Magnetized Dusty Plasma Research Articles

Propagation of Nonlinear Dust-Acoustic Waves in a Self-Gravitating Collision Magnetized Dusty Plasma in Earth’s Magnetosphere

The nonlinear propagation of different types of DANW acoustic dust nonlinear waves has been investigated in a magnetized dusty plasma consisting of negatively charged dust particles, Maxwellian electrons, and ions. Application of the standard reductive perturbation theory is used to derive the corresponding three-dimensional nonlinear a complex Ginzburg–Landau (3D-CGLE) equation which governs the dynamics of the dust-acoustic wave packets. The stationary analytical solutions of the CGLE are numerically analysed where the effect of the physical parameters of the dusty plasma model on the wave’s propagation is taken into account. It has been found that there can be a relationship between the appearance of soliton waves and electromagnetic waves, as well as between shock-like waves and periodic travelling waves. Expression of the importance of these findings is the cornerstone of explaining the true relationship between the propagation of nonlinear waves in the physics of space, for example, the Earth’s magnetic field.

Propagation of nonlinear dust-acoustic solitary waves under the effect of non-extensive electrons in inhomogeneous collisional magnetized dusty plasma

Propagation of nonlinear dust-acoustic solitary waves under the effect of non-extensive electrons in inhomogeneous collisional magnetized dusty plasma

Dust density effects on electron density gradient driven lower hybrid waves in magnetized plasma

AbstractElectrostatic lower hybrid waves propagating transverse to the external magnetic field in magnetized dusty plasma are investigated, using the fluid equations and also including the effect of density gradient in plasma. Lower hybrid modes are considered important in laboratory, astrophysical as well as space plasmas in interpreting low frequency noises. Unlike other electrostatic waves, lower hybrid waves can resonantly interact with electrons as well as ions in plasma. The dust and gradient terms lead to novel growth of these waves in dusty plasma. A theoretical model is developed to investigate density gradient effects on lower hybrid waves in plasma comprised of electrons, ions and dust particles. The dependence of plasma components' density, strength of magnetic field, temperature and charge of electrons, ions and dust grains on the frequency and growth rate of electrostatic lower hybrid waves has been investigated and presented graphically. It has been observed that the number density of each plasma components directly affects the growth rate. The electrostatic waves are found to grow along the positive electron gradient and the dust effect depends on the gradient length chosen. Above a certain threshold value of gradient length, the waves are found to stabilize. A correlation of the obtained theoretical results with the experimental observations is also discussed.

Small amplitude dust acoustic solitary waves in a magnetized dusty plasma with nonthermal distribution for both electrons and ions

The propagation of dust acoustic solitary waves (DASWs) has been investigated in a magnetized dusty plasma consisting of negatively charged dust particles, nonthermal ions and nonthermal electrons. Using reductive perturbation method, the Korteweg-de-Vries (K-dV) equation is derived. It is found that the basic structures (such as polarity, amplitude, width) of DASWs are influenced by nonthermal ions and nonthermal electrons. The results show that both compressive and rarefactive DASWs exist in such dusty plasma. It is observed that by increasing the nonthermality parameter of ions and electrons, the nonlinear wave phase velocity increases. Furthermore, nonthermal distributed ions have more effect on the nonlinear wave phase velocity of the DASWs than nonthermal distributed electrons. The dependence of the angle that the external magnetic field makes with the propagation direction of wave on the amplitude and width of DASWs has been also investigated. It was concluded that this angle strongly affects the DASWs. Finally, the effect of the magnetic field appears only in the width and not in the amplitude of the DASWs. The findings of this study can be helpful in understanding the structures of DASWs in the dusty plasma in which both nonthermal ions and nonthermal electrons exist. Such structures can be found in different regions of space and astrophysics mediums such as the upper ionosphere and Saturn’s E-ring.

Beltrami fields in partially ionized magnetized dusty plasma

The relaxed state of a magnetized four-component partially ionized dusty (PID) plasma is explored. PID plasma is composed of inertial electrons, positive ions, neutrals, and static negatively charged dust particles. When the neutrals are dragged along with the ions, the steady-state solution of vortex dynamic equations for inertial electron and ion species yields a triple Beltrami relaxed state, which is a linear combination of three single force-free fields and is characterized by three self-organized structures. The impact of plasma parameters such as Beltrami parameters and neutral (degree of ionization) and dust species densities on the nature of the relaxed state is investigated. Furthermore, the role of scale separation and its implication in space plasma are also presented. The present research will aid in elucidating the role of neutral and dust species in space, astrophysical, and laboratory plasmas.

