In this work all the dessins d'enfant with no more than 4 edges are listed and their Belyi pairs are computed. In order to enumerate all dessins the technique of matrix model computations was used. The total number of dessins is 134; among them 77 are spherical, 53 of genus 1 and 4 of genus 2. The orders of automorphism groups of all the dessins are also found.Dessins are listed by the number of edges. Dessins with the same number of edges are ordered lexicographically by their lists of 0-valencies. The corresponding matrix model for any list of 0-valencies is given and computed. Complex matrix models for dessins with 1 -3 edges are used. For the dessins with 4 edges we use Hermitian matrix model, correlators for which are computed in [1].
Generation of spontaneous magnetic fields (SMFs) is one of the most interesting phenomena accompanying an intense laser–matter interaction. One method of credible SMFs measurements is based on the magneto-optical Faraday effect, which requires simultaneous measurements of an angle of polarization plane rotation of a probe wave and plasma electron density. In classical polaro-interferometry, these values are provided independently by polarimetric and interferometric images. Complex interferometry is an innovative approach in SMF measurement, obtaining information on SMF directly from a phase–amplitude analysis of an image called a complex interferogram. Although the theoretical basis of complex interferometry has been well known for many years, this approach has not been effectively employed in laser plasma research until recently; this approach has been successfully implemented in SMF measurement at the Prague Asterix Laser System (PALS). In this paper, proprietary construction solutions of polaro-interferometers are presented; they allow us to register high-quality complex interferograms in practical experiments, which undergo quantitative analysis (with an original software) to obtain information on the electron density and SMFs distributions in an examined plasma. The theoretical foundations of polaro-interferometric measurement, in particular, complex-interferometry, are presented. The main part of the paper details the methodology of the amplitude–phase analysis of complex interferograms. This includes software testing and examples of the electron density and SMF distribution of a laser ablative plasma generated by irradiating Cu thick planar targets with an iodine PALS laser at an intensity above about 1016 W/cm2.
Laser plasma created by intense light interaction with matter plays an important role in high-energy density fundamental studies and many prospective applications. Terawatt laser-produced plasma related to the low collisional and relativistic domain may form supersonic flows and is prone to the generation of strong spontaneous magnetic fields. The comprehensive experimental study presented in this work provides a reference point for the theoretical description of laser-plasma interaction, focusing on the hot electron generation. It experimentally quantifies the phenomenon of hot electron retention, which serves as a boundary condition for most plasma expansion models. Hot electrons, being responsible for nonlocal thermal and electric conductivities, are important for a large variety of processes in such plasmas. The multiple-frame complex-interferometric data providing information on time resolved spontaneous magnetic fields and electron density distribution, complemented by particle spectra and x-ray measurements, were obtained under irradiation of the planar massive Cu and plastic-coated targets by the iodine laser pulse with an intensity of above 1016 W cm−2. The data shows that the hot electron emission from the interaction region outside the target is strongly suppressed, while the electron flow inside the target, i.e. in the direction of the incident laser beam, is a dominant process and contains almost the whole hot electron population. The obtained quantitative characterization of this phenomenon is of primary importance for plasma applications spanning from ICF to laser-driven discharge magnetic field generators.
Recently developed three-frame complex-interferometry system driven by a Ti:Sa laser with 40 fs pulse has been installed at the PALS (Prague Asterix Laser System) laser facility. This unique diagnostic allows for the first time to perform simultaneous measurements of B-field in the coil region of the capacitor-coil targets (CCT) and the self-generated B-field (SMF) of the diode plasma in between the CCT-plates. CCT were irradiated by the PALS iodine laser (λ = 1315 nm) with energy in the range 250–500 J and pulse duration of 350 ps at full width at half maximum. The operation of this diagnostic system and methodologies for quantitative data analysis are presented in this study, including: (i) obtaining information about the induction of the magnetic field in the CCT coil based on measurements of the Faraday effect in the TGG (Terbium Gallium Garnet) paramagnetic crystal at the coil vicinity and (ii) determining magnetic field and current density distributions in the capacitor region of the CCT by analysis of the complex interferograms. The preliminary measurements confirmed the high potential of the reported setup for optimization studies of CCT targets.
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