Saha Equation Research Articles

Algorithms for Solving the Equilibrium Composition Model of Arc Plasma.

In the present study, the Homotopy Levenberg-Marquardt Algorithm (HLMA) and the Parameter Variation Levenberg-Marquardt Algorithm (PV-LMA), both developed in the context of high-temperature composition, are proposed to address the equilibrium composition model of plasma under the condition of local thermodynamic and chemical equilibrium. This model is essentially a nonlinear system of weakly singular Jacobian matrices. The model was formulated on the basis of the Saha and Guldberg-Waage equations, integrated with Dalton's law of partial pressures, stoichiometric equilibrium, and the law of conservation of charge, resulting in a nonlinear system of equations with a weakly singular Jacobian matrix. This weak singularity primarily arises due to significant discrepancies in the coefficients between the Saha equation and the Guldberg-Waage equation, attributed to differing chemical reaction energies. By contrast, the coefficients in the equations derived from the other three principles within the equilibrium composition model are predominantly single-digit constants, further contributing to the system's weak singularity. The key to finding the numerical solution to nonlinear equations is to set reasonable initial values for the iterative solution process. Subsequently, the principle and process of the HLMA and PV-LMA algorithms are analyzed, alongside an analysis of the unique characteristics of plasma equilibrium composition at high temperatures. Finally, a solving method for an arc plasma equilibrium composition model based on high temperature composition is obtained. The results show that both HLMA and PV-LMA can solve the plasma equilibrium composition model. The fundamental principle underlying the homotopy calculation of the (n-1) -th iteration, which provides a reliable initial value for the n-th LM iteration, is particularly well suited for the solution of nonlinear equations. A comparison of the computational efficiency of HLMA and PV-LMA reveals that the latter exhibits superior performance. Both HLMA and PV-LMA demonstrate high computational accuracy, as evidenced by the fact that the variance of the system of equations ||F|| < 1 × 10-15. This finding serves to substantiate the accuracy and feasibility of the method proposed in this paper.

The influence of continuum lowering on the equilibrium composition of plasma: case study of laser-induced plasma on a WC–Cu target

Abstract Composition of plasma obtained by laser ablation of cermet WC-Cu is calculated under the assumption of local thermodynamical equilibrium. Special attention is paid to the effect of lowering the ionization potential, the influence of which in the Saha equations is reflected both through the exponential Boltzmann term and through the partition functions of atomic and ionic species present in the plasma. The effect on these two terms are separated and quantified. It has been shown that the correction of the partition functions due to the reduction of the ionization potential is of greater importance than the correction of Boltzmann term, at higher temperatures for atomic species. It is thus necessary for the precise determination of the plasma composition, especially at higher temperatures. The effect of lowering the ionization potential on different types of atoms as well as on different ionic states is analyzed. Тhe change of the partition function due to the lowering of ionization energy affects also the concentration of single charged ions in an amount comparable to the correction of the Boltzmann term.

Driven two-fluid slow magnetoacoustic waves in the solar chromosphere with a realistic ionisation profile

Context. This study was carried out in the context of chromosphere heating. Aims. This paper aims to discuss the evolution of driven slow magnetoacoustic waves (SMAWs) in the solar chromosphere modelled with a realistic ionisation profile and to consider their potential role in plasma heating and the generation of plasma outflows. Methods. Two-dimensional (2D) numerical simulations of the solar atmosphere are performed using the JOANNA code. The dynamic behaviour of the atmospheric plasma is governed by the two-fluid equations (with ionisation and recombination terms taken into account) for neutrals (hydrogen atoms) and ions (protons)+electrons. The initial atmosphere is described by a hydrostatic equilibrium (HE) supplemented by the Saha equation (SE) and embedded in a fanning magnetic field. This initial equilibrium is perturbed by a monochromatic driver which operates in the chromosphere on the vertical components of the ion and neutral velocities. Results. Our work shows that the HE+SE model results in time-averaged (net) plasma outflows in the top chromosphere, which are larger than their pure HE counterpart. The parametric studies demonstrate that the largest chromosphere temperature rise occurs for smaller wave driving periods. The plasma outflows exhibit the opposite trend, growing with the driver period. Conclusions. We find that the inclusion of the HE+SE plasma background plays a key role in the evolution of SMAWs in the solar atmosphere.

