Small amplitude ion-acoustic double layers with cold electron beam and q-nonextensive electrons

Small amplitude ion-acoustic double layers in an unmagnetized and collisionless plasma consisting of cold positive ions, q-nonextensive electrons, and a cold electron beam are investigated. Small amplitude double layer solution is obtained by expanding the Sagdeev potential truncated method. The effects of entropic index q, speed and density of cold electron beam on double layer structures are discussed.     

Nonlinear structures for extended Korteweg–de Vries equation in multicomponent plasma

Using the fluid hydrodynamic equations of positive and negative ions, as well as q-nonextensive electron density distribution, an extended Korteweg–de Vries (EKdV) equation describing a small but finite amplitude dust ion-acoustic waves (DIAWs) is derived. Extended homogeneous balance method is used to obtain a new class of solutions of the EKdV equation. The effects of different physical parameters on the propagating nonlinear structures and their relevance to particle acceleration in space plasma are reported.     

Ion-acoustic solitary waves in e-p-i plasmas with (r,q)-distributed electrons and kappa-distributed positrons

In this paper, we have studied the propagation of non-linear ion-acoustic waves in a plasma comprising of (r, q) -distributed electrons and kappa-distributed positrons. We have investigated the effect of complete electron distribution profile on the propagation of small, as well as arbitrary, amplitude solitons (via pseudopotential technique) by using generalized (r, q) distribution, which exhibits a spiky and flat top nature at low energies and a super-thermal tail at high energies. Interestingly, for negative values of r , solitons are formed with both polarities, positive (compressive) and negative (rarefactive), separately within a small amplitude limit and exist simultaneously in an arbitrary amplitude limit. We also found that the propagation of solitons has been affected by the change in parameters r , q , positron concentration, and electron to positron temperature ratio. The results presented in this study add to the fundamental understanding of the complete profile of the electron distribution function, high- and low-energy parts, and in the formation of compressive and rarefactive small and finite amplitude solitons in both space and astrophysical plasmas.     

Solar wind driven electrostatic instabilities with generalized (r,q) distribution function

Using Boltzmann–Vlasov kinetic model, a currentless ion acoustic instability driven by stream of solar wind plasma is studied in a non‐thermal distributed electrons and ions. The non‐thermal distribution considered here is the generalized distribution which has low energetic flat‐top and velocity power law tail at higher energies. The instability threshold is found to be affected and depends upon the spectral indices r and q . It is found that the growth rate increases with the decrease in the value of r and increase with q . Moreover, such kinetic instability has also been discussed for three species electron–ion–dust plasma using the generalized (r, q) distribution function. Such case is of interest when the solar wind is streaming through the cometary plasma in the presence of interstellar dust and excites electrostatic instabilities. The dispersion properties and growth rates for ion‐acoustic and dust‐acoustic mode are calculated analytically and plotted for different values of the spectral indices r and q .     

Effect of non‐extensivity parameter q on the damping rate of dust ion acoustic waves in non‐extensive dusty plasma

Kinetic theory has been applied to study the damping characteristics of dust ion acoustic waves (DIAWs) in a dusty plasma comprising q‐non‐extensive distributed electrons and ions, while the dust particles are considered extensive following the Maxwellian velocity distribution function. It is found that the results of the three‐dimensional velocity distribution function are more accurate compared to the results of the one‐dimensional velocity distribution function. The numerical solution of the dispersion relation is carried out to study the effect of the non‐extensivity parameter q on the dispersion, the damping rate, and the range of the values of the normalized wavenumber ( k λ_D) for which the DIAWs are weakly damped. It is found that the change in the value of the electron non‐extensivity parameter q_e has a minor effect on the dispersion, the damping rate, and the range of the values of the normalized wavenumber ( k λ_D) for which the DIAWs are weakly damped, while on the other hand, ion non‐extensivity parameter q_i has a strong effect on these arguments. The effect of other parameters, such as the ratio of electron to ion number density and ratio of electron to ion temperature, on the damping characteristics of DIAWs is also highlighted.     

Effect of nonextensivity on the characteristics of supersolitons in a two-temperature electron plasma

Ion-acoustic supersolitons are investigated in an unmagnetized two-temperature electron plasma comprising cold fluid ions, hot nonextensive electrons, and cool Maxwellian electrons by using the Sagdeev pseudopotential technique. Existence domain of positive polarity supersolitons in terms of Mach number is computed, which is found to exist for Mach numbers beyond the existence of positive double layers. The domain of existence of supersolitons diminishes with the decrease of the nonextensive parameter (q ). The amplitude and width of the supersolitons are dependent on the cool-to-hot electron temperature ratio (τ ), cool electron density (f ), and nonextensive parameter (q ). The increase of cool electron density increases the amplitude of the supersolitons. For fixed values of f , q _, and Mach numbers, the decrease of τ exhibits more distinct wiggles in the electric fields of supersolitons. The present work may be helpful for further study of supersolitons in the auroral plasma.     

