Superthermal Distribution Research Articles

Super-thermal light for imaging applications

AbstractWe report on a new classical light source useful for ghost-imaging applications. The light is obtained by frequency doubling a conventional speckle pattern having an overall multi-mode thermal distribution. The frequency-doubled light acquires a super-thermal distribution, which induces higher correlations at a beam splitter and, as a consequence, a higher visibility in ghost-imaging protocols.

Fluid simulation of dispersive and nondispersive ion acoustic waves in the presence of superthermal electrons

One-dimensional fluid simulation is performed for the unmagnetized plasma consisting of cold fluid ions and superthermal electrons. Such a plasma system supports the generation of ion acoustic (IA) waves. A standard Gaussian type perturbation is used in both electron and ion equilibrium densities to excite the IA waves. The evolutionary profiles of the IA waves are obtained by varying the superthermal index and the amplitude of the initial perturbation. This simulation demonstrates that the amplitude of the initial perturbation and the superthermal index play an important role in determining the time evolution and the characteristics of the generated IA waves. The initial density perturbation in the system creates charge separation that drives the finite electrostatic potential in the system. This electrostatic potential later evolves into the dispersive and nondispersive IA waves in the simulation system. The density perturbation with the amplitude smaller than 10% of the equilibrium plasma density evolves into the dispersive IA waves, whereas larger density perturbations evolve into both dispersive and nondispersive IA waves for lower and higher superthermal index. The dispersive IA waves are the IA oscillations that propagate with constant ion plasma frequency, whereas the nondispersive IA waves are the IA solitary pulses (termed as IA solitons in the stability region) that propagate with the constant wave speed. The characteristics of the stable nondispersive IA solitons are found to be consistent with the nonlinear fluid theory. To the best of our knowledge, this is the first fluid simulation study that has considered the superthermal distributions for the plasma species to model the electrostatic solitary waves.

Obliquely propagating electromagnetic waves in magnetized kappa plasmas

Velocity distribution functions (VDFs) that exhibit a power-law dependence on the high-energy tail have been the subject of intense research by the plasma physics community. Such functions, known as kappa or superthermal distributions, have been found to provide a better fitting to the VDFs measured by spacecraft in the solar wind. One of the problems that is being addressed on this new light is the temperature anisotropy of solar wind protons and electrons. In the literature, the general treatment for waves excited by (bi-)Maxwellian plasmas is well-established. However, for kappa distributions, the wave characteristics have been studied mostly for the limiting cases of purely parallel or perpendicular propagation, relative to the ambient magnetic field. Contributions to the general case of obliquely propagating electromagnetic waves have been scarcely reported so far. The absence of a general treatment prevents a complete analysis of the wave-particle interaction in kappa plasmas, since some instabilities can operate simultaneously both in the parallel and oblique directions. In a recent work, Gaelzer and Ziebell [J. Geophys. Res. 119, 9334 (2014)] obtained expressions for the dielectric tensor and dispersion relations for the low-frequency, quasi-perpendicular dispersive Alfvén waves resulting from a kappa VDF. In the present work, the formalism is generalized for the general case of electrostatic and/or electromagnetic waves propagating in a kappa plasma in any frequency range and for arbitrary angles. An isotropic distribution is considered, but the methods used here can be easily applied to more general anisotropic distributions such as the bi-kappa or product-bi-kappa.

Nonlinear Electron Acoustic Waves in Dissipative Plasma with Superthermal Electrons

The nonlinear properties of small amplitude electron-acoustic ( EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and superthermal hot electrons obeying superthermal distribution, and stationary ions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili-Burgers (KP-Brugers) equation. Some solutions of physical interest are obtained. These solutions are related to soliton, monotonic and oscillatory shock waves and their behaviour are shown graphically. The formation of these solutions depends crucially on the value of the Burgers term and the plasma parameters as well. By using the tangent hyperbolic (tanh) method, another interesting type of solution which is a combination between shock and soliton waves is obtained . The topology of phase portrait and potential diagram of the KP-Brugers equation is investigated.The advantage of using this method is that one can predict different classes of the travelling wave solutions according to different phase orbits. The obtained results may be helpful in better understanding of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.