Non-gaussian Saha’s ionization in Rindler spacetime and the equivalence principle

We investigate the non-Gaussian effects of the Saha equation in Rindler space via Tsallis statistics. By considering a system with cylindrical geometry, we deduce the non-Gaussian Saha ionization equation for a partially ionized hydrogen plasma that expands with uniform acceleration. We demonstrate conditions for the validity of the equivalence principle within the realms of both Boltzmann–Gibbs and Tsallis statistics. In the non-Gaussian framework, our findings reveal that the effective binding energy exhibits a quadratic dependence on the frame acceleration, in contrast to the linear dependence predicted by Boltzmann–Gibbs statistics. We show that an accelerated observer shall notice a more pronounced effect on the effective binding energy for a>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a>0$$\\end{document} and a more attenuated one when a<0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a<0$$\\end{document}. We also ascertain that an accelerated observer will measure values of q smaller than those measured in the rest frame. Besides, assuming the equivalence principle, we examine the effects of the gravitational field on the photoionization of hydrogen atoms and pair production. We show that both photoionization and pair production are more intensely suppressed in regions with a strong gravitational field in a non-Gaussian context than in the Boltzmann–Gibbs framework. Lastly, constraints on the gravitational field and the electron and positron chemical potentials are derived.

Influence of Ionization on the Polytropic Index of the Solar Atmosphere within Local Thermodynamic Equilibrium Approximation

An initial theoretical attempt to explain the observed decrease of the polytropic/adiabatic index γ in the solar corona has been accomplished. The chemical reactions of the ionization–recombination processes in local thermodynamic equilibrium (LTE) of a solar plasma cocktail containing heavy elements are found to cause 1.1 < γ ≤ 5/3 in the quiet solar atmosphere. It is also shown that the quiet solar atmosphere is in LTE, justifying this theoretical study. This result is obtained by numerically solving the Saha equation and subsequently using a newly derived equation for calculation of the polytropic index from thermodynamic partial derivatives of the enthalpy and pressure with respect to density and temperature. In addition, a comparison measured from spectroscopic observations of propagating slow magnetohydrodynamic waves in coronal loops shows that LTE ionization accounts for a very small part of the observed decrease of γ, meaning that the solar plasma in the active region is not in LTE as expected. However, the observed dependency of higher polytropic index at higher temperatures is confirmed by the current theoretical approach. It is concluded that in order to account for the polytropic index decrease in the active regions of the solar corona, it is necessary for kinetic non-LTE ionization calculations to be performed.

Non-equilibrium modeling on the aerothermodynamic characteristics of hypersonic inflatable reentry vehicle

In this study a 2D two-temperature chemical non-equilibrium model is established to investigate the flow characteristics and chemical reactions processes around hypersonic inflatable reentry vehicle at different flight altitudes and reentry velocities. This chemical kinetic model is based on the Gupta model and modified by comparing the species mole fractions at thermal equilibrium condition with the results obtained by Saha equation. In order to validate the model, the calculations are performed for a blunt cone ELECTRE and a cylinder, the predicted heat flux and pressure are compared with experimentally measured data and the maximum differences on heat flux and wall pressure are less than 20% and 5%, respectively. Then the flow characteristics behind the shock wave and wall heat flux are discussed in detail for Titans vehicle. It is found that the pressure declines with the increase of altitude and reentry velocity, this variation trend is opposite to the wall heat flux, whose maximum value increases from 58 kw/m2 to 107 kw/m2 with the rise of flight altitude from 79 to 88 km due to the large temperature and component gradients. This indicates that the aerodynamic force and heat flux should be taken into account simultaneously for the design of inflatable reentry vehicle. By analyzing the chemical reactions processes behind the strong shock wave, it is seen that not only the dissociation reactions of N2 and O2 molecules play an important role, but also the neutral species exchange reactions contribute to the density change of species. The dominant ionization reactions are N+O→NO++e and NO+M→4NO++e+M4, while the ionization processes are weak, and the maximum ionization degree is smaller than 1%. The analysis of dominant chemical reactions can provide a reference for the numerical modeling study of hypersonic reentry vehicle.

