Κ-distributed Electrons Research Articles

Ion temperature gradient mode and its solitons with regularized κ-distributed electrons

The linear and the non-linear behaviors of the ion temperature gradient (ITG) mode in a plasma with regularized κ-distributed electrons are investigated using the fluid model. The dispersion relation of the ITG mode obtained on the basis of the local approximation shows that the growth rate of the ITG mode decreases with the increase in the spectral index κ and the exponential cut-off parameter α. It indicates that the presence of the superthermal electron leads to destabilization of the ITG mode, especially in the low κ (κ < 1.5) region. In addition, the existence and the nature of the soliton structure driven by the ITG are studied using the pseudopotential technology. The soliton amplitude increases with the increase in the exponential cut-off parameter α and the spectral index κ, whereas the width of the soliton varies inversely. The present results will help to understand the low-frequency electrostatic wave and nonlinear structure in space and experimental plasmas with non-thermal electrons.

The Ultraviolet C ii Lines as a Diagnostic of κ-distributed Electrons in Planetary Nebulae

Non-Maxwellian κ electron energy distributions (EEDs) have been proposed in recent years to resolve the so-called “electron temperature and abundance discrepancy problem” in the study of planetary nebulae (PNs). Thus the need to develop diagnostic tools to determine from observations the EED of PNs is raised. Arising from high-energy levels, the ultraviolet (UV) emission lines from PNs present intensities that depend sensitively on the high-energy tail of the EED. In this work, we investigate the feasibility of using the C ii]λ2326/C ii λ1335 intensity ratios as a diagnostic of the deviation of the EED from the Maxwellian distribution (as represented by the κ index). We use a Maxwellian decomposition approach to derive the theoretical κ-EED-based collisionally excited coefficients of C ii, and then compute the C ii UV intensity ratio as a function of the κ index. We analyze the archival spectra acquired by the International Ultraviolet Explorer and measure the intensities of C ii UV lines from 12 PNs. By comparing the observed line ratios and the theoretical predictions, we can infer their κ values. With the Maxwellian-EED hypothesis, the observed C ii]λ2326/C ii λ1335 ratios are found to be generally lower than those predicted from the observed optical spectra. This discrepancy can be explained in terms of the κ EED. Our results show that the κ values inferred range from 15 to infinity, suggesting a mild or modest deviation from the Maxwellian distribution. However, the κ-distributed electrons are unlikely to exist throughout the whole nebulae. A toy model shows that if just about 1%–5% of the free electrons in a PN had a κ EED as small as κ = 3, it would be sufficient to account for the observations.

Transcritical bifurcation of nonlinear electrostatic waves in a superthermal dusty plasma

The phase portraits and bifurcation properties of nonlinear dust ion-acoustic waves are studied in a complex plasma comprising cold dust particles, warm adiabatic ions, and κ-distributed electrons. A characteristic equation is obtained and solved numerically. The existence domain of fixed points and the stability of traveling wave solutions are discussed in the parameter space of Mach number M and dust concentration δ over a wide range of values of κ and ion temperature σ. It is shown that the motion dynamics of homoclinic orbits and nonlinear periodic orbits undergo a transcritical bifurcation at critical points of and , where two fixed points coalesce, and then switch their stabilities. We observe that at these bifurcation values with half-stable fixed points, the system supports a new analytical solitary wave solutions with much fatter tails than regular solitons. Furthermore, the existence domain of transcritical bifurcation parameters and transition between solitary and nonlinear periodic waves has been determined for different values of M and δ. It is found that the Mach number broadens the region prior to the bifurcation point, and enhances the onset of transition between modes, while the dust concentration has an opposite influence.

Small amplitude ion-acoustic solitons with regularized κ-distributed electrons

A theoretical investigation of ion-acoustic solitons in an unmagnetized plasma consisting of cold ions and regularized κ-distributed electrons has been carried out. The properties of stationary solitary structures are briefly studied by the reductive perturbation method in the small amplitude limit. It is found that in the small κ region, the ion-acoustic solitary waves propagate more slowly in the case of regularized κ distribution than in the case of standard κ distribution. The regularized κ-distributed electrons affect the width and amplitude of the solitary waves. As the cutoff parameter α increases, the amplitudes of both the compressive and rarefactive solitary waves decrease, and their widths also decrease. In addition, for a given value of κ, positive potential solitons will appear at large α, while negative potential solitons will appear at small α. The results of this paper may be useful for understanding nonlinear electrostatic phenomena in space plasmas.

