non-Maxwellian Energy Distribution Research Articles

Enhancement of fusion reactivities using non-Maxwellian energy distributions.

We discuss conditions for the enhancement of fusion reactivities arising from different choices of energy distribution functions for the reactants. The key element for potential gains in fusion reactivity is identified in the functional dependence of the tunneling coefficient on the energy, ensuring the existence of a finite range of temperatures for which reactivity of fusion processes is boosted with respect to the Maxwellian case. This is shown using a convenient parametrization of the tunneling coefficient dependence on the energy, analytically in the simplified case of a bimodal Maxwell-Boltzmann distribution, and numerically for kappa distributions. We then consider tunneling potentials progressively better approximating fusion processes and evaluate in each case the average reactivity in the case of kappa distributions.

Maxwellian and non-Maxwellian rate coefficients of the tungsten ions: W46+–W55+

This study focuses on the significance of suprathermal (‘hot’) electrons in the tokamak device. Hot electrons, which follow a non-Maxwellian energy distribution, are high-energy electrons that exert a substantial influence on various processes taking place within the plasma. Our aim was to investigate the influence of non-Maxwellian distribution on the rate coefficients of highly charged tungsten ions. This paper presents Maxwellian and non-Maxwellian electron impact ionization rate coefficients for W46+ to W55+ ions. The cross sections were calculated using the fully relativistic flexible atomic code with level-to-level distorted-wave method. We found that even for a small fraction of hot electrons, the contribution of hot electrons to the rate coefficients is still dominant at low bulk temperature.

Discussion on the transport processes in electrons with non-Maxwellian energy distribution function in partially-ionized plasmas

In a previous work (Alvarez Laguna et al 2022 Phys. Plasmas 29 083507), we have developed a non-linear moment model for electrons that self-consistently captures non-Maxwellian electron energy distribution function effects. The model does not rely in the local approximation and the transport coefficients are calculated by expanding the distribution function into Hermite polynomials and by taking moments of the Boltzmann equation, including the collision operator for elastic and inelastic collisions with arbitrary cross sections. This model captures the classical Fick’s, Fourier’s, and Ohm’s law as well as Soret, Dufour, and Peltier effects. In addition, novel non-local transport phenomena appear as a result of spatial gradients of the kurtosis of the distribution function. In this paper, we discuss on the transport effects by analyzing two collisional models: constant collision frequency and constant cross section. We estimate the order of magnitude of the transport processes in non-equilibrium electrons by analyzing the Langmuir probe measurements of a low-pressure argon inductively-coupled discharge. The results show that, under these conditions, the transport produced by the spatial gradients in the kurtosis of the distribution function produces a heat-flux contribution that is of the same order of magnitude as the Fourier and Dufour’s effects. These transport effects are beyond the local field or the electron gradient expansions, commonly used in the low-temperature plasma modeling.

The Influence of Hot Electrons on the Calculation of Ionization Rates

Electron-Impact Ionization (EII) is considered one of the most important ionization methods in dynamic systems, in which elements and ions are suddenly exposed to energetic electrons. In many plasma types, it has been observed that some electrons (hot) are governed by a non-Maxwellian energy distribution. This study illustrates the effects of a non-Maxwellian distribution on beryllium and Be+2 emission lines and their effective ionization rate coefficients. The focus on beryllium as an impacted material by electron flux aimed to evaluate the EII rates for Be and generate the corresponding datasets needed for Be+2 data analysis. An interaction cross-section was generated using the Flexible Atomic Code (FAC) and used in the estimation of the EII distribution energy functions to estimate the ionization rates for a non-Maxwellian distribution. The use of non-Maxwellian energy distributions for different fractions of hot electrons showed the sensitivity of these rates to the fraction of hot electrons and the forms of the electron energy distribution. The results were in good agreement with those found in the literature.

