Exponential Energy Distribution Research Articles

Unruh Entropy with Exponential Energy Distribution for a Spherically Symmetric Source

Unruh Entropy with Exponential Energy Distribution for a Spherically Symmetric Source

Estimation of Energy Spectrum of Precipitating Magnetospheric Electrons Based on Bremsstrahlung X‐Ray Fluxes Recorded in the Atmosphere

AbstractNumerous energetic electron precipitation events were recorded since 1963 in the atmosphere at polar latitudes in the course of regular measurements of charged particle fluxes in the Earth's atmosphere being performed by the Lebedev Physical Institute. The experimental data obtained represent the only uniform database in the world on electron precipitation events recorded directly in the atmosphere well below satellite orbits. The precipitating electrons are absorbed in the upper atmosphere. However, they generate X‐rays that can penetrate deep into the atmosphere sometimes down to altitudes of 20–35 km accessible to balloon measurements. These experimental data allow studying energy, temporal and spatial characteristics of electron precipitation events. In particular, based on PLANETOCOSMICS/GEANT4 we developed a method for evaluating the energy spectra of the primary flux of precipitating electrons. This method was used for evaluation of primary spectra of precipitating electrons assuming exponential energy distribution of incident electrons. Now, for the development of the method, we present the possibility of determining the energy spectra of electrons in the power‐law form, using new software RUSCOSMICS code. This new method, based on the GEANT4 software, makes it possible to describe the transport of precipitating electrons in the atmosphere taking into account the evolution of the energy and pitch‐angle distributions of electrons and X‐ray photons.

Collimation of fast electron beams by strong external magnetic field in laser–solid interaction using Monte Carlo simulation

In this paper, the effect of the external magnetic field on the fast electron beam angular spread and spatial divergence in laser–solid interaction were investigated and energy deposition of these electrons into the high-density fuel was evaluated using Monte Carlo simulation by Geant4 simulation toolkit. In our simulation, two types of the energy distribution function, exponential energy distribution, and quasi-two temperature energy distribution function, for electrons were considered. Our simulations in the presence of an external magnetic field show that the dynamics and spatial divergence of the high energy electrons are strongly affected by the external magnetic field. It was shown that in the case with the two-temperature energy distribution, the number of electrons (electron number density) with a large angular spread in the momentum space which were trapped by the magnetic fields lines and collimated toward the fuel were more populated than that of the exponential function. Comparison of the results indicate that the acceptable condition is obtained for the density in the presence of a magnetic field of about with a laser wavelength and laser intensity . It was presented that in the case with the sufficiently strong external fields, , it seems that the optimal results for suppression of electron spatial divergence, electron beam collimation, and energy deposition rate are obtained.

New Adsorption Models for Entirely Describing the Adsorption Isotherm and Heat of Methane in Heterogeneous Nanopore Structures of Coal.

To understand the adsorption mechanism of methane in heterogeneous nanopore structures of coal, integral adsorption models based on linear, exponential, hyperbolic and quadratic energy distribution functions are established. The adsorption energy domain of the new models is assumed to be a finite interval. These new adsorption models can describe both the adsorption isotherm and the adsorption heat. A volumetric method of adsorption with a microcalorimetry system is used to measure the adsorption isotherms and integral heat, and then the parameters of the new models are obtained by fitting the experimental data. Since the adsorption heat can be different for different adsorption models, it is necessary to fit the adsorption isotherms and heat simultaneously. The fitting results of the adsorption isotherms and heat show that the new models are able to describe the experimental data better than the Langmuir model. By comparing the fitting results and the effective range of adsorption energy of the different adsorption models, it is shown that the exponential energy distribution function is the most reasonable model for methane adsorption in coals, which can be used to evaluate the energetic heterogeneity of nanopores in coal samples. The decreasing exponential energy distributions of three coal samples indicate that a larger adsorption energy corresponds to fewer adsorption sites in the coal samples. The proportion of high adsorption energy is related to the micro-nanopore volume in the coal samples.