Large-time behavior of global solutions to the Cauchy problem of one-dimensional viscous and heat-conducting ionized gas

This paper is concerned with the Cauchy problem of one-dimensional viscous and heat-conducting ionized gas when the viscosity is a positive constant or depends on the density. According to Saha's ionization equation, the equations of state for the basic thermodynamic variables of an ionized gas depend also on the degree of ionization, which leads to the loss of concavity of the physical entropy in some small bounded domain. Such a property of the ionized gas together with the unboundedness of the domain under our consideration makes it hard to derive the desired dissipative estimates on the first-order spatial derivative of both the bulk velocity and the absolute temperature, thus making the problem more challenging.In this paper, for a class of constant non-vacuum equilibrium states with positive temperature, we succeed in deducing the desired uniform-in-time bounds on the above mentioned dissipative estimates on both the bulk velocity and the absolute temperature. Based on such an estimate, we can then establish the global existence of solutions to the Cauchy problem of one-dimensional viscous and heat-conducting ionized gas with positive constant or density-dependent viscosity and show that such a class of constant non-vacuum equilibrium states is time asymptotically nonlinear stable.

Fluid–solid coupled simulation of hypervelocity impact and plasma formation

Previous theoretical and computational studies on hypervelocity impact have mainly focused on the dynamic response of the solid materials that constitute the projectile and the target, while the surrounding environment is often assumed to be a vacuum. In this paper, we consider impact events that occur in a fluid (e.g., gas) medium, and present a computational model that includes the dynamics, thermodynamics, and ionization of the surrounding fluid material. The model couples the compressible Navier–Stokes equations with the Saha equations to predict the onset and extent of ionization in the surrounding fluid. An extended level set method with two signed distance functions is employed to track the three material interfaces between the projectile, the target, and the ambient fluid. This method accommodates the large deformation, contact, and separation of the interfaces, while avoiding spurious overlapping of different material subdomains. The advective fluxes across material interfaces are computed by constructing and solving bimaterial Riemann problems, thereby taking into account the discontinuities in both state variables (e.g., density) and thermodynamic relations. The computational model is first verified for an infinite ideal plasma and a one-dimensional three-material impact problem. Next, the model is employed to analyze the impact of a tantalum rod projectile onto a soda lime glass (SLG) target in an argon gas environment. In different analyses, the impact velocity is varied between 3 and 6km/s, and the radius of the projectile is varied between 2.5 and 10mm. Each analysis starts with a steady-state fluid dynamics simulation that generates the shock-dominated hypersonic flow around the projectile. This flow field is then used as an initial condition to start the fluid–solid coupled impact simulation. The predicted maximum temperature and pressure within the SLG target agree reasonably well with published experimental data for a similar material (fused quartz). Within the ambient gas, the impact-generated shock wave is found to be stronger than the initial bow shock in front of the projectile. Behind this shock wave, a region of high pressure and temperature forms in the early stage of the impact, mainly due to the hypersonic compression of the fluid between the projectile and the target. The temperature within this region is significantly higher than the peak temperature in the solid materials. For impact velocities higher than 4km/s, ionization is predicted. This finding indicates that the ambient gas may be a nontrivial contributor to the plasma formed in terrestrial and atmospheric hypervelocity impact events.

