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Dust Acoustic Shock Waves in a Warm Magnetized Dusty Plasma with Kappa Distributed Electrons and Ions
... From the theoretical framework perspective, numerous authors have investigated the nonlinear structures of DAWs in various dust plasma environments, e.g., dust-acoustic (DA) soliton and DA shock waves, using the Korteweg-de Vries (KdV) and Burger equations. [15][16][17][18][19] However, the validity of using these equations to model a plasma system is conditional on specific values of the plasma parameters for which the first-order nonlinear term is neither equal nor tends to zero. When the value of the first-order nonlinear term is equal to or tends toward zero as the waves evolve with very large amplitudes, the reductive perturbation method fails. ...
... For instance, the consideration of the Physics of Fluids ARTICLE pubs.aip.org/aip/pof values a ¼ 1=2; b ¼ 1, and c > 1=2 produced the KdV equation (18), while a ¼ 0:5; b ¼ 1, c ¼ 0:5 and the equilibrium or neutrality condition is satisfied lead to the Burgers' equation (20). The coexistence of dispersion and dissipation can be observed at a ¼ 1=2; b ¼ 1 and c ¼ 1=2, leading to the KdV-Burgers' equation (22). ...
... The soliton solution u KdV ðn; sÞ (19) satisfies the KdV equation (18) under the condition of the balance between the nonlinear and dispersion terms. In Figs. 1 and 2, we study the electrostatic potential u KdV ðn; 0:01Þ as a function of the position n under the effects of the thermal r and non-extensive q parameters. ...
A variety of dust acoustic (DA) waves like solitons, shock waves, and double-layer structures can generate and propagate in dusty plasma systems depending on the plasma composition and their particle distributions. In this paper, a refined fluid model is proposed to provide a general description of all possible DA waves that may propagate in complex dusty plasmas with thermally distributed heavy ions and non-extensive light species. The DA waves are characterized using the Further-Burger equation with three newly induced arbitrary parameters, enabling the identification of the different plasma waves. The DA wave's structures are found to be highly sensitive to the thermal parameter σ of the heavy ions and the non-extensive parameter “q” of the light species. Moreover, these two parameters act as key factors that control the polarity of the waves around their critical values, i.e., around σ = 0.11 and “q = 1.146.” The potential relevance of our results in space and astrophysics plasma setups is briefly discussed.
... Additionally, they concluded that although the steepness of the positive and negative shock waves decreases with kinematic viscosity, their amplitudes stay constant in magnitude. Worm-viscous dust fluid in a magnetized dusty plasma system with superthermal electrons and ions is studied by Berbri et al. [27]. They observed that when the magnetic field intensity grew, so did the amplitude of the dust acoustic shock waves. ...
In this work, we have studied the propagation of nonlinear electrostatic shock waves in an anisotropically pressured magnetized plasma containing positive and negative ions, trapped electrons, and positrons. A reductive perturbation technique is used to generate the trapped Zakharov-Kuznetsov Burgers’ equation is generated for nonlinear analysis. We study and debate the effects of positron and electron trapping on shock structures. In addition, the influence of an external magnetic field and an anisotropic pressure on the shock waves for both positive and negative ions is thoroughly discussed. It is shown that the amplitude and magnitude of the shock wave are affected by changes in the bulk viscosity and kinematic viscosity for both ions. The paper examines the unique characteristics of rarefactive shock-like formations under various plasma conditions, including ion bulk and kinematic viscosities, electrons and positron trapping with the influence of magnetic fields. This result of this study will provide a better understanding of the nonlinear transmission of ion acoustic shock waves in astrophysical environments, such as neutron stars and pulsar magnetospheres.
... They also deduced that although the steepness of the positive and negative shock waves decreases with kinematic viscosity, their amplitudes stay the same in magnitude. Berbri et al. [41] study the characteristics of a magnetized dusty plasma system that consists of superthermal electrons and ions. They specifically focus on the properties of a fluid made up of worm-like viscous dust particles. ...
