Vortex-like Distribution Research Articles

Nonlinear Dynamics of Ion-Acoustic Waves in a Magnetized Plasma With Trapped Electrons

The dynamics of obliquely propagating ion-acoustic waves (IAWs) in a collisionless, magnetized plasma consisting of free and trapped electrons, having a vortex-like distribution and fluid ions immersed in an external static magnetic field, has been investigated. The reductive perturbation technique (RPT) has been used to derive a Schamel’s modified Laedke–Spatschek (S–LS) equation. Several nonlinear structures have been obtained, like solitary waves, periodic and quasi-periodic oscillations, as well as chaotic structures. The effects of the magnetic field strength, the wave propagation obliqueness, the Mach number, and the electrons trapping on these nonlinear structures have been explored. The increase in the magnetic field strength has been found to reduce the soliton width and enhance its amplitude, while the role of rising the trapping parameter is only to increase the solitary wave amplitude. For a relatively weak magnetic field, the increase in the Mach number may change the solitonic structure to a periodic oscillation and the latter to a quasi-periodic one, while the decrease in the propagation angle to the magnetic field direction may bring about the second transition (periodic <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\rightarrow$</tex-math> </inline-formula> quasi-periodic). Furthermore, depending on the plasma parameters, the intensification of the magnetic field can lead to the transition from a quasi-periodic to a chaotic behavior of the electrostatic wave.

Instability of opposite polarity charged dusty plasma with vortex-like distributed electrons

Electrons in space plasma may follow vortex-like distribution, that is why we have derived the three-dimentional (3D) nonlinear modified Zakharov–Kuznetsov (mZK), describing the propagation of dust acoustic solitary to the plasma system composed of four components, magnetized charged dust plasma with electrons modelled by vortex-like distribution. By using the reductive perturbation method, it has been found that both solitary wave amplitude and width are affected by the plasma parameters: graim charge ratio ρ, population parameter β, and temperature ratio σ. The small-k perturbation technique has also been applied to study the instability criterion and growth rate of this instability. Cyclotron frequency Ω, temperature ratio , direction cosine ( and ), and grain charge ratio ρ are found to modify the instability growth rate Γ.

Large-amplitude electrostatic fluctuations at the Earth’s magnetopause with a vortex-like distribution of hot electrons

Large-amplitude electrostatic solitary waves (ESWs) associated with asymmetric magnetic reconnection at the Earth’s magnetopause are studied in a four-component plasma composed of a mixture of the magnetosheath and magnetosphere plasma of a cold, warm and hot electron populations, and background ions. The species are modeled as adiabatic fluids except for the hot electrons which have a kinetic vortex-like velocity distribution. The hybrid model uses the Sagdeev pseudopotential technique to study the arbitrary amplitude ion- and electron-acoustic solitons and double layers. The numerical computations reveal that for the parameters corresponding to magnetosphere side of the ion diffusion region, only slow electron-acoustic solitons and double layer can exist. On the magnetosheath side of the ion diffusion region, only the electron-acoustic/beam solitons can exist. The electric field amplitude of the electrostatic solitary waves (ESWs) predicted by our model are consistent with the Magnetospheric Multiscale (MMS) observations.

Transverse instability of dust acoustic solitary waves in magnetized dusty plasma composed of vortex-like distribution ions

The dynamical behaviors of dusty plasma can be described by a (3+1)-dimensional modified Zakharov-Kuznetsov equation (mZKE) when the distribution of ions is vortex-like. The critical stable conditions for the line solitons are obtained by the linear stability analysis, which are also confirmed by the nonlinear dynamic evolution. An interesting phenomenon is found from the numerical results, maybe the first time, that the unstable line solitons of the mZKE will evolve into one or more completely localized soliton(s) after a long time evolution. Subsequently, we numerically studied the collision process of two line solitons. The results show that two stable line solitons can restore to their original states. However, if one of the two solitons or both of them are unstable, one or more completely localized solitons will appear during the collision. The results indicate that there are both elastic and inelastic collisions between line solitons.