Exciton Formation Dynamics and Band‐Like Free Charge‐Carrier Transport in 2D Metal Halide Perovskite Semiconductors

AbstractMetal halide perovskite (MHP) semiconductors have driven a revolution in optoelectronic technologies over the last decade, in particular for high‐efficiency photovoltaic applications. Low‐dimensional MHPs presenting electronic confinement have promising additional prospects in light emission and quantum technologies. However, the optimisation of such applications requires a comprehensive understanding of the nature of charge carriers and their transport mechanisms. This study employs a combination of ultrafast optical and terahertz spectroscopy to investigate phonon energies, charge‐carrier mobilities, and exciton formation in 2D (PEA)2PbI4 and (BA)2PbI4 (where PEA is phenylethylammonium and BA is butylammonium). Temperature‐dependent measurements of free charge‐carrier mobilities reveal band transport in these strongly confined semiconductors, with surprisingly high in‐plane mobilities. Enhanced charge‐phonon coupling is shown to reduce charge‐carrier mobilities in (BA)2PbI4 with respect to (PEA)2PbI4. Exciton and free charge‐carrier dynamics are disentangled by simultaneous monitoring of transient absorption and THz photoconductivity. A sustained free charge‐carrier population is observed, surpassing the Saha equation predictions even at low temperature. These findings provide new insights into the temperature‐dependent interplay of exciton and free‐carrier populations in 2D MHPs. Furthermore, such sustained free charge‐carrier population and high mobilities demonstrate the potential of these semiconductors for applications such as solar cells, transistors, and electrically driven light sources.

Expansion and line-binned opacities of samarium ions for the analysis of early kilonova emission from neutron star mergers

ABSTRACTOpacity calculations performed within the expansion and the line-binned formalisms are reported for Sm V–X ions in this paper. These were determined by means of new large-scale atomic structure and radiative rate computations carried out using the pseudo-relativistic Hartree-Fock (HFR) method from which energy levels, wavelengths, and oscillator strengths were deduced for more than 100 millions of spectral lines in the considered samarium ions. In the absence of any experimental data, the reliability of HFR results was roughly estimated by comparison with those obtained with an independent theoretical approach, namely the fully relativistic multiconfiguration Dirac-Hartree-Fock method, in Sm VI and Sm VII. The opacities were estimated for typical conditions corresponding to early phases of kilonovae following neutron star mergers, i.e. for a density ρ = 10−10 g cm−3, a time after the merger t = 0.1 day and temperatures ranging from 25 000 to 70 000 K. In addition, the atomic calculations allowed us to establish the ground level for each of the Sm ions considered (still unknown until now), as well as reliable partition functions that are crucial for the determination of the ionization balance by solving the Saha equation and for accurate opacity calculations.

Analytical study of ionizing blast waves in atomic hydrogen

The ionization effect on both the evolution and internal structure of a blast wave (BW) is determined in laboratory conditions. In a first step, the Rankine–Hugoniot equations describing the structure of the shock front together with the Saha equation modeling ionization are solved analytically in a consistent way for the conditions of a cold initial atomic hydrogen gas. In a second step, a simplified approach is used by introducing an effective adiabatic index γ * that takes into account ionization arising at the shock front. Finally, γ * is used as input data in the self-similar model derived formerly by Barenblatt to describe the structure and the dynamics of the ionizing BW. For the typical laboratory conditions of blast wave experiments, ionization achieves a hydrogen gas compression up to about 11 times at the shock front of the blast wave where a thin and dense shell forms. For such a compression, the value of the effective adiabatic index is γ * ≃ 1.2 leading to a self-similar evolution of the BW where its radius R(t) varies according to R ( t ) ∝ t α * with α * ≃ 0.33. This value of α * is lower than the adiabatic expansion stage α = 2 / 5, where the total energy of the BW is conserved. Thus, ionization is found to act as a cooling effect at the shock front where a fraction of kinetic energy is absorbed to ionize the gas.