Dusty plasmas are plasmas containing solid particles in the size range of about 10 nm—10 μm. The particles acquire an electrical charge by collecting electrons and ions from the plasma, or by photo-electron emission if they are exposed to UV radiation. The charged dust particles interact with the electrons and ions, forming a multi-component plasma. Dusty plasmas occur in a number of natural environments, including planetary rings, comet tails, and solar nebulae; as well as in technological devices used to manufacture semiconductor chips, and in magnetic fusion devices. This article focuses on the physics underlying dusty plasmas, which are studied by plasma physicists, aeronomists, space physicists, and astrophysicists. The article begins with an introduction explaining what we mean by a dusty plasma, where they are found, and a summary of their basic properties. The article then presents the fundamental physics of dust charging, forces on dust particles, a description of devices used to produce dusty plasmas, strongly coupled dusty plasmas, collective phenomenon (waves) in dusty plasmas, magnetized dusty plasmas, and the emerging technologies based on dusty plasmas. It concludes with a few perspective comments on how the field has developed historically and the prospects for future advances.
The characteristics of low-frequency shocks in a magnetized dusty plasma comprising of negatively charged dust fluid, kappa-distributed electrons and ions have been investigated. Using the reductive perturbation method, the nonlinear Korteweg de–Vries–Burgers (KdV–B) equation which governs the dynamics of the dust acoustic (DA) shock waves is derived. The characteristics of shock structures are studied under the influence of various plasma parameters, viz. superthermality of ions, magnetic field, electron-to-dust-density ratio, kinematic viscosity, ion-to-electron-temperature ratio and obliqueness. The combined effects of these physical parameters significantly influence the characteristics of DA shock structures. It is observed that only negative potential shocks exist in a plasma environment comprising of dust fluid and superthermal electrons and ions such as that of Saturn’s magnetosphere.
In this paper, a theoretical investigation has been made of obliquely propagating dust acoustic solitary wave (DASW) structures in a cold magnetized dusty plasma consisting of a negatively charged dust fluid, electrons, and two different types of nonthermal ions. The Zakharov-Kuznetsov (ZK) and modified Zakharov-Kuznetsov (MZK) equations, describing the small but finite amplitude DASWs, are derived using a reductive perturbation method. The combined effects of the external magnetic field, obliqueness (i.e. the propagation angle), and the presence of second component of nonthermal ions, which are found to significantly modify the basic features (viz. amplitude, width, polarity) of DASWs, are explicitly examined. The results show that the external magnetic field, the propagation angle, and the second component of nonthermal ions have strong effects on the properties of dust acoustic solitary structures. The solitary waves may become associated with either positive potential or negative potential in this model. As the angle between the direction of external magnetic field and the propagation direction of solitary wave increases, the amplitude of the solitary wave (for both positive potential and negative potential) increases. With changing this angle, the width of solitary wave shows a maximum. The magnitude of the external magnetic field has no direct effect on the solitary wave amplitude. However, with decreasing the strength of magnetic field, the width of DASW increases.
The propagation of linear and nonlinear dust acoustic (DA) waves in a homogeneous unmagnetized, collisionless and dissipative dusty plasma consisted of extremely massive, micron-sized, negatively 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 η_{d} and the ratio of the ions to the electrons temperatures σ_{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 (tanh) 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.
A nonlinear dust acoustic solitary wave (DASW) in a magnetized dusty plasma with superthermal electrons is studied analytically. In this model hot electrons are described by the kappa distribution function, but ions are taken to be Maxwellian and plasma pressure and dust-natural collisions have been taken into account. Using the reductive perturbation method the Zakharov–Kuznetsov equation is derived and effect of electrons’ hotness on the amplitude and width of soliton in dusty plasma is investigated. With decreasing energy of the hot electrons in the system, κ > 100, results coincide with the results of the dusty plasma system containing Maxwellian electrons. In this model anisotropy is caused by an external magnetic field while inhomogeneity is generated by ion density gradient in the plasma. The initial density decreases exponentially in the space along one direction. The amplitude of DASW is mainly affected by density inhomogenity rather than the electrons’ energy. With increasing energy of the system, the width of DASW increases significantly. Applying the effect of pressure in the model only rarefactive DASW may be generated in the dusty plasma.