Modulational instability of dust-ion-acoustic waves and associated first and second-order rogue waves in a super-thermal plasma

A proper theoretical research has been carried out to explore the modulational instability (MI) conditions of dust-ion-acoustic (DIA) waves (DIAWs) in a three-component dusty plasma system containing inertialess κ-distributed electrons, and inertial warm positive ions and negative dust grains. The nonlinear Schrödinger equation (NLSE) has been derived by employing the reductive perturbation method. The numerical analysis under consideration demonstrates two types of modes, namely, fast and slow DIA modes. The MI conditions of DIAWs and the configuration of the energetic rogue waves (RWs) associated with DIAWs in the modulationally unstable parametric regime have been rigorously changed by the variation of various plasma parameters, namely, charge, mass, temperature, and number density of the plasma species. The findings of our present investigation will be useful in understanding the criteria for the formation of electrostatic RWs in both astrophysical environments (viz., Jupiter’s magnetosphere, cometary tails, pulsar magneto-sphere, interstellar medium, Earth’s mesosphere, Saturn’s rings, etc.) and laboratory experiments.

Dust-Ion-Acoustic waves in unmagnetized 4-component plasma

A theoretical study is presented for the propagation of Dust Ion Acoustic Waves in an unmagnetized four-component plasma, consisting of Maxwellian negative ions, cold mobile positive ions, κ-distributed electrons and positively charged dust grains. Based on the characteristics of Sagdeev pseudopotential and phase portraits, three types of nonlinear waves are observed – solitons, double layers and supersolitons. The conditions for the existence of such nonlinear waves are highly sensitive to the plasma parameters. The results obtained in this study may be of wide relevance in the field of space plasma as well as ultrasmall semiconductor devices in the laboratory.

Soliton turbulence in electronegative plasma due to head-on collision of multi solitons

Abstract Head-on interaction of four dust ion acoustic (DIA) solitons and the statistical properties of the wave field due to head-on interaction of solitons moving in opposite direction is studied in the framework of two Korteweg de Vries (KdV) equations. The extended Poincaré–Lighthill–Kuo (PLK) method is applied to obtain two opposite moving KdV equations from an unmagnetized four component plasma model consisting of Maxwellian negative ions, cold mobile positive ions, κ-distributed electrons and positively charged dust grains. Hirota’s bilinear method is adopted to obtain two-soliton solutions of both the KdV equations and accordingly act of soliton turbulence is presented due to head-on collision of four solitons. The amplitude and shape of the resultant wave profile at the point of strongest interaction are obtained. To see the effect of head-on collision on the statistical properties of wave field the first four moments are computed. It is observed that the head-on collision has no effect on the first integral moment while the second, third and fourth moments increase in the dominant interaction region of four solitons, which is a clean indication of soliton turbulence.

Can the Kappa-distributed Electron Energies Account for the Intensity Ratios of O ii Lines in Photoionized Gaseous Nebulae?

Abstract A vexing puzzle in the study of planetary nebulae and H ii regions is that the plasma diagnostic results based on collisionally excited lines systematically differ from those based on recombination lines. A fairly speculative interpretation is the presence of nonthermal electrons with the so-called κ energy distributions, yet there is little observational evidence to verify or disprove this hypothesis. In this paper, we examine the influence of κ-distributed electrons on the emissivities of O ii recombination lines using an approximate method, where the rate coefficients for a κ distribution are computed by summing Maxwellian–Boltzmann rate coefficients with appropriate weights. The results show that if invoking κ-distributed electrons, the temperatures derived from the [O iii] (λ4959 + λ5007)/λ4363 ratios could coincide with those estimated from the O ii λ4649/λ4089 ratios. However, the estimated temperatures and κ values are not in agreement with those obtained through comparing the [O iii] (λ4959 + λ5007)/λ4363 ratios and the hydrogen recombination spectra, suggesting that the electron energy is unlikely to follow the κ-distributions over a global scale of the nebular regions. Nevertheless, based on this observation alone, we cannot definitely rule out the presence of κ-distributed electrons in some microstructures within nebulae.

