Stationary Ion Research Articles

Coupled nonlinear Schrödinger (CNLS) equations for two interacting electrostatic wavepackets in a non-Maxwellian fluid plasma model

The nonlinear dynamics of two co-propagating electrostatic wavepackets in a one-dimensional non-magnetized plasma fluid model is considered, from first principles. The coupled waves are characterized by different (carrier) wavenumbers and amplitudes. A plasma consisting of non-thermalized (κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document}-distributed) electrons evolving against a cold (stationary) ion background is considered. The original model is reduced, by means of a multiple-scale perturbation method, to a pair of coupled nonlinear Schrödinger (CNLS) equations for the dynamics of the wavepacket envelopes. For arbitrary wavenumbers, the resulting CNLS equations exhibit no known symmetry and thus intrinsically differ from the Manakov system, in general. Exact analytical expressions have been derived for the dispersion, self-modulation (nonlinearity) and cross-modulation (coupling) coefficients involved in the CNLS equations, as functions of the wavenumbers (k1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_1$$\\end{document}, k2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_2$$\\end{document}) and of the spectral index κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document} characterizing the electron profile. An analytical investigation has thus been carried out of the modulational instability (MI) properties of this pair of wavepackets, focusing on the role of the intrinsic (variable) parameters. Modulational instability is shown to occur in most parts of the parameter space. The instability window(s) and the corresponding growth rate are calculated numerically in a number of case studies. Two-wave interaction favors MI by extending its range of occurrence and by enhancing its growth rate. Growth rate patterns obtained for different κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document} index (values) suggest that deviation from thermal (Maxwellian) equilibrium, for low κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document} values, leads to enhance MI of the interacting wave pair. To the best of our knowledge, the dynamics of two co-propagating wavepackets in a plasma described by a fluid model with κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document}-distributed electrons is investigated thoroughly with respect to their MI properties as a function of κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document} for the first time, in the framework of an asymmetric CNLS system whose coefficients present no obvious symmetries for arbitrary k1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_1$$\\end{document} and k2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_2$$\\end{document}. Although we have focused on electrostatic wavepacket propagation in non-thermal (non-Maxwellian) plasma, the results of this study are generic and may be used as basis to model energy localization in nonlinear optics, in hydrodynamics or in dispersive media with Kerr-type nonlinearities where MI is relevant.

Theoretical estimation of multiple hydrogen isotope content in metal layers slowly co-deposited from plasmas

A probabilistic and diffusion-based model describing concentrations of multiple hydrogen isotopes simultaneously co-depositing with slowly grown metal layer is given. The conditions modeled are identical to stationary ion implantation into bulk material with infinite fluence. Ratios of different multiple hydrogen isotopes occupying same trapping sites in metal layers co-deposited from plasma are estimated. It is shown that if hydrogen isotopes have different detrapping energies in regards to the same trap (vacancy, dislocation, etc.), only the concentration of the isotope with highest detrapping energy decreases monotonously with deposition temperature. The uncertainty of tritium concentration in co-deposited layer based on the uncertainty in detrapping energy of tritium and deuterium is evaluated; for an 0.01 eV difference, a >10% tritium concentration uncertainty is predicted.

Exact Shearing Flow Magnetized Hybrid Kinetic Equilibria with Inhomogeneous Temperature

Magnetized plasmas with shearing flows are found in many natural contexts, such as around Earth’s magnetopause. In collisionless plasmas where physical quantities vary on a scale of the order of or larger than ion scales, the hybrid Vlasov−Maxwell description (kinetic ions coupled to a neutralizing electron fluid via electromagnetic fields) represents a suitable approach. When crossing the magnetopause, the ion temperature, density, and direction of magnetic field vary. We derive a form for an exact stationary solution of the hybrid Vlasov−Maxwell equations that represent a magnetized plasma with a quasi-planar shearing flow, variable density and ion temperature, and variable magnetic field direction. A stationary ion distribution function is expressed as a suitable combination of particle constants of motion and evaluated numerically in such a way to obtain configurations with variable density and temperature and two quasi-planar oppositely directed velocity shear layers. Properties of particular configurations are derived from Magnetospheric Multiscale measures during crossings of Earth’s magnetopause. In the first case a quasi-uniformly directed, nearly perpendicular magnetic field is present, while in the second case, going from the magnetosheath to the magnetosphere, the magnetic field makes a wide rotation from one side to the other of the shearing flow plane. In both cases, the ion distribution function departs from a Maxwellian in the shear layers, displaying temperature anisotropy and agyrotropy, with a nonsymmetric behavior in the two shear layers. The configurations considered here can be used as models for Earth’s magnetopause in simulations of the Kelvin–Helmholtz instability.