Plasma fluctuations arise in the boundary region between charged dust clouds and background plasmas. A self-consistent computational model is developed to study expansion of a charged dust cloud across a magnetic field, creation of the inhomogeneous boundary layer and associated processes. The charging of the dust particulates produces a boundary layer and associated ambipolar electric field. This ambipolar field provides a source for low frequency dust acoustic waves in unmagnetized plasmas. A background magnetic field if sufficiently strong, may impact the dust acoustic wave evolution and dust density structures due to E×B and diamagnetic current generation. The dust acoustic density fluctuation generation across a strong magnetic field (ωpe/Ωce≪1) may be suppressed as compared to an unmagnetized dusty plasma, which will be discussed. Fluctuations generated at longer timescales propagating along the dust boundary layer will also be investigated in the lower hybrid and dust lower hybrid frequency range. Applications to space and laboratory plasmas are discussed.
We describe experiments on (1) nonlinear dust acoustic waves and (2) dust acoustic shocks performed in a direct current (DC) glow discharge dusty plasma. First, we describe experiments showing nonlinear dust acoustic waves characterized by waveforms of the dust density that are typically sharper in the wave crests and flatter in the wave troughs (compared to sinusoidal waves), indicating the development of wave harmonics. We discuss this behavior in terms of a second-order fluid theory for dust acoustic waves. Second, experimental observations of the propagation and steepening of large-amplitude dust acoustic waves into dust acoustic shock waves are presented. The observed shock wave evolution is compared with numerical calculations based on the Riemann solution of the fully nonlinear fluid equations for dust acoustic waves.
The Korteweg-deVries (KdV) equation that describes the evolution of nonlinear ion-acoustic solitary waves in plasmas with Kappa-distributed electrons is derived by using a reductive perturbation method in the small amplitude limit. We identified a dip-type (negative) electrostatic KdV solitary wave, in addition to the hump-type solution reported previously. The two types of solitary waves occupy different domains on the κ (Kappa index)-V (propagation velocity) plane, separated by a curve corresponding to singular solutions with infinite amplitudes. For a given Kappa value, the dip-type solitary wave propagates faster than the hump-type. It was also found that the hump-type solitary waves cannot propagate faster than V = 1.32.
Recent analysis of the excitation of dust Bernstein–Greene–Kruskal modes [Tribeche et al., Phys. Plasmas 7, 4013 (2000)] is extended to include self-consistently the dust charge variation. The grain charge becomes a new self-consistent dynamical variable, leading to some new and interesting results such as threshold lowering, mode damping, and spatially localized nonlinear structures. © 2002 American Institute of Physics.
The basic features of dusty plasmas, particularly basic characteristics of dust in a plasma, and typical dusty plasma parameters for different space and laboratory plasma conditions, are presented. The complexity and the diversity of the field of dusty plasma physics are briefly discussed. Theoretical and experimental discoveries of linear and nonlinear features of waves, particularly dust-ion-acoustic and dust-acoustic waves, in dusty plasmas are reviewed.
We analyze the radial distribution of electron populations inside 20 Rs in Saturn's magnetosphere, and we calculate moments for these populations by a forward modeling method using composite spectra produced by the CAPS/ELS (0.6 eV to 26 keV) and the MIMI/LEMMS (15 keV to 10 MeV) instruments on board Cassini. We first calculate and harmonize both data sets in physical units and apply corrections taking into account biases introduced by spacecraft interaction with the magnetospheric environment. We then test different bimodal isotropic electron distribution models, deciding on a model with two kappa distributions. We adjust our isotropic model to the flux composite spectra with a least square method to produce three sets of fluid parameters (density, temperature, spectral index) per electron population. The radial profiles are then analyzed, revealing a relevant boundary at 9 Rs in both thermal and suprathermal electron populations. Observed discontinuities in the moment profiles (sudden drop-off in cold density profile outside 9 Rs, hot electrons drop-off inside 9 Rs) coincide with the known outer edge of Saturn's neutral OH cloud. Farther out, thermal electrons disappear completely beyond 15 Rs while suprathermal electrons are still observed in the middle and outer magnetosphere.