On the rogue waves propagation in non-Maxwellian complex space plasmas

The implications of the non-Maxwellian electron distributions (nonthermal/or suprathermal/or nonextensive distributions) are examined on the dust-ion acoustic (DIA) rogue/freak waves in a dusty warm plasma. Using a reductive perturbation technique, the basic set of fluid equations is reduced to a nonlinear Schrödinger equation. The latter is used to study the nonlinear evolution of modulationally unstable DIA wavepackets and to describe the rogue waves (RWs) propagation. Rogue waves are large-amplitude short-lived wave groups, routinely observed in space plasmas. The possible region for the rogue waves to exist is defined precisely for typical parameters of space plasmas. It is shown that the RWs strengthen for decreasing plasma nonthermality and increasing superthermality. For nonextensive electrons, the RWs amplitude exhibits a bit more complex behavior, depending on the entropic index q. Moreover, our numerical results reveal that the RWs exist with all values of the ion-to-electron temperature ratio σ for nonthermal and superthermal distributions and there is no limitation for the freak waves to propagate in both two distributions in the present plasma system. But, for nonextensive electron distribution, the bright- and dark-type waves can propagate in this case, which means that there is a limitation for the existence of freak waves. Our systematic investigation should be useful in understanding the properties of DIA solitary waves that may occur in non-Maxwellian space plasmas.

Direct detection of super-thermal photon-number statistics in second-harmonic generation.

Changes in the statistical properties of light undergoing second-harmonic generation are investigated in the photon-number-resolving domain. We theoretically demonstrate that when a portion of multimode thermal light produced by parametric down-conversion is up-converted, both the second-harmonics and the residual beam at the fundamental wavelength are endowed with super-thermal photon-number distributions. The experimental results, which were obtained by exploiting the photo-number-resolving capability of hybrid photodetectors, are in excellent agreement with the theoretical expectations.

Revisiting the thermal and superthermal two-class distribution of incomes

This paper offers a two-pronged critique of the empirical investigation of the income distribution performed by physicists over the past decade. Their finding rely on the graphical analysis of the observed distribution of normalized incomes. Two central observations lead to the conclusion that the majority of incomes are exponentially distributed, but neither each individual piece of evidence nor their concurrent observation robustly proves that the thermal and superthermal mixture fits the observed distribution of incomes better than reasonable alternatives. A formal analysis using popular measures of fit shows that while an exponential distribution with a power-law tail provides a better fit of the IRS income data than the log-normal distribution (often assumed by economists), the thermal and superthermal mixture's fit can be improved upon further by adding a log-normal component. The economic implications of the thermal and superthermal distribution of incomes, and the expanded mixture are explored in the paper.

The dispersion relations of dispersive Alfvén waves in superthermal plasmas

AbstractThe effects of velocity distribution functions (VDFs) that exhibit a power law dependence on the high‐energy tail have been the subject of intense research by the space plasma community. Such functions, known as superthermal or kappa distributions, have been found to provide a better fitting to the VDF measured by several spacecraft in the plasma environment of the solar wind. In the literature, the general treatment for waves excited by (bi‐)Maxwellian plasmas is well established. However, for kappa distributions, either isotropic or anisotropic, the wave characteristics have been studied mostly for the limiting cases of purely parallel or perpendicular propagation. Contributions for the general case of obliquely propagating waves have been scarcely reported so far. In this work we introduce a mathematical formalism that provides expressions for the dielectric tensor components and subsequent dispersion relations for oblique propagating dispersive Alfvén waves (DAWs) resulting from a kappa VDF. We employ an isotropic distribution, but the methods used here can be easily applied to more general anisotropic distributions, such as the bi‐kappa or product‐bi‐kappa. The effect of the kappa index and thermal corrections on the dispersion relations of DAW is discussed.

Vlasov-kinetic computer simulations of electrostatic waves in dusty plasmas: an overview of recent results

A series of numerical simulations based on a recurrence-free Vlasov kinetic model using kinetic phase point trajectories are presented. Electron-ion plasmas and three-component (electron-ion-dust) dusty or complex plasmas are considered, via independent simulations. Considering all plasma components modeled through a kinetic approach, the linear and nonlinear behavior of ion-acoustic excitations is investigated. Maxwellian and kappa-type (superthermal) distribution functions are assumed, as initial conditions, in separate simulations for the sake of comparison. The focus is on the parametric dependence of ion-acoustic waves on the electron-to-ion temperature ratio and on the dust concentration.

Gardner solitons in dusty plasmas with nonextensive ions and two-temperature superthermal electrons

Nonlinear propagation of dust-acoustic waves in an unmagnetized dusty plasma consisting of negatively charged mobile dust, nonextensive ions following nonextensive q-distribution and two distinct temperature superthermal electrons following superthermal kappa distribution each, is investigated by employing lower and higher order nonlinear equations, namely the Korteweg-de-Vries (K-dV), the modified Korteweg-de-Vries (mK-dV) and the Gardner equations. The characteristic features of the hump (positive potential) and dip (negative potential) shaped dust-acoustic (DA) Gardner solitons are found to exist beyond the K-dV limit. The effects of two superthermal temperature electrons and ions nonextensivity on the basic characteristics of DA K-dV, mK-dV and Gardner solitons have also been investigated. It has been found that the DA Gardner solitons exhibit either negative or positive potential solitons only for q<q c where, q c is the critical value of the nonextensive parameter q. The possible applications of our results in understanding the localized nonlinear electrostatic structures existing in solar atmosphere, Saturn’s magnetosphere etc. (where the tails of the high energetic particles at different temperatures follow power-law like distribution) are also briefly discussed.