Coupling of ‘cold’ electron plasma wave via stationary ion inhomogeneity to the plasma bulk

Using high resolution kinetic (VPPM-OMP 1.0) and fluid (BOUT++) solvers, evolution of long-wavelength electron plasma wave (EPW) in the presence of stationary periodic ion background non-uniformity is investigated. Mode coupling dynamics between long-wavelength EPW mode of scale k and ion inhomogeneity of scale k 0 is illustrated. Validity of well known Bessel function J n (x) scaling in the cold plasma approximation (i.e., when phase velocity ω/k ≫ v thermal ) alongwith the effect of ion inhomogeneity amplitude (A) on temporal evolution of energy density in the long-wavelength EPW mode is investigated. Effect of finite system sizes on the Bessel J n (x) scaling is examined and scaling law for τ FM i.e the time required to attain first minimum of energy density of the corresponding perturbed mode (also called phase mixing time for k ⟶ 0 modes) versus ion inhomogeneity amplitude A obtained from both kinetic and fluid solutions for each of the cases studied, alongwith some major differences in τ FM scaling for small system sizes is also reported.

Application of electric thrusters in a spacecraft propulsion system

The place of electric rocket thrusters in a spacecraft propulsion system is pointed out; the tasks for such propulsion system are described. The modern classification of electric thrusters is given, in accordance of that one there are four classes, dissimilar due to a nature of processes that impart a kinetic energy to a propellant: electrothermal, electrostatic, pulsed and magnetoplasmodynamic. In order to illustrate an electric rocket thrusters sate of art, examples different classes electric rocket thrusters for modern spacecrafts are presented; the technical characteristics, such a thrust, specific impulse, powered energy and efficiency are systematized. As a general electric rocket thrusters for spacecraft propulsion system were chosen electrostatic thrusters: stationary plasma (Hall thrusters) and ion thusters. For the different classes of electric rocket thrusters the common characteristics are defined as a set of: specific impulse (that describes thruster propellant efficiency), thrust cost (determines electric power consumption per unit thrust) and propellant type (combines thruster’s technical and economical characteristics). A necessity is stated to take into account the cost parameters of an electric rocket thruster design and a manufacturing during a propulsion system developing for a next generation spacecraft. The tasks are determined for the further research in the area of a techno-economic efficiency of electric rocket thrusters exploiting as a part of a spacecraft’s propulsion system.

Low frequency Compressional modes in degenerate semiconductor plasmas

Properties of low frequency compressional electromagnetic wave pulse in a magnetized semiconductor hole-electron plasma, are investigated. The quantum mechanical effects such as Fermi pressure, quantum tunneling and exchange-correlation potential of inertialess electrons, inertial holes and stationary charged ion particulates are considered in the presence of the magnetic field. A new type of dispersion relation is derived for low-frequency compressional waves by employing quantum magneto-hydrodynamic model and Maxwell equations; the dispersion relation is then analyzed for parallel, perpendicular and oblique propagation of compressional electromagnetic wave pulse to the external magnetic field direction. We have analyzed the obtained dispersion relations numerically, for different semiconductor plasma such as GaAs, GaSb and, GaN, the graphs shows that the frequency of compressional electromagnetic wave pulse decreases with increase of electron-hole density concentration, whereas the frequency increases with the increase of angle of propagation compressional electromagnetic wave pulse. Our results are applicable to understanding the dynamics of semiconductor plasma to produce high power, high band-width devices in contrast to the existing gas plasma devices. Keywords: degenerate semiconductor plasma, quantum mechanical effects, compression electromagnetic wave, gas plasma device.

Стабильные формы и стационарная эмиссия ионов танталового полевого эмиттера в процессе воздействия внешним электрическим полем при высоких температурах

Using the methods of field electron microscopy, the change in the form of the field emitter from Ta was studied when exposed to high temperatures T and strong electric fields F. The aim of the study was to obtain a stable form of the emitter surface that would give a stationary ion current during field evaporation. Such a stable form was found at a certain combination of T and F, it could provide a stable constant ion current, but of relatively small magnitude.

Double-Electromagnetically-Induced-Transparency Ground-State Cooling of Stationary Two-Dimensional Ion Crystals.

