Editorial

3 pages, 170 KiB

Open AccessEditorial

Special Issue Editorial “Atomic Processes in Plasmas and Gases: Symmetries and Beyond”

by Eugene Oks

Symmetry 2022, 14(8), 1497; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14081497 - 22 Jul 2022

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Atomic processes in plasmas and gases encompass broad areas in theoretical and experimental atomic and molecular physics [...] Full article

(This article belongs to the Special Issue Atomic Processes in Plasmas and Gases: Symmetries and Beyond)

Research

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14 pages, 929 KiB

Open AccessArticle

Space-Time Coupling: Current Concept and Two Examples from Ultrafast Optics Studied Using Exact Solution of EM Equations

by Nikolay L. Popov and Alexander V. Vinogradov

Symmetry 2021, 13(4), 529; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13040529 - 24 Mar 2021

Cited by 4 | Viewed by 1751

Abstract

Current approach to space-time coupling (STC) phenomena is given together with a complementary version of the STC concept that emphasizes the finiteness of the energy of the considered pulses. Manifestations of STC are discussed in the framework of the simplest exact localized solution [...] Read more.

Current approach to space-time coupling (STC) phenomena is given together with a complementary version of the STC concept that emphasizes the finiteness of the energy of the considered pulses. Manifestations of STC are discussed in the framework of the simplest exact localized solution of Maxwell’s equations, exhibiting a “collapsing shell”. It falls onto the center, continuously deforming, and then, having reached maximum compression, expands back without losing energy. Analytical solutions describing this process enable to fully characterize the field in space-time. It allowed to express energy density in the center of collapse in the terms of total pulse energy, frequency and spectral width in the far zone. The change of the pulse shape while travelling from one point to another is important for coherent control of quantum systems. We considered the excitation of a two-level system located in the center of the collapsing EM (electromagnetic) pulse. The result is again expressed through the parameters of the incident pulse. This study showed that as it propagates, a unipolar pulse can turn into a bipolar one, and in the case of measuring the excitation efficiency, we can judge which of these two pulses we are dealing with. The obtained results have no limitation on the number of cycles in a pulse. Our work confirms the productivity of using exact solutions of EM wave equations for describing the phenomena associated with STC effects. This is facilitated by rapid progress in the search for new types of such solutions. Full article

(This article belongs to the Special Issue Atomic Processes in Plasmas and Gases: Symmetries and Beyond)

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10 pages, 526 KiB

Open AccessArticle

Polarization of Lyman-α Line Due to the Anisotropy of Electron Collisions in a Plasma

by Motoshi Goto and Nilam Ramaiya

Symmetry 2021, 13(2), 297; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13020297 - 09 Feb 2021

Cited by 2 | Viewed by 1615

Abstract

We have developed an atomic model for calculating the polarization state of the Lyman-

α

line in plasma caused by anisotropic electron collision excitations. The model assumes a nonequilibrium state of the electron temperature between the directions parallel (

T_{‖}

) and [...] Read more.

We have developed an atomic model for calculating the polarization state of the Lyman-

α

line in plasma caused by anisotropic electron collision excitations. The model assumes a nonequilibrium state of the electron temperature between the directions parallel (

T_{‖}

) and perpendicular (

T_{⊥}

) to the magnetic field. A simplified assumption on the formation of an excited state population in the model is justified by detailed analysis of population flows regarding the upper state of the Lyman-

α

transition with the help of collisional-radiative model calculations. Calculation results give the polarization degree of several percent under typical conditions in the edge region of a magnetically confined fusion plasma. It is also found that the relaxation of polarization due to collisional averaging among the magnetic sublevels is effective in the electron density region considered. An analysis of the experimental data measured in the Large Helical Device gives

T_{⊥} / T_{‖} = 7.6

at the expected Lyman-

α

emission location outside the confined region. The result is derived with the absolute polarization degree of 0.033, and

T_{⊥} = 32

eV and

n_{e} = 9.6 \times 10^{18} m^{- 3}

measured by the Thomson scattering diagnostic system. Full article

(This article belongs to the Special Issue Atomic Processes in Plasmas and Gases: Symmetries and Beyond)

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12 pages, 7197 KiB

Open AccessFeature PaperArticle

Data for Beryllium–Hydrogen Charge Exchange in One and Two Centres Models, Relevant for Tokamak Plasmas

by Petr A. Sdvizhenskii, Inga Yu. Tolstikhina, Valery S. Lisitsa, Alexander B. Kukushkin and Sergei N. Tugarinov

Symmetry 2021, 13(1), 16; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13010016 - 23 Dec 2020

Cited by 2 | Viewed by 1609

Abstract

Data on the cross section and kinetic rate of charge exchange (CX) between the bare beryllium nucleus, the ion Be(+4) and the neutral hydrogen atom are of great interest for visible-range high-resolution spectroscopy in the ITER tokamak because beryllium is intended as the [...] Read more.