Cosmic ray-driven magnetohydrodynamic waves in magnetized self-gravitating dusty molecular clouds

ABSTRACT The impact of galactic cosmic rays (CRs) in terms of CR pressure and parallel CR diffusion has been investigated on the low-frequency magnetohydrodynamic (MHD) waves and linear gravitational instability in the typical dusty plasma environment of molecular clouds (MCs). The dusty fluid model is formulated by combining the equations of the magnetized electrons/ions and dust particles, including the CR effects. The interactions between CR fluid and gravitating magnetized dusty plasma have been studied with the help of modified dispersion properties of the MHD waves and instabilities using the hydrodynamic fluid–fluid (CR–plasma) approach. CR diffusion affects the coupling of CR pressure-driven mode with dust-Alfvén MHD mode and causes damping in the MHD waves. It persists in its effect along the direction of the magnetic field and is diminished across the magnetic field. The phase-speed diagram shows that for super-Alfvénic wave, the slow mode becomes the intermediate Alfvén mode. The fundamental Jeans instability criterion remains unaffected due to CR effects, but in the absence of CR diffusion, the effects of dust-acoustic speed and CR pressure-driven wave speed are observed in the instability criterion. It is found that CR pressure stabilizes while CR diffusion destabilizes the growth rates of Jeans instability and significantly affects the gravitational collapse of dusty MCs. The charged dust grains play a dominant role in the sub-Alfvénic and super-Alfvénic MHD waves and the collapse of MCs, triggering gravitational instability. The consequences have been discussed to understand the gravitational instability in the dense photodissociation regions of dusty MCs.

Stability of dust-acoustic solitary waves in magnetized dusty plasmas: effect of polarization force and degenerate electron temperature

The influence of polarization force, trapped degenerate electrons, and nonthermal ions on the propagation characteristics of dust acoustic solitary waves (DASWs) in a magnetized dusty plasma is investigated. The reductive perturbation approach has been adopted to derive the extended Zakharov-Kuznetsov (eZK) equation and the solitary pulse solution is obtained to investigate the characteristics of DASWs. Pulse stability has also been analysed following the method proposed by Allen and Rowlands. Influence of different relevant plasma parameters on the growth rate of DASWs is studied. It is also found that the relevant plasma parameters have significant impact on the instability criteria of DASWs. This investigation is useful in explaining the nonlinear structures in ultra-dense degenerate plasma media which may exist in astrophysical compact objects (e.g., white dwarfs, neutron stars, etc.) and high density plasma experiments in which plasma degeneracy and relativistic effects play an important role.

Dynamics and head-on collisions of multidimensional dust acoustic shock waves in a self-gravitating magnetized electron-depleted dusty plasma

The dynamics and collisions of dust acoustic (DA) shock excitations traveling in opposite directions are theoretically investigated in a three-dimensional self-gravitating magnetized electron-depleted dusty plasma whose ingredients are extremely warm positively and negatively charged massive dust grains as well as ions that follow the q-nonextensive distribution. A linear analysis and the extended Poincare–Lighthill–Kuo method are used to derive the dispersion relation, the two-sided Korteweg–de Vries Burgers equations, and the phase shift that occurs due to the wave interaction. It is found that gravitation introduces Jeans-like instability, reduces the wave damping rate, decays the aperiodic oscillatory structure of DA excitations, and strongly affects the amplitude, steepness, and occurrence of monotonic compressive and rarefactive shocks. Numerical simulations also highlighted the stabilizing role of the magnetic field and the singularities of the collision process of monotonic shock fronts as well as the undeniable influence of viscosity, ion nonextensivity, and obliqueness between counter-traveling waves on the phase shift and collision profiles. The present results may be useful to better understand interactions of dust acoustic shock waves in the laboratory and astrophysical scenarios, such as dust clouds in the galactic disk, photo-association regions separating H II regions from dense molecular clouds, Saturn's planetary ring, and Halley Comet.

Application of the scattering matrix method for investigating the propagation characteristics of terahertz waves in magnetized dusty plasma

A scattering matrix method is applied to investigate propagation characteristics of oblique incident terahertz waves into magnetized dusty plasmas. The numerical results agree well with those given by the Wenzell–Kramer–Brillouin method. Three different electron density distributions are taken into account, and both the right- and left-hand circularly polarized (RCP and LCP) waves are analyzed. Transmission properties of terahertz (THz) waves with different physical parameters, such as external magnetic, dust particle density, and dust particle radius, are discussed systematically. There exists a transmissivity peak at the lower-frequency band for RCP waves when an external magnetic field is presented. The value of the peak nearly keeps invariant, and its location moves toward the higher-frequency direction if the magnetic field enhances. Increasing the dust particle density or radius can make the value of a transmissivity peak larger. The transmissivity of higher-frequency RCP THz waves decreases if the external magnetic field increases. However, for LCP waves, there is no transmissivity peak. It increases monotonously as the frequency of a THz wave increases. Different from the RCP waves, enhancing the external magnetic field is better for the LCP waves to penetrate the dusty plasma. Our results may provide some theoretical basis for alleviating the problem of “blackout.”