We report first in situ multispacecraft observations of nonlinear steepening of compressional pulses in the solar wind upstream of Earth's bow shock. The magnetic field of a compressional pulse formed at the upstream edge of density holes is shown to suddenly break and steepen into a shocklike structure. During the early phase of development thermalization of ions is insignificant. Substantial thermalization of ions occurs as gyrating ions are observed at the steepened edge. These observations indicate that the mechanisms causing the dissipation of magnetic fields (currents) and ions are different in the early phase of shock development.
The results on shock phenomena in dusty plasmas of the Solar System are reviewed. The problems of dust ion acoustic bow shock in interaction of the solar wind with dusty cometary coma and formation of transient atmospheres of atmosphereless cosmic bodies such as Moon, Mercury, asteroids and comets are considered. The latter assumes the evolution of meteoroid impact plumes and production of charged dust grains due to the condensation of both the plume substance and the vapor thrown from the crater and the surrounding regolith layer. Physical phenomena occurring during large meteoroid impacts can be modeled with the aid of active rocket experiments, which involve the release of some gaseous substance in near-Earth space. New vistas in investigation of shock processes in natural dusty plasmas are determined.
A statistical analysis of density fluctuations in a cylindrical non-fusion device is performed. The experimental setup is implemented in order to reach a turbulent behavior of the linear plasma column. Two different turbulent regimes are obtained corresponding to two selected sets of values for the discharge parameters. The first regime displays a rotating column characterized by the presence of a shear layer separating the plasma bulk from the tenuous plasma in the shadow of the limiter, the latter showing a strong intermittent behavior and superdiffusion. The second regime corresponds to a weakly rotating column in which coherence is lost in the plasma bulk and a standard diffusive process takes place in the shadow region. These findings are supported by the calculation of the Hurst's exponent using wavelet-analysis techniques. Furthermore the intermittent behavior is characterized and related to the diffusive process. Finally the shape of the probability distribution function of density fluctuations seems to be well described by an analytical form suggested on the basis of Tsallis generalized statistics.
Formation of ion-acoustic shock waves (IAShWs) and their propagation nature in a magnetized plasma in the presence of superthermal trapped electrons are investigated for the first time via the fluid dynamical approach. A magnetized plasma system, comprising of inertial ions and non-inertial electrons following κ-superthermal trapped distribution, is considered to examine the basic features (amplitude, width, phase speed, etc.) of IAShWs in such a plasma. A diffusion effect (due to the ion kinematic viscosity) is taken into account. The reductive perturbation technique is adopted to derive the modified Korteweg de-Vries Burgers’ (mKdVB) equation and the solution of mKdVB equation (derived by adopting the tangent hyperbolic method) is used to investigate the dynamical and structural characteristics (speed, amplitude, width, etc.) of IAShWs. The influence of relevant plasma (configuration) parameters (e.g., the superthermality index κ, concentration of trapped electrons, external magnetic field, and obliquity angle, etc.) on the nature of IAShWs is examined. The applications of the results in space and laboratory plasma environments, where nonthermal trapped electrons are available, are briefly discussed.
By considering the continuity, the Navier-Stokes and Poisson's equations in a nonrelativistic framework for plasmas, we study the behavior of small amplitude ion acoustic solitary waves in plasmas under the influence of a varying magnetic field. The result is a nonlinear wave equation which complies with the modified Korteweg-de Vries-Burgers equation, surprisingly in the absence of thermal pressure or any dissipative effects. We show that the complete set of equations, by considering the varying magnetic field, creates solitary waves which radiate energy during their travel in the medium. An interesting result is the existence of small amplitude localized shock profiles beside the solitary waves. Properties of this solitaire solution are studied by considering different values for the environmental characters.