Relativistic transformation of thermodynamic parameters and refined Saha equation

The relativistic transformation rule for temperature is a debated topic for more than 110 years. Several incompatible proposals exist in the literature but a final resolution is still missing. In this work, we reconsider the problem of relativistic transformation rules for a number of thermodynamic parameters including temperature, chemical potential, pressure, entropy and enthalpy densities for a relativistic perfect fluid using relativistic kinetic theory. The analysis is carried out in a fully relativistic covariant manner, and the explicit transformation rules for the above quantities are obtained in both Minkowski and Rindler spacetimes. Our results suggest that the temperature of a moving fluid appears to be colder, supporting the proposal by de Broglie, Einstein, and Planck, in contrast to other proposals. Moreover, in the case of a Rindler fluid, our findings suggest that the total number of particles and the total entropy of a perfect fluid in a box whose bottom is parallel to the Rindler horizon are proportional to the area of the bottom, but are independent of the height of the box, provided the bottom of the box is sufficiently close to the Rindler horizon. The area dependence of the particle number implies that the particles tend to be gathered toward the bottom of the box, and hence implicitly determines the distribution of the chemical potential of the system, whereas the area dependence of the entropy indicates that the entropy is still additive and may have potential applications in explaining the area law of black hole entropy. As a by-product, we also obtain a relativistically refined version of the famous Saha equation which holds in both Minkowski and Rindler spacetimes.

An analytical model for organic bulk heterojunction solar cells based on Saha equation for exciton dissociation.

The power conversion efficiencies of organic solar cells (OSCs) have been greatly improved in recent years. However, latest experimental data of high efficiency OSCs, the sublinear relationship between the short circuit current density (Jsc) and light intensity (Pin), and the effects of energetic disorder in bulk heterojunction organic solar cells have not been understood. An analytical model for high-efficiency OSCs is proposed, which takes most physical factors into account that have been ignored in most previous models, including practical solar spectra and absorption spectra, degeneracy effect, exciton effect, space charge limited current, and unified mobility expression dependent on temperature, electric field and density, etc. Three analytical iterative methods are proposed to solve the strong non-linear Poisson equation and the drift-diffusion equations. The method for the drift-diffusion equations involves introducing two constant coefficients and determining their values self-consistently by demanding the space averages of approximate drift and diffusion currents equal to the averages of accurate ones. The theoretical results for five high-efficiency OSCs are in good agreement with experimental data, including current-voltage curves, light intensity-dependent Jsc and open-circuit voltage (Voc) curves. The effects of energetic disorder in bulk heterojunction organic solar cells, and the sublinear relationship Jsc ∝ Pαin (α < 1) can be well explained. The Saha equation for exciton dissociation and the space-charge-limited-current (SCLC) effect are important for modelling high-efficiency OSCs. The Voc ∼ Pin relationship can be influenced by many factors. But, the Jsc ∼ Pin relationship can be mainly and slightly influenced by the exciton effect and energetic disorder, respectively. When aiming to realize higher performance OSCs, one should decrease six material parameters, including the energetic disorder, exciton mass, deep level impurity concentration, the ratios of electron and hole mobilities, densities of states for electrons and holes, and potential barriers at the anode and cathode. The performance parameters of 15 triad compounds are predicted by using ab initio Eg and absorption spectra from the literature along with other input parameters taken from previous optimized values, and the efficiency of two compounds was found to exceed 35%.

Semi-analytic model for plasma production and Cherenkov radiation emission from hypervelocity impacts on soda–lime glass

A semi-analytic method is proposed to compute the produced plasma and the emitted Cherenkov radiation from hypervelocity impacts on soda–lime glass for various projectiles and impact velocities. First, the Taylor–von Neumann–Sedov blast wave model, coupled with the system of nonlinear Saha equations for multispecies, strongly coupled plasma, is adopted to estimate the hydrodynamic profiles and the ionization state of the target material in the early stage of the impact. Second, the Frank–Tamm formula is considered to investigate the onset of the Cherenkov radiation and to compute the emitted energy. The present approach predicts a linear dependence of the produced total electric charge on the projectile density and a quadratic dependence on the projectile velocity, whereas the emitted Cherenkov radiation scales quadratically with the produced charge if the onset conditions are met.

