Dielectric Function Method Research Articles

Stopping power of high-density alpha-particle clusters in partially degenerated deuterium–tritium fuels

The state of burning plasma had been achieved in inertial confinement fusion (ICF), which was regarded as a great milestone for high-gain laser fusion energy. In the burning plasma, alpha particles incident on the cryogenic (warm dense) fuels cannot be simply regarded as single particles, and the new physics brought about by the density effects of alpha particles should be considered. In this work, the collective interaction between them has been considered, namely, the effect of the superposition of wake waves. The stopping power of alpha-particle clusters, i.e., the rate of energy loss per unit distance traveled has been calculated using both analytical and simulation approaches. In theory, we obtain the stopping power of alpha clusters in cryogenic (warm dense) fuel by the dielectric function method, which illustrates the importance of the effective interaction between particles. Simulation results using the LAPINS code show that the collective stopping power of the alpha cluster is indeed increased via coherent superposition of excitation fields (the excitation of high-amplitude wake waves). However, the comparison between simulation and theoretical results also illustrates a coherent–decoherent transition of the stopping power of the cluster. The initial conditions with various sizes and densities of the alpha clusters have been considered to verify the condition of decoherence transition. Our work provides a theoretical description of the transport properties of high-density alpha particles in warm dense cryogenic fuel and might give some theoretical guidance for the design of actual fusion processes.

Calculation of thermodynamic properties of hot dense plasma based on generalized Hulthen potential

In the dielectric response function method, the equation of state and thermodynamic properties of plasma can be calculated by defining the effective potential. In this method, it is necessary to determine the extent of its effect on plasma with the help of a suitable primary potential, and then the effective potential is determined by applying these effects. In this paper, for the first time, the Hulthen potential is used as the primary potential in describing hot dense plasma by the dielectric response function method. For this reason, to find a suitable relation between the screening parameters of Hulthen potential, De, and the Debye shielding parameter, μD, a comparison is made between the two potentials Hulthen and Debye. With this comparison, the parameter De is known and specified for each specific value of the coupling (Γ) and density (rs) parameters. The Hulthen potential with the specified screening parameter using the dielectric response function method is used to achieve the effective interaction potential for hot dense plasma. In the following, the equation of different states of fully ionized plasma is defined using the effective potential and the analytical calculation of the internal energy of the plasma particles is determined. Finally, the thermodynamic properties of hot dense plasma such as; free energy, pressure, specific heat, entropy, and enthalpy energy of the plasma system are calculated analytically.

Calculation of effective potential of Hulthen interaction for a nonideal dense plasma using dielectric response method

The interactions of hot dense plasma particles are calculated using the dielectric response method. The key element in this method is a function called the dielectric response function, which depends on the use of the proper external potential. This external potential provides the basis for deriving the dielectric function that leads to the effective potential of the plasma particles. In this paper, the well-known Hulthen potential is used to describe non-ideal plasmas. For this purpose, a comparison between Hulthen and Debye potentials is performed to find the relation between the Hulthen potential screening parameter,Dh, and the Debye shielding parameter, μD. As a result of this comparison, parameter Dh is specified for each specific value of the Coupling, Γ, and Density, rs, parameters. Then, to obtain the effective interaction potential, the Hulthen potential function with a specific screening parameter is used in the dielectric response function method with the help of Coulomb potential. In this work, in order to increase the effective potential flexibility, a relation is created between screening and shielding parameters. Finally, the results are compared with a number of experimental and theoretical works.

TM Standing Wave Solution of Maxwell Equations in a Self-Defocusing Kerr Media and its Application to a Thin-Film Waveguide

We applied the dielectric function method to solve analytically L-NL-L structure problems with negative Kerr nonlinearity. A damped wave in linear and a periodic standing wave in non-linear media had to be matched at boundaries. We gave a formulation of boundary conditions that did not explicitly include a film thickness. The boundary-value of a dielectric function can be expressed through the constant of non-trivial integral of motion. Using it, one generates a family of matched solutions satisfying boundary conditions. Then arbitrary film thickness can be checked against this family of solutions in search of matches. As a result, all fitted solutions are determined straightforwardly.

Plasmonic Cooper pairing in single layer graphene

The dielectric function method (DFM), which uses a non-adiabatic approach to calculate the critical temperatures for superconductivity, has been quite successful in describing superconductors at low carrier densities. This regime of carrier densities causes other theories, such as BCS and Migdal-Eliashberg theory, to violate their assumption of a small Debye window. We investigate the application of DFM to the linear dispersion of single layer graphene. We derive the gap equation of DFM for a Dirac cone and calculate the critical temperature as a function of carrier density. This is done using an interaction potential that utilizes the Random Phase Approximation dielectric function and thus allows for plasmonic interactions. Our results show a significantly different behaviour of the critical temperature as a function of carrier density when compared to the BCS result. Thus, we find the DFM approach to be better suited when considering graphene systems at low carrier densities.