A Generalized Method for Calculating Atmospheric Ionization by Energetic Electron Precipitation

AbstractAccurate specification of ionization production by energetic electron precipitation is critical for atmospheric chemistry models to assess the resultant atmospheric effects. Recent model‐observation comparison studies have increasingly highlighted the importance of considering precipitation fluxes in the full range of electron energy and pitch angle. However, previous parameterization methods were mostly proposed for isotropically precipitation electrons with energies up to 1 MeV, and the pitch angle dependence has not yet been parameterized. In this paper, we first characterize and tabulate the atmospheric ionization response to monoenergetic electrons with different pitch angles and energies between ∼3 keV and ∼33 MeV. A generalized method that fully accounts for the dependence of ionization production on background atmospheric conditions, electron energy, and pitch angle has been developed based on the parameterization method of Fang et al. (2010, https://doi.org/10.1029/2010GL045406). Moreover, we validate this method using 100 random atmospheric profiles and precipitation fluxes with monoenergetic and exponential energy distributions, and isotropic and sine pitch angle distributions. In a suite of 6,100 validation tests, the error in peak ionization altitude is found to be within 1 km in 91% of all the tests with a mean error of 2.7% in peak ionization rate and 1.9% in total ionization. This method therefore provides a reliable means to convert space‐measured precipitation energy and pitch angle distributions into ionization inputs for atmospheric chemistry models.

Broad-band study of high-synchrotron-peaked BL Lac object 1ES 1218+304

ABSTRACT The origin of the multiwavelength emission from the high-synchrotron-peaked BL Lac 1ES 1218+304 is studied using the data from SwiftUVOT/XRT, NuSTAR, and Fermi-LAT. A detailed temporal and spectral analysis of the data observed during 2008–2020 in the γ-ray (>100 MeV), X-ray (0.3–70 keV), and optical/UV bands is performed. The γ-ray spectrum is hard with a photon index of 1.71 ± 0.02 above 100 MeV. The SwiftUVOT/XRT data show a flux increase in the UV/optical and X-ray bands; the highest 0.3–3 keV X-ray flux was (1.13 ± 0.02) × 10−10 erg cm−2 s−1. In the 0.3–10 keV range, the averaged X-ray photon index is >2.0 which softens to 2.56 ± 0.028 in the 3–50 keV band. However, in some periods, the X-ray photon index became extremely hard (<1.8), indicating that the peak of the synchrotron component was above 1 keV, and so 1ES 1218+304 behaved like an extreme synchrotron BL Lac. The hardest X-ray photon index of 1ES 1218+304 was 1.60 ± 0.05 on MJD 58489. The time-averaged multiwavelength spectral energy distribution is modelled within a one-zone synchrotron self-Compton leptonic model using a broken power law and power law with an exponential cutoff electron energy distributions. The data are well explained when the electron energy distribution is $E_{\rm e}^{-2.1}$ extending up to γbr/cut ≃ (1.7 − 4.3) × 105, and the magnetic field is weak (B ∼ 1.5 × 10−2 G). By solving the kinetic equation for electron evolution in the emitting region, the obtained electron energy distributions are discussed considering particle injection, cooling, and escape.

Charge carrier injection and transport in QLED layer with dynamic equilibrium of trapping/de-trapping carriers

A theoretical analysis on carrier injection and transport through layers of quantum dot light emitting display (QLED) device was attempted assuming dynamic equilibrium of trapping and detrapping charge carriers. Assuming traps in exponential or Gaussian energy distribution, the effect of parameters on the current-voltage relationship for the device was investigated. The energy level and distribution of charge traps, a Schottky barrier, and the ratio of detrapping rate constant to the trapping rate constant were found to affect the current-voltage relationship significantly in the charge transport layer. The results suggest that the parameters must be modulated simultaneously in order to achieve a charge balance in the quantum dot layer of the QLED device.