Study on electrical conductivity of detonation products of aluminized explosives

Using the thermodynamic equilibrium constant method and JWL-Miller equation of state, based on the calculation of the thermodynamic parameters such as the composition, pressure, and explosion temperature of the detonation products of aluminized explosives in the Magnetocumulative generator, the Saha ionization equation, and gas conductivity calculation model are used to write Matlab code to calculate the electron density and conductivity of the detonation products of the magnetic flux compression generator. The temporal and spatial variation law of electron density and conductivity is revealed. The simulation shows that the thickness of the maximum conductivity layer in the detonation process is about 1 mm and moves at a uniform speed following the CJ surface. The maximum conductivity of HMX/Al (70/30) is 1.88e5 Ω−1·m−1, with an error of 6%, and the maximum conductivity of RA1 (HMX / DNAN / Al) is 2.7e4 Ω−1·m−1

Impact of Coulomb correction factor on rate of change of lepton fraction during presupernova evolution

We re-examine the weak interaction nuclei having largest contribution to the lepton-to-baryon fraction (Ye) by coupling the stellar weak rates and mass abundances for post silicon burning conditions during the presupernova evolution of massive stars. The stellar weak rates were recently calculated by Nabi et al. (2021) employing the fully microscopic pn-QRPA model without invoking the Brink-Axel hypothesis. We compute the mass abundances for a total of 728 nuclei, with A = 1–100, using Saha's equation and assuming nuclear statistical equilibrium with the incorporation of Coulomb correction factor to the chemical potential. We compile a list of top 50 electron capture (ec) and β-decay (bd) nuclei, on the basis of largest contribution to Y˙e for post silicon burning conditions, where 11 ec and 6 bd nuclei debuted due to Coulomb corrections. The calculated mass abundances and corresponding Y˙e values are enhanced up to 3 orders of magnitude for heavier nuclei once Coulomb corrections were incorporated. This enhancement led to an increment in total Y˙ebd and Y˙eec values, at Ye = 0.425 (ρ = 2.20×109 g/cm3), of 80% and 91%, respectively. After incorporating the Coulomb corrections, we propose a revised interval of Ye = 0.423-0.455, where bd rates surpass the competing ec rates, and is 3.2% bigger than the one suggested by Nabi et al. (2021).

Ionization of heavy elements and the adiabatic exponent in the solar plasma

Context. The adiabatic exponent Γ1 is studied as a thermodynamic quantity in the partially ionized plasma of the solar convection zone. Aims. The aim of this study is to understand the impact of heavy elements on the Γ1 profile. We calculated Γ1 with the SAHA-S equation of state for different chemical compositions of plasma, and we analyzed contributions of individual elements to Γ1. We attempted to determine the mass fractions of the heavy elements using our analysis of the Γ1 profile. Methods. We studied the decrease in Γ1 due to the ionization of heavy elements in comparison with the value obtained for a pure hydrogen-helium plasma. These types of differences are denoted as “Z contributions”, and we analyzed them for eight elements (C, N, O, Ne, Mg, S, Si, and Fe) as well as for a mixture of elements corresponding to the solar chemical composition. The contributions of the heavy elements are studied on an adiabat in the lower part of the convection zone, where the influence of hydrogen and helium to the Z contribution is minimal. The Z-contribution profiles are unique for each chemical element. We compared linear combinations of individual Z contributions with the exact Z contribution. Applying a least-squares technique to the decomposition of the full Z contribution to a basis of individual-element contributions, we obtained the mass fractions of the heavy elements. Results. The Z contribution of heavy elements can be described by a linear combination of individual-element Z contributions with a high level of accuracy of 5 × 10−6. The inverse problem of estimating the mass fractions of heavy elements from a given Γ1 profile was considered for the example of solar-type mixtures. In ideal numerical simulations, the mass fractions of the most abundant elements could be determined with a relative accuracy better than a few tenths of a percent. In the presence of random or systematic errors in the Γ1 profile, abundance estimations become remarkably less accurate, especially due to unknown features of the equations of state. If the amplitude of the errors does not exceed 10−4, we can expect a determination of at least the oxygen abundance with a relative error of about 10%. Otherwise, the results of the method would not be reliable.

