Linear propagation of dust acoustic modes in the presence of an electron beam

The physical and optical properties of plasmas are depended on dynamics of species in the discharge volume. Then, the presence of an electron beam, as a separate component, in a dusty plasma can modify the plasma structures through altering the discharge parameters. In this report, the linear propagation of acoustic modes in a collisionless dusty plasma contains electrons, ions and charged dust grains is investigated in the presence of an electron beam. Our analysis indicates that the electron beam can modify the dispersion relations of dust acoustic modes which resulted different data transportation in dusty plasmas. The obtained results are also examined for negative and positive charged dust grains with different number densities. The charge of dust grains represents an important role in the dynamics of the low frequency waves. Additionally, our findings reveal that the propagation of acoustic waves in dusty plasmas can be controlled by adjusting the electron number density of the beam and the cathode potential. Lastly, we obtian the destabilizing effects, originated from dust charge fluctuation, by reconsidering the dispersion relations of both dust acoustic modes.     

Twisted electrostatic waves in a self‐gravitating dusty plasma

A generalized response (dielectric) function for twisted electrostatic waves is derived for an un‐magnetized self‐gravitating thermal dusty plasma, whose constituents are the Boltzmann‐distributed electrons and positive ions in the presence of negatively charged micrometre‐sized massive dust particulates. For this purpose, a set of Vlasov–Poisson coupled equations is solved along with the perturbed Laguerre–Gauss distribution function, as well as the electrostatic and gravitational potentials in the limit of paraxial approximation. For plane wave solution, the wavefronts of the dust‐acoustic (DA ) wave are assumed to have a constant phase with electric and gravitational field lines propagating straight along the propagation axis. On the other hand, non‐planar wave solutions show helical (twisted) wavefronts, in which field lines spiral around the propagation axis owing to the azimuthal velocity component to account for the finite orbital angular momentum (OAM ) states. The dispersion relation and damping rate for twisted DA waves are studied both analytically and numerically. It is shown that finite OAM states, the dust to electron temperature ratio, and dust self‐gravitation effects significantly affect the linear dispersion and Landau damping frequencies. In particular, the phase speed of twisted DA waves is reduced with the variation of the twist parameter η (= k /lq_ϕ ), dust concentration δ (= n_{d 0}/n_{i 0}), and dust self‐gravitation α (= ω_Jd /ω_pd ). The relevance of our findings to interstellar dust clouds is also discussed for micrometre‐sized massive dust grains.     

Self-focusing of electromagnetic waves in a degenerate electron-hole plasma

The free carrier nonlinear dielectric constant of a degenerate electron-hole plasma (e.g., Ge) in the presence of a Gaussian electromagnetic beam has been studied by a kinetic treatment. The redistribution of carriers (electrons and holes) is the source of nonlinearity and is effective in causing the self-focusing of the beam. The rise in carrier temperature due to the wave field is almost unaffected by the degeneracy, whereas the nonlinearity is considerably affected by it. The increase of degeneracy (by increasing the equilibrium carrier concentration at the fixed lattice temperature) increases the nonlinear dielectric constant. Hence self-focusing is enhanced by degeneracy. This work was supported by NSF (USA) and CSIR (India).     

Theoretical analysis for transmission of Gaussian and sine time irradiance of electromagnetic beam in collisional dusty plasmas

A theoretical model of propagation of Gaussian and Sine time irradiance of an electromagnetic beam in collisional dusty plasma has been done in the present analysis. It contains equilibrium of dust charge, particle density, and energy of plasma ingredients having charge neutrality. Ionization of neutral particles, recombination of free electrons with ions, adsorption and emission of electrons from dust grain surface, and binary collisions between plasma components are also considered in this treatment. Time varying behaviour of modified electron temperature and collision frequency has been illustrated numerically as a function of dust densities. Also, the comparative analyses of variation of beam waist parameter with the dimensionless length of transmission for both the Gaussian and Sine time irradiance are involved in this model as a function of distinguishable time width, collision frequencies, and dust densities under the condition that the size of dust nebulous is greater than the electrons mean free path for the adsorption on the dust grain surface. The observed results are significant for the applications in industry and astrophysics.     

Theory of mach cones in magnetized dusty plasmas with strongly correlated charged dust grains

A theory for the formation of Mach cones in a magnetized dusty plasma with strongly correlated charged dust grains has been presented. We use the electron and ion susceptibilities for weakly correlated magnetized electrons and ions as well as the strongly correlated unmagnetized dust grain susceptibilities which are obtained by means of the quasilocalized charge approximation and a generalized hydrodynamic model. The plasma dielectric response of the present system reveals the parametric regimes for which Mach cones in a strongly coupled laboratory dusty magnetoplasma can be formed. We suggest conducting experiments in radiofrequency dusty plasma discharges with superconducting magnets for verifying the theoretical prediction of Mach cones that is made herein.     