Numerical study of instabilities in magnetized inhomogeneous collisional dusty plasmas under dust dynamics

Numerical study of instabilities in magnetized inhomogeneous collisional dusty plasmas under dust dynamics

Study of magnetized multi-component plasma sheath containing charged dust particles in presence of oblique magnetic field: a fluid approach

The dynamics of low-temperature magnetized multi-component dusty plasma sheath structures have been investigated with finite ion temperature in presence of an oblique magnetic field using the one-dimensional multi-fluid model. The parametric changes inside the sheath are estimated in presence of charged dust species having nano-meter (nm) sizes. In presence of charged dust inside the sheath, the ions are found to get accumulated near the sheath edge, hence the ion density is decreased towards the wall. Further, with the increase in magnetic field strength, the peaking of ion densities near the sheath edge has been found to be intensified. The magnetic field orientation has also played a crucial role in the bunching of the ions near the sheath edge. An increase in the magnetic field obliqueness has also contributed to intensifying the ion bunching. It has also been observed that the sheath potential is substantially changed. In addition, we also investigated and presented the influence of dust species presence on the electron density inside the sheath. A qualitative explanation of the phenomenon that occurs due to the presence of dust species is presented.

Dust Acoustic Shock Waves in a Warm Magnetized Dusty Plasma with Kappa Distributed Electrons and Ions

Dust Acoustic Shock Waves in a Warm Magnetized Dusty Plasma with Kappa Distributed Electrons and Ions

Sagdeev Potential Approach for Dust Acoustic Solitary Waves in a Magnetized Dusty Plasma with Low and High Temperature for Both Electrons and Ions

Sagdeev Potential Approach for Dust Acoustic Solitary Waves in a Magnetized Dusty Plasma with Low and High Temperature for Both Electrons and Ions

The time‐fractional generalized Z‐K equation: Analysis of Lie group, similarity reduction, conservation laws, and explicit solutions

In this paper, we consider the three‐dimensional non‐linear time‐fractional generalized Zakharov‐Kuznetsov (Z‐K) equation that describes the dust‐ion acoustic solitary waves in a magnetized dusty plasma. Based on the definition of the Riemann‐Liouville (R‐L) fractional derivatives, the analysis of the Lie group method can be applied to find the symmetries for the considered equation. After that, these symmetries enable us to transform the equation under study into a two‐dimensional non‐linear ordinary differential equation of fractional order in the sense of ErdLélyi‐Kober (E‐K) fractional operator. Also, we obtain a set of new analytical solutions for the time‐fractional generalized Z‐K equation via the power series and the fractional sub‐equation methods. Furthermore, we compute the conservation laws for this equation with a detailed derivation based on the formal Lagrangian.

Dust-acoustic periodic travelling waves in a magnetized dusty plasma with trapped ions and nonthermal electrons in astrophysical situations: oblique excitations

Obliquely propagating three-dimensional dust-acoustic periodic travelling waves (DAPTWs) in a magnetized dusty plasma composed of negatively charged inertial dust particles, trapped ions, and nonthermal fast electrons have been undertaken. In the dusty plasma model at hand, the dynamic behaviors of DAPTWs are governed by a Schamel equation. The presence of dust acoustic solitary waves (DASWs) and DAPTWs is investigated via bifurcation analysis of the Hamiltonian system. In the nonlinear regime, the Sagdeev potential and phase portrait structures indicate the presence of small-amplitude DAPTW solutions. The influences of intrinsic physical parameters include the strength of the static magnetic field, the obliqueness of propagation, the thermal pressure of charged dust grains, the electron to dust density ratio, the trapping parameter of trapped ions, and the degree of nonthermality of fast electrons on the characteristics of DAPTWs are simulated numerically. In particular, the findings illustrate that the amplitude of DAPTWs is reduced as the numerical values of the trapping parameter are decreased. Interestingly, the theoretical simulations of numerical results can significantly highlight the physical nature of DAPTWs in astrophysical situations such as Earth’s magnetosphere, auroral region, and heliospheric environments.

Influence of quantum particles on self-gravitational magnetic dust acoustic double layers

The impact of Fermi–Dirac distributed electrons and ions on the features of dust acoustic double layers in a four-component magnetized dusty plasma was investigated. In this model, the plasma consists of Fermi–Dirac distributed electrons and ions and negative and positive dust particles. The plasma species experience electrical, magnetical, and self-gravitational forces as well as the degeneracy pressure force that is caused by the Pauli exclusion law and the quantum tunneling force due to Bohm force. Employing a reductive perturbation method, the quantum extended Korteweg-de Vries equation was extracted from the set of fluid equations. The results show that the energy of generated dust acoustic double layers is extremely smaller than that in similar classical plasmas. The ratio of the Fermi temperature of ions to electrons is an effective parameter in the structure of double layers. With the variation of this parameter, the structure of double layers changes from compressive to rarefactive, and its polarity switches from negative to positive.