Data on the cross section and kinetic rate of charge exchange (CX) between the bare beryllium nucleus, the ion Be(+4) and the neutral hydrogen atom are of great interest for visible-range high-resolution spectroscopy in the ITER tokamak because beryllium is intended as the material for the first wall in the main chamber. Here an analysis of available data is presented, and the data needs are formulated. Besides the active probe signal produced by the CX of the diagnostic hydrogen neutral beam with impurity ions in plasma, a passive signal produced by the CX of impurity ions with cold edge plasma is also important, as it shows in observation data from the JET (Joint European Torus) tokamak with an ITER-like beryllium wall. Data in the range of a few eV/amu to ~100 eV/amu (amu stands for the atomic mass unit) needed for simulations of level populations for principal and orbital quantum numbers in the emitting beryllium ions Be(+3) can be obtained with the help of two-dimensional kinetic codes. The lack of literature data, especially for data resolved in orbital quantum numbers, has instigated us to make numerical calculations with the ARSENY code. A comparison of the results obtained for the one-centre Coulomb problem using an analytic approach and for the two-centre problem using numerical simulations is presented. Full article

(This article belongs to the Special Issue Atomic Processes in Plasmas and Gases: Symmetries and Beyond)

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22 pages, 16219 KiB

Open AccessArticle

Hypersonic Imaging and Emission Spectroscopy of Hydrogen and Cyanide Following Laser-Induced Optical Breakdown

by Christian G. Parigger, Christopher M. Helstern and Ghaneshwar Gautam

Symmetry 2020, 12(12), 2116; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12122116 - 19 Dec 2020

Cited by 4 | Viewed by 2393

Abstract

This work communicates the connection of measured shadowgraphs from optically induced air breakdown with emission spectroscopy in selected gas mixtures. Laser-induced optical breakdown is generated using 850 and 170 mJ, 6 ns pulses at a wavelength of 1064 nm, the shadowgraphs are recorded [...] Read more.

This work communicates the connection of measured shadowgraphs from optically induced air breakdown with emission spectroscopy in selected gas mixtures. Laser-induced optical breakdown is generated using 850 and 170 mJ, 6 ns pulses at a wavelength of 1064 nm, the shadowgraphs are recorded using time-delayed 5 ns pulses at a wavelength of 532 nm and a digital camera, and emission spectra are recorded for typically a dozen of discrete time-delays from optical breakdown by employing an intensified charge-coupled device. The symmetry of the breakdown event can be viewed as close-to spherical symmetry for time-delays of several 100 ns. Spectroscopic analysis explores well-above hypersonic expansion dynamics using primarily the diatomic molecule cyanide and atomic hydrogen emission spectroscopy. Analysis of the air breakdown and selected gas breakdown events permits the use of Abel inversion for inference of the expanding species distribution. Typically, species are prevalent at higher density near the hypersonically expanding shockwave, measured by tracing cyanide and a specific carbon atomic line. Overall, recorded air breakdown shadowgraphs are indicative of laser-plasma expansion in selected gas mixtures, and optical spectroscopy delivers analytical insight into plasma expansion phenomena. Full article

(This article belongs to the Special Issue Atomic Processes in Plasmas and Gases: Symmetries and Beyond)

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6 pages, 1635 KiB

Open AccessCommunication

Chirped Laser Pulse Effect on a Quantum Linear Oscillator

by Valeriy A. Astapenko and Evgeniya V. Sakhno

Symmetry 2020, 12(8), 1293; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081293 - 04 Aug 2020

Cited by 2 | Viewed by 1980

Abstract

We present a theoretical study of the excitation of a charged quantum linear oscillator by chirped laser pulse with the use of probability of the process throughout the pulse action. We focus on the case of the excitation of the oscillator from the [...] Read more.