Ударное и "задержанное" повреждение поверхности керамики ZnS-CVD

Impact and impeded damage of ZnS-CVD ceramics surface I.P. Shcherbakov, A.A. Dunaev, A.B. Sinani, A.E. Chmel Localized damage of the surface of ductile ZnS ceramics synthesized by the chemical vapor deposition (CVD) method was performed by either impact of a pointed striker or by the impeded indenting of a Vickers pyramid. In both cases, the time series of acoustic emission pulses were recorded. The duration of the impact-induced sound emission was of 0.3-0.5 ms, while the indenting-produced active phase of emission was of 3-5 ms in length. The primary emission followed by the irradiation of weak acoustic signals during 80-100 ms. The statistical analysis of the time series showed the exponential (poissonian) energy distribution in impact-induced pulses, while in indented specimens, the distribution function followed a power law of the Gutenberg-Richter type. Considering that dislocation clusters serve as weak points for the crack nucleation, the difference in the mode of energy yield was explained by varying temporal pattern characteristics of the strain-stimulated dislocation motion in different time domains.

Statistical Regularities of Formation of a Main Crack in a Structurally Inhomogeneous Material under Various Deformation Conditions

The peculiarities of the formation of a main crack in the Westerly granite samples under quasistatic uniaxial compression without any lateral upthrust have been studied using the data of acoustic emission (AE) and X-ray computer microtomography (CT). The multifractal analysis of pauses between acoustic emission events and the analysis of the energy distribution functional forms of the AE signal have been performed. According to the computer tomography data, defects form only near a future main crack; i.e., no stage of disperse accumulation of defects over entire sample volume has been revealed. Two stages of the main crack formation have been observed: the first stage is characterized by an exponential energy distribution of AE signals and the second stage is characterized by a power low of the AE signal energy distribution. The multifractal analysis of the pauses between neighboring AE signals demonstrate the transition from the multifractal dynamics of the acoustic emission to the monofractal dynamics when approaching a fracture moment.

Статистические закономерности формирования магистральной трещины в структурно-неоднородном материале при различных условиях деформирования

AbstractThe peculiarities of the formation of a main crack in the Westerly granite samples under quasistatic uniaxial compression without any lateral upthrust have been studied using the data of acoustic emission (AE) and X-ray computer microtomography (CT). The multifractal analysis of pauses between acoustic emission events and the analysis of the energy distribution functional forms of the AE signal have been performed. According to the computer tomography data, defects form only near a future main crack; i.e., no stage of disperse accumulation of defects over entire sample volume has been revealed. Two stages of the main crack formation have been observed: the first stage is characterized by an exponential energy distribution of AE signals and the second stage is characterized by a power low of the AE signal energy distribution. The multifractal analysis of the pauses between neighboring AE signals demonstrate the transition from the multifractal dynamics of the acoustic emission to the monofractal dynamics when approaching a fracture moment.

Effect of the state of internal boundaries on granite fracture nature under quasi-static compression

Based on an analysis of the spatial distribution of hypocenters of acoustic emission signal sources and an analysis of the energy distributions of acoustic emission signals, the effect of the liquid phase and a weak electric field on the spatiotemporal nature of granite sample fracture is studied. Experiments on uniaxial compression of granite samples of natural moisture showed that the damage accumulation process is twostage: disperse accumulation of damages is followed by localized accumulation of damages in the formed macrofracture nucleus region. In energy distributions of acoustic emission signals, this transition is accompanied by a change in the distribution shape from exponential to power-law. Granite water saturation qualitatively changes the damage accumulation nature: the process is delocalized until macrofracture with the exponential energy distribution of acoustic emission signals. An exposure to a weak electric field results in a selective change in the damage accumulation nature in the sample volume.

