Magnetized Dusty Plasma Research Articles

Excitation of upper-hybrid waves by a gyrating relativistic electron beam in a magnetized dusty plasma cylinder

A gyrating relativistic electron beam propagating through a magnetized dusty plasma cylinder drives an upper-hybrid wave to instability via cyclotron interaction. Numerical calculations of the growth rate and unstable mode frequencies have been carried out for the typical parameters of dusty plasma experiments. It is found that as the density ratio of negatively charged dust grains to electrons increases, the unstable mode frequency of the upper-hybrid waves increases. Moreover, the growth rate of the instability also increases with the density ratio. The growth rate of the unstable mode has the largest value for the modes whose eigenfunctions peak at the location of the beam. The growth rate of the unstable mode scales as the one-third power of the beam density.

On the stability of obliquely propagating dust ion-acoustic solitary waves in hot adiabatic magnetized dusty plasmas

Obliquely propagating dust ion acoustic solitary waves (DIASWs) are investigated in hot adiabatic magnetized dusty plasmas consisting of hot adiabatic inertial ions, hot adiabatic inertialess electrons, and negatively/positively charged static dust grains. Using a reductive perturbation method, a nonlinear Zakharov–Kuznetsov equation is derived. The effects of the concentration of negatively/positively charged dust particles and ion-neutral collision on the basic characteristics of DIASWs are studied. The three-dimensional stability of these waves is examined by the use of small-k (long wavelength plane wave) perturbation expansion technique. It is shown that the instability criterion and their growth rate depend on external magnetic field, obliqueness, the concentration of charged dust grains, ion-neutral, and ion-dust collisions.

Obliquely propagating cnoidal waves in a magnetized dusty plasma with variable dust charge

We have studied obliquely propagating dust-acoustic nonlinear periodic waves, namely, dust-acoustic cnoidal waves, in a magnetized dusty plasma consisting of electrons, ions, and dust grains with variable dust charge. Using reductive perturbation method and appropriate boundary conditions for nonlinear periodic waves, we have derived Korteweg–de Vries (KdV) equation for the plasma. It is found that the contribution to the dispersion due to the deviation from plasma approximation is dominant for small angles of obliqueness, while for large angles of obliqueness, the dispersion due to magnetic force becomes important. The cnoidal wave solution of the KdV equation is obtained. It is found that the frequency of the cnoidal wave depends on its amplitude. The effects of the magnetic field, the angle of obliqueness, the density of electrons, the dust-charge variation and the ion-temperature on the characteristics of the dust-acoustic cnoidal wave are also discussed. It is found that in the limiting case the cnoidal wave solution reduces to dust-acoustic soliton solution.

Excitation of surface plasma waves by an electron beam in a magnetized dusty plasma

An electron beam drives surface plasma waves to instability on a vacuum magnetized dusty plasma interface and in a magnetized dusty plasma cylinder via Cerenkov and fast cyclotron interaction. The dispersion relation of a surface plasma wave has been derived and it has been shown that the phase velocity of waves increases with increase in relative density δ(=ni0/ne0)), where ni0 is the ion plasma density and ne0 is the electron plasma density of negatively charged dust grains. The frequency and the growth rate of the unstable wave instability also increases with δ. The growth rate of the instability increases with beam density and scales as the one-third power of the beam density in Cerenkov interaction and is proportional to the square root of beam density in fast cyclotron interaction. The dispersion relation of surface plasma waves has been retrieved from the derived dispersion relation by considering that the beam is absent and there is no dust in the plasma cylinder.

Three-dimensional dust acoustic solitary waves in nonuniform magnetized dusty plasmas with adiabatic dust charge fluctuation

Using a standard reductive perturbation theory, a modified variable coefficients Korteweg–de Vries (MKdV) equation governing the three-dimensional dust acoustic solitary waves is derived in inhomogeneous dusty plasmas comprising negatively charged dust grains of equal radii, Boltzmann distributed electrons and ions. The incorporation of the combined effects of adiabatic dust charge fluctuation, the external magnetic field and the inhomogeneity caused by nonuniform equilibrium values of particle density, charging variable and particle potential on the waves leads to a significant modification of the nature of dust acoustic solitary waves and excites both dust acoustic solitary holes (solitons with a density dip) and positive solitons (solitons with a density hump).

Effects of Two-Temperature Electrons and Trapped Ions on Multidimensional Instability of Dust-Acoustic Solitary Waves

The basic features of obliquely propagating dust-acoustic solitary waves (DASWs), and their multidimensional instability in a magnetized dusty plasma containing negatively charged dust, two-temperature electrons, and trapped ions, have been theoretically investigated by the reductive-perturbation method and small-k perturbation-expansion technique. The combined effects of external magnetic field (obliqueness), two-electron temperature, and trapped-ion distribution, which are found to significantly modify the basic properties (amplitude and width) of small but finite-amplitude DASWs, are explicitly examined. It is also found that the instability criterion and the growth rate are significantly modified by the external magnetic field and the propagation directions of both the nonlinear waves and their perturbation modes. The implications of our results in space plasmas are briefly discussed.

