atoms Stark Broadening of Spectral Lines in Plasmas Edited by Eugene Oks Printed Edition of the Special Issue Published in Atoms www.mdpi.com/journal/atoms Stark Broadening of Spectral Lines in Plasmas Stark Broadening of Spectral Lines in Plasmas Special Issue Editor Eugene Oks MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade Special Issue Editor Eugene Oks Auburn University USA Editorial Office MDPI St. Alban-Anlage 66 4052 Basel, Switzerland This is a reprint of articles from the Special Issue published online in the open access journal Atoms (ISSN 2218-2004) in 2018 (available at: https://www.mdpi.com/journal/atoms/special issues/ stark broadening plasmas) For citation purposes, cite each article independently as indicated on the article page online and as indicated below: LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. Journal Name Year, Article Number, Page Range. ISBN 978-3-03897-455-0 (Pbk) ISBN 978-3-03897-456-7 (PDF) Cover image courtesy of Eugene Oks. c 2018 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND. Contents About the Special Issue Editor ...................................... vii Preface to ”Stark Broadening of Spectral Lines in Plasmas” ..................... ix Eugene Oks Review of Recent Advances in the Analytical Theory of Stark Broadening of Hydrogenic Spectral Lines in Plasmas: Applications to Laboratory Discharges and Astrophysical Objects Reprinted from: Atoms 2018, 6, 50, doi:10.3390/atoms6030050 .................... 1 Christian G Parigger, Kyle A Drake, Christopher M Helstern, and Ghaneshwar Gautam Laboratory Hydrogen-Beta Emission Spectroscopy for Analysis of Astrophysical White Dwarf Spectra Reprinted from: Atoms 2018, 6, 36, doi:10.3390/atoms6030036 .................... 70 Elisabeth Dalimier, Tatiana A. Pikuz and Paulo Angelo Mini-Review of Intra-Stark X-ray Spectroscopy of Relativistic Laser–Plasma Interactions Reprinted from: Atoms 2018, 6, 45, doi:10.3390/atoms6030045 .................... 87 V. A. Astapenko and V. S. Lisitsa Interaction of Ultrashort Laser Pulses with Atoms in Plasmas Reprinted from: Atoms 2018, 6, 38, doi:10.3390/atoms6030038 ....................102 Ashraf M. EL Sherbini, Ahmed E. EL Sherbini and Christian G. Parigger Measurement of Electron Density from Stark-Broadened Spectral Lines Appearing in Silver Nanomaterial Plasma Reprinted from: Atoms 2018, 6, 44, doi:10.3390/atoms6030044 ....................111 Paul Sanders and Eugene Oks Improving the Method of Measuring the Electron Density via the Asymmetry of Hydrogenic Spectral Lines in Plasmas by Allowing for Penetrating Ions Reprinted from: Atoms 2018, 6, 21, doi:10.3390/atoms6020021 ....................120 Alexander B. Kukushkin, Vladislav S. Neverov, Petr A. Sdvizhenskii and Vladimir V. Voloshinov Automodel Solutions of Biberman-Holstein Equation for Stark Broadening of Spectral Lines Reprinted from: Atoms 2018, 6, 43, doi:10.3390/atoms6030043 ....................129 Paul Sanders and Eugene Oks Correcting the Input Data for Calculating the Asymmetry of Hydrogenic Spectral Lines in Plasmas Reprinted from: Atoms 2018, 6, 9, doi:10.3390/atoms6010009 .....................144 Ghaneshwar Gautam and Christian G. Parigger Plasma Expansion Dynamics in Hydrogen Gas Reprinted from: Atoms 2018, 6, 46, doi:10.3390/atoms6030046 ....................148 Elisabeth Dalimier and Eugene Oks X-ray Spectroscopy Based Diagnostic of GigaGauss Magnetic Fields during Relativistic Laser-Plasma Interactions Reprinted from: Atoms 2018, 6, 60, doi:10.3390/atoms6040060 ....................154 v About the Special Issue Editor Eugene Oks received his Ph.D. degree from the Moscow Institute of Physics and Technology and, later, the highest degree of Doctor of Sciences from the Institute of General Physics of the Academy of Sciences of the USSR by the decision of the Scientific Council led by the Nobel Prize winner, academician A.M. Prokhorov. Oks worked in Moscow (USSR) as the head of a research unit at the Center for Studying Surfaces and Vacuum, then at the Ruhr University in Bochum (Germany) as an invited professor, and, for the last 28 years at the Physics Department of Auburn University (USA) in the position of Professor. He has conducted research in five areas: atomic and molecular physics, plasma physics, laser physics, nonlinear dynamics, and astrophysics. He founded/co-founded and developed new research fields, such as intra-Stark spectroscopy (new class of nonlinear optical phenomena in plasmas), masing without inversion (advanced schemes for generating/amplifying coherent microwave radiation), and quantum chaos (nonlinear dynamics in the microscopic world). He also developed a large number of advanced spectroscopic methods for diagnosing various laboratory and astrophysical plasmas, methods that were then used and are used by many experimental groups around the world. He published over 400 papers and 5 books, the latest one, published in 2017, being titled “Diagnostics of Laboratory and Astrophysical Plasmas Using Spectral Lineshapes of One-, Two-, and Three-Electron Systems”. He is the Chief Editor of the journal International Review of Atomic and Molecular Physics. He is a member of the Editorial Boards of the two other journals: International Journal of Spectroscopy and Open Journal of Microphysics. He is also a member of the International Program Committees of the two conferences: “Spectral Line Shapes” and Zvenigorod Conference on “Plasma Physics and Controlled Fusion”. vii Preface to ”Stark Broadening of Spectral Lines in Plasmas” Stark broadening of spectral lines remains an important tool for spectroscopic diagnostics of various types of laboratory and astrophysical plasmas. This is because laboratory and astrophysical plasmas contain various types of electric fields, such as the ion microfield, the electron microfield, fields of different kinds of electrostatic plasma turbulence, and laser/maser fields penetrating into plasmas. All these kinds of electric fields, differing by their statistical properties, strength, frequency, and possible polarization, cause a variety of types of Stark broadening of spectral lines in plasmas. Therefore, this research area is very important both fundamentally and practically, the latter being due to the numerous applications of plasmas. The practical applications range from the controlled thermonuclear fusion to plasma-based lasers and plasma sources of incoherent x-ray radiation as well as technological microwave discharges. Spectroscopic diagnostics based on Stark broadening are also indispensable tools for analyzing various astrophysical objects, such as solar plasmas (both for the quiet Sun and in solar flares), flare stars, white dwarfs, and so on. This book presents the latest research achievements in the area of Stark broadening of spectral lines in plasmas. It opens with three reviews describing the latest advances in analytical theory (with applications to various laboratory and astrophysical plasmas), in experimental studies of relativistic laser–plasma interactions, and in laboratory experiments facilitating the analysis of white dwarfs in astrophysics. These reviews are followed by seven original research papers devoted to a number of issues concerning Stark broadening of spectral lines in plasmas. They cover various experimental studies of laser-produced plasmas and theoretical studies presenting, in particular (but not exclusively), a new method for measuring ultra-strong magnetic fields, an improved method for measuring the electron density, as well as an advanced description of the radiative transfer. Eugene Oks Special Issue Editor ix atoms Review Review of Recent Advances in the Analytical Theory of Stark Broadening of Hydrogenic Spectral Lines in Plasmas: Applications to Laboratory Discharges and Astrophysical Objects Eugene Oks Physics Department, 206 Allison Lab, Auburn University, Auburn, AL 36849, USA; [email protected] Received: 26 June 2018; Accepted: 1 August 2018; Published: 3 September 2018 Abstract: There is presented an overview of the latest advances in the analytical theory of Stark broadening of hydrogenic spectral lines in various types of laboratory and astrophysical plasmas. They include: (1) advanced analytical treatment of the Stark broadening of hydrogenic spectral lines by plasma electrons; (2) center-of-mass effects for hydrogen atoms in a nonuniform electric field: applications to magnetic fusion, radiofrequency discharges, and flare stars; (3) penetrating-ions-caused shift of hydrogenic spectral lines in plasmas; (4) improvement of the method for measuring the electron density based on the asymmetry of hydrogenic spectral lines in dense plasmas; (5) Lorentz–Doppler broadening of hydrogen/deuterium spectral lines: analytical solution for any angle of observation and any magnetic field strength, and its applications to magnetic fusion and solar physics; (6) Revision of the Inglis-Teller diagnostic method; (7) Stark broadening of hydrogen/deuterium spectral lines by a relativistic electron beam: analytical results and applications to magnetic fusion; (8) Influence of magnetic-field-caused modifications of the trajectories of plasma electrons on shifts and