Time evolution of nonplanar electron acoustic shock waves in a plasma with superthermal electrons

The propagation of cylindrical and spherical electron acoustic (EA) shock waves in unmagnetized plasmas consisting of cold fluid electrons, hot electrons obeying a superthermal distribution and stationary ions, has been investigated. The standard reductive perturbation method (RPM) has been employed to derive the cylindrical/spherical Korteweg-de-Vries-Burger (KdVB) equation which governs the dynamics of the EA shock structures. The effects of nonplanar geometry, plasma kinematic viscosity and electron suprathermality on the temporal evolution of the cylindrical and spherical EA shock waves are numerically examined.

Head-on collision of ion-acoustic solitons in an ultracold neutral plasma

Properties of ion acoustic solitons head-on collision in an ultracold neutral plasma composed of ion fluid and non-Maxwellian electron distributions are investigated. For this purpose, the extended Poincare-Lighthill-Kuo (PLK) method is employed to derive coupled Kortweg-de Vries (KdV) equations describing the system. The nonlinear evolution equations for the colliding solitons and corresponding phase shifts are investigated both analytically and numerically. It is found that the polarity of the colliding solitons strongly depends on the type of the non-Maxwellian distribution (via nonthermal or superthermal electron distributions). Especially the phase shift due to solitons collision is strongly influenced by the non-Maxwellian distribution. A new critical nonthermal parameter β c , characterizing the nonthermal electron distribution, and which is not present for superthermal particle distributions, allows the existence of double polarity of the solitons. The phase shift increases below β c for compressive solitons, but it decreases above β c for rarefactive soliton. For superthermal distribution the phase shift increases rapidly for low spectral index κ, whereas for higher values of κ, the phase shift decreases smoothly and becomes nearly stable for κ>10. Around β c and small values of κ, the deviation from the Maxwellian state is strongest, and therefore the phase shift has unexpected behavior due to the presence of more energetic electrons that are represented by the non-Maxwellian distributions. The nonlinear structure, as reported here, could be useful for controlling the solitons that may be created in future ultracold neutral plasma experiments.

Head-on collision of electron-acoustic solitary waves in a plasma with superthermal hot electrons

The head-on collision between two electron-acoustic solitary waves in an unmagnetized plasma is investigated, including a cold electron fluid, hot electrons obeying a superthermal distribution and stationary ions. By using extended Poincare′-Lighthill-Kuo perturbation method, the analytical phase shifts following head-on collision are derived. Effects of the ratio of number density of hot electrons to number density of cold electrons α and superthermal parameter k on phase shifts are studied. It is found that hot-to-cold electron density ratio significantly modifies the phase shifts.

Spectral characteristics of the plasma dispersionless injection during the storm recovery phase on 11 March 1998

A substorm dispersionless injection event observed during the storm recovery phase on 11 March 1998 at geosynchronous orbit is carefully studied. The event shows the notable characteristics that for energetic ions the flux enhancement ratio before and after injection increases and remains elevated with increasing energy, while for energetic electrons it tends to decrease with increasing energy. In order to explain the unique injection feature, the authors propose a possible mechanism that velocity space diffusion in common to electric acceleration adjusts the particle injection state. Spectral characteristics of four different phases (pregrowth phase, the growth phase, the substorm expansion phase, and the recovery phase) have been investigated. The differential fluxes of electrons from 50 keV to 1.5 Mev and ions from 50 keV to 1.2 MeV measured by Synchronous Orbit Plasma Analyzer (SOPA) instrument onboard LANL satellite 1991–080 are found to be best fitted with the three‐parameter kappa distribution function (f ∼ A0 · E[1 + E / (κE0)]−κ−1) by Levenberg‐Marquardt and Universal Global Optimization methods. The evolutions of the three parameters in the above kappa distribution in different substorm phases have been depicted for both electrons and ions. In each phase, E0 and κ show an approximately linear relationship κ(E0) = κ0 + ηE0. This linear relationship can be obtained by solving the velocity space diffusion equation with an initial superthermal kappa distribution. Ion and electron are found to have opposite trend of parameters κ0 and η in each phase, which indicates that the different species of particles exert different velocity space diffusion processes so that their flux enhancement ratios before and after injection are rather different. This implies that not only electric field acceleration, but also velocity space diffusion plays a very important role in the particle injection.

Obliquely propagating electron acoustic solitons in a magnetized plasma with superthermal electrons

The problem of small amplitude electron acoustic solitary waves is discussed using the reductive perturbation theory in magnetized plasmas consisting of cold electrons, hot electrons obeying superthermal distribution and stationary ions. The effects of superthermal electrons, the population ratio of hot to cool electrons and also the magnetic field on the behavior of plasma are investigated. The results show that only rarefactive solitary waves propagated in this plasma and the presence of superthermal electrons reduces the soliton amplitude and its width.