We theoretically and experimentally investigate double-electromagnetically-induced transparency (double-EIT) cooling of two-dimensional ion crystals confined in a Paul trap. The double-EIT ground-state cooling is observed for ^{171}Yb^{+} ions with a clock state, for which EIT cooling has not been realized like many other ions with a simple Λ scheme. A cooling rate of n[over ¯][over ˙]=34(±1.8) ms^{-1} and a cooling limit of n[over ¯]=0.06(±0.059) are observed for a single ion. The measured cooling rate and limit are consistent with theoretical predictions. We apply double-EIT cooling to the transverse modes of two-dimensional (2D) crystals with up to 12 ions. In our 2D crystals, the micromotion and the transverse mode directions are perpendicular, which makes them decoupled. Therefore, the cooling on transverse modes is not disturbed by micromotion, which is confirmed in our experiment. For the center of mass mode of a 12-ion crystal, we observe a cooling rate and a cooling limit that are consistent with those of a single ion, including heating rates proportional to the number of ions. This method can be extended to other hyperfine qubits, and near ground-state cooling of stationary 2D crystals with large numbers of ions may advance the field of quantum information sciences.

Exact hybrid-kinetic equilibria for magnetized plasmas with shearing flows

Context.Magnetized plasmas characterized by shearing flows are present in many natural contexts, such as the Earth’s magnetopause and the solar wind. The collisionless nature of involved plasmas requires a kinetic description. When the width of the shear layer is on the order of ion scales, the hybrid Vlasov-Maxwell approach can be adopted for this purpose.Aims.The aim of this work is to derive explicit forms for stationary configurations of magnetized plasmas with planar shearing flows within the hybrid Vlasov-Maxwell description. Two configurations are considered: the first with a uniform magnetic field obliquely directed with respect to the bulk velocity and the second with a uniform-magnitude variable-direction magnetic field.Methods.We obtained stationary ion distribution functions by combining single-particle constant of motions, which are derived through the study of particle dynamics. Preliminary information about the form of the distribution functions were analytically derived in considering a local approximation for the background electromagnetic field. Then a numerical method was set up to obtain a solution for general profiles.Results.We determined explicit distribution functions that allow us to obtain profiles of density, bulk velocity, temperature, and heat flux. Anisotropy and agyrotropy in the distribution function were also evaluated. The stationarity of the solution during numerical simulations was checked in the uniform oblique magnetic field case.Conclusions.The configurations considered here can be used as models for the Earth’s magnetopause in simulations of the Kelvin-Helmholtz instability.

Изменение электропроводности стекла, кварца и пленок Au, C, МоS2 под влиянием непрерывной инжекции протонов

Changes in the electrical conductivity of a wide range of materials with different crystal-chemical types and electrophysical properties (quartz, glass, molybdenum disulfide, graphite, gold) under continuous proton injection are studied. Film samples of layered MoS2 and graphite compounds were obtained on rough surfaces of glass or quartz by mechanical rubbing of powder. Gold films are formed on glass substrates by magnetron sputtering of a gold target. To create a continuous stream of protons injected into the test sample, a stationary ion source with a cold cathode and a magnetic field forming an ion beam of relatively low intensity was used. The current in the ion beam is up to 1.2 mA, the pressure of hydrogen in the chamber is ~10 – 2 Pa, the energy of hydrogen ions is from 1 to 4 keV. The experimental results indicate that under conditions of continuous proton injection, the electrical conductivity of thin films with a layered structure (MoS2 and graphite) increases sharply (by 4 – 5 orders of magnitude). This effect increases when the temperature decreases from ~ 293 to ~ 77 K, as well as when the number of charges supplied to the sample increases. In the case of continuous injection of protons into massive dielectrics (glass, quartz) and thin films of gold, no noticeable change in electrical conductivity was detected.

A Water-Stable Cationic Metal-Organic Framework with Hydrophobic Pore Surfaces as an Efficient Scavenger of Oxo-Anion Pollutants from Water.

Water contamination due to heavy metal-based toxic oxo-anions (such as CrO42- and TcO4-) is a critical environmental concern that demands immediate mitigation. Herein, we present an effort to counter this issue by a novel chemically stable cationic metal-organic framework (iMOF-2C) with strategic utilization of a ligand with hydrophobic core, known to facilitate such oxo-anion capture process. Moreover, the compound exhibited very fast sieving kinetics for such oxo-anions and a very high uptake capacity for CrO42- (476.3 mg g-1) and ReO4- (691 mg g-1), while the latter being employed as a surrogate analogue for radioactive TcO4- anions. Notably, the compound showed excellent selectivity even in the presence of other competing anions such as NO3-, Cl-, SO42-, ClO4-. etc.. Furthermore, the compound possesses excellent reusability (up to 10 cycles) and is also employed to a stationary phase ion column to decontaminate the aforementioned oxo-anions from water.