A fractal process of hydrogen diffusion in a-Si:H with exponential energy distribution

Hydrogen diffusion in a-Si:H with exponential distribution of the states in energy exhibits the fractal structure. It is shown that a probability [Formula: see text] of the pausing time [Formula: see text] has a form of [Formula: see text] ([Formula: see text]: fractal dimension). It is shown that the fractal dimension [Formula: see text]/[Formula: see text] ([Formula: see text]: hydrogen temperature, [Formula: see text]: a temperature corresponding to the width of exponential distribution of the states in energy) is in agreement with the Hausdorff dimension. A fractal graph for the case of [Formula: see text] is like the Cantor set. A fractal graph for the case of [Formula: see text] is like the Koch curves. At [Formula: see text], hydrogen migration exhibits Brownian motion. Hydrogen diffusion in a-Si:H should be the fractal process.

Laser-driven micro-Coulomb charge movement and energy conversion to relativistic electrons

Development of robust instrumentation has shown evidence for a multi-μC expulsion of relativistic electrons from a sub-μm-thick foil, laser illuminated with 60–70 J on target at 2 × 1020 W/cm2. From previous work and with electron spectroscopy, it is seen that an exponential electron energy distribution is accurate enough to calculate the emitted electron charge and energy content. The 5–10-μC charge for the >100-TW Trident Laser represents the first active measurement of the >50% laser-light-to-electron conversion efficiency. By shorting out the TV/m electric field usually associated with accelerating multi-MeV ions from such targets, one finds that this charge is representative of a multi-MA current of relativistic electrons for diverse applications from electron fast ignition to advanced radiography concepts. Included with the details of the discoveries of this research, shortcomings of the diagnostics and means of improving their fidelity are discussed.

The Meyer–Neldel Rule in Conduction Mechanism of the Electrospun ZnO Nanofibers

An analytical model describing the conductivity of ZnO nanofibers depending on the grains size is proposed. The research is based on the thermal dc electrical measurements of a single electrospun ZnO nanofiber calcined at different temperatures. In the our previous research, we showed that electrical conduction of ZnO nanofibers is mainly thermally activated. The activation energy of conductivity was strongly dependent on the grain size, which in turn depended on the calcination temperature. This could be due to migration of a point defect in the grain of ZnO and could change the carrier concentration. Our recent studies have shown that ZnO nanofibers behavior is consistent with the Meyer–Neldel rule. This indicates an exponential energy distribution of deep level traps in the material. Based on the theoretical assumptions and experimental data, the improved model of conductivity in a single ZnO nanofiber calcined at different temperatures was proposed.

Universality of charge-carrier transport in molecularly doped polymers

The charge-carrier transport model based on the multiple-trapping quasi-band theory with the Gaussian or exponential energy distributions of traps for the two-layer structure of the molecularly doped polymer sample is used to explain the experimentally observed constancy of the flat plateau on time-of-flight curves in a wide electric-field range. The constant shape of the time-of-flight curve under the condition of nonequilibrium transport is observed for the exponential, rather than Gaussian, energy trap distribution. This observation may be used to distinguish between these trap distributions. Finding the true Poole–Frenkel constant requires that the nonequilibrium transport in molecularly doped polymers be taken into account during treatment of the data on the field dependence of mobility.

Determination of active oxide trap density and 1/f noise mechanism in RESURF LDMOS transistors

The physical origin of majority charge carrier fluctuations in the SiO2 interface of Si at accumulation has been investigated and analyzed for differently processed and voltage-rated reduced surface field (RESURF), lateral-double-diffused MOS (LDMOS) transistors. Surface carrier mobility fluctuation due to remote Coulomb scattering by the trapped charge in the gate oxide is identified as the dominant physical mechanism for LDMOS 1/f noise irrespective of process technologies. A significant contribution to the measured noise has been noted from the surface majority carrier mobility fluctuation due to trapped charge at the accumulation region of the extended drain region, dominant over other sources including the surface minority charge carrier fluctuations in the channel. Active oxide trap density was characterized spatially and for the first time up to ∼0.4eV above the conduction band-edge of Si. The interface trap density in the unstressed devices (∼8×106cm−2) increased more than an order of magnitude (∼1×108cm−2) after the devices were stressed for 10,000sec at their individual worst drain current and on-resistance degradation conditions. The extracted Si/SiO2 interface trap density above the silicon conduction band edge was found to be several orders of magnitude lower than that reported for silicon mid-gap energies, even after stressing. Since the traps near the quasi-Fermi level for electrons are active in trapping–detrapping, and the Fermi level is energetically positioned above the conduction band edge of Si in the investigated devices as compared to the previously reported observations, the lower trap density obtained here is an indication for reversal of the well-known exponential trap energy distribution beyond the conduction band-edge of Si. These findings shift the focus from the channel to the gate overlap section of the extended drain and the quality of the Si/SiO2 interface in that region.

