Maxwellian Velocity Distribution Research Articles

Inverse Bremsstrahlung absorption coefficient in inhomogeneous plasma with nonextensive electron velocity distribution and Tsallis exponential electron density profile

AbstractInverse bremsstrahlung (collisional) absorption of the laser beam is studied in plasma with a generalized (q‐nonextensive) electron velocity distribution and some kind of generalized electron density profile. It is shown that for some values of parameters designating the q‐nonextensive electron velocity distribution function and its generalized density profile, the calculated absorption coefficient reduces to the already known cases with Maxwellian velocity distribution with linear and exponential density profiles.

Volatilization and condensation behavior of magnesium vapor during magnesium production via a silicothermic process with magnesite

The condensation behavior of magnesium vapor produced by metal Mg or pellets for magnesium production is investigated at heat source temperatures of 1173–1473 K under vacuum. The possibility of reduction of magnesite in vacuum was analyzed by means of thermodynamics. The results indicate that the thermal motion of magnesium is violent, and the volatilization rate increased with high heat source temperature, the results accord with Maxwell's velocity distribution law. Magnesium vapor condensation products were obtained with flake and powder macromorphologies, where the flake products accounted for more than 80% (in mass). Scanning electron microscopic analysis revealed that the main factor affecting the magnesium vapor condensed particles was the vapor pressure, which was determined by temperature and reaction. The end condensation temperature was between 528.1 and 637.1 K when the heat source temperature was 1173–1473 K. Increasing the temperature gradient decreases the condensation temperature range. X-ray diffraction results showed that the magnesium condensation products were more crystalline at lower vapor pressure and a small temperature gradient. The presence of Ca2SiO4 in the reduction slag indicated the occurrence of the reduction reaction. The experimental results from pellets for magnesium production were consistent with those involving Mg metal.

Fundamental Rarefied Gas Flows

The study of rarefied gas flows based on kinetic theory of gases is one of the important foundations of vacuum technology. By contrast, “rarefied gas dynamics”, which is specialized for the study of rarefied gas flows, is an established field related to fluid dynamics. However, the knowledge accumulated in rarefied gas dynamics does not seem to have been well utilized in vacuum technology. The present note aims to review some results on fundamental rarefied gas flows, obtained in rarefied gas dynamics, that may be useful for vacuum technology. In addition, the definition of the Maxwell velocity distribution in a manner of rarefied gas dynamics, which differs slightly from that in vacuum technology, is given for reference.

On the approximate solutions of a damped nonplanar modified Korteweg–de Vries equation for studying dissipative cylindrical and spherical solitons in plasmas

In this work, the effect of both nonplanar (cylindrical and spherical) geometry and the dust-neutral collision on the propagation of dissipative nonplanar electrostatic dust-acoustic solitary waves (DASWs) in a strongly coupled complex plasma (SCCP) is examined. The electrons and ions are assumed to follow a Maxwellian and non-Maxwellian trapped velocity distributions, respectively. The fluid governing equations of the plasma species are reduced to an evolution equation using the reductive perturbation technique (RPT). For describing the dynamical mechanism of the dissipative nonplanar DASWs, the evolution equation (the damped nonplanar Shamel Korteweg–de Vries (SKdV)) is solved numerically using both homotopy perturbation method (HPM) and the improved multistage homotopy perturbation method (MsHPM). The numerical solutions of the integrable planar Shamel-KdV (SKdV) equation using both HPM and MsHPM is compared with the exact solution of the SKdV. Also, the comparison between the numerical solutions of the damped nonplanar SKdV using both HPM and MsHPM is discussed. Moreover, the maximum global residual error for both HPM and MsHPM is estimated for measuring the accuracy of the obtained numerical solutions. Furthermore, the dependence of dissipative nonplanar solitons characteristics on various plasma parameters are investigated.