Correction to: Stationary and Nonstationary Ion and Water Flux Interactions in Kidney Proximal Tubule: Mathematical Analysis of Isosmotic Transport by a Minimalistic Model.

The chapter 'Stationary and Nonstationary Ion and Water Flux Interactions in Kidney Proximal Tubule: Mathematical Analysis of Isosmotic Transport by a Minimalistic Model' has now been made available open access under a CC BY 4.0 license.

Genesis of non-uniformity of plasma fluxes over emissive wall in low-temperature plasmas

Origins of spatial modulation of stationary electron and ion currents to the wall in discharge plasma with/without magnetic field at low gas pressure are studied in the experiments and 2D PIC MCC simulations. It is shown that a non-uniformity of ion and electron fluxes to the wall is induced by (a) a non-planar topology on the emissive wall, (b) a difference in the secondary electron emission yields of materials in segmented wall or (c) an inclination of the external magnetic field. The transition in the sheath structure over the grooved emissive surface from a developed sheath to a collapsed one caused by the increase of electron energy enlarges the alteration of the ion and electron currents over the grooved or segmented surfaces. The experimental study of the plasma-emissive wall sheath transition was carried out with hexagonal boron nitride wall samples grooved with the characteristic size of 1 mm and 5 mm, which is about of the Debye length. In kinetic simulations, this phenomenon is analyzed in terms of the electron and ion energy distribution functions. An external oblique magnetic field applyed to the dc discharge is found to redistribute the plasma and the periodical structure with the spikes of electron and ion densities forms This phenomena causes the non-uniform spatial distribution of electron and ion currents to the wall. The spikes in electron and ion densities became more pronounced with an increase of magnetic field incidence angle.

Why and under which conditions can running and standing ionization-diffusion shock waves appear in the direct current gas discharge plasma?

It is shown that the modern synergy viewpoint on striations offers an explanation of how backward, forward, and fixed ionization waves (striations) in a direct current (dc) gas discharge come into being. Striations always propagate in the direction of majority carriers, namely, electrons with respect to the stationary ion skeleton, but particular experimental conditions in gas discharge tubes associated with cataphoretic and electrophoretic phenomena determine the actual propagation direction of striations.

Optimization of ion transport from atmospheric pressure ion sources

An experimental study and numerical calculations of the influence of geometric and electrical parameters of ion sources with ionization at atmospheric pressure on the motion of ions from ionization site to an entrance orifice were carried out. The effect of space charge on the current-voltage characteristics of an electrode configuration of the ion source was experimentally shown. The results of numerical calculations of ion motion with allowance for the space charge in a stationary ion flow based on the statistical diffusion simulation model were shown to agree well with the experiment. The possibility of 100% ion transportation from the ionization area to a collector was demonstrated experimentally and numerically.

Stationary and Nonstationary Ion and Water Flux Interactions in Kidney Proximal Tubule: Mathematical Analysis of Isosmotic Transport by a Minimalistic Model.

Our mathematical model of epithelial transport (Larsen et al. Acta Physiol. 195:171-186, 2009) is extended by equations for currents and conductance of apical SGLT2. With independent variables of the physiological parameter space, the model reproduces intracellular solute concentrations, ion and water fluxes, and electrophysiology of proximal convoluted tubule. The following were shown: 1. Water flux is given by active Na+ flux into lateral spaces, while osmolarity of absorbed fluid depends on osmotic permeability of apical membranes. 2. Following aquaporin "knock-out," water uptake is not reduced but redirected to the paracellular pathway. 3. Reported decrease in epithelial water uptake in aquaporin-1 knock-out mouse is caused by downregulation of active Na+ absorption. 4. Luminal glucose stimulates Na+ uptake by instantaneous depolarization-induced pump activity ("cross-talk") and delayed stimulation because of slow rise in intracellular [Na+]. 5. Rate of fluid absorption and flux of active K+ absorption would have to be attuned at epithelial cell level for the [K+] of the absorbate being in the physiological range of interstitial [K+]. 6. Following unilateral osmotic perturbation, time course of water fluxes between intraepithelial compartments provides physical explanation for the transepithelial osmotic permeability being orders of magnitude smaller than cell membranes' osmotic permeability. 7. Fluid absorption is always hyperosmotic to bath. 8. Deviation from isosmotic absorption is increased in presence of glucose contrasting experimental studies showing isosmotic transport being independent of glucose uptake. 9. For achieving isosmotic transport, the cost of Na+ recirculation is predicted to be but a few percent of the energy consumption of Na+/K+ pumps.