Possibility of weakly charged nonlinear solitary dust clouds near the continuum threshold of dust population in a quasi-neutral dusty plasma

Considering the Boltzmann response of the plasma ions and electrons and inertial dynamics of the charged dust grains, the possibility of very weak compressive soliton near the continuum limit of the dust population has been inferred. It is concluded that the behaviour of such coherent structures could be well described by the numerical analysis of the derived nonlinear classical energy integral equation for bounded solutions. These seem to be higher order dispersive structures within acoustic limit of the nonlinear turbulence. It is observed that the dust density enhancement beyond the continuum threshold causes regular increment in width and amplitude of the soliton structures. It is found that the soliton amplitude sensitively depends on the massive impurity’s population. These coherent structures could be visualized as weakly charged solitary dust clouds of finite extension (∼ plasma Debye length) within Boltzmann environment of plasma particles in their local surroundings. The seeding mechanism of such clouds may be attributed to some plasma instabilities driven by either internal or external free energy sources. Numerical analysis of the problem concludes that the experimental observations of such clouds could be possible in low density plasma regime. It is deduced that for plasma density ∼ 10⁶ cm^-3 at temperatures of a few electron volts and for micron to l0nm sized dust grains, the observation of such structures could be possible within wide range variability of the dust population density.     

Dispersion of Dust Acoustic Modes and Perturbations of Plasma Flux Balance

Previous considerations of dust acoustic waves is demonstrated to be inconsistent ‐ the required equilibrium state for perturbations was not defined since balance of plasma fluxes was neglecting. The self‐consistent treatment shows that plasma flux perturbations are accompanying any collective waves propagating in dusty plasmas and can play an important role in wave dispersion, wave damping and can create instabilities. This is illustrated by the derivation of dispersion relation for dust acoustic modes taking into account the plasma flux balances and plasma flux perturbations by waves. The result of this approach shows that the dust acoustic waves with linear dependence of wave frequency on the wave number exist only in restricted range of the wave numbers. Only for wave numbers larger than some critical wave number for low frequency modes the frequency can be have approximately a linear dependence on wave number and can be called as dust acoustic wave but the phase velocity of these waves is different from that which can be obtained neglecting the flux balance and depends on grain charge variations which are determined by the balance of fluxes. The presence of plasma fluxes previously neglected is the main typical feature of dusty plasmas. The dispersion relation in the range of small wave numbers is found to be mainly determined by the change of the plasma fluxes and is quite different from that of dust acoustic type, namely it is found to have the same form as the well known dispersion relation for the gravitational instability. This result proves in general way the existence of the collective grain attractions of negatively charged grains for for large distances between them and for any source of ionization. The attraction of grains found from dispersion relation of the dust acoustic branch coincides with that found previously for pair grain interactions using some models for the ionization source. For the existing experiments the effective Jeans length for such attraction is estimated to be about 8 – 10 times larger than the ion Debye length and the effective gravitational constant for the grain attraction is estimated to be several orders of magnitude larger than the usual gravitational constant. The grain attraction at large inter‐grain distances described by the gravitationlike grain instability is considered as the simplest explanation for observed dust cloud clustering, formation of dust structures including the plasma crystals. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Formation of dust-acoustic shock waves in a strongly coupled cryogenic dusty plasma

The nonlinear propagation of ultra-low-frequency dust-acoustic (DA) waves in a strongly coupled cryogenic dusty plasma has been investigated, by using the Boltzmann distributed electrons and ions, as well as modified hydrodynamic equations for strongly coupled charged dust grains. The reductive perturbation technique is used to derive the Burger equation. It is shown that strong correlations among negatively charged dust particles acts like a dissipation, which is responsible for the formation of the DA shock waves. The latter are associated with the negative potential, i.e. with the compression of negatively charged cryogenic dust particle density. It is also found that the effective dust-temperature, which arises from electrostatic interactions among negatively charged dust particles, significantly affects the height of the DA shock structures. New laboratory experiments at cryogenic temperature should be conducted to verify our theoretical prediction.     