Finite amplitude electron-acoustic waves in the electron diffusion region

The electron-acoustic solitons are studied with two temperature electrons (a hot trapped having vortex-like velocity distribution and a warm adiabatic fluid) and stationary ions. The theoretical model is based on the observations of a mixture of the hot, tenuous magnetospheric and warm, dense magnetosheath plasma particles associated with the asymmetric magnetic reconnection at the Earth’s magnetopause by Magnetospheric Multiscale (MMS). Using the reductive perturbation technique, the model supports the existence of nonlinear electron-acoustic structures derived from the mKdV-like equation. The electron-acoustic waves propagate at supersonic speeds above the electron sound speed. The results are applied to observations of electric field structures in the electron diffusion region (EDR).

Effect of particle trapping in a three-component plasma sheath model containing Tsallis distributed electrons

In this paper, the effect of particle trapping in a three-component plasma sheath model has been investigated analytically. The behavior of plasma sheath is studied with cold fluid ions, trapped/vortex-like hot electrons and cold q-nonextensive electrons. The trapped hot electrons follow Schamel’s vortex-like distribution. A modified Bohm sheath criterion and a sheath width equation have been analytically derived. It is seen that the thickness of the sheath explicitly depends on q-nonextensivity parameter, Bohm velocity, cold electron fraction, temperature and densities of cold and hot electrons; while the Bohm velocity depends on nonextensive parameter, fraction of cold electrons, temperature and densities of cold and hot electrons. It is observed that as the electron nonextensivity as well as fraction of cold electron increases, the Bohm velocity decreases and also the sheath width decreases. As the ratio between hot electrons temperature to cold electrons temperature increases, the Bohm velocity increases and the sheath thickness also increases. The increasing values of the ratio of cold electrons to hot electrons concentration results in the decrease of sheath width.

Three-dimensional modified Korteweg-de Vries equation in a magnetised relativistic plasma with positron beam and vortex-like electron distribution

The nonlinear features of Ion Acoustic (IA) waves are studied in a fully relativistic three-dimensional (3-D) plasma system with consideration of effect of both positron beam and trapped electrons. We consider a set of 3-D magnetised hydrodynamic equations with pressure expansion for our plasma model along with kinetic Vlasov equation for electrons. Applying the perturbative expansion technique, a Modified Korteweg-de Vries (m-KdV)-like equation is derived, exhibiting the evolution of small amplitude IA waves in plasma. The modified coefficient of nonlinear term in K-dV equation has arrived due to impact of vortex-like distribution of electrons. An analytical and numerical investigation of the nonlinear evolution equations is exhibited with external magnetic field effects, the time derivative pressure expansion as well as other parameters like relativistic effect, mass variation, beam velocity and temperature effect have been taken into consideration. The presence of vortex like trapped electron distribution and positron beam governs the influence of soliton structure quite significantly. The present result should help us to understand the experiments that involve particle trapping and also the salient features of astrophysical environment like ionospheric plasma together with situations in plasma describing the electrostatic solitary structures usually seen in antimatter-related environment in interplanetary region.

Electric modulation of magnetic anisotropy on the granule/matrix interface of a permalloy/PZT composite

In this work, the electric modulation of magnetic anisotropy is investigated on a granule/matrix interface of a Py/PZT composite. Outside the Py/PZT interface, the electric polarization is derived through the Thomas-Fermi model and mean field approximation. Inside the Py/PZT interface, the magnetizing energy is derived through the spin-split model and spherical shell approximation. As the Py volume fraction varies from 0.0% to 0.8%, the electric polarization evolves from radiationlike to vortexlike distribution, while the magnetizing energy evolves from symmetric-type to asymmetric-type distribution. Under downward and upward polarization, parallel and perpendicular magnetization are preferred, respectively. As the granule diameter or matrix thickness is varied, the downward polarization induces unstable parallel magnetic anisotropy, while the upward polarization induces stable perpendicular magnetic anisotropy. This work is beneficial for achieving electrostatic manipulation of a magnetic vortex.