Charge fluctuations and Hall effect in dusty plasmas

In a magnetized dusty plasma, Hall effect can arise due to collisional processes when, e.g., ion-dust collision decouples the ions from the magnetic field. In this case, due to the dust stoppage of the ions, the Hall electric field can be generated over large scales. The same collisional processes are also responsible for dust charge fluctuations. Therefore, the Hall effect and dust charge fluctuations are intricately linked to each other through the same mechanism. The inertial scale over which the Hall effect is dynamically important depends not only on the value of the grain charge times the ratio of the grain to the plasma (ion) number densities but also on the ratio of the ion-dust to the electron-dust collision frequencies. This scale can become arbitrarily large when these collision frequencies are comparable. We show that the charge dynamics, though linked to the Hall scale, does not directly affect the low frequency waves in the medium. Since charge fluctuation modifies the length scale over which Hall operates, the normal mode in such a medium is only indirectly affected although wave suffers weak damping due to collision.

Multi-dimensional instability of dust-ion-acoustic solitary waves in a multi-ion dusty plasma

AbstractThe basic features of obliquely propagating dust-ion-acoustic (DIA) solitary waves, and their multi-dimensional instability in a magnetized multi-ion dusty plasma containing hot adiabatic inertia-less electrons, cold positive and negative ions, and negatively charged static dust have been theoretically investigated by the reductive perturbation method, and the small-k perturbation expansion technique. The combined effects of electron adiabaticity, external magnetic field (obliqueness), and negative ions, which are found to significantly modify the basic properties (speed, amplitude, width, and instability) of small but finite-amplitude DIA solitary waves, are explicitly examined. It is also found that the instability criterion and the growth rate are significantly modified by the external magnetic field, the propagation directions of both the nonlinear waves and their perturbation modes, and the presence of negative ions. The implications of our results in space and laboratory dusty plasmas are briefly discussed.

Collisional phase shifts between two colliding solitary waves in a three-dimensional magnetized dusty plasma

Interaction of dust acoustic solitary waves in two different directions in a three-dimensional dusty plasma is investigated. The phase shifts after collision of two solitary waves with arbitrary angle in a three-dimensional magnetized dusty plasma are studied. By using the extended Poincaré–Lighthill–Kuo perturbation method, two Korteweg–de Vries equations for nonlinear waves in both ξ and η directions are obtained. The effects of the collision angle θ, the ratio of dust temperature to ion temperature σ, the ratio of ion temperature to electron temperature β, the ratio of effective temperature to ion temperature s, and the ratio of the number densities of both ion and electron to the density of dust particles μ and ν on the phase shifts are discussed.

Nonlinear Ion Acoustic Waves in a Magnetized Dusty Plasma in the Presence of Nonthermal Electrons

The Kadomtsev-Petviashili (KP) equation is derived for weakly nonlinear ion acoustic waves in a magnetized dusty plasma in the presence of nonthermal electrons. Soliton solutions are obtained in both the one-dimensional and two-dimensional framework. For the one-dimensional soliton solution the ‘tanh’ method is considered while the two-dimensional solution is obtained by a method introduced by S.V. Manacov et al., Phys. Lett. A 63, 205 (1977). It is found that in case of the onedimensional solution, both compressive and rarefactive solitary waves exist which could be obtained depending on the ratio of the electron and ion density. It is also seen that the nonthermal distribution of electrons has some significant effect in the shape of both the one-dimensional and two-dimensional solitary wave.

Study of the dust acoustic waves in a magnetized dusty plasma with many different dust grains

The nonlinear dust waves in a magnetized dusty plasma with many different dust grains are analytically investigated. New analytical solutions for the governing equation of this system have been obtained for the dust acoustic waves in a dusty plasma for the first time. We derive exact mathematical expressions for the general case of the nonlinear dust waves in magnetized dusty plasma which contains different dust grains.

Effects of Adiabatic Dust Charge Fluctuation and Particles Collisions on Dust-Acoustic Solitary Waves in Three-Dimensional Magnetized Dusty Plasmas

Taking into account the combined effects of the external magnetic field, adiabatic dust charge fluctuation and collisions occurring between the charged dust grains and neutral gas particles (dust-neutral collisions), the dust-acoustic solitary waves in three-dimensional uniform dusty plasmas are investigated analytically. By using the reductive perturbation method, the Korteweg–de Vries (KdV) equation governing the dust-acoustic solitary waves is obtained. The present analytical results show that only rarefactive solitary waves exist in this system. It is also found that the effects of the wave vector along the z-direction, dust charge variation, collisional frequency, the plasma density, and temperature ratio can significantly influence the characteristics of low-frequency wave modes. Moreover, for the collisional dusty plasmas, there is a certain critical value μc of the plasma density ratio μ, if μ < μc, the width of the waves increases with μ, otherwise the width of waves decreases with μ.