Electrostatic sheath at the boundary of a collisional dusty plasma

Considering the Boltzmann response of the ions and electrons in plasma dynamics and inertial dynamics of the dust charged grains in a highly collisional dusty plasma, the nature of the electrostatic potential near a boundary is investigated. Based on the fluid approximation, the formation as well as the characteristic behaviours of the sheath is studied. It is expected that the presence of dust charged grains will lead to a very different behaviour of the sheath as compared to that of electron-ion plasma. Moreover, the collisions of the dust charged grains with the neutrals are expected to exhibit novel features.     

Self-focusing of a laser beam in a strongly ionized plasma

In the presence of a strong Gaussian laser beam, the non-linearity in the dielectric constant of a strongly ionized plasma has been investigated. The non-linearity arises due to the heating and redistribution of the electrons; the loss of electron energy gained from the field has been assumed to be due to thermal conduction. This self-induced non-linearity causes a self-focusing and oscillatory waveguide propagation of the beam even when the non-linear dielectric constant does not fall in the saturating range. In a typical case of a 10¹⁰ W laser, the enhancement of axial intensity by a factor of 25 has been predicted in a length of 0.6 cm.Works supported by N.S.F. (USA).On leave from Malviya Regional Engeeniring College, Jaipur-4, India.     

Nonlinear oscillatory waveguide propagation in a plasma

The presence of an intense Gaussian laser beam gives rise to a ponderomotive force on electrons in a collisionless plasma, leading to a redistribution of electron density along the wave-front and consequently to an intensity dependent dielectric constant which saturates with increasing intensity. The intensity dependent dielectric constant is responsible for beam propagation in an oscillatory waveguide. It is seen that (i) a beam of radiusr ₀ less thanr _0min (?c/ω _p) cannot be focused in the plasma regardless of its power, (ii) minimum dimension of oscillatory waveguide increases with increasing power of the beam. Similar results are also obtained for collisional plasma where nonlinearity arises due to nonuniform heating and consequent redistribution of carriers.     

Effects of non‐extensive electrons on the sheath of dusty plasmas with variable dust charge

In this study, a detailed investigation of the problem of sheath is presented using the fluid model in a magnetized three‐component dusty plasma system comprising positive ions, dust grains with variable charge and q‐non‐extensive electrons (i.e., the electrons evolve far away from their Maxwellian thermodynamic equilibrium [q = 1]). The effects of q‐non‐extensivity parameter on the plasma sheath parameters are studied numerically. A significant change is observed in the quantities characterizing the sheath with the presence of the super‐extensive electrons (q < 1) and sub‐extensive electrons (q > 1). In addition, based on the orbital motion limited theory, by taking various forces acting on the dust particle into consideration, the dynamics of the dust located within the sheath, that is, the dust grain charging inside the sheath, is examined under different values of q. It is found that the q‐non‐extensivity has affected significantly the dynamics and the charging process of the dust grains in the sheath.     

On the role of dust in the cometary plasma

The cometary coma consists of neutral gas, plasma, and dust grains. The dust grains can influence both the neutral and charged coma’s constituents. Usually, the presence of dust particles in a plasma results in additional losses of both electrons and ions due to the plasma recombination on the particle surfaces. Solar radiation makes the impact of dust even more complicated depending on the solar flux, the dust number density, the photoelectric properties of the dust particles, the dust particle composition, the distribution of the sizes, etc. We propose a simple kinetic model evaluating the role of dust particles in the coma plasma chemistry and demonstrate that this role can be crucial, resulting in a nontrivial behavior of both the electron and ion densities of the plasma. We show that a coma’s dust particles can be negatively as well as positively charged depending on their composition. These opposite charges of the grains can result in fast coagulation of dust particles, thus, forming complex aggregate shapes of cometary grains. The text was submitted by the authors in English.     

Second Harmonic Generation of Self Focused Cosh‐Gaussian Laser Beam in Collisionless Plasma

This paper presents an investigation of self‐focusing of a Cosh‐Gaussian (ChG) laser beam and its effect on second harmonic generation in collisionless plasma. In the presence of ChG laser beam the carriers get redistributed from high field region to low field region on account of ponderomotive force as a result of which a transverse density gradient is produced in the plasma which in turn generates an electron‐plasma wave at pump frequency. Generated plasma wave interacts with the incident laser beam and hence generates its second harmonics. Moment theory has been used to derive differential equation governing the evolution of spot size of ChG laser beam propagating through collisionless plasma. The differential equation so obtained has been solved numerically. The effect of decentered parameter, intensity of ChG laser beam and density of plasma on self‐focusing of the laser beam and second harmonic yield has been investigated. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Streaming instability in quantum dusty plasmas

By using a quantum hydrodynamic (QHD) model, we derive a generalized dielectric constant for an unmagnetized quantum dusty plasma composed of electrons, ions, and charged dust particulates. Neglecting the electron inertial force in comparison with the electron pressure, and the force associated with the electron correlations at a quantum scale, we discuss two classes of electrostatic instabilities that are produced by streaming ions, and dust grains. The effects of the plasma streaming speeds, the thermal speed of electrons, and the quantum parameter are examined on the growth rates. The relevance of our investigation to dense astrophysical plasmas is discussed.     