A rigorous theoretical investigation has been made on dust-acoustic (DA) shock structures in an unmagnetized dusty plasma system whose constituents are negatively charged cold mobile dust fluid, electrons following Boltzmann distribution, and positively charged ions of two distinct temperatures following nonextensive (q) and nonthermal distributions, respectively. In this paper, the Burgers' equation has been derived by employing reductive perturbation technique which is valid for small but finite amplitude limit. It is observed that both the nonextensive and nonthermal ions of two distinct temperatures and dust kinematic viscosity significantly modify the basic properties (amplitudes, width, and polarities) of the DA shockwaves (DASHWs). The effects of low (high) temperature ions following nonextensive (nonthermal) and dust kinematic viscosity on DASHWs are examined both analytically and numerically. The implications of these results to some astrophysical environments and space plasmas (e.g., stellar polytropes, peculiar velocity distributions of galaxies, and collisionless thermal plasma), and laboratory dusty plasma systems are briefly mentioned.
A theoretical investigation is carried out to study the basic properties of dust-acoustic (DA) shock waves propagating in a magnetized non-thermal dusty plasma (containing cold viscous dust fluid, non-thermal ions, and non-thermal electrons). The reductive perturbation method is used to derive the Korteweg–de Vries–Burgers equation. It is found that the basic properties of DA shock waves are significantly modified by the combined effects of dust fluid viscosity, external magnetic field, and obliqueness (angle between external magnetic field and DA wave propagation direction). It is shown that the dust fluid viscosity acts as a source of dissipation, and is responsible for the formation of DA shock structures in the dusty plasma system under consideration. The implications of our results in some space and laboratory plasma situations are briefly discussed.
A theoretical investigation has been made of obliquely propagating nonlinear electrostatic shock structures. The reductive perturbation method has been used to derive the Korteweg-de Vries-Burger (KdV-Burger) equation for dust acoustic shock waves in a homogeneous system of a magnetized collisionless plasma comprising a four-component dusty plasma with massive, micron-sized, positively, negatively dust grains and non-extensive electrons and ions. The effect of dust viscosity coefficients of charged dusty plasma of opposite polarity and the non-extensive parameters of electrons and ions have been studied. The behavior of the oscillatory and monotonic shock waves in dusty plasma has been investigated. It has been found that the presence of non-extensive parameters significantly modified the basic properties of shock structures in space environments.
A recent paper [L.-N. Hau and W.-Z. Fu, Phys. Plasmas 14, 110702 (2007)]
deals with certain mathematical and physical properties of the kappa
distribution. We comment on the authors' use of a form of distribution
function that is different from the ``standard'' form of the kappa
distribution, and hence their results, inter alia for an expansion of
the distribution function and for the associated number density in an
electrostatic potential, do not fully reflect the dependence on κ
that would be associated with the conventional kappa distribution. We
note that their definition of the kappa distribution function is also
different from a modified distribution based on the notion of
nonextensive entropy.
A laboratory observation of the dust-acoustic instability is reported. The results are compared with available theories. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.
An investigation into both small and large amplitude dust acoustic solitary waves in dusty plasmas with cold negative dust grains and kappa-distributed ions and/or electrons is discussed. Existence conditions for the arbitrary amplitude case are found in an appropriate parameter space, viz., an effective Mach number of the structure speed and the fraction of the charge density that resides with the free electrons, expressed in terms of the ion density. Results indicate that the kappa distribution has only a quantitative, not a qualitative effect on the existence domains and only negative potential solitons exist regardless of whether the electrons or the ions, or both, have a kappa distribution. Despite a wide-ranging search, we have not found double layers in such a plasma. In the case of positive dust, an equivalent set of results holds.