Generation of energetic ions with non-Maxwellian energy distribution from a double-layer target irradiated by an ultra-intense laser pulse

Generation of energetic ions with non-Maxwellian energy distribution from a double-layer target irradiated by an ultra-intense laser pulse

On the calculation of superstatistics ionization rates of neutral Hélium

Electron-impact ionization (EII) can be important in dynamic systems where atoms are suddenly exposed to higher electron temperatures. EII can also have a significant effect on the charge state distribution for plasmas with a non-thermal electron energy distribution. In this paper, we present the effects of hot electrons on the calculation of ionization rates for neutral Helium using superstatistics. We also exchange the distribution function with the effective Boltzmann factor of superstatistics. The ionization rates of neutral Helium are obtained from cross sections obtained by FAC code, are weighted by a non-maxwellian distribution function. The results are compared to those reported by Kato. et. al. We note that non-maxwellian energy distribution for different fractions of hot electrons showed the effects of these rates on the fractions of hot electrons and the forms of ionization rates.

Calculation of ionization rates of Beryllium ions (Be2+) using the superstatistics distributions

Electron-impact ionization (EII) can be important in dynamic systems where ions are suddenly exposed to higher electron temperatures. EII can also have a significant effect on the charge state distribution for plasmas with a non-thermal electron energy distribution. In this paper, we present the effects of hot electrons on the calculation of ionization rates for Be2+ using the superstatistics, and we also exchange the distribution function with the effective Boltzmann factor of superstatistics. The ionization rates of Be2+ generate from cross sections obtained by FAC code, weighted by a non–Maxwellian distribution function. We note that non-Maxwellian energy distribution for different fractions of hot electrons showed the effects of these rates on the fractions of hot electrons and the forms of ionization rates.

Estimation of Electron Impact Ionization Rates of Li Using a Non-Maxwellian Distribution Function

We report an estimate of the cross-section and rate of electron-impact ionization of Li. The FAC code (Flexible Atomic Code) is used in order to determine the cross-section and to calculate the level of energy. We evaluate the effect of electron energy distribution functions on the measurement of the ionization rate for a non-Maxwellian energy distribution, if the fraction of hot electrons is small. In several types of plasma, it has been observed that certain (hot) electrons are governed by a non-Maxwellian energy distribution. These electrons affect the line spectra and other characteristics of plasma. By using a non-Maxwellian distribution of energies, we revealed the sensitivity of the electron-impact ionization rate of Li to types of the electron energy distribution and to the fraction of hot electrons.

Numerical Modeling of Non-equilibrium Plasma Discharge of Hydrogenated Silicon Nitride (SiH4/NH3/H2)

In this work, we model a radiofrequency discharge of hydrogenated silicon nitride in a capacitive coupled plasma reactor using Maxwellian and non-Maxwellian electron energy distribution function. The purpose is to investigate whether there is a real advantage and a significant contribution using non-Maxwellian electron energy distribution function rather than Maxwellian one for determining the fundamental characteristics of a radiofrequency plasma discharge. The results show the evolution of the non-Maxwellian electron energy distribution function, the mobility and the diffusion coefficient required to determine the fundamental characteristics of the radiofrequency plasma discharge of a hydrogenated silicon nitride deposit at low pressure and low temperature, between the two electrodes of the capacitive coupled plasma reactor. By comparing these results using non-Maxwellian electron energy distribution function with those calculated using the Maxwellian one, we conclude that the use of non-Maxwellian electronic energy distribution function is more efficient for describing the evolution of a radiofrequency plasma discharge in a capacitive reactor, which will improve the quality of the deposition of thin films.

Kinetic neoclassical transport in the H-mode pedestal

Multi-species kinetic neoclassical transport through the QH-mode pedestal and scrape-off layer on DIII-D is calculated using XGC0, a 5D full-f particle-in-cell drift-kinetic solver with self-consistent neutral recycling and sheath potentials. Quantitative agreement between the flux-driven simulation and the experimental electron density, impurity density, and orthogonal measurements of impurity temperature and flow profiles is achieved by adding random-walk particle diffusion to the guiding-center drift motion. The radial electric field (Er) that maintains ambipolar transport across flux surfaces and to the wall is computed self-consistently on closed and open magnetic field lines and is in excellent agreement with experiment. The Er inside the separatrix is the unique solution that balances the outward flux of thermal tail deuterium ions against the outward neoclassical electron flux and inward pinch of impurity and colder deuterium ions. Particle transport in the pedestal is primarily due to anomalous transport, while the ion heat and momentum transport are primarily due to the neoclassical transport. The full-f treatment quantifies the non-Maxwellian energy distributions that describe a number of experimental observations in low-collisionallity pedestals on DIII-D, including intrinsic co-Ip parallel flows in the pedestal, ion temperature anisotropy, and large impurity temperatures in the scrape-off layer.