Superconductivity in SrTiO3: Dielectric Function Method for Non-Parabolic Bands

The dielectric function method for superconductivity has been applied to SrTiO$_{3}$ accounting for the non-parabolic dispersion of charge carriers in the conduction band and for the dispersion of optical phonons based on density functional theory calculations. The obtained critical temperatures of the superconducting phase transition in SrTiO$_{3}$ are in agreement with experiments in the density range $n\sim5\times10^{18}$ to $5\times10^{20}$ cm$^{-3}$. The dielectric function method predicts also the sign of the anomalous isotope effect in strontium titanate, in line with recent observations.

THERMODYNAMIC PROPERTIES OF PARTIALLY IONIZED HYDROGEN PLASMA

This paper considers dense partially ionized hydrogen plasma. The model of interaction between particles was used to study properties of plasma. Interaction potentials were obtained through the dielectric response function method. Effective potentials, taking into account the screening effects at large distances and the quantum-mechanical diffraction effect at small distances, were used to model the interaction between particles. Another effective screening potential was chosen to describe the charge interaction with neutral atoms. This potential takes into account the interaction between free charge and atomic nucleus with centrally symmetric distribution of the electron density. The degree of ionization was calculated through solving the system of Saha equations. Pair correlation functions were studied in the exponential approximation. Thermodynamic properties for hydrogen plasma were calculated using the effective potentials and obtained on their base pair correlation functions. Internal energy and equation of state of partially ionized hydrogen plasma were compared with the results from previous research. The results indicated that the difference observed with high values of parameters was due to increase in the concentration of atoms.

DNA strand breaks induced by electrons simulated with Nanodosimetry Monte Carlo Simulation Code: NASIC.

The method of Monte Carlo simulation is a powerful tool to investigate the details of radiation biological damage at the molecular level. In this paper, a Monte Carlo code called NASIC (Nanodosimetry Monte Carlo Simulation Code) was developed. It includes physical module, pre-chemical module, chemical module, geometric module and DNA damage module. The physical module can simulate physical tracks of low-energy electrons in the liquid water event-by-event. More than one set of inelastic cross sections were calculated by applying the dielectric function method of Emfietzoglou's optical-data treatments, with different optical data sets and dispersion models. In the pre-chemical module, the ionised and excited water molecules undergo dissociation processes. In the chemical module, the produced radiolytic chemical species diffuse and react. In the geometric module, an atomic model of 46 chromatin fibres in a spherical nucleus of human lymphocyte was established. In the DNA damage module, the direct damages induced by the energy depositions of the electrons and the indirect damages induced by the radiolytic chemical species were calculated. The parameters should be adjusted to make the simulation results be agreed with the experimental results. In this paper, the influence study of the inelastic cross sections and vibrational excitation reaction on the parameters and the DNA strand break yields were studied. Further work of NASIC is underway.

Interaction potentials and thermodynamic properties of two component semiclassical plasma

In this paper, the effective interaction potential in two component semiclassical plasma, taking into account the long-range screening and the quantum-mechanical diffraction effects at short distances, is obtained on the basis of dielectric response function method. The structural properties of the semiclassical plasma are considered. The thermodynamic characteristics (the internal energy and the equation of state) are calculated using two methods: the method of effective potentials and the method of micropotentials with screening effect taken into account by the Ornstein-Zernike equation in the HNC approximation.

Comparison of direct DNA strand breaks induced by low energy electrons with different inelastic cross sections

In order to study the influence of inelastic cross sections on the simulation of direct DNA strand breaks induced by low energy electrons, six different sets of inelastic cross section data were calculated and loaded into the Geant4-DNA code to calculate the DNA strand break yields under the same conditions. The six sets of the inelastic cross sections were calculated by applying the dielectric function method of Emfietzoglou’s optical-data treatments, with two different optical datasets and three different dispersion models, using the same Born corrections. Results show that the inelastic cross sections have a notable influence on the direct DNA strand break yields. The yields simulated with the inelastic cross sections based on Hayashi’s optical data are greater than those based on Heller’s optical data. The discrepancies are about 30–45% for the single strand break yields and 45–80% for the double strand break yields. Among the yields simulated with cross sections of the three different dispersion models, generally the greatest are those of the extended-Drude dispersion model, the second are those of the extended-oscillator-Drude dispersion model, and the last are those of the Ashley’s δ-oscillator dispersion model. For the single strand break yields, the differences between the first two are very little and the differences between the last two are about 6–57%. For the double strand break yields, the biggest difference between the first two can be about 90% and the differences between the last two are about 17–70%.

Evaluation of thermal radiation dependent performance of GaSb thermophotovoltaic cell based on an analytical absorption coefficient model

Applying the model dielectric function method, we have expressed the absorption coefficient of GaSb analytically at room temperature relating to the contribution of various critical points of its electronic band structure. The calculated absorption spectrum shows good agreement with the reported experimental data obtained by spectral ellipsometry on nominally undoped sample. Based on this analytical absorption spectrum, we have qualitatively evaluated the response of active absorbing layer structure and its photoelectric conversion properties of GaSb thermophotovoltaic device on the perturbation of external thermal radiation induced by the varying radiator temperature or emissivity. Our calculation has demonstrated that desirable thickness to achieve the maximum conversion efficiency should be decreased with the increment of radiator temperature and the performance degradation brought by any structure deviation from its optimal one would be stronger meanwhile. For the popular radiator temperature, no more than 1500 K in a real solar thermophotovoltaic system, and typical doping profile in GaSb cell, a reasonable absorbing layer structure parameter should be controlled within 100–300 nm for the emitter while 3000–5000 nm for the base.