Equatorially confined warm trapped ions at around 100 eV near the plasmapause

Near the equatorial plasmapause at around 4–5 Earth radius (RE) geocentric distance, pancake distributed tens of eV ions are sometimes found, as previously reported by Olsen et al. (1987). Cluster CIS data during perigee traversals in 2001–2002 (nearly 200 traversals) revealed new features of these equatorially‐trapped warm ions. (1) The characteristic energy of He+ is often higher than that of H+. (2) Some events show non‐thermal ring distribution for He+ rather than superthermal pancake distribution. H+can also have the ring distribution in such events. (3) While majority of the events are dispersion‐free, some events show energy‐time dispersion, indicating drifts from different local times. (4) The time scale of the development is about an hour, which is much shorter than the drifting time of these ions around the Earth. Cluster statistics also confirmed some results from the previous studies: (5) These ions are confined within a few degrees of latitudinal range near the equator, and have nearly 90° pitch angles. (6) At a geocentric distance of about 4–4.5 REwhere Cluster traversed the equator during its perigee, the probability of observing clear events is about 40–45% in the noon and dusk sectors and about 20–25% in the night‐to‐dawn sector. (7) They are dominated by H+ with variable content of He+. The He+/H+ ratio is much less than 5% for the majority of the cases.

Dust acoustic shock waves in strongly coupled dusty plasmas with kappa-distributed ions

Dust acoustic shock waves (DASWs) have been studied in an unmagnetized dusty plasma system consisting of coupled negatively charged dust and ions obeying superthermal distribution. Korteweg-deVries-Burger equation (KdV-Burgers) has been derived using small amplitude perturbation expansion method to study the nonlinear propagation of the DASWs. The behavior of the shock waves in the plasma has been investigated. It is found that the coefficients of the KdV-Burgers equation are significantly modified by k-parameter (k is a spectral index for superthermal distribution).

Cylindrical and spherical electron acoustic solitary waves in the presence of superthermal hot electrons

Propagation of cylindrical and spherical electron-acoustic solitary waves in unmagnetized plasmas consisting of cold electron fluid, hot electrons obeying a superthermal distribution and stationary ions are investigated. The standard reductive perturbation method is employed to derive the cylindrical/spherical Korteweg-de-Vries equation which governs the dynamics of electron-acoustic solitons. The effects of nonplanar geometry and superthermal hot electrons on the behavior of cylindrical and spherical electron acoustic soliton and its structure are also studied using numerical simulations.

Cylindrical and spherical dust acoustic solitary waves in dusty plasma with superthermal ions and electrons

Nonlinear propagation of cylindrical and spherical dust-acoustic solitons in an unmagnetized dusty plasma consisting of cold dust grains, superthermal ions and electrons are investigated. For this purpose, the standard reductive perturbation method is employed to derive the cylindrical/spherical Korteweg-de-Vries equation which governs the dynamics of dust-acoustic solitons. The effects of nonplanar geometry and superthermal distributions on the cylindrical and spherical dust acoustic solitons structures are also studied by numerical calculation of the cylindrical/spherical Korteweg-de-Vries equation.

NONLINEAR DYNAMICS OF ACOUSTIC INSTABILITY IN A COSMIC RAY SHOCK PRECURSOR AND ITS IMPACT ON PARTICLE ACCELERATION

An acoustic instability of a shock precursor driven by the pressure gradient of accelerated particles is studied in the nonlinear regime. The nonlinearity steepens unstable acoustic waves and turns them into shocks. The shocks form a shocktrain but they may merge into each other. Traveling wave solutions are obtained analytically in two different cases. In the first case, only acoustic instability is included and the characteristic scale (distance between the shocks) is limited only by the system size (while shocks merge). In the second case, the instability develops out of cyclotron unstable seed magnetohydrodynamic (MHD) waves. The spatial distance between the MHD wave packets sets the scale of the acoustic shocktrain. The internal structure of the individual shocks is presumably determined by the ion skin depth c/ω pi and by the relaxation length of slightly superthermal particle distributions near these shocks. The shocks are assumed to be arbitrarily thin compared with the distance between them which is ensured by a small viscous term. Both types of solutions are dynamically verified by numerical calculations. The hydromagnetic flow in the shock precursor emerging from the acoustic instability is crucial for two recently suggested phenomena in diffusive shock acceleration. One phenomenon is the enhancement of the acceleration rate well above its standard (Bohm) value due to the narrowing of the shock precursor. The second phenomenon is the amplification of the long-scale magnetic field by an inverse cascade of Alfven waves generated by accelerated particles and scattered in k-space on the acoustic perturbations.