Anomalous emission behavior of excitons at low temperature in monolayer WS2

We report on the anomalous emission behavior of excitons (X) in monolayer WS2 using temperature dependent photoluminescence spectroscopy. In general, PL emission from excitons enhances with decreasing temperature due to suppression of phonon mediated non-radiative transitions. Here, we observe that excitonic PL is temperature independent, although with decreasing temperature, the emission intensity for trion (X −) and biexciton or defect-bound excitons (XX/L 1) increases up to 123 K and then decreases. Analysis of experimental data with a model derived from the Boltzmann distribution and Saha equation reveal conversion of excitons into trions, biexcitons or defect-bound excitons and an increase of spin forbidden dark state with reduction in temperature. These findings could provide better strategies for designing future quantum devices.

Non-Gaussian effects of the Saha\u2019s ionization in the early universe

Tsallis’ thermostatistical has received increasing attention due to its success in describing phenomena that manifest unusual thermodynamic properties. In this context, the generalized Saha equation must follow a condition of generalized thermal equilibrium of matter and radiation. The present work aims to explore the non-Gaussian effects on Saha’s ionization via Tsallis statistics. To accomplish this, we generalized the number density taking into account a non-Gaussian Fermi-Dirac distribution and then set out the Saha equation for the cosmological recombination. As a result, we highlight two new non-Gaussian effects: (i) two generalized chemical equilibrium conditions, one for the relativistic regime and the other for the non-relativistic one; and (ii) the hydrogen binding q-energy. We demonstrated that to yield smooth shifts in the binding energy, the a-parameter must be very small. We also showed that binding q-energy exhibits symmetrical behavior around the value of the standard binding energy. Besides, we used the q-energy in order to access other hydrogen energy levels, and we ascertained the values of the a-parameter that access those levels and their relationship to temperature. Finally, we employed these results to examine the non-Gaussian effects of the deuterium bottleneck, recombination, and the particle anti-particle excess.

Relativistic Transformation of Thermodynamic Parameters and Refined Saha Equation

The relativistic transformation rule for temperature is a subject under debate for more than 110 years. Several incompatible proposals exist in the literature, but a final resolution is still missing. In this work, we reconsider the problem of relativistic transformation rules for a number of thermodynamic parameters, including temperature, chemical potential, pressure, entropy and enthalpy densities for a relativistic perfect fluid using relativistic kinetic theory. The analysis is carried out in a fully relativistic covariant manner, and the explicit transformation rules for the above quantities are obtained in both Minkowski and Rindler spacetimes. Our results suggest that the temperature of a moving fluid appears to be colder, supporting the proposal by de Broglie, Einstein and Planck in contrast to other proposals. Moreover, in the case of Rindler fluid, our work indicates that, the total number of particles and the total entropy of a perfect fluid in a box whose bottom is parallel to the Rindler horizon are proportional to the area of the bottom, but are independent of the height of the box, provided the bottom of the box is sufficiently close to the Rindler horizon. The area dependence of the particle number implies that the particles tend to be gathered toward the bottom of the box and hence implicitly determines the distribution of chemical potential of the system, whereas the area dependence of the entropy indicates that the entropy is still additive and may find some applications in explaining the area law of black hole entropy. As a by product, we also obtain a relativistically refined version of the famous Saha equation which holds in both Minkowski and Rindler spacetimes.