Dust‐ion‐acoustic solitary waves in a magnetized dusty pair‐ion plasma with Cairns‐Gurevich electrons and opposite polarity dust particles

The nonlinear dust‐ion‐acoustic (DIA) solitary structures have been studied in a dusty plasma, including the Cairns‐Gurevich distribution for electrons, both negative and positive ions, and immobile opposite polarity dust grains. The external magnetic field directed along the z‐axis is considered. By using the standard reductive perturbation technique and the hydrodynamics model for the ion fluid, the modified Zakharov–Kuznetsov equation was derived for small but finite amplitude waves and was provided the solitary wave solution for the parameters relevant. Using the appropriate independent variable, we could find the modified Korteweg–de Vries equation. By plotting some figures, we have discussed and emphasized how the different plasma values, such as the trapping parameter, the positive (or negative) dust number density, the non‐thermal electron parameter, and the ion cyclotron frequency, can influence the solitary wave structures. In addition, using the bifurcation theory of planar dynamical systems, we have extracted the centre and saddle points and illustrated the phase portrait of such a system for some particular plasma parameters. Finally, we have graphically investigated the behaviour of the solitary energy wave by changing the plasma values as well as by calculating the instability criterion; we have also discussed the growth rate of the solitary waves. The results could be useful for studying the physical mechanism of nonlinear propagation of DIA solitary waves in laboratory and space plasmas where non‐thermal electrons, pair‐ions, and dust particles can exist.     

Small amplitude double layers in an electronegative dusty plasma with q-distributed electrons

The small amplitude dust ion-acoustic double layers in a collisionless four-component unmagnetized dusty plasma system containing nonextensive electrons, inertial negative ions, Maxwellian positive ions, and negatively charged static dust grains are investigated theoretically. Using the pseudo-potential approach and reductive perturbation method, an energy integral equation for the system has been derived and its solution in the form of double layers is obtained. The results appear that the existence regime of the double layer is very sensitive to the plasma parameters, e.g., electron nonextensivity,negative-to-positive ion number density ratio etc. It has been observed that for the selected set of parameters, the system supports rarefactive,(compressive) double layers depending upon the degree of nonextensivity of electrons.     

Laser-Plasma Interaction in Presence of an Obliquely External Magnetic Field: Application to Laser Fusion without Radioactivity

In this paper, the nonlinear interaction of ultra-high power laser beam with fusion plasma at relativistic regime in the presence of obliquely external magnetic field has been studied. Imposing an external magnetic field on plasma can modify the density profile of the plasma so that the thermal conductivity of electrons reduces which is considered to be the decrease of the threshold energy for ignition. To achieve the fusion of Hydrogen-Boron (HB) fuel, the block acceleration model of plasma is employed. Energy production by HB isotopes can be of interest, since its reaction does not generate radioactive tritium. By using the inhibit factor in the block model acceleration of plasma and Maxwell's as well as the momentum transfer equations, the electron density distribution and dielectric permittivity of the plasma medium are obtained. Numerical results indicate that with increasing the intensity of the external magnetic field, the oscillation of the laser magnetic field decreases, while the dielectric permittivity increases. Moreover, the amplitude of the electron density becomes highly peaked and the plasma electrons are strongly bunched with increasing the intensity of external magnetic field. Therefore, the magnetized plasma can act as a positive focusing lens to enhance the fusion process. Besides, we find that with increasing θ-angle (from oblique external magnetic field) between 0 and 90°, the dielectric permittivity increases, while for θ between 90° and 180°, the dielectric permittivity decreases with increasing θ.     

Rogue wave triplets in an ion-beam dusty plasma with superthermal electrons and negative ions

A new dust ion-acoustic wave structure called ‘Rogue wave triplets’ is investigated in an unmagnetized plasma consisting of stationary negatively charged dust grains, charged positive and negative ions, and electrons obeying kappa distribution, which is penetrated by an ion beam. The reductive perturbation theory is used to derive the nonlinear Schrödinger equation governing the dynamics as well as the modulation of wave packets. The rogue wave triplets which are composed of three separate Peregrine breathers can be generated in the modulation instability region. It has been suggested that a laboratory experiment be performed to test the theory presented here.