Diffusion coefficient using pausing time of hydrogen in a-Si:H with exponential energy distribution

The diffusion coefficient of hydrogen is obtained for exponential energy distribution in hydrogenated amorphous silicon (a-Si:H). It is shown that the diffusion coefficient follows the form of τα-1 (τ: diffusion time) in the case of α < 1 and a larger τ, in which α is the ratio of hydrogen temperature to width for energy distribution function. In the case of α ≥ 1, as α reaches infinity at the limit, the hydrogen diffusion approaches Brownian motion.

Numerical modeling of the polarization current of geminate pairs in disordered polymers with traps

The time dependences of the polarization current of geminate pairs in disordered media are simulated by the Monte Carlo numerical method. A model of hopping transport with exponential energy distribution of the hopping centers is considered. The dependence of the polarization-current kinetics on the initial geminate-pair separation, the relative concentration of traps, the temperature, and the strength of the applied electric field is investigated. The limits of the applicability of an analytical theory based on the driftdiffusion description of electron and hole motion of the geminate pair in the dispersive-transport mode are discussed. The range of parameters is determined in which the existence of the negative current is possible.

Advanced percolation solution for hopping conductivity

Hopping of carriers between localized states dominates charge transport in amorphous organic and inorganic semiconductors. We suggest a comprehensive description of this transport regime based on the percolation approach that allows one to determine not only very pronounced exponential dependencies of the hopping conductivity on material parameters, but also the more weakly dependent pre-exponential factors. The problem of the variable-range hopping (VRH) via sites with exponential energy distribution is mapped onto a universal geometrical problem of percolation via spheres with distributed sizes. An exact solution of the latter problem provides accurate results for the VRH in systems with exponential density-of-states (DOS). Our analytical results are confirmed by straightforward computer simulations and compared to former results present in the literature. We also discuss the case of nearest-neighbor hopping on a lattice, where the pre-exponential factors are provided by the percolation approach for any shape of the DOS.

Analysis of the experiment on registration of X-rays from the stepped leader of a cloud-to-ground lightning discharge

[1] Using a Monte Carlo technique to simulate the transport of runaway electrons (REs) and X-rays in the atmosphere and through attenuators covering detectors, we have modeled the results of experiments to detect X-rays from triggered lightning and stepped leaders of a natural cloud-to-ground lightning. In the model, bremsstrahlung of high-energy runaway electrons (REs) generated at the leader front is assumed to be the origin of X-rays. Specific fluxes (per one RE) of photons and bremsstrahlung energy at the detectors were calculated. The analysis was executed with monoenergetic and exponential initial energy distributions of REs with different angular distributions. To reproduce the detected radiation energy of ~1–2 MeV, a generation of ~1010–1011 REs per flash is required in the case with the beam angular distribution of monoenergetic REs with the energy in the range 1–10 MeV. The same result was obtained with the exponential energy distribution of REs with the average energy 7 MeV, i.e., with the average energy in the RE avalanche. The electric field amplifies the flux of the radiation energy, and the amplification becoming stronger as the RE source approaches the ground. In the case with an isotropic angular distribution of REs in the bottom hemisphere, with no electric field, (4–5) × 109 REs are required for reproducing ~1–2 MeV of detected X-ray energy. In addition, fluxes of photons and fluxes of their energy at the detectors, energy distributions of photons and their average energy were calculated.