Theoretical results of the dust acoustic waves in a magnetized dusty plasma with different dust particles

In this paper, the nonlinear dust acoustic waves (DAW) in a magnetized dusty plasmas with different dust grains are analytically investigated. New analytical solutions of the governing equation for this system have been obtained for the first time. The exact mathematical expressions of the nonlinear dust waves have been canvassed for the general case in magnetized dusty plasma containing different dust particles.

Obliquely propagating ion acoustic solitary waves in magnetized dusty plasma in the presence of nonthermal electrons

Obliquely propagating dust ion acoustic solitary waves subjected to an external magnetic field are studied using Sagdeev’s pseudopotential technique. Nonthermal distribution for electrons is considered. The pseudopotential is derived without considering the quasineutrality condition. It is obtained from the Poisson equation instead. Using Sagdeev’s technique, the ranges of parameters for which solitary waves exist are studied in detail.

Propagation of the three-dimensional dust acoustic solitons in magnetized quantum plasmas with dust polarity effect

The quantum hydrodynamical model is employed to investigate the nonlinear properties of the quantum dust acoustic waves in a magnetized dusty plasma composed of inertialess electrons, ions, and mobile positive/negative charged dust particles. For this purpose, a quantum Zakharov–Kuznetsov equation is derived and the basic features of the electrostatic excitations are investigated by applying the direct method. It is found that positive and negative bell-shaped solitary pulses become explosive pulses depending mainly upon the angles of propagation and dust polarity. Furthermore, the effects due to nondimensional quantum parameter and the external magnetic field are examined on the width of the quantum dust acoustic solitary pulses. The relevance of the present results to semiconductor quantum wells is mentioned.

Dressed ion-acoustic solitons in magnetized dusty plasmas

In the present research paper, the characteristics of ion acoustic solitary waves are investigated in hot magnetized dusty plasmas consisting of negatively charged dust grains, positively charged ion fluid, and isothermal electrons. Applying a reductive perturbation theory, a nonlinear Korteweg–de Vries (KdV) equation for the first-order perturbed potential and a linear inhomogeneous KdV-type equation for the second-order perturbed potentials are derived. Stationary solutions of these coupled equations are obtained using a renormalization method. The effects of the external oblique magnetic field, hot ion fluid, and higher-order nonlinearity on the nature of the ion acoustic solitary waves are discussed. The results complement and provide new insights into previously published results on this problem [R. S. Tiwari and M. K. Mishra, Phys. Plasmas 13, 062112 (2006)].

Obliquely propagating ion acoustic solitary waves and double layers in a magnetized dusty plasma with anisotropic ion pressure

Obliquely propagating dust ion acoustic solitary waves and double layers in an external magnetic field is studied by using Sagdeev’s pseudo-potential technique. Anisotropic ion pressure is considered, which is defined by applying the Chew–Goldberger–Low theory. The Sagdeev pseudo-potential is derived considering the Poisson equation instead of the charge neutrality condition so that the length scales of the solitary waves and double layers may be shorter than the Debye length. The ranges of parameters for which solitary waves and double layers can exist are studied in detail.

Jeans instability in a magneto-radiative dusty plasma

AbstractThe importance of thermal radiation on the Jeans instability is discussed for a magnetized dusty plasma with gravitational effects. The one-fluid MHD equations are developed by assuming that the entropy of each subsystem of plasma is conserved, when the temperature of the plasma species is non-relativistic. The dispersion relation in this case shows that thermal radiation helps to stabilize the Jeans instability. It is shown that the plasma is stable in a certain range of wavelengths. The magnetic field stabilizes the Jeans instability when the wave propagates across the magnetic field. However, for oblique propagation it is seen that the magnetic field does not stabilize the Jeans instability.

Electrostatic solitary waves in a magnetized dusty plasma

The nonlinear evolution of driven low-frequency electrostatic waves is investigated in a three-component magnetized dusty plasma comprised of a warm dust fluid, electrons, and ions. Electrons as well as ions are considered to have Boltzmann distributions. The fluid equations for the dust along with the quasineutrality condition are used to obtain a single nonlinear differential equation for the electric field. Periodic solutions of the nonlinear differential equation yield sinusoidal, sawtooth and bipolar structures which are similar to nonlinear structures supported in electron-ion plasmas. Results of our findings are applied to Saturn’s rings.

Multidimensional Instability of Dust-Ion-Acoustic Solitary Waves

The basic features of obliquely propagating dust-ion-acoustic (DIA) solitary waves (SWs), and their multidimensional instability in a hot adiabatic magnetized dusty plasma (containing adiabatic inertialess electrons, adiabatic inertial ions, and negatively charged static dust), have been investigated by the reductive perturbation method. The combined effects of plasma particle (electron and ion) adiabaticity and external magnetic field (obliqueness), which are found to significantly modify the basic properties (speed, amplitude, and width) of small but finite-amplitude DIA SWs, are explicitly examined. It is also found that the instability criterion and the growth rate are significantly modified by the external magnetic field and the propagation directions of both the nonlinear waves and their perturbation modes. The implications of our results in space and laboratory dusty plasmas are briefly discussed.