Group velocity of obliquely propagating Alfvén waves in a magnetized dusty plasma

ABSTRACT In this work, we investigate the characteristics of the group velocity of obliquely propagating Alfvén waves in a dusty plasma typical of a stellar wind. The dispersion relation is derived with the aid of the kinetic theory for a magnetized dusty plasma consisting of electrons and ions, with distribution of momenta described by a Maxwellian function. The dust particles are considered to be immobile and have all the same size; they are electrically charged by absorption of plasma particles via inelastic collisions and by photoionization. We numerically solve the dispersion relation and calculate the components of group velocity (along and transverse to the magnetic field) for the normal modes, namely the compressional and shear Alfvén waves (CAW and SAW). The results show that the direction of the group velocity of CAWs is greatly modified with the wave-vector direction. On the other hand, SAWs will present group velocity propagating practically along the magnetic field. The changes in dust parameters, such as number density and equilibrium electrical charge, may significantly change the waves’ characteristics. It is seen that for sufficiently high dust to ion number density ratio, the SAWs may present perpendicular group velocity propagating in opposite direction to the perpendicular phase velocity, in a small interval of wavenumber values; we also notice that this interval may change, or even vanish, when the flux of radiation incident on the dust is altered, changing the equilibrium electrical charge of the grains.

In the existence of a transverse dc electric field, the kinetic theory of current‐driven electrostatic ion cyclotron waves excitation in a magnetized dusty plasma

AbstractThe theoretical modelling for the electrostatic ion cyclotron (EIC) waves in the existence of a transverse direct current (dc) electric field in a collisionless magnetized dusty plasma has been investigated using the kinetic theory model. It is examined that after incorporation of dc electric field with the dust grains can alter the dispersion properties of EIC waves in a magnetized dusty plasma. Our model developed accounts for the critical drift velocity, electron‐to‐ion temperature ratio, magnetic field, the number density of dust grains, relative density of negatively charged dust grains, and finite gyroradius parameter. Our investigation found that normalized growth rate and frequency increase with the relative density ratio and electric field. Moreover, the critical drift velocity for the excitation of the mode with negatively charged dust grains and electron‐to‐ion temperature ratio has been studied, and it was found that critical drift velocity decreases with the increase in negatively charged dust grains. The impact of dust grains on the low‐frequency waves has also been studied, and it was found that an increase in dust grain number density results in the reduction of growth rate. Some of our theoretical findings are consistent with the experimental observations.

Completely Localized Stable Elliptic and Vortex Solitons in Magnetized Dusty Plasma

We numerically and theoretically investigated the elliptic and vortex solitons, and their dynamical stabilities in a magnetized dusty plasma. By using the Petviashvili method, a type of completely localized solitons, which are also confirmed analytically, is found numerically. Numerical results indicate that the amplitude is proportional to its velocity and inverse proportional to the nonlinear interaction strength. The linear stability analysis shows that these solitons are always linearly stable, which agrees well with the nonlinear dynamic evolution. Finally, we find that both elastic and inelastic collisions exist when two localized solitons collide. It is an elastic one when the collision occurs between a localized soliton and a stable line soliton. However, a series of localized solitons will be excited if a localized soliton and an unstable line soliton collide, suggesting that inelastic collisions also exist. This finding may be helpful to understand the nonlinear phenomena in magnetized dusty plasma.

Instabilities in magnetized inhomogeneous dusty plasmas with the effect of recombination

An analytical formalism to understand the impact of various parameters on evolving instabilities in inhomogeneous collisional dusty plasmas is presented here under the effect of recombination. The basic fluid dynamics for electrons and singly charged cold ions is carried out including recombination and collision at constant rate at the surface of dust particles. Dust particles are considered to be static with unperturbed density. Normal mode analysis method has been used along with linear approximation to get perturbed densities (n i1, n e1) which are used along with quasi-neutrality condition to get perturbed potential using Poisson’s equation to obtain dispersion relation. While other authors have detected instabilities in unmagnetized plasmas, here this method has been successfully realized in presence of static magnetic field at various propagation angle and allowed the straightforward calculation of growth rates of observed instability. An extensive study of the unstable modes has been done which are well discriminated and plotted with respect to different plasma parameters like dust charge, dust density, propagation angle, magnetic field, electrostatic potential along with plasma oscillation wavelength to Debye wavelength ratio. We have observed in the said model that the presence of dust particles and propagation angle of applied magnetic field are affecting significantly the growth rate of instability as compared to magnetic field and recombination.