Effective potentials for ion-ion and charge-atom interactions of dense semiclassical plasma

Using the dielectric function method, the effective interaction potential between ions in a dense semiclassical plasma is investigated. For the case of a partially ionized strongly coupled plasma, the effective potential of charge-unperturbed atom interaction is presented. Both effective potentials are screened. To obtain these potentials the dielectric function is used, taking into account the quantum diffraction effects in electron-electron interactions.

Effective polarization interaction potential “charge-atom” for partially ionized dense plasma

The pseudopotentials of particle interaction, taking into account quantum-mechanical effects of diffraction at short distances and also screening effects at large distances, are obtained for a partially ionized plasma. The dielectric function method was used.

Energy Loss of Slow H- to Be-Like Ions in Electron Gas

The electronic stopping power and the energy loss straggling of low velocity H-. He-, Li- and Be-like ions in the degenerate electron gas were calculated. The Hartree-Fock-Slater description of the ion and the dielectric function method were used. The stopping and straggling effective charges Z eff of an ion were analysed. They are found to differ with each other and to depend on the electron gas density r s , on the ion atomic number Z i and on N i , the number of electrons carried by the ion.

Energy loss of slow single-centre projectiles in electron gas

Calculations of the electronic energy loss and the straggling of the energy loss for slow single-centre projectiles in the degenerate electron gas are reported. The Hartree-Fock-Slater description of the projectile (few bound electrons) and the density function formalism (many electrons) together with the dielectric function method are used. The stopping and straggling effective charges for the energy loss are analysed and found to differ from each other and to depend on the one-electron radius , on the projectile atomic number and on the number of electrons carried by the projectile. Results of calculations are compared with available experimental data and a good agreement is found.

Stopping of Slow Projectiles in Electron Gas

New analytical formulas for the electronic stopping power and the energy loss straggling of low velocity extended charge projectiles in the degenerate electron gas are calculated within the dielectric function method. The stopping and straggling effective charges Z eff of a projectile were analysed. They are found to differ one from the other and to depend on the electron gas density r s , on the projectile atomic number Z l and on the projectile degree of ionization ζ. For small Z i , due to antiscreening Z eff > 1.

Energy loss of partially stripped ions in pre-equilibrium frozen charge states

The inelastic energy loss of swift single-atom hydrogenlike, heliumlike, and lithiumlike ions, and hydrogen-molecule ions is investigated under charge state pre-equilibrium conditions. During their passage, those charge states are assumed to be frozen. The stopping-power values and the effective charges calculated on the basis of the dielectric function method, the wave-packet method, and the recently derived analytical formula, are compared with existing experimental data.

Density effects of heavy-ion stopping power in high temperature matter

Abstract The stopping power and range for Xe ions in high temperature matter (partially ionized plasmas) have been calculated using the dielectric response function method. Calculations have been made for a target matter Al (Z = 13) over a wide range of temperatures and densities considering a finite temperature model. The stopping powers obtained have smaller values in comparison with those of a zero temperature model. The stopping power strongly depends on the density and temperature of the target material, and the projectile ion energy.

Energy distribution of secondary electrons emitted from solid surfaces under electron bombardment: I. Theory

A dielectric-function method has been presented for the energy distribution of secondary electrons (SE's) emitted from metal surfaces. The quantities appearing in our theory are the energy-dependent inelastic mean free path λ(E), the stopping power S(E) for excited electrons inside, and the internal SE energy distribution per unit primary path, d2ndE0dz. It is found that di from a classical pure Coulomb treatment, the quantity d2ndE0dz does not diverge at the Fermi level, due to the dynamical screening effect. Dealing with the problem of surface transmission in a quantum-mechanical way, the energy distribution of emitted SE's is calculated and compared with the result using a classical particle-transmission.

Energy loss and straggling of low-velocity heavy atoms in matter

Based on the dielectric-function method, we have investigated the energy loss and straggling of heavy atoms with atomic number ${\mathit{Z}}_{1}$ passing through the degenerate electron gas at low velocities. The size parameter \ensuremath{\Lambda} of the electron cloud on the projectile is newly determined according to the statistical variational method by taking into account the static screening effect of conduction electrons. The analytical formulas obtained here have ${\mathit{Z}}_{1}$ dependences different from those of existing theories in spite of the same velocity dependence. It is found that the screening effect on \ensuremath{\Lambda} enlarges the electronic stopping of the media by a constant value regardless of ${\mathit{Z}}_{1}$. Numerical results show agreement with the trends of the available data.