Effect of superbanana diffusion on fusion reactivity in stellarators

Fusion reactivity is usually obtained using a Maxwellian distribution. However, energy-dependent radial diffusion can modify the energy distribution. Superbanana diffusion is energy-dependent and occurs in nonaxisymmetric magnetic confinement devices, such as stellarators, because of ripple-trapped particles which can take large steps between collisions. In this paper, the D-T fusion reactivity is calculated using a non-Maxwellian energy distribution obtained by solving the Fokker-Planck equation numerically, including radial superbanana diffusion as well as energy scattering. The ions in the tail of the distribution, with energies larger than thermal, which are most needed for fusion, are depleted by superbanana diffusion. In this paper, it is shown that the D-T fusion reactivity is reduced by tail ion depletion due to superbanana diffusion, by roughly a factor of 0.5 for the parameters used in the calculation.

Charge storage and electron/light emission properties of silicon nanocrystals

Monodispersed silicon nanocrystals show novel electrical and optical characteristics of silicon quantum dots, such as single-electron tunneling, ballistic electron transport, visible photoluminescence and high-efficiency electron emission. Single-electron memory effects have been studied using a short-channel MOSFET incorporating Si quantum dots as a floating gate. Surface nitridation of Si nanocrystal memory nodes extends the charge-retention time significantly. Single-electron storage in individual Si dots has been evaluated by Kelvin probe force microscopy. Photoluminescence and electron emission are observed for surface-oxidized silicon nanocrystals. Efficiency of the no-phonon-assisted transition increases with decreasing core Si size. Electron emission efficiency as high as 5% has been achieved for the Si-nanocrystal-based cold electron emitter devices. The non-Maxwellian energy distribution of emitted electrons suggests that the mechanism of electron emission is due to ballistic transport through arrays of surface-oxidized Si nanocrystals. Combined with the ballistic electron emission, the quasi-direct light emission properties can be used for developing Si-based lasers.

Prethermalization, non-extensive statistics and hydrodynamics

We argue that the success of hydrodynamic description does not necessarily imply realization of the local thermodynamical equilibrium in relativistic heavy ion reactions. A simple and general argument shows that a class of dynamical correlations give rise to the so-called Tsallis non-extensive statistics for which the usual thermodynamical relations are valid. An example of a system having such a dynamics is given, exhibiting a non-Maxwellian energy distribution.

Energy transport gate current model accounting for non-Maxwellian energy distribution

A new formulation to describe hot-electron tunnelling through dielectrics is presented. It is based on an expression for the electron energy distribution function which is characterised by its first three even moments. The model is simplified to make it applicable for energy-transport simulations, yielding a modified supply function in Tsu-Esaki's equation. Simulations show excellent agreement with Monte Carlo results.

Analysis of the oxygen nightglow measured by the Hopkins Ultraviolet Telescope: Implications for ionospheric partial radiative recombination rate coefficients

The Hopkins Ultraviolet Telescope (HUT) recorded nighttime ultraviolet O+ spectra in the tropical ionosphere during the December 1990 Astro 1 space shuttle mission. We reexamine the HUT 911‐Å radiative recombination continuum spectra and the relative 911‐Å and 1356‐Å intensities in order to address questions raised in a previous study. First, we find that the radiative recombination of O+ to the ground state of O accounts for nearly all of the continuum emission. The need for a second component beyond the ionization threshold is eliminated by allowing for an instrumental wavelength shift. Second, we find that certain low‐count spectral features in some of the data are not due to a non‐Maxwellian energy distribution because of the fast electron thermalization in the nighttime F region. Instead, we show that these features are consistent with random fluctuations alone. Third, the best known O+ – O− mutual neutralization chemistry gives good agreement between theoretical and measured 1356/911 ratios, thereby demonstrating the consistency among the various determinations of the O− photodetachment cross section. We update the 911‐Å radiative recombination rate coefficient using recent photoionization cross section information, and the 1356‐Å rate coefficient by fitting HUT 1356/911 ratio data. The derived rate coefficient agrees very closely with our interpretation of independent 7774‐Å data. Both the three‐parameter fit to the 911‐Å radiative recombination continuum and the updated 911 and 1356‐Å radiative recombination rate coefficients improve the agreement between the model and measured 1356/911 ratios. The updated radiative recombination rate coefficients are 3.5 × 10−13 cm3 s−1 for 911‐Å, and 7.3 × 10−13 cm3 s−1 for 1356‐Å, both at 1160 K.

