Maxwellian Electron Distribution Research Articles

Non-Maxwellian electron distributions in time-dependent simulations of low-Z materials illuminated by a high-intensity X-ray laser

The interaction of high intensity X-ray lasers with matter is modeled. A collisional-radiative time-dependent module is implemented to study radiation transport in matter from ultrashort and ultraintense X-ray bursts. Inverse bremsstrahlung absorption by free electrons, electron conduction or hydrodynamic effects are not considered. The collisional-radiative system is coupled with the electron distribution evolution treated with a Fokker-Planck approach with additional inelastic terms. The model includes spontaneous emission, resonant photoabsorption, collisional excitation and de-excitation, radiative recombination, photoionization, collisional ionization, three-body recombination, autoionization and dielectronic capture. It is found that for high densities, but still below solid, collisions play an important role and thermalization times are not short enough to ensure a thermal electron distribution. At these densities Maxwellian and non-Maxwellian electron distribution models yield substantial differences in collisional rates, modifying the atomic population dynamics.

Plasma expansion into vacuum assuming a steplike electron energy distribution

The expansion of a semi-infinite plasma slab into vacuum is analyzed with a hydrodynamic model implying a steplike electron energy distribution function. Analytic expressions for the maximum ion energy and the related ion distribution function are derived and compared with one-dimensional numerical simulations. The choice of the specific non-Maxwellian initial electron energy distribution automatically ensures the conservation of the total energy of the system. The estimated ion energies may differ by an order of magnitude from the values obtained with an adiabatic expansion model supposing a Maxwellian electron distribution. Furthermore, good agreement with data from experiments using laser pulses of ultrashort durations τ(L)</~80fs is found, while this is not the case when a hot Maxwellian electron distribution is assumed.

The incomplete plasma dispersion function: Properties and application to waves in bounded plasmas

The incomplete plasma dispersion function is a generalization of the plasma dispersion function in which the defining integral spans a semi-infinite, rather than infinite, domain. It is useful for describing the linear dielectric response and wave dispersion in non-Maxwellian plasmas when the distribution functions can be approximated as Maxwellian over finite, or semi-infinite, intervals in velocity phase-space. A ubiquitous example is the depleted Maxwellian electron distribution found near boundary sheaths or double layers, where the passing interval can be modeled as Maxwellian with a lower temperature than the trapped interval. The depleted Maxwellian is used as an example to demonstrate the utility of using the incomplete plasma dispersion function for calculating modifications to wave dispersion relations.

Low intensity dust ion-acoustic shock waves due to dust charge fluctuation in a nonextensive dusty plasma

The properties of low intensity dust ion acoustic shock waves are studied in a charge varying dusty plasma with nonextensive electrons. Owing to the departure from the Maxwellian electron distribution to a nonextensive one, the modified electrostatic charging of a spherical dust particle in plasma with ion streaming speed is considered. Based on the weakly nonlinear analysis, a new relationship between the low intensity localized disturbances and nonextensive electrons is derived. It is found that both strength and steepness of shock structures arise as the electrons evolve far from their thermodynamic equilibrium in such plasma with parameter ranges corresponding to Saturn’s rings. It is also shown that the ion temperature and population of electrons reduce the possibility of the formation of the shock profile.

Equilibrium theory of cylindrical discharges with special application to helicons

Radiofrequency discharges used in industry often have centrally peaked plasma density profiles n(r) although ionization is localized at the edge, even in the presence of a dc magnetic field. This can be explained with a simple cylindrical model in one dimension as long as the short-circuit effect at the endplates causes a Maxwellian electron distribution. Surprisingly, a universal profile can be obtained, which is self-similar for all discharges with uniform electron temperature Te and neutral density nn. When all collisions and ionizations are radially accounted for, the ion drift velocity toward the wall reaches the Bohm velocity at a radius which can be identified with the sheath edge, thus obviating a pre-sheath calculation. For non-uniform Te and nn, the profiles change slightly but are always peaked on axis. For helicon discharges, iteration with the HELIC code for antenna-wave coupling yields profiles consistent with both energy deposition and diffusion profiles. Calculated density is in absolute-value agreement with experiment.