Effects of Vortex-Like Ion Distribution on Dust-Acoustic Solitary Waves in a Self-Gravitating Opposite Polarity Dusty Plasmas

A self-gravitating opposite polarity dust plasma (SGOPDP) medium (containing both positively and negatively charged dust, vortex-like distributed ions and Maxwellian electrons) has been considered in order to examine the effect of vortex-like (trapped) ion distribution on dust-acoustic (DA) solitary waves (SWs) propagating in SGOPDP medium. The reductive perturbation method, which is valid for small but finite amplitude SWs, is employed to derive a modified Korteweg-de Vries equation having stronger nonlinearity. The basic features of the DA SWs in SGOPDP medium are found to be significantly modified by the combined effect of self-gravitational field and vortex-like ion distribution. The results of this paper have many implications in space and laboratory dusty plasmas.

Nonlinear dust ion acoustic waves behaviors analysis in warm viscous dusty plasma with trapped ions

The nonlinear excitation of a dust ion acoustic (DIA) wave packet in a viscous dusty plasma consisting of Boltzmann distributed electrons, trapped ions, and variable charged dust is investigated. The dependence of the damping rate of the waves on the plasma parameters is discussed via the linear stability analysis. The standard reductive perturbation method is employed to derive the modified Korteweg-de Vries-Burgers equation due to an interplay among the nonlinearity, dispersion, and dissipation effects, and, the non-dissipative case gives the modified Korteweg-de Vries equation. Bifurcation analysis is discussed for the non-dissipative and dissipative systems assuming a Boltzmann distribution for electrons and a vortex-like distribution for ions. The effects of plasma parameters, among which the dusty plasma viscosity ν, trapping ion parameter β, and dust charge variation γ1 on solitary waves (SWs) and shock wave solutions, are discussed. It is observed that parameters ν and β significantly influence the characteristics of nonlinear dust ion acoustic solitary structures. It is seen that without viscosity (ν = 0), the system has the DIA solitary wave solutions, whereas, the viscous system supports DIA shock waves. By increasing the kinematic viscosity, the opportunity for formation of higher energy shock solitary waves increases and the solitary waves become monotonic shock waves.

Existence and stability of alternative dust ion acoustic solitary waves in a dusty plasma consisting of nonthermal electrons having vortex-like velocity distribution

The recent work of Sardar et al. [Phys. Plasmas 23, 073703 (2016)] on the existence and stability of the small amplitude dust ion acoustic solitary waves in a collisionless unmagnetized plasma consisting of warm adiabatic ions, static negatively charged dust grains, isothermal positrons, and nonthermal electrons due to Cairns et al. [Geophys. Res. Lett. 22, 2709 (1995)] has been extended by considering nonthermal electrons having a vortex-like velocity distribution due to Schamel [Plasma Phys. 13, 491 (1971); 14, 905 (1972)] instead of taking nonthermal electrons. This distribution takes care of both free and trapped electrons. A Schamel's modified Kadomtsev Petviashvili (SKP) equation describes the nonlinear behaviour of dust ion acoustic waves in this plasma system. The nonlinear behaviour of the dust ion acoustic wave is described by the same Kadomtsev Petviashvili (KP) equation of Sardar et al. [Phys. Plasmas 23, 073703 (2016)] when B = 0, where B is the coefficient of nonlinear term of the SKP equation. A combined SKP-KP equation more efficiently describes the nonlinear behaviour of dust ion acoustic waves when B → 0. The solitary wave solution of the SKP equation and the alternative solitary wave solution of the combined SKP-KP equation having profile different from both sech4 and sech2 are stable at the lowest order of the wave number. It is found that this alternative solitary wave solution of the combined SKP-KP equation and its lowest order stability analysis are exactly the same as those of the solitary wave solution of the KP equation when B → 0.