Calculation of the inverse bremsstrahlung absorption in unmagnetized plasmas

Inverse bremsstrahlung is one important way to deliver laser energy to the plasma in inertial confinement fusion. In this article, we study the collisional absorption rate as obtained from the Fokker–Planck treatment of an unmagnetized plasma in harmonic laser field. The electron–ion collision rate is considered in the Krook approximation, and the electron distribution function is considered a Maxwellian function. We evaluate the inverse bremsstrahlung absorption near the irradiated plasma surface in the critical layer. We observe that absorption increases with shorter laser wavelength and lower electron temperatures. When the maximum electron velocity in the limit of q → 1 reaches infinity, the q-non-extensive distribution function reduces to the standard Maxwell-Boltzmann distribution.     

Determination of the profile of energy release from a high-power electron beam in an aerogel

Optical methods are used to investigate the dynamics of the interaction of a high-current electron beam with an aerogel (a highly porous transparent dielectric with a low density ρ=0.36 g/cm³). The measured profile of the glow of the aerogel and the pattern of its expansion are compared with the results of a numerical simulation. The influence of the space charge on the profile of the energy absorption from the high-current relativistic electron beam is discussed. Zh. Tekh. Fiz. 67, 26–32 (November 1997)     

Variable‐size dust grains with generalized (r,q) electrons in a dusty plasma

The effect of the generalized (r, q) distribution on the non‐linear propagation of dust acoustic waves (DAWs) in a dusty plasma consisting of variable‐size dust grains is discussed. A Korteweg–de Vries (KdV) equation is derived using the reductive perturbation technique (RPT). The dust size obeys the power‐law dust size distribution (DSD). The present results reveal that rarefactive and compressive waves can propagate in the proposed plasma model. It is found that the spectral indices r and q influence the main properties of DAWs. Especially, the velocity, amplitude, and width of the DAW change drastically with r compared to changes in q.     

Two-dimensional drift solitary structures in inhomogeneous magnetized O?H ion plasmas with generalized (r,q) distributed electrons

In this paper, the effect of generalized (r, q) distributed electrons on the linear and nonlinear coupling of drift and ion acoustic waves in a nonuniform plasma containing Hydrogen and Oxygen ions is investigated. In the linear regime, it is observed that increasing the percentage of flat-topped (i.e. r > 0) electrons enhances the frequency of the coupled drift-ion acoustic waves, whereas the increasing values of the spectral index q mitigates it. In the nonlinear regime, one- and two-dimensional Korteweg de Vries-like and Kadomtsev-Petviashvili-like equations are derived and their solutions are plotted for different ratios of ion number densities and for different values of double spectral indices r and q of the generalized distribution of electrons. It is found that only rarefactive structures exist for two-dimensional solitons, however, both rarefactive and compressive structures are observed for the one-dimensional case. The limiting cases of kappa and Maxwellian distributions are also discussed and their comparison with the generalized (r, q) distribution is thoroughly investigated. Spatial scales for the formation of rarefactive and compressive solitary structures are also discussed with reference to the changing electron distribution functions. The possible applications of the present study are also spelled out with special reference to space plasmas.     

Cross sections of Oq+（q=1-4） electron loss in collisions with He,Ne and Ar

Electron-loss cross sections of O q+(q = 1 4) colliding with He,Ne and Ar atoms are measured in the intermediate velocity regime.The ratios of the cross sections of two-electron loss to that of one-electron loss R 21 are presented.It is shown that single-channel analysis is not sufficient to explain the results,but that projectile electron loss,electron capture by the projectile and target ionization must be considered together to interpret the experimental data.The screening and antiscreening effects can account for the threshold velocity results,but cannot explain the dependence of the ratio R 21 on velocity quantitatively.In general,the effective charge of the target atom increases with velocity increasing because the high-speed projectile ion can penetrate into the inner electronic shell of target atom.Ne and Ar atoms have similar effective charges in this velocity regime,but He atoms have smaller ones at the same velocities due to its smaller nuclear charge.     

Landau damping of longitudinal oscillation in ultra- relativistic plasmas with nonextensive distribution

The generalized dispersion equation for longitudinal oscillation in an unmagnetized, collisionless, isotropic and relativistic plasma is derived in the context of nonextensive q-distribution. An analytical expression for the Landau damping is obtained in an ultra-relativistic regime, which is related to q-parameter. In the limit q → 1, the result based on the relativistic Maxwellian distribution is recovered. It is shown that the interactions between the wave and particles are stronger and the waves are more strongly damped for lower values of q-parameter. The results are explained by the increased number of superthermal particles or low velocity particles contained in the plasma with the nonextensive distribution.     