Dust-ion-acoustic solitary waves in dusty plasma with arbitrarily charged dust and vortex-like electron distribution

The nonlinear propagation of dust-ion-acoustic (DIA) waves in a dusty plasma containing trapped electrons following vortex-like distribution, cold mobile ions, and arbitrarily charged static dust is theoretically investigated. The properties of small but finite amplitude DIA solitary waves (SWs) are studied by employing the reductive perturbation technique. It is found that owing to the departure from the Maxwellian electron distribution to a vortex-like one, the dynamics of such DIA SWs is governed by a modified Korteweg-de Vries equation. The basic features (amplitude, width, speed, etc.) of such DIA SWs, which are found to be significantly modified by the vortex-like electron distribution and dust polarity, are also examined. The implications of our results to space and laboratory dusty plasmas are briefly discussed.

Diagnostics of theκ-distribution using Si III lines in the solar transition region

Aims. The solar transition region satisfies the conditions for appearance of the non-thermal κ-distribution. We aim to prove the occurrence of the non-thermal κ-distribution in the solar transition region and diagnose its parameters. Methods. The intensity ratios of Si iii lines observed by SUMER in 1100‐1320 A region do not correspond to the line ratios computed under the assumption of the Maxwellian electron distribution. We computed a set of synthetic Si iii spectra for the electron κ-distributions with different values of the parameter κ. We had to include the radiation field in our calculations to explain the observed line ratios. We propose diagnostics of the parameter κ and other plasma parameters and analyze the effect of the different gradient of differential emission measures (DEM) on the presented calculations. Results. The used line ratios are sensitive to T, density and the parameter κ. All these parameters were determined from the SUMER observations for the coronal hole (CH), quiet Sun (QS) and active region (AR) using our proposed diagnostics. A strong gradient of DEM influences the diagnosed parameters of plasma. The essential contributions to the total line intensities do not correspond to single T but a wider range of T, and they originate in different atmospheric layers. The amount of the contributions from these atmospheric layers depends on the gradient of DEM and the shape of the electron distribution function. Conclusions. The κ-distribution is able to explain the observed Si iii line spectrum in the transition region. The degree of nonthermality increases with the activity of the solar region, it is lower for CH and higher for the AR. The DEM influences the diagnosed T and Ne but it has only little effect on the diagnostics of the parameter κ.

Modelling of Kα X‐Ray Yield From a Foil Under the Vacuum Heating of Hot Electrons by a Femtosecond Laser Pulse

AbstractEnhancement of characteristic x‐ray yield from a metal foil, coated with spherical clusters, irradiated by a p ‐polarized Gaussian femtosecond laser beam, is investigated depending on the cluster size, laser pulse intensity and the foil thickness. Simulations were carried out both for the hot electrons, accelerated in accordance with the Brunel model of vacuum heating, and for corresponding Maxwellian distribution of hot electrons. Existence of an interval of cluster sizes with respect to the laser wavelength, in which the number of emitted photons from the foil with clustered surface exceeds one from the polished foil, and increase of Kα yield with growth of the laser field angle of incidence is most pronounced, is shown (© 2011 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Electrostatic solitary waves in the presence of excess superthermal electrons: modulational instability and envelope soliton modes

The nonlinear dynamics of electrostatic solitary waves in the form of localized modulated wavepackets is investigated from first principles. Electron-acoustic (EA) excitations are considered in a two-electron plasma, via a fluid formulation. The plasma, assumed to be collisionless and uniform (unmagnetized), is composed of two types of electrons (inertial cold electrons and inertialess kappa-distributed superthermal electrons) and stationary ions. By making use of a multiscale perturbation technique, a nonlinear Schrödinger equation is derived for the modulated envelope, relying on which the occurrence of modulational instability (MI) is investigated in detail. Stationary profile localized EA excitations may exist, in the form of bright solitons (envelope pulses) or dark envelopes (voids). The presence of superthermal electrons modifies the conditions for MI to occur, as well as the associated threshold and growth rate. The concentration of superthermal electrons (i.e., the deviation from a Maxwellian electron distribution) may control or even suppress MI. Furthermore, superthermality affects the characteristics of solitary envelope structures, both qualitatively (supporting one or the other type, for different κ) and quantitatively, changing their characteristics (width, amplitude). The stability of bright and dark-type nonlinear structures is confirmed by numerical simulations.