The ‘SXR—Pit’ paradox as an indicator of electron transport in tokamaks

A phenomenon is analyzed, which is observed at some laboratory-scale tokamaks and seems to be unexplained: a strong drop in the soft x-ray radiation (SXR) after it passed through the ‘thick’ Be foils (the pit in the SXR spectrum). This phenomenon becomes more pronounced as the foil thickness increases and the plasma electron density decreases. The explanation for this phenomenon is proposed, which involves the assumption that the Maxwellian electron velocity distribution becomes ‘depleted’ in the range of velocities that are 3–5 times higher than the thermal one. The anomalous electron heat transport along the weakly perturbed toroidal magnetic field of the tokamak (the ‘magnetic flutter’ model) seems to be the most probable reason for this depletion. Thus, the ‘SXR—Pit’ can be a new tool for studying the physical nature of the anomalous electron transport in tokamaks.

Performance and simulated moment uncertainties of an ion spectrometer with asymmetric 2π field of view for ion measurements in space.

Space plasma instruments provide 3D particle velocity distribution functions. Because of telemetry limitations, these cannot be transmitted in high time resolution and the plasma needs to be characterized by moments of the velocity distribution function. These moment uncertainties have vital effects on the reliability and accuracy of onboard plasma moments. We assess the measurement accuracy for magnetosheath and solar wind ions using an ion spectrometer with an asymmetric field of view designed for the all-sky measurement of low-energy ions in the magnetosheath and solar wind. We focus on moment uncertainties for the ideal spectrometer, not considering the background counts, which may have considerable effects on the uncertainties in real life. To obtain number density, bulk velocity, and temperature, different orders of moments are integrated assuming a Maxwellian velocity distribution. Based on the design specifications, we use simulations to estimate systematic and random errors for typical plasma conditions. We find that the spectrometer resolution is adequate for determining the density of solar wind (∼7% error) and magnetosheath ions (∼4% error). The resolution is also adequate for determining the temperature of solar wind (∼10% error) and magnetosheath ions (∼2% error). For high speed flows with a bulk velocity of 750 km/s and a temperature of 20 eV, the maximum density and temperature errors become 9% and 7%, respectively. The bulk velocity errors are less than 2% for all cases. The contributions of heavy ions to the systematic errors are less than 5% for magnetosheath ions and less than 8% for solar wind ions.

Holistic numerical calibration of the iMESA electrostatic analyzer.

A drifted Maxwellian velocity distribution is the most common model used to interpret the data from low-energy charged-particle instruments onboard spacecraft that are used to investigate the ambient plasma environment in the low Earth orbit (LEO). An original method is presented for determining the flow parameters (density, temperature, and flow energy) of such a distribution from the output of the integrated miniaturized electrostatic analyzer, which has been successfully flown on several LEO missions. Rather than attempting to deconvolve from the on-orbit data the analyzer's response to an ideal, monoenergetic input, numerical simulation is used to predict and parameterize the response of the device to an input distribution that includes an isotropic, non-zero temperature, yielding a straightforward method for extracting the flow parameters from the spacecraft data. The method is computationally simple enough to be incorporated into a robust algorithm suitable for rapid batch processing or real-time analysis of data.

Exothermic dark matter for XENON1T excess

Motivated by the recent excess in the electron recoil from XENON1T experiment, we consider the possibility of exothermic dark matter, which is composed of two states with mass splitting. The heavier state down-scatters off the electron into the lighter state, making an appropriate recoil energy required for the Xenon excess even for the standard Maxwellian velocity distribution of dark matter. Accordingly, we determine the mass difference between two component states of dark matter to the peak electron recoil energy at about 2.5 keV up to the detector resolution, accounting for the recoil events over ER = 2 − 3 keV, which are most significant. We include the effects of the phase-space enhancement and the atomic excitation factor to calculate the required scattering cross section for the Xenon excess. We discuss the implications of dark matter interactions in the effective theory for exothermic dark matter and a massive Z′ mediator and provide microscopic models realizing the required dark matter and electron couplings to Z′.

