ion energy exchange due to a super-Gaussian electron velocity distribution function

An analytical description of electron–ion energy exchange in plasmas in which the electron velocity distribution is super-Gaussian due to heating by a strong laser field is presented. The ion to electron temperature ratio at which collisional electron–ion energy exchange cancels increases from 1 in a Maxwellian plasma to 1.98 in a strongly super-Gaussian plasma. Numerical examples illustrating this dependence in nonequilibrium laser heated plasmas are presented.

Active laser resonator performance: formation of a specified intensity output

We discuss the formation of a specified super-Gaussian intensity distribution of a fundamental mode by means of an intracavity controlled mirror, which is a water-cooled bimorph flexible mirror equipped with four controlling electrodes. Analysis has confirmed the possibility to form fourth-, sixth-, and eighth-order super-Gaussian intensity distributions at the output of the stable resonators of industrial cw CO(2) and YAG:Nd(3+) lasers. We present the results of the experimental formation of fourth-order and sixth-order super-Gaussian fundamental modes at the output of a cw CO(2) laser by means of an intracavity flexible mirror. We observed an increase in power up to 12% and an enlargement of the peak value of the far-field intensity by as much as 1.6 times that with a Gaussian TEM(00) mode of the cw CO(2) laser.

Ion acceleration during adiabatic plasma expansion: Renormalization group approach

The renormalization group approach is applied to derive an exact solution to self-consistent Vlasov kinetic equations for plasma particles in the quasineutral approximation. The solution obtained describes the one-dimensional adiabatic expansion into vacuum of a plasma bunch with arbitrary initial velocity distributions of the electrons and ions. The ion acceleration is investigated for both a Maxwellian two-temperature initial electron distribution and a super-Gaussian initial electron distribution.

Effects of non-Maxwellian (super-Gaussian) electron velocity distribution on the spectrum of Thomson scattering

The dynamic form factor for Thomson scattering with a non-Maxwellian (super-Gaussian) electron velocity distribution is analytically and numerically studied for the first time. Both the ion and electron features of the spectra for α>1 are found to be affected strongly. For the ion feature, the use of the usual theoretical spectra with the assumption of a Maxwellian distribution for fitting the measured Thomson scattering spectra may have resulted in some errors in calculating the plasma parameters in high-Z plasmas irradiated with high intensity light. However, it is impossible to use the ion feature of the measured spectra alone to deduce the form of the electron distribution. For the electron feature, the spectral shape (in particular the peak amplitude) changes sensitively with the distribution index. It would be possible to detect the super-Gaussian distribution by simultaneously measuring the ion and electron features of the spectra.

Techniques for fabrication of multilayer dielectric graded-reflectivity mirrors and their use enhancement of the brightness of the radiation from a multimode Nd3+:YAG laser with a stable cavity

Techniques for fabrication of multilayer dielectric mirrors with the reflectivity varying over their surfaces are described. They were used at the output of the cavity of a high-power industrial Nd3+:YAG laser to form a beam with a Gaussian or super-Gaussian intensity distribution. The permissible range of variation of the mirror reflectivity was 40-90% and it was reproducible from sample to sample to within 5%. A mirror with the reflectivity of 84% was used at the output of a plane—plane cavity of a cw Nd3+:YAG laser (output power 12 W) to increase the axial brightness by a factor of 17.

YAG:Nd3+laser with mirrors characterized by a radially distributed reflection coefficient

A new class of mirrors with a super-Gaussian reflection coefficient distribution was investigated. A technique was developed for fabricating such mirrors in a standard evaporation apparatus. The efficiency of a YAG:Nd3+ laser utilizing such mirrors was demonstrated.