He-like Ions as Practical Astrophysical Plasma Diagnostics: From Stellar Coronae to Active Galactic Nuclei

We review X-ray plasma diagnostics based on the line ratios of He-like ions. Triplet/singlet line intensities can be used to determine electronic temperature and density, and were first developed for the study of the solar corona. Since the launches of the X-ray satellites Chandra and XMM-Newton, these diagnostics have been extended and used (from C v to Si xiii) for a wide variety of astrophysical plasmas such as stellar coronae, supernova remnants, solar system objects, active galactic nuclei, and X-ray binaries. Moreover, the intensities of He-like ions can be used to determine the ionization process(es) at work, as well as the distance between the X-ray plasma and the UV emission source for example in hot stars. In the near future thanks to the next generation of X-ray satellites (e.g., Astro-H and IXO), higher-Z He-like lines (e.g., iron) will be resolved, allowing plasmas with higher temperatures and densities to be probed. Moreover, the so-called satellite lines that are formed closed to parent He-like lines, will provide additional valuable diagnostics to determine electronic temperature, ionic fraction, departure from ionization equilibrium and/or from Maxwellian electron distribution.

Floating harmonics method for measuring electron temperature in non-Maxwellian plasmas

Electron temperatures obtained from the slope of the electron energy probability function (EEPF) at the floating potential were compared with those measured by the floating harmonics method in various electron distributions. Basically, these two types of the electron temperatures should be same in a Maxwellian electron distribution. As expected, discrepancies were observed between them in cases of non-Maxwellian distribution. In this study, the second and third harmonics of probe current were used to obtain the electron temperature in non-Maxwellian distribution. The experimental results were shown that the electron temperature obtained using this method was in good agreement with the electron temperature from the slope of the EEPF at floating potential, regardless of the electron distribution.

Double layer formation in a two-region electronegative plasma

The formation of a double layer (DL) in a two-dimensional (2D) electronegative plasma with a source (heating) section connected to a larger downstream section is described. A 2D particle-in-cell (PIC) code is used to exhibit the DL, which appears near the transition between the source and downstream chambers, over a range of pressures and electronegativities. Diagnostics of the PIC code allow the calculation of various plasma parameters, not easily measured in experiments, to be compared with an analytic theory. The theory consists of a collisionless one-dimensional model of a DL connected to 2D source and downstream global models. The conditions of positive and negative ion balance upstream and downstream, and the downstream energy balance determine the DL potential, electron temperatures, and other plasma parameters. A rescaled oxygen reaction set is used both for the simulation and for the analytic comparison. The PIC simulations exhibit a Maxwellian electron distribution in the source region at temper...

On the influence of high energy electron populations on metal abundance estimates in galaxy groups and clusters

<i>Aims. <i/>Spectral line emissivities have usually been calculated for a Maxwellian electron distribution. But many theoretical works on both galaxy groups and clusters and the solar corona consider modified Maxwellian electron distribution functions when fitting observed X-ray spectra. Here we examine the influence of high energy electron populations on measurements of metal abundances.<i>Methods. <i/>A generalized approach proposed by ourselves is used to calculate the line emissivities for a modified Maxwellian distribution. We study metal abundances in galaxy groups and clusters in which hard X-ray excess emission was observed. <i>Results. <i/>We found that for modified Maxwellian distributions the argon abundance decreases for the HCG 62 group, the iron abundance decreases for the Centaurus cluster, and the oxygen abundance decreases for the solar corona with respect to the case of a Maxwellian distribution. Therefore, metal abundance measurements are a promising tool for testing the presence of high energy electron populations.

Signatures of a Maxwellian component in shock-accelerated electrons in GRBs

Recent particle-in-cell simulations suggest that a large fraction of the energy dissipated in a relativistic shock is deposited into a Maxwellian distribution of electrons that is connected to the high-energy power-law tail. Here, we explore the observational implications of such a mixed thermal-nonthermal particle distribution for the afterglow and prompt emission of gamma-ray bursts. When the Maxwellian component dominates the energy budget, the afterglow lightcurves show a very steep decline phase followed by a more shallow decay when the characteristic synchrotron frequency crosses the observed band. The steep decay appears in the X-rays at ~100 sec after the burst and is accompanied by a characteristic hard-soft-hard spectral evolution that has been observed in a large number of early afterglows. If internal shocks produce a similar mixed electron distribution, a bump is expected at the synchrotron peak of the nu*f_nu spectrum.

EUV filter responses to plasma emission for the nonthermalκ-distributions

The responses to plasma emission of the TRACE EUV filters are computed by integrating their spectral responses over the synthetic spectra obtained from the CHIANTI database. The filter responses to emission are functions of temperature, electron density, and the assumed electron distribution function. It is shown here that, for the nonthermal κ-distributions, the resulting responses to emission are more broadly dependent on T , and their maxima are flatter than for the Maxwellian electron distribution. The positions of the maxima can also be shifted. Filter reponses to T are density-dependent as well. The influence of the nonthermal κ-distributions on the diagnostics of T from the observations in all three EUV filters is discussed.