Derivation of Multicomponent Lattice Boltzmann Equations by Introducing a Nonequilibrium Distribution Function into the Maxwell Iteration Based on the Convective Scaling

This study firstly proposes a simple recursive method for deriving the macroscale equations from lattice Boltzmann equations. Similar to the Maxwell iteration based on the convective scaling, this method is used to expand the lattice Boltzmann (LB) equations with the time step $$\delta _{t}$$ . It is characterised by the incorporation of a nonequilibrium distribution function not appearing in the Maxwell iteration to considerably reduce the mathematical manipulations required. Next, we define the kinetic equations of a multicomponent (i.e. N-component) system based on a model using the Maxwell velocity distribution law for the equilibrium distribution function appearing in the cross-collision terms. Then, using this simple recursive method, we derive the generalized Stefan–Maxwell equation, which is the macroscale governing equation of a multicomponent system while ensuring the mass conservation. In short, our objective is to firstly define the kinetic equations of a multi-component system having a clear physical interpretation and then formulate the LB equations of any N-component system deductively.

Effect of quantization and positron concentration on shielding potentials in electron‐positron‐ion plasma

AbstractThe kinetic theory of plasma has been employed to compute the test‐charge potential distributions accounting for quantization effects in magnetized electron‐positron‐ion (EPI) plasmas. In this regard, the degenerate positrons and electrons are assumed to follow the Fermi‐Dirac distribution, while inertial ions are modelled by Maxwellian velocity distribution. By solving the Fourier‐transformed Vlasov–Poisson equations, a modified dielectric function and electrostatic potential is obtained. By imposing various constraints on the test‐charge speed, the potential profile has been analysed in terms of Debye–Hückel (DH), far‐field (FF), and wake‐field (WF) potentials. It has been found that the amplitude of DH and FF potentials increases by the inclusion of quantization effects, and it becomes the opposite for the WF potential profile. Furthermore, the variation of positron concentration significantly affects the DH, FF, and WF potentials. The present findings are important to understand the shielding phenomenon in degenerate multi‐species plasmas.

Formation of mass gap compact object and black hole binary from Population III stars

Abstract We performed population synthesis simulations of Population III binary stars with Maxwellian kick velocity distribution when MGCOs (mass gap compact objects, with mass $2$–$5\,M_{\odot}$) are formed. We found that for eight kick velocity dispersion models of $\sigma_{\rm k}=0$–$500\>$km$\>$s$^{-1}$, the mean mass of black hole (BH)-MGCO binary is $\sim (30 \,M_\odot,\,2.6 \,M_\odot)$. In numerical data of our simulations, we found the existence of a BH-MGCO binary with mass $(22.9 \,M_\odot,\,2.5 \,M_\odot)$ which looks like GW190814.

Magnetic confinement of effectively unmagnetized plasma particles

A purely magnetic applied field may provide plasma confinement under conditions where the bulk of the plasma is effectively free of the applied magnetic field. The applied magnetic field surrounds the bulk of the plasma, and plasma particles that are incident on the applied magnetic field can be reflected back into the effectively unmagnetized region of plasma. The concept belongs to a class of magnetic plasma confinement approaches studied long ago, for which some experimental results indicated that classical (collision-based) cross-magnetic-field transport may occur. However, multiple magnetic coils are required to be immersed within the confined plasma, and rapid plasma loss may occur if material structures are present, which pass through the plasma (e.g., to hold the immersed coils in place). In the work reported, the concept is studied in combination with magnetic plasma expulsion [R. E. Phillips and C. A. Ordonez, Phys. Plasmas 25, 012508 (2018)], which would be employed to keep plasma away from material structures that pass through the plasma. A planar model is used for the study. A classical trajectory Monte Carlo simulation is carried out on particles that are independently incident on the applied magnetic field. With monoenergetic incident particles, the results indicate that the applied magnetic field can reflect all independently incident particles in certain regions of parameter space. Prospects for achieving three-dimensional magnetic confinement of an effectively unmagnetized plasma with a Maxwellian velocity distribution are discussed.

