High-brightness Metal Vapour Lasers Vol. 1 Physical Fundamentals and Mathematical Models High-brightness Metal Vapour Lasers Vol. 1 Physical Fundamentals and Mathematical Models V. M. Batenin, V. V. Buchanov, A. M. Boichenko M. A. Kazaryan, I. I. Klimovskii, E. I. Molodykh CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2017 by CISP CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper Version Date: 20161109 International Standard Book Number-13: 978-1-4822-5004-6 (Hardback) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint. Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying, microfilming, and recording, or in any information stor- age or retrieval system, without written permission from the publishers. For permission to photocopy or use material electronically from this work, please access www.copy- right.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that pro- vides licenses and registration for a variety of users. For organizations that have been granted a photo- copy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Contents Foreword 1 Notations, indexes and abbreviations 7 Introduction 13 1 Devices and methods for producing metal vapours 22 1.1. First designs of metal vapour lasers 22 1.2. Self-heated lasers 23 1.2.1. Thermal regime of discharge laser tubes 23 1.2.2. Design of structures with self-heating laser tubes 25 1.3. The explosive method for producing metal vapours 29 1.4. Pumping laser systems 31 1.5. The flow of fine particles as the active medium of metal vapour lasers 34 1.6. Methods for affecting the output characteristics of lasers 37 1.7. Laser cells for copper vapour lasers with a transverse discharge 39 1.8. Laser tubes with a hollow cathode 43 1.9. Modified cells for gas discharge lasers 46 1.10. Laser cells pumped by electron beams 51 1.11. Metal vapour salts lasers 58 1.11.1. Methods for introducing metal atoms into the working zone 58 1.11.2. Gas discharge tubes 59 1.11.3. Methods for producing vapours for hybrid metal vapour lasers 62 1.12. The principles of calculating the thermal regime of emitters 64 2 Excitation circuit and its effect on the lasing characteristics of self-heating copper vapour lasers 73 2.1. Electrical characteristics of the discharge 77 2.2. Distribution of electrical energy consumed by a rectifier in different elements of the charger and discharge circuits 78 2.3. Effect of the charging circuit on the lasing characteristics of self-contained lasers 78 2.4. Influence of the discharge circuit on the lasing characteristics of self-contained lasers 81 2.5. Features of the thyratron in pulse-periodic copper vapour lasers 92 3 Excitation circuits of self-contained lasers 105 3.1. Discharge circuits that increase the steepness of the leading edge of the voltage pulse on electrodes of gas discharge tubes 105 vi Contents 3.2. Excitation circuits with pulse transformers 110 3.3. Thyratron excitation units with higher excitation pulse repetition frequency and increased switching capacity 115 3.4. Excitation units with Blumlein circuits 124 3.5. Excitation units reducing the effect of cataphoresis on the loss of working metal from GDT 127 3.6. Thyratron–thyristor excitation drive units 128 3.7. Generators of dual pulses and excitation pulse trains 132 3.8. Excitation pulse generators on tacitrons and vacuum triodes 134 3.9. Excitation circuits of pulse-periodic lasers with dischargers as switches 136 3.10. Excitation circuits with semiconductor switches 139 3.11. Methods for controlling the characteristics of metal vapour lasers 145 3.12. Prospects for the development of excitation pulse generators of self-contained lasers 149 4 Repetitively pulsed self-contained lasers 154 4.1. The history of research of repetitively pulsed metal vapour lasers 154 4.2. The radial inhomogeneity of the plasma parameters in the repetitively pulsed self-contained lasers 162 4.2.1. The heterogeneity of the temperature distribution of gas 163 4.2.2. Heterogeneity of prepulse density distributions of the concentration of the atoms of inert gas and working metal in the ground state 166 4.2.3. The heterogeneity of prepulse electron concentration distribution 167 4.2.4. The heterogeneity of prepulse electron temperature distribution and concentration of metastable atoms 169 4.2.5. The heterogeneity of the distribution of plasma parameters during the excitation pulse 170 4.3. The gas temperature in repetitively pulsed copper vapour lasers 172 4.4. The results of measurements of concentrations of metastable and resonance-excited atoms of working metal in lasers at self-contained transitions of metal atoms 183 4.5. The concentration and temperature of electrons in self- contained lasers 195 4.5.1. The concentration and temperature of the electrons during the excitation pulse 195 4.5.2. Concentration and temperature of electrons in the interpulse interval in lasers with a GDT of small Contents vii diameters (d < 2 cm) 199 p 4.5.3. Concentration and temperature of electrons in large-diameter GDTs 207 4.6. The concentration of atoms of the working metal in self-contained lasers 211 5 The results of analytical studies of self-contained lasers 228 5.1. The characteristics of the lasing pulse of the self-contained lasers 229 5.2. Lasing