Non-Maxwellian electron distributions in clusters of galaxies

<i>Context. <i/> Thermal X-ray spectra of clusters of galaxies and other sources are commonly calculated assuming Maxwellian electron distributions. There are situations where this approximation is not valid, for instance near interfaces of hot and cold gas and near shocks. <i>Aims. <i/> The presence of non-thermal electrons affects the X-ray spectrum. To study the role of these electrons in clusters and other environments, an efficient algorithm is needed to calculate the X-ray spectra. <i>Methods. <i/> We approximate an arbitrary electron distribution by the sum of Maxwellian components. The decomposition uses either a genetic algorithm or an analytical approximation. The X-ray spectrum is then evaluated with a linear combination of those Maxwellian components. <i>Results. <i/> Our method is fast and leads to an accurate evaluation of the spectrum. The Maxwellian components allow the use of the standard collisional rates that are available in plasma codes such as SPEX. We give an example of a spectrum for the supra-thermal electron distribution behind a shock in a cluster of galaxies. The relative intensities of the satellite lines in such a spectrum are sensitive to supra-thermal electrons. These lines can only be investigated with high spectral resolution. We show that the instruments on future missions like Astro-H and IXO will be able to demonstrate the presence or absence of these supra-thermal electrons.

The characteristics of ion acoustic solitons in non-Maxwellian plasmas

Ion acoustic solitons may be associated with the electrostatic solitary structures observed in the space plasma environment. Earlier models describing these solutions assume Maxwellian distribution for electrons imbedded in the fluid ions and predict enhanced density that have difficulty in explaining some of the observed features of depleted density associated with electrostatic solitons. Improved models incorporating nonthermal electrons are shown to be able to produce solitary structures with depleted density [R. A. Cairns et al., Geophys. Res. Lett. 22, 2709 (1995)]. In this paper general solutions of ion acoustic solitons are derived for which the electrons are modeled by the kappa distribution characterized by the κ parameter that has been found to well represent the particle distribution observed in space plasmas. It is shown that solitary structures with depleted density are unlikely to exist in non-Maxwellian plasmas with general κ distribution. Detailed comparisons are made of the solutions base...

An analysis of electron distributions in galaxy clusters by means of the flux ratio of iron lines FeXXV and XXVI

The interpretation of hard X-ray emission from galaxy clusters is still ambiguous and different models proposed can be probed using various observational methods. Here we explore a new method based on Fe line observations. Spectral line emissivities have usually been calculated for a Maxwellian electron distribution. In this paper a generalized approach to calculate the iron line flux for a modified Maxwellian distribution is considered. We have calculated the flux ratio of iron lines for the various possible populations of electrons that have been proposed to account for measurements of hard X-ray excess emission from the clusters A2199 and Coma. We found that the influence of the suprathermal electron population on the flux ratio is more prominent in low temperature clusters (as Abell 2199) than in high temperature clusters (as Coma).

Heating and Acceleration of Intracluster Medium Electrons by Turbulence

In this paper we investigate the feasibility of bremsstrahlung radiation from `nonthermal' electrons as a source of hard X-rays from the intracluster medium of clusters of galaxies. With an exact treatment of the Coulomb collisions in a Fokker-Planck analysis of the electron distribution we find that the severe difficulties with lifetimes of `nonthermal' particles found earlier by Petrosian (2001) using a cold target model remain problematic. We then address possible acceleration of background electrons into a nonthermal tail. We assume a simplified but generic acceleration rate and determine the expected evolution of an initially Maxwellian distribution of electrons. We find that strong nonthermal components arise only for rapid rate of acceleration which also heats up the entire plasma. These results confirm the conclusion that if the observed `nonthermal' excesses are due to some process accelerating the background thermal electrons this process must be short lived.

Electron impact collision strengths in Sn XXIII

The energy levels, multipole (E1, M1, E2, and M2) transition rates, and electron-impact collision strengths are calculated for Sn XXIII. The data refer to 107 fine-structure levels belonging to the configurations (1s 22s 22p 6)3s 23p 63d 10, 3s 23p 63d 94ℓ, 3s 23p 53d 104ℓ, and 3s3p 63d 104ℓ(ℓ = s, p, d, and f). The collision strengths are calculated with a 20-collision-energy grid in terms of the energy of the scattered electron between 37.5 and 8436 eV by using the distorted-wave approximation. Effective collision strengths are obtained at five electron temperatures, T e (eV) = 193.89, 387.78, 581.67, 775.57, and 969.46, by integrating the collision strengths over a Maxwellian electron distribution.