Transition Probabilities and Collision Strengths for Fine-structure Levels Excitation of Ti II

Abstract Several spectral features from the stellar and nebular objects arise due to the iron-peak Ti II fine-structure excitations. Transition probabilities and electron excitation collision strengths of iron-peak elements are important for a meaningful interpretation and analysis of the observed astrophysical spectra. Accurate description of atomic structure with open 3d-shell elements is the key to the reliable and accurate computation of radiative and collision rates. The term-dependent one-electron orbitals in the multiconfiguration Hartree–Fock approach with adjustable configuration expansions and semi-empirical fine-tuning for energy corrections have been used in achieving highly accurate target description. A total of 314 Ti II fine-structure levels of the ground 3d 24s and excited 3d 3, 3d4s 2, 3d 24p, 3d 25s, 3d4s4p, 3d 24d, 3d 25p, and 3d 24f configurations have been included in the calculations of these atomic parameters. The present calculation of collision strengths has been performed in a close-coupling approximation based on the B-spline Breit–Pauli R-matrix method with inclusion of spin–orbit interaction term in the Hamiltonian matrices. Effective collision strengths over a Maxwellian distribution of electron velocities at temperatures in the range from 103 to 105 K have been reported for transitions between the 314 fine-structure levels. These wide array of transitions give rise to many main Ti II infrared, optical, and ultraviolet lines from a variety of astrophysical objects. Our calculated parameters are compared with the available other theoretical and experimental results, and through this comparison likely uncertainties in our results have been estimated, especially for transitions among the low-lying fine-structure levels of astrophysical importance.

Exact solutions of plasma flow on a rigid oscillating plate under the effect of an external non-uniform electric field

The paper is concerned with the flow behavior of a helium-plasma bounded by a rigid, oscillating flat plate. The influences of an unsteady nonlinear external electric field (NEEF) on the plasma fluid were investigated. Attention has been focused on the Bhatnagar-Gross-Krook (BGK)–type of the Boltzmann kinetic equation (BKE) to study the gas dynamics with the Maxwellian velocity distribution function (VDF). An analytical solution of the model equations was given using the moment and the traveling wave methods. The role of the mean velocity, shear stress, viscosity coefficient, and electromagnetic fields are investigated. We found that the effect of the NEEF is powerful in plasma. It made it fluctuate and perturbed strongly compared to the effect of the nonlinear external magnetic field (NEMF). So, in the plasma controlling process, we should use NEMF instead of NEEF to save the equilibrium state (ES) for a plasma fluid. The thermodynamic properties were investigated, and qualitative agreements with previous related papers were demonstrated using 3-Dimensional graphics for the calculating variables. This study's significance was due to its vast applications in numerous fields, such as in physics, electrical engineering, micro-electro-mechanical systems (MEMS), or Nano-electro-mechanical systems (NEMS) devices, and various commercial-industrial applications.

On Analytical Solution of a Plasma Flow over a Moving Plate under the Effect of an Applied Magnetic Field

Our objective of this investigation is to mainly focus on the behavior of a plasma gas that is bounded by a moving rigid flat plate; its motion is damping with time. The effects of an external magnetic field on the electrons collected with each other, with positive ions, and with neutral atoms in the plasma fluid are studied. The BGK type of the Boltzmann kinetic equation is used to study the gas dynamics various regimes with Maxwellian velocity distribution functions. An analytical solution of the model equations for the unsteady flow was given using the moment and the traveling wave methods. The manner of the mean velocity of plasmas is illustrated, which is compatible with the variation of the shear stress, viscosity coefficient, and the initial and boundary conditions. Besides, the thermodynamic prediction is investigated by applying irreversible thermodynamic principles and extended Gibbs formula. Finally, qualitative agreements with previous related papers were demonstrated using 3-dimensional graphics for calculating the variables. The significance of this study is due to its vast applications in numerous fields such as in physics, engineering, commercial, and industrial applications.