Ion-acoustic solitary waves in a positron beam plasma with electron trapping and nonextensivity effects

Ion-acoustic solitary waves (IASWs) are investigated in a plasma having a cold positron beam fluid, electrons following a vortex-like distribution with entropic index q, and dynamic ions. Using a standard procedure, a pseudo-potential energy equation is derived. The presence of nonextensive q- distributed trapped electrons and cold positron beam has been shown to influence the small amplitude soliton structure quite significantly. From the analysis of our results, it is shown that compressive IASWs are supported in this plasma model. As the real plasma situations are observed with plasma species having a relative flow, our present analysis should be beneficial for comprehending the electrostatic solitary structures observed in fusion plasma devices and positron winds observed in astrophysical plasmas.

Electron-acoustic solitary waves in a beam plasma with electron trapping and nonextensivity effects

A theoretical investigation is carried out for understanding the properties of electron-acoustic solitary waves (EASWs) in a beam plasma whose constituents are a cold beam electron fluid, hot nonextensive electrons obeying a vortex-like distribution with nonextensive factor q, and stationary ions. An energy integral (Schamel KdV) equation is derived by employing pseudo-potential (reductive perturbation) approach. The presence of nonextensive q-distributed hot trapped electrons and cold electron beam has been shown to influence the soliton structure quite significantly. The nonlinear dispersion relation is derived to analyze the dependency of the electron acoustic solitary wave quantities. From the analysis of our results, it is shown that the present plasma model supports the compressive EASWs. As the real plasma situations are observed with plasma species having a relative flow, so our present analysis should be useful for understanding the electrostatic solitary structures observed in the dayside auroral zone and other regions of the magnetosphere.

Random sources for beams with azimuthally varying polarization properties.

We develop analytical model for statistically stationary sources that radiate beam-like far fields with polarization properties separately controllable in both radial and azimuthal variables. In particular, we demonstrate that for a suitable choice of source parameters a vortex-like far-field distribution of the degree of polarization (DOP) can be obtained. Furthermore, we report the experimental generation of such sources using an optical setup with Mach-Zehnder interferometer having two independent spatial light modulators in its branches. The experimental results agree well with the theoretical predictions. The new class of sources may find uses in imaging, communication and sensing applications based on source polarization diversity.

The effect of trapped electrons on the three-dimensional ion-acoustic shock wave in magnetized ionic-pair plasma

The effect of trapped electrons featuring vortex-like distribution on the nonlinear behavior of a three-dimensional ion-acoustic shock wave is investigated in a magnetized ionic-pair plasma. In the long-wave approximation, the dynamics of the shock wave is governed by the -dimensional Schamel-Zakharov-Kuznetsov-Burgers' equation due to the presence of trapped electrons and ion kinematic viscosity. By using the homogeneous balance principle and tanh function method, we obtain a novel exact shock wave solution of the equation. It is found for the first time that the trapped electrons can support a shock wave with only positive polarity.

ROLE OF TRAPPED ELECTRONS IN THE PROPAGATION OF DUST-ION ACOUSTIC WAVES IN MAGNETIZED DUSTY ELECTRONEGATIVE PLASMA

A theoretical investigation has been conducted concerning the nonlinear propagation of dust-ion acoustic waves in magnetized three-component dusty electronegative plasma consisting of Boltzmann negative ions, adiabatic positive ions, & negatively charged stationary dust & vortex-like distributed electrons. In this paper, the nonlinear propagation of dust-ion acoustic (DIA) solitary waves in a magnetized dusty electronegative plasma with trapped electrons is investigated. Due to the presence of trapped electrons, the electron distribution function with the vortex-like distribution has been introduced. The stationary solution of the KdV equation (i.e. DIA solitons) in this plasma is found & the influence of different parameters on the amplitude & width of DIA solitons is investigated. In these regions, due to the presence of a high density of dust grains, different types of collective processes exist & very rich wave modes can be excited. One of these is low-frequency dust ion-acoustic (DIA) waves. Shukla & Silin have shown the existence of dust-ion-acoustic (DIA) waves in a dusty plasma containing boltzmann electrons, mobile ions, & negatively charged stationary dust theoretically.