Solitary ion acoustic waves in a plasma with regularized κ-distributed electrons

This work has been focused on the investigation of the existence conditions and the characteristics of ion acoustic soliton (IAS) in a plasma, which is composed of cold ions and regularized κ-distributed electrons. It is found that the propagation speed of the IAS should be larger than the actual ion acoustic velocity in the model. When the superthermal spectral index κ > 1.5, there exists IAS with only positive potential. In that case, the impact of the cutoff parameter α on the IAS is rather small. When κ < 1.5, however, the properties of IAS will exhibit a completely different behavior. The most significant change is that there will be IAS with negative potential if κ is small enough. The value of κ for the presence of the negative potential IAS decreases with the increase in α. The width of the IAS is determined by the Mach number, the superthermal index κ, and the cutoff parameter α. In addition, there is no singularity for the existence conditions of the IAS in the whole range κ > 0. It indicates that the regularized κ-distribution introduced by Scherer et al. (2017) can be relevant to the fluid description of the nonthermal plasma. The results obtained in the present study might be useful for the understanding of the nonlinear electrostatic phenomena in space plasmas.

Ion acoustic solitons in magnetized collisional non-thermal dusty plasmas

The oblique propagation of ion-acoustic solitary waves (IASWs) is considered, in a magnetized non-thermal collisional dusty plasma, composed of non-Maxwelian κ-distributed electrons, inertial ions, and stationary dust. The reductive perturbation approach is adopted to derive the damped Korteweg de-Vries (dKdV) equation, and the dissipative oblique ion-acoustic wave properties are investigated in terms of different key plasma parameters via the numerical solution of the dKdV equation. The collisional effect, describing the ion-neutral collision in the plasma, is taken into account, and seen to influence the dynamics of IASWs significantly. The basic features of IASWs are observed to modify, and the polarity of the wave is seen to change due to the variation of dust to that of ion number density and also due to the variation of the supethermality index κ in the considered plasma system.

Double layers and solitary structures in electron-positron-ion plasma with Kappa distributed trapped electrons

The effect of electron trapping in an electron-positron-ion plasma is modeled with κ-distributed electrons. The trapped electron number density is truncated to some finite order of the electrostatic potential Φ. Small amplitude solitary structures with Sagdeev potential approach and reductive perturbation method (through Schamel equation) are found to be modified under the impact of superthermality index κ and trapping efficiency β. A modified Schamel equation which gives rise to the small amplitude double layers (SIADLs) is obtained. The role of various plasma parameters in particular, the superthermality index, the positron concentration, and the electron trapping efficiency on the small amplitude ion acoustic double layers (SIADLs) has been investigated. It can be inferred from this investigation that these parameters play modifying character in the formation of nonlinear structures like solitary waves and SIADLs in e–p–i plasma.

Small amplitude double layers in a warm electronegative plasma with trapped kappa distributed electrons

We employ quasipotential analysis to derive the Sagdeev potential which accounts for the effect of electron trapping in a warm electronegative plasma with κ-distributed electrons. The trapped electron density is truncated to some finite order of the electrostatic potential Φ. This consequently leads to an extended KdV equation which gives rise to small amplitude double layers (SIADLs). The effects of various plasma parameters, e.g., superthermality index, the electron trapping efficiency, the mass ratio of negative to positive ion, the number density ratio of electron to positive ion, and temperature ratio of positive ion to electron on the small amplitude ion acoustic double layers (SIADLs), have been investigated. It has been found that these parameters have a significant modifying role in the SIADLs.

ON THE NONTHERMAL κ-DISTRIBUTED ELECTRONS IN PLANETARY NEBULAE AND H ii REGIONS: THE κ INDEX AND ITS CORRELATIONS WITH OTHER NEBULAR PROPERTIES

ABSTRACT Recently, a suspicion arose that the free electrons in planetary nebulae (PNs) and H ii regions might have nonthermal energy distributions. In this scenario, a κ index is introduced to characterize the electron energy distributions, with smaller κ values indicating larger deviations from Maxwell–Boltzmann distributions. Assuming that this is the case, we determine the κ values for a sample of PNs and H ii regions by comparing the intensities of [O iii] collisionally excited lines and the hydrogen Balmer jump. We find the average κ indices of PNs and H ii regions to be 27 and 32, respectively. Correlations between the resultant κ values and various physical properties of the nebulae are examined to explore the potential origin of nonthermal electrons in photoionized gaseous nebulae. However, no positive result is obtained. Thus, the current analysis does not lend support to the idea that κ-distributed electrons are present in PNs and H ii regions.