Velocity independent constraints on spin-dependent DM-nucleon interactions from IceCube and PICO

Adopting the Standard Halo Model (SHM) of an isotropic Maxwellian velocity distribution for dark matter (DM) particles in the Galaxy, the most stringent current constraints on their spin-dependent scattering cross-section with nucleons come from the IceCube neutrino observatory and the PICO-60 hbox {C}_3hbox {F}_8 superheated bubble chamber experiments. The former is sensitive to high energy neutrinos from the self-annihilation of DM particles captured in the Sun, while the latter looks for nuclear recoil events from DM scattering off nucleons. Although slower DM particles are more likely to be captured by the Sun, the faster ones are more likely to be detected by PICO. Recent N-body simulations suggest significant deviations from the SHM for the smooth halo component of the DM, while observations hint at a dominant fraction of the local DM being in substructures. We use the method of Ferrer et al. (JCAP 1509: 052, 2015) to exploit the complementarity between the two approaches and derive conservative constraints on DM-nucleon scattering. Our results constrain sigma _{mathrm{SD}} lesssim 3 times 10^{-39} mathrm {cm}^2 (6 times 10^{-38} mathrm {cm}^2) at gtrsim 90% C.L. for a DM particle of mass 1 TeV annihilating into tau ^+ tau ^- (bbar{b}) with a local density of rho _{mathrm{DM}} = 0.3~mathrm {GeV/cm}^3. The constraints scale inversely with rho _{mathrm{DM}} and are independent of the DM velocity distribution.

Electromagnetic Ion–Ion Instabilities in Space Plasmas: Effects of Suprathermal Populations

Abstract In collision-poor plasmas from space, three distinct ion–ion instabilities can be driven by the proton beams streaming along the background magnetic field: left-hand resonant, nonresonant, and right-hand resonant instabilities. These instabilities are in general investigated considering only idealized proton beams with Maxwellian velocity distributions, and ignoring the implications of suprathermal populations, usually reproduced by the Kappa power laws. Moreover, the existing theories minimize the kinetic effects of electrons, assuming them isotropic and Maxwellian distributed. In an attempt to overcome these limitations, in the present paper we present the results of an extended investigation of ion–ion instabilities, which show that their dispersion and stability properties (e.g., growth rates, wave frequencies, and the unstable wavenumbers) are highly sensitive to the influence of suprathermal populations and anisotropic electrons. These results offer valuable explanations for the origin of the enhanced low-frequency fluctuations, frequently observed in space plasmas and associated with proton beams.

DNA Model with Non-Local Inter-Site Interaction in Collisional Thermostat

A modified Peyrard-Bishop-Dauxios model with non-local nature of the inter-site potential was studied in a collisional thermostat with a Maxwell velocity distribution of short-lived virtual particles at a temperature of 310 K. Introduction of non-locality to the inter-site potential was found to reduce significantly the equilibrium constants for the denaturation bubble formation reaction. This property improves the agreement of calculated data with experiments. The effect is especially pronounced for large bubbles. The end effects in the new version of the model are investigated. The significant contribution of entropy and the important role of the processes of transfer and localization of mechanical energy at the end sections of DNA are shown.

Saturation of trapped particle instability induced by vortex-merging in electron plasma waves

Phase space vortex merging in electron plasma waves is researched by applying a periodically changing electric field in plasma space with Maxwellian velocity distribution. The pump electric field excites the electron plasma wave with large amplitude and electron phase space vortices are formed. The electron plasma wave can be transited to longer wave modes through vortex merging processes. Excepting the fundamental mode of electron plasma waves, two or more modes appear and grow exponentially before vortex merging. After merging, another mode replaces the initial pumping wave as the strongest wave mode. It is verified that the growth of this new strong mode is related to trapping particle instability. Vortex merging is one of the saturation mechanisms of trapped particle instability.

A Note on the Opacity of the Sun’s Atmosphere

The opacity of the atmosphere of the Sun is due to processes such as Thomson scattering, bound–bound transitions and photodetachment (bound–free) of hydrogen and positronium ions. The well-studied free–free transitions involving photons, electrons, and hydrogen atoms are re-examined, while free–free transitions involving positrons are considered for the first time. Cross sections, averaged over a Maxwellian velocity distribution, involving positrons are comparable to those involving electrons. This indicates that positrons do contribute to the opacity of the atmosphere of the Sun. Accurate results are obtained because definitive phase shifts are known for electron–hydrogen and positron–hydrogen scattering.