We present a theoretical study of the excitation of a charged quantum linear oscillator by chirped laser pulse with the use of probability of the process throughout the pulse action. We focus on the case of the excitation of the oscillator from the ground state without relaxation. Calculations were made for an arbitrary value of the electric field strength by utilizing the exact expression for the excitation probability. The dependence of the excitation probability on the pulse parameters was analyzed both numerically and by using analytical formulas. Full article

(This article belongs to the Special Issue Atomic Processes in Plasmas and Gases: Symmetries and Beyond)

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12 pages, 1709 KiB

Open AccessFeature PaperArticle

Oscillatory-Precessional Motion of a Rydberg Electron Around a Polar Molecule

by Eugene Oks

Symmetry 2020, 12(8), 1275; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081275 - 02 Aug 2020

Cited by 5 | Viewed by 2142

Abstract

We provide a detailed classical description of the oscillatory-precessional motion of an electron in the field of an electric dipole. Specifically, we demonstrate that in the general case of the oscillatory-precessional motion of the electron (the oscillations being in the meridional direction (θ-direction) [...] Read more.

We provide a detailed classical description of the oscillatory-precessional motion of an electron in the field of an electric dipole. Specifically, we demonstrate that in the general case of the oscillatory-precessional motion of the electron (the oscillations being in the meridional direction (θ-direction) and the precession being along parallels of latitude (φ-direction)), both the θ-oscillations and the φ-precessions can actually occur on the same time scale—contrary to the statement from the work by another author. We obtain the dependence of φ on θ, the time evolution of the dynamical variable θ, the period T_θ of the θ-oscillations, and the change of the angular variable φ during one half-period of the θ-motion—all in the forms of one-fold integrals in the general case and illustrated it pictorially. We also produce the corresponding explicit analytical expressions for relatively small values of the projection p_φ of the angular momentum on the axis of the electric dipole. We also derive a general condition for this conditionally-periodic motion to become periodic (the trajectory of the electron would become a closed curve) and then provide examples of the values of p_φ for this to happen. Besides, for the particular case of p_φ = 0 we produce an explicit analytical result for the dependence of the time t on θ. For the opposite particular case, where p_φ is equal to its maximum possible value (consistent with the bound motion), we derive an explicit analytical result for the period of the revolution of the electron along the parallel of latitude. Full article

(This article belongs to the Special Issue Atomic Processes in Plasmas and Gases: Symmetries and Beyond)

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12 pages, 575 KiB

Open AccessArticle

Application of the Generalized Hamiltonian Dynamics to Spherical Harmonic Oscillators

by Eugene Oks

Symmetry 2020, 12(7), 1130; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12071130 - 07 Jul 2020

Cited by 4 | Viewed by 1735

Abstract

Dirac’s Generalized Hamiltonian Dynamics (GHD) is a purely classical formalism for systems having constraints: it incorporates the constraints into the Hamiltonian. Dirac designed the GHD specifically for applications to quantum field theory. In one of our previous papers, we redesigned Dirac’s GHD for [...] Read more.

Dirac’s Generalized Hamiltonian Dynamics (GHD) is a purely classical formalism for systems having constraints: it incorporates the constraints into the Hamiltonian. Dirac designed the GHD specifically for applications to quantum field theory. In one of our previous papers, we redesigned Dirac’s GHD for its applications to atomic and molecular physics by choosing integrals of the motion as the constraints. In that paper, after a general description of our formalism, we considered hydrogenic atoms as an example. We showed that this formalism leads to the existence of classical non-radiating (stationary) states and that there is an infinite number of such states—just as in the corresponding quantum solution. In the present paper, we extend the applications of the GHD to a charged Spherical Harmonic Oscillator (SHO). We demonstrate that, by using the higher-than-geometrical symmetry (i.e., the algebraic symmetry) of the SHO and the corresponding additional conserved quantities, it is possible to obtain the classical non-radiating (stationary) states of the SHO and that, generally speaking, there is an infinite number of such states of the SHO. Both the existence of the classical stationary states of the SHO and the infinite number of such states are consistent with the corresponding quantum results. We obtain these new results from first principles. Physically, the existence of the classical stationary states is the manifestation of a non-Einsteinian time dilation. Time dilates more and more as the energy of the system becomes closer and closer to the energy of the classical non-radiating state. We emphasize that the SHO and hydrogenic atoms are not the only microscopic systems that can be successfully treated by the GHD. All classical systems of N degrees of freedom have the algebraic symmetries O_N+1 and SU_N, and this does not depend on the functional form of the Hamiltonian. In particular, all classical spherically symmetric potentials have algebraic symmetries, namely O₄ and SU₃; they possess an additional vector integral of the motion, while the quantal counterpart-operator does not exist. This offers possibilities that are absent in quantum mechanics. Full article

(This article belongs to the Special Issue Atomic Processes in Plasmas and Gases: Symmetries and Beyond)

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