Plasmonically induced magnetic field in graphene-coated nanowires.

In this Letter, we investigate a magnetic field induced by guiding plasmonic modes in graphene-coated nanowire via an inverse Faraday effect. Magnetic field distribution for different plasmonic modes has been calculated. It has been shown that a magnetic field has a vortex-like distribution for some plasmonic modes. The possibility of producing magnetic field distribution that rotates along the nanowire axis and periodically depends on azimuthal angle has been demonstrated.

Time-fractional Schamel–KdV equation for dust-ion-acoustic waves in pair-ion plasma with trapped electrons and opposite polarity dust grains

Nonlinear propagation of dust-ion-acoustic (DIA) waves is investigated in a one-dimensional, unmagnetized plasma containing positive ions, negative ions, trapped electrons featuring vortex-like distribution, and immobile dust grains having both positive and negative charges. Via reductive perturbation method, Agrawal's method, and Euler–Lagrange equation, the time-fractional Schamel–KdV equation under the sense of Riesz fractional derivative is derived to describe nonlinear behavior of DIA waves. The approximate solution of the time-fractional Schamel–KdV equation is constructed in terms of Jacobi elliptic functions by variational iteration method. The effect of the plasma parameters on the DIA solitary waves is also discussed in detail.

The nonadiabatic dust charge variation on dust acoustic solitary and shock waves in strongly coupled dusty plasmas

The combined effects of nonadiabatic dust charge fluctuation and strongly coupled dust particles on the nonlinear propagation of dust acoustic (DA) waves in dusty plasma consisting of nonthermal electrons and trapped ions with vortex-like distribution are presented here. We use generalized viscoelastic hydrodynamic model for dust particles. In the weak nonlinearity limit, a modified Korteweg–de Vries (KdV) equation with a damping term and a KdV–Burger equation have been derived in the kinetic regime and hydrodynamic regime, respectively. The approximate analytical solitary solution of modified KdV equation is derived in the weak nonadiabatic dust charge variation limit, which shows that the amplitude of DA solitary waves decreases with time. The presence of viscosity due to strong coupling stands for the formation of DA shock waves in the hydrodynamic regime. The results show that the DA shock waves will be oscillating one for weak viscosity and will become monotonic ones for large viscosity.

Linear and nonlinear analysis of dust acoustic waves in dissipative space dusty plasmas with trapped ions

The propagation of linear and nonlinear dust acoustic waves in a homogeneous unmagnetized, collisionless and dissipative dusty plasma consisted of extremely massive, micron-sized, negative dust grains has been investigated. The Boltzmann distribution is suggested for electrons whereas vortex-like distribution for ions. In the linear analysis, the dispersion relation is obtained, and the dependence of damping rate of the waves on the carrier wave number \(k\), the dust kinematic viscosity coefficient \(\eta _{d}\) and the ratio of the ions to the electrons temperatures \(\sigma _{i}\) is discussed. In the nonlinear analysis, the modified Korteweg–de Vries–Burgers (mKdV–Burgers) equation is derived via the reductive perturbation method. Bifurcation analysis is discussed for non-dissipative system in the absence of Burgers term. In the case of dissipative system, the tangent hyperbolic method is used to solve mKdV–Burgers equation, and yield the shock wave solution. The obtained results may be helpful in better understanding of waves propagation in the astrophysical plasmas as well as in inertial confinement fusion laboratory plasmas.