Bridging Child–Langmuir and Warren: exact and approximate solutions for the unipolar sheath of intermediate pressure

The stationary unipolar ion sheath is investigated in the regime of intermediate gas pressure. A mathematical model is consulted which describes the motion of a single species of positive ions under the influence of the self-generated electric field and accounts for ion inertia and collisional ion-neutral friction assuming a constant mean free path. In the collisionless limit, the model reduces to the power law of Child and Langmuir (1911 Phys. Rev. 32 492; 1913 Phys. Rev. II 2 450); in the collisional case, to that of Warren (1955 Phys. Rev. 98 1658). The general case, however, resists a power law ansatz, and an exact analytical solution is currently not known. This study will close the gap by constructing such a solution in terms of Airy functions. An approximation based on the quadratic order harmonic mean of the limiting velocities and an earlier potential interpolation by Riemann et al (1992 J. Phys. D: Appl. Phys. 25 620) are critically assessed.

Exploring competitive features of stationary sodium ion batteries for electrochemical energy storage

Owing to the four features summarized in this review, i.e., low-cost resource, high-power performance, all-climate adaptability and full-batty recyclability, sodium ion batteries show great promise for large-scale energy storage systems used for the application of renewable energy sources and smart grids.

Determining the Radius of the Magnetic Vortex Core of YBCO123 and Bi2212

A plasma has been defined as a quasi-neutral gas of charged particles showing collective behaviour. Plasmas can support waves depending on the local condi-tions, the presence of external electric and magnetic fields. A characteristic property of plasmas is their ability to transfer momentum and energy via col-lective motion. An example in this case, is the Langmuir waves where plasma electrons oscillate against a stationary ion background. In a superconductor, two plasma electrons arise one that is made up of normal electrons and the other that is made up of super-electrons. In this study, we consider a system of super-electrons forming a super-particle. The motion of the plasma su-per-particles around a magnetic vortex core has been studied in the YBCO123 and Bi2212 systems.

Dissipative high-frequency envelope soliton modes in nonthermal plasmas

The linear and nonlinear properties of modulated high-frequency (electron-acoustic) electrostatic wave packets are investigated via a fluid-dynamical approach. A three-component plasma is considered, composed of two types of electrons at different temperatures (``cold'' and ``hot'' electrons) evolving against a cold stationary ion background. A weak dissipative effect is assumed, due to electron-neutral collisions. While the cold electrons are treated as an inertial fluid, the hot electrons are assumed to be in a non-Maxwellian state, described by a kappa ($\ensuremath{\kappa}$) type distribution. The linear characteristics of electron-acoustic waves are analyzed in detail, and a linear dispersion relation is obtained. Weakly damped electrostatic waves are shown to propagate above a wave number $k$ threshold, whose value is related to dissipation (and reduces to zero in its absence). Long-wavelength values (i.e., for $k$ below that threshold) are heavily damped and no propagation occurs. The nonlinear dynamics (modulational self-interaction) of wave packets in the propagating region is modeled via a dissipative nonlinear Schr\odinger type equation, derived via a multiscale perturbation technique for the wave envelope, which includes a dissipative term associated with the finite imaginary part of the nonlinearity term. The dynamical and structural characteristics (speed, amplitude, width) of dissipative localized modes representing the amplitude of modulated electron-acoustic wave packets in a collisional plasma are thus investigated for various values of relevant plasma (configuration) parameters, namely the superthermality index $\ensuremath{\kappa}$, the cold-to-hot electron density ratio, and collisionality (strength). Our analytical predictions are tested by computer simulations. A quasilinear perturbation method for near-integrable systems leads to a theoretical prediction for the wave amplitude decay, which is shown to match our numerical result. The results presented in this paper should be useful in understanding the dynamics of localized electrostatic disturbances in space plasmas, and also in laboratory plasmas, where the combined effect(s) of excess energetic (suprathermal) electrons and (weak) electron-neutral collisions may be relevant.