Electron beam effects on the spectroscopy of multiply charged ions in plasma focus experiments

Argon–hydrogen mixture plasma focus experiments performed at the Warsaw Institute of Plasma Physics and Laser Microfusion show detailed space resolved spectra for Ar K-shell satellite lines up to F-like Ar and K-alpha of Ar. These transitions originating from autoionizing levels are caused by collisions of ions with the energetic electron beams which are created by the constrictions of the plasma column due to the development of magnetohydrodynamic instabilities. A collisional-radiative model was constructed using a non-Maxwellian eletron energy distribution consisting of a thermal Maxwellian part plus a Gaussian part to represent the high-energy electron beam. The shapes of the observed satellite structures are consistent with the calculated spectrum for electron temperatures between 20 and 230 eV, and beam densities of about 10 -3 times the plasma electron density.

Spectroscopic signature of non-Maxwellian and nonstationary effects in plasmas heated by intense, ultrashort laser pulses.

The interaction of an intense (${10}^{16}$ W/${\mathrm{cm}}^{2}$), ultrashort (400 fs) 1.06 \ensuremath{\mu}m laser pulse normally incident on an aluminum preformed plasma was simulated with an electron kinetic code. Postprocessing with a detailed atomic model predicted the resulting K-shell x-ray spectrum. Both the very rapid time variation and the non-Maxwellian energy distribution (due to the steep gradients, energetic electrons stream from the hot into the cold plasma and enhance the excitation of Li-like satellite there) greatly modify the line ratios, even without any addition of hot electrons.

Nonequilibrium exciton kinetics in Cu2O

We have observed the energy distribution of nonthermalized excitons in the semiconductor Cu2O on a time scale of 10 ps following near-resonant creation by a short (5ps) laser pulse. We see a non-Maxwellian energy distribution with four discrenible hot-luminescence peaks at early times due to emission of both acoustic and optic phonons, which had previously been identified as multi-phonon Raman scattering lines. We fit the energy distribution of the excitons at all times by numerically integrating an exact Boltzmann equation. From this we deduce the deformation potential for acoustic phonon emission, which agrees with the results of hydrostatic-stress and uniaxial-stress measurements, and we deduce the rate for single optic phonon emission, which turns out to be rather slow, about 30 ps.

Simulation of EPROM programming characteristics

An efficient method for the simulation of EPROM programming, based on hydrodynamic calculations of electron energy within the device, is described. After the nonMaxwellian energy distribution is calculated, an expression for injected gate current is integrated to find the total gate charge, and hence the threshold voltage shift, as a function of time. Comparison of theoretical and experimental results for actual EPROM programming validates this method.

Charge exchange neutral sputtering in ASDEX

Neutral fluxes to the wall of ASDEX were measured with a new energy-resolving carbon resistance probe, CRP, combined with a mechanical shutter, providing time resolution. With the new CRP having two silicon overlayers of different thickness the non-Maxwellian energy distribution of the charge exchange neutrals can be approximately determined. Using the flux and the mean energy of the particles from the resistance probe measurements, one can calculate the flux of impurities generated by sputtering. Various discharges were investigated. High impurity fluxes were observed in discharges with high power auxiliary heating. Low impurity fluxes were observed in pellet-refuelled discharges and during neutral beam heating in counter direction and H-mode discharges refuelled with pellets, Charge exchange neutral sputtering is an important impurity source representing a lower limit for impurity generation.