Ion acoustic drift solitons and shocks with κ-distributed electrons

The impact of superthermal particles on nonlinear drift solitary and shock like structures are presented in an inhomogeneous electron-ion plasma with κ-distributed electrons. It is shown that the amplitude of the drift solitons and shocks is modified significantly in the presence of superthermal particles. The condition for the existence of drift solitons is found modified in the presence of higher energy particles. Furthermore, Kadomtsev–Petviashvili (KP) equation is also derived for the present plasma model.

Dust-acoustic solitons in quantum plasma with kappa-distributed ions

Arbitrary amplitude dust-acoustic (DA) solitary waves in an unmagnetized and collisionless quantum dusty plasma comprising cold dust particles, kappa (κ)-distributed ions and degenerate electrons are investigated. The influence of suprathermality and quantum effects on the linear dispersion relation of DA waves is investigated. Then, the effect of κ-distributed ions and degenerate electrons on the existence domain of solitons is discussed in the space of (M, f). The comparison of the existence domain for higher and lower values of κ shows that suprathermality results in propagation of solitons with lower Mach number, and the quantum effects, lead to a higher values of Mach number. The existence domain of solitons for nondegenerate κ-distributed electrons is considered for comparison with effect of degenerate electrons. Also, we found that the Sagdeev potential well becomes deeper and wider as e F − i decreases, as for lower κ values, the influence of quantum effects on the Sagdeev pseudopotential profile is smaller.

Drift and ion acoustic wave driven vortices with superthermal electrons

Linear and nonlinear analysis of coupled drift and acoustic mode is presented in an inhomogeneous electron-ion plasma with κ-distributed electrons. A linear dispersion relation is found which shows that the phase speed of both the drift wave and the ion acoustic wave decreases in the presence of superthermal electrons. Several limiting cases are also discussed. In the nonlinear regime, stationary solutions in the form of dipolar and monopolar vortices are obtained. It is shown that the condition for the boundedness of the solution implies that the speed of drift wave driven vortices reduces with increase in superthermality effect. Ignoring density inhomogeniety, it is investigated that the lower and upper limits on the speed of the ion acoustic driven vortices spread with the inclusion of high energy electrons. The importance of results with reference to space plasmas is also pointed out.

Langmuir solitons in plasma with κ-distributed electrons in the kinetic regime

Superthermal electrons are often observed in space and astrophysics, and can be appropriately modeled by the family of kappa distribution functions. The Langmuir solitons are studied in the plasma with kappa-distributed electrons based on the Zakharov equation in the kinetic regime. It is shown that the presence of additional superthermal particles does not make qualitative changes to the important aspect of soliton behavior, but modifies the thickness of solitons.

Arbitrary amplitude ion-acoustic solitary excitations in the presence of excess superthermal electrons

Velocity distribution functions with an excess of superthermal particles are commonly observed in space plasmas, and are effectively modeled by a kappa distribution. They are also found in some laboratory experiments. In this paper we obtain existence conditions for and some characteristics of ion-acoustic solitary waves in a plasma composed of cold ions and κ-distributed electrons, where κ>3/2 represents the spectral index. As is the case for the usual Maxwell–Boltzmann electrons, only positive potential solitons are found, and, as expected, in the limit of large κ one recovers the usual range of possible soliton Mach numbers, viz., 1<M<1.58. For lower values of κ, modeling the presence of a greater superthermal component, the range of accessible Mach numbers is reduced. It is found that the amplitude of the largest possible solitons that may be generated in a given plasma (corresponding to the highest allowed Mach number for the given plasma composition) falls off with decreasing κ, i.e., an increasing superthermal component. On the other hand, at fixed Mach number, both soliton amplitude and profile steepness increase as κ is decreased. These changes are seen to be important particularly for κ<4, i.e., when the electrons have a “hard” spectrum.