characteristics of copper vapour laser 235 5.3. Analytical solution of the characteristics of lasing pulse of copper vapour lasers with the development of ionization taken into account 242 5.4. The influence of self-absorption of stimulated emission on the lasing characteristics 249 5.5. Similarity relations for pulsed metal vapour lasers 253 6 Numerical studies of pulsed metal vapour lasers 260 6.1. Physical and mathematical formulation of the problem 261 6.2. The calculated dependences of the coefficients, cross sections, rate constants and frequencies of elementary physical processes 265 6.3. Methods of solution, software and results of numerical experiments 275 6.4. Copper vapour laser 289 6.4.1. Monopulse operating mode of a copper vapour laser with a Maxwellian electron energy distribution function 289 6.4.2. Calculation of single-pulse operating mode a of copper vapour laser with the non-Maxwellian electron energy distribution function 291 6.4.3. Frequency operating mode of a copper vapour laser with neon in the mixture 281 6.4.4. Operation of a copper vapour laser at high buffer gas pressure 304 6.4.5. A parametric study of the effect of initial data on the energy characteristics of a CVL 314 6.5. Europium vapour laser 320 6.6. Optimization of parameters of metal vapour lasers 332 7 Numerical modeling of repetitively pulsed copper vapour lasers taking into account the heterogeneity of distribution of plasma parameters (inhomogeneity of discharge) over the cross section of the gas discharge tube 345 7.1. The place and role of model studies of repetitively pulsed copper vapour lasers, taking into account the radial inhomogeneity of the plasma parameters [1–6] in a number viii Contents of other numerical studies of such lasers 345 7.2. The results of numerical studies of repetitively pulsed CVLs, assuming uniform distribution of plasma parameters over the cross section of the GDT [1–3] 347 7.3. Typical radial distributions of the prepulse plasma parameters in the repetitively pulsed copper vapour lasers 356 7.4. The equations for calculating the lasing characteristics in the conditions of inhomogeneous distribution of plasma parameters over the cross section of the GDT 358 7.5. Dynamics of lasing in a radially inhomogeneous active medium of a copper vapour laser 361 7.6. Effect of radial inhomogeneity of the plasma parameters on the efficiency and specific lasing energy and efficiency of the CVL 365 7.7. Effect of the excitation pulse shape on the lasing characteristics of a CVL 371 7.8. Lasing characteristics of repetitively pulsed CVLs 374 7.9. Comparison of the results of calculations [4–6] and experiment 385 7.10. Self-consistent models, taking into account radial inhomogeneities 392 8 Simulation of copper vapour lasers. Kinetically enhanced lasers 397 8.1. Introduction 397 8.2. The kinetic model 397 8.3. The electron distribution function 400 8.4. Restrictions on pulse repetition rate 416 8.5. Lasers with modified kinetics (kinetically enhanced lasers) 444 8.5.1 Additions of hydrogen 445 8.5.2. Hydrogen chloride additives 479 8.6. Formation of high-quality radiation of the copper vapour laser in the master oscillator–amplifier system 510 8.6.1. The dependence of the additional power, taken from the amplifier, on the pump power 520 Index 529 Foreword The lasing at self-contained transitions of metal atoms was achieved for the first time in lead vapours [1] in 1965, at the transition between the resonant level 6p7s 3P01 and one of the levels 6p2 1D2 of the basic configuration, at a wavelength of 722.9 nm. Since then, many studies have been published that contain the results of research and development of lasers on self-contained transitions of metal atoms. Moreover, in the meantime numerous attempts have been made (see [2–7]) in some way to summarize the results of studies carried out by different groups, primarily in the USA and the former USSR. 12 years has passed since the publication of the monograph [6], which made at that time a significant contribution to the development of research and development of the self-contained metal vapour lasers. During this time the investigations were almost completed of the physical processes taking place in the active medium of self-contained lasers and determining their lasing parameters; mathematical models of these lasers were developed with different degrees of accuracy so that it was possible to transfer from physical investigations to numerical experiments in order to determine the optimum operating conditions as regards the efficiency or the mean lasing power of the self-contained lasers; new methods of development of these lasers have been formulated. Constant interest in the lasers at self-contained transitions of metal vapours has been maintained by the extensive possibilities of using them in solving various applied problems. The last and relatively successful attempt for the collective generalization of the results of investigations of self-contained lasers is a collection of the Proceedings of the International Scientific School: Pulsed metal vapour lasers, organised in 1995 at the St. Andrews University (Scotland) under the supervision of NATO. The proceedings, published for this scientific school [8], provides quite complete