We fit Kappa functions to 16,000 velocity distribution functions measured in the solar wind by the electron plasma instrument on board Ulysses. Statistically, the electron distributions are observed to have important high velocity tails in the fast solar wind but are closer to a Maxwellian in the slow wind. We also discuss how this result could support a recent kinetic model of the solar wind proposed by Maksimovic, Pierrard and Lemaire [1997].
DOI:https://doi.org/10.1103/PhysRevLett.17.996
Linear and nonlinear dust ion-acoustic waves are studied experimentally in a homogeneous unmagnetized dusty plasma. In the linear regime, the phase velocity of the wave increases and the wave suffers heavy damping with increasing dust density. An oscillatory ion-acoustic shock wave in usual Ar plasma transforms into a monotonic shock front when it travels through the dusty plasma column. The Korteweg-de Vries-Burgers equation is numerically integrated taking experimental parameters into account, and the results are compared with the experimental findings.
An experimental investigation of the effect of negatively charged dust on ion acoustic shock formation in a Q machine is described. Ion acoustic compressional pulses were observed to steepen as they traveled through a dusty plasma if the percentage of the negative charge in the plasma on the dust grains was ≳75%.
The detection of a new LF electrostatic wave in an unmagnetized collisionless dusty plasma is reported. This new wave should have relevance to LF noise in the F-ring of Saturn. Due to the special feature of the dusty plasma in this ring, the present dust acoustic wave can exist as a normal mode of the system.
The dissipation caused by fluid viscosity is investigated for unmagnified dusty plasma with two-temperature ions in a spherical geometry. Analytical investigation shows that the propagation of a small-amplitude wave is governed by the spherical Kadomtsev-Petviashvili-Burgers equation. The shock wave solutions for dust-acoustic shock waves with two types of charged dust grains, that is, constant charged dust grains and adiabatic variable charged dust grains, are studied. The effects caused by dissipation and transverse perturbations are also discussed.
The effects of the external magnetized field, nonadiabatic dust charge fluctuation, and nonthermally distributed ions on three-dimensional dust acoustic shock wave in dusty plasmas have been investigated. By using the reductive perturbation method, a Korteweg–de Vries (KdV) Burger equation governing the dust acoustic shock wave is derived. The results of numerical integrations of KdV Burger equation show that the external magnetized field, nonthermally distributed ions, and nonadiabatic dust charge fluctuation have strong influence on the shock structures.
In this paper, we consider an unmagnetized plasma consisting of warm adiabatic ions, superthermal electrons, and thermal positrons. Nonlinear cylindrical and spherical modified Korteweg-de Vries (KdV) equations are derived for ion acoustic waves by using reductive perturbation technique. It is observed that an increasing positron concentration decreases the amplitude of the waves. Furthermore, the effects of the superthermal parameter (k) on the ion acoustic waves are found. (C) 2011 American Institute of Physics. [doi:10.1063/1.3613675]
It is commonly accepted that supernova-explosions are the dominant source of cosmic rays up to an energy of 10 to the 14th power eV/nucleon. Moreover, these high energy particles provide a major contribution to the energy density of the interstellar medium (ISM) and should therefore be included in calculations of interstellar dynamic phenomena. For the following the first order Fermi mechanism in shock waves are considered to be the main acceleration mechanism. The influence of this process is twofold; first, if the process is efficient (and in fact this is the cas) it will modify the dynamics and evolution of a supernova-remnant (SNR), and secondly, the existence of a significant high energy component changes the overall picture of the ISM. The complexity of the underlying physics prevented detailed investigations of the full non-linear selfconsistent problem. For example, in the context of the energy balance of the ISM it has not been investigated how much energy of a SN-explosion can be transfered to cosmic rays in a time-dependent selfconsistent model. Nevertheless, a lot of progress was made on many aspects of the acceleration mechanism.