Vibrational Feshbach resonances in electron attachment to carbon dioxide clusters

Using a high resolution ( meV) laser photoelectron attachment method, we have studied the formation of (CO ₂) _q ⁻ ions (q = 4−22) in collisions of low energy electrons (1−180 meV) with (CO₂) _N () clusters. The previously reported “zero energy resonance”, observed at much larger electron bandwidths, actually consists of several narrow vibrational Feshbach resonances of the type [(CO ₂) _{N −1}CO which involve a vibrationally-excited molecular constituent ( denotes vibrational mode) and a diffuse electron weakly bound to the cluster by long range forces. The resonances occur at energies below those of the vibrational excitation energies of the neutral clusters [(CO ₂) _{N −1}CO ]; the redshift rises with increasing cluster ion size q by about 12 meV per unit; these findings are recovered by a simple model calculation for the size dependent binding energies. The size distribution in the cluster anion mass spectrum, resulting from attachment of very slow electrons, mainly reflects the amount of overlap of solvation-shifted vibrational resonances with zero energy; the cluster anion size q is identical with or close to that of the attaching neutral cluster. Received 11 January 2000 and Received in final form 10 April 2000     

Single electron capture in collisions of N^q＋ （q = 5, 6, 7） ions with helium

Close-coupling calculations are carried out for cross sections of the single electron capture in collisions of N^q+ (q = 5, 6, 7) ions with helium atoms in the collision velocity range from 0.3 a.u. to 1.8 a.u. The relative importances of the single ionization (SI) to the single capture (SC) are investigated for the N^q+ (q = 5, 6, 7) projectiles, respectively. The SI/SC cross section ratio for the N⁷⁺ projectile obtained from our calculations is in excellent agreement with the experimental data. The ratio curves also show us distinct behaviours when the charge of the projectile is different. The partial electron capture cross sections for different projectiles indicate that the electron on the target He atom tends to be captured by the projectile into its lower orbital of the outer shell with the decreasing projectile charge.     

Towards information theory for q-nonextensive statistics without q-deformed distributions

In this paper we extend our recent results [P. Jizba, T. Arimitsu Physica A 340 (2004) 110] on q-nonextensive statistics with non-Tsallis entropies. In particular, we combine an axiomatics of Rényi with the q-deformed version of Khinchin axioms to obtain the entropy which accounts both for systems with embedded self-similarity and q-nonextensivity. We find that this entropy can be uniquely solved in terms of a one-parameter family of information measures. The corresponding entropy maximizer is expressible via a special function known under the name of the Lambert W-function. We analyze the corresponding “high” and “low-temperature” asymptotics and make some remarks on the possible applications.     

Quantization in generalized coordinates III-Lagrangian formulation

It is shown that if one incorporates the generalized coordinate quantum velocitiesQ ¹ as given byQ ¹=l[H,Q ¹](h=1) into the generalized classical Lagrangian for a free particle (the total energy),L=1/2Q ¹ g _tk Q ^k one does not obtain (no matter what ordering of the operatorsq ^l ,q ^k andg _lkwe choose the correct quantum Lagrangian operator which is a transformation from -1/2V² to generalized coordinates (Gruber, 1971, 1972).q ^l as given byq ^l=i[H,q ^l] turns out to be the Hermitian part of a more generaiized operator which we call the total generalized velocity operator similar to the notation in ear previous articles (Gruber, 1971, 1972). This total velocity operator really determines the fundamental structure governing our system in the Lagrangian formulation. We show that ft is through the total velocity operator that we make the transition from classical to quantum mechanics and through our procedure we arrive at the correct quantum Lagrangian operator.     

Modulation of ion sound excitations in electron–ion plasmas with double spectral index distribution function

Theoretical investigation of amplitude modulation of ion sound waves is presented here for an electron–ion plasma where the electrons are dictated by the double spectral index (r, q) distribution function. Using the standard reductive perturbative technique, a non-linear Schrödinger (NLS) equation is derived that describes the evolution of modulated ion sound envelope excitations. Stability analysis of the NLS equation shows that the ion sound waves remain stable for the flat-topped and kappa-like distributions, but they can become unstable for the spiky electron velocity distribution. It is shown that changing the electron population in regions of low and high phase space density regions results in remarkable features that have no equivalent in ion sound waves with Boltzmannian electrons. Different types of localized ion sound excitations are plotted for the different shapes of the distribution functions controlled by the double spectral indices, and the underlying physics is discussed in detail. The present investigation may be beneficial to understand ion sound excitations in space plasmas where the distribution functions of the shapes presented here are frequently encountered by the satellite missions.     

Radiative transfer in the lyman α spectral line with self-consistent electron velocity distribution

Radiative transfer in the Ly α spectral line in a stationary, plane-parallel plasma of constant temperature and electron density is studied using model H-atoms with only two bound levels and a continuum. For this purpose, the equation of radiative transfer is solved simultaneously with the steady-state equations of the atomic levels and the kinetic equation of the electrons. The numerical results indicate that, in hydrogen plasmas with temperatures T ? 12,000°K and electron densities n_e ? 10¹⁶cm^?3, the high-energy tail of the electron velocity distribution deviates from a Maxwell distribution, even in cases of rather large optical thicknesses and that therefore the deviations from local thermodynamic equilibrium are increased compared with estimates based on the assumption of a Maxwellian electron velocity distribution. This qualitative conclusion should hold in spite of some deficiencies of the model which are discussed.     

Phenomenological representation of correlations in an electron gas

An expression of the form (a₁q² + a₂q⁴ + a₃q⁶)/(1 + b₂q⁴ + b₃q⁶) for the function G(q) describing exchange and correlation effects in an electron gas is considered. The dependence of the coefficients on the electron density is estimated from known theoretical results.