The screening of dust particles immersed in the sheath of a parallel plate rf discharge in helium is studied by excitation of waves in a linear chain arrangement. The waves are excited by the radiation pressure of a modulated laser beam. The measured dispersion relation is compared with a one-dimensional dust lattice wave to obtain the shielding length. Dust acoustic waves are not compatible with the measured dispersion relation.
The tanh (or hyperbolic tangent) method is a powerful technique to search for travelling waves coming out from one-dimensional nonlinear wave and evolution equations. In particular, in those problems where dispersive effects, reaction, diffusion and/or convection play an important role. To show the strength of the method, an overview is given to find out which kind of problems are solved with this technique and how in some nontrivial cases this method, adapted to the problem at hand, still can be applied. Single as well as coupled equations, arising from wave phenomena which appear in different scientific domains such as physics, chemical kinetics, geochemistry and mathematical biology, will be treated. Next, attention is focussed towards approximate solutions. As a result, solitary- and shock-wave profiles are derived together with the associated width and velocity. The same method can be easily extended so that difference-differential equations can be similarly solved. Finally, some extensions of the method are discussed.
It is shown that after a sufficiently long propagation time, the nonlinear dust-acoustic waves appear as a stationary shock wave structure. The latter arises as a result of a balance between the nonlinear wave breaking and the dissipation of the wave energy due to the variation of the dust particle charges. The presented analytical theory shows that a necessary condition for the shock formation demands that the dust acoustic wave frequency ω is considerably smaller than the dust charging frequency ωq0. In this frequency regime, the shock wave propagation is described by the well-known Burgers equation. Furthermore, the breakdown of the analytical theory has been studied by solving the basic set of fluid equations numerically. The numerical solutions exhibit that shock waves may also occur for ω of the order of ωq0, viz in a wave frequency regime that is not covered by our analytical theory.
New acoustic waves originating from a balance of dust particle inertia and plasma pressure are investigated. It is shown that these waves can propagate linearly as a normal mode in a dusty plasma, and non-linearly as supersonic solitons of either positive or negative electrostatic potential.
Repeated, self-excited dust acoustic shock waves (DASWs) have been observed in a dc glow discharge dusty plasma using high-speed video imaging. Two major observations are reported: (1) The self-steepening of a nonlinear dust acoustic wave (DAW) into a saw-tooth wave with sharp gradient in dust density, very similar to those found in numerical solutions of the fully nonlinear fluid equations for a nondispersive DAW [B. Eliasson and P. K. Shukla, Phys. Rev. E 69, 067401 (2004)], and (2) the collision and confluence of two DASWs.
Low energy electron spatial distribution in magnetosphere obtained with OGO 1 and 3 indicate lower energies and higher densities occur during geomagnetic disturbances
The average charge on a particle in a particle-plasma cloud, the plasma potential inside the cloud, and the Coulomb force acting on the particle are calculated. The net repulsive electrostatic force on a particle depends on the plasma density, temperature, density of particles, particle size, and the gradient of the particle density. In a uniformly dense ring the electrostatic repulsion is zero. It is also shown that the electrostatic force acts like a pressure force, that even a collisionless ring can be stable against gravitational collapse, and that a finite ring thickness does not necessarily imply a finite velocity dispersion. A simple criterion for the importance of electrostatic forces in planetary rings is derived which involves the calculation of the vertical ring thickness which would result if only electrostatic repulsion were responsible for the finite ring thickness. Electrostatic forces are entirely negligible in the main rings of Saturn and the E and G rings. They may also be negligible in the F ring. However, the Uranian rings and Jupiter's ring seem to be very much influenced by electrostatic repulsion. In fact, electrostatic forces could support a Jovian ring which is an order of magnitude more dense than observed.
The low energy plasma electron environment within Saturn's magnetosphere was surveyed by the Plasma Science Experiment (PLS) during the Voyager encounters with Saturn. Over the full energy range of the PLS instrument (10 eV to 6 keV) the electron distribution functions are clearly non-Maxwellian in character; they are composed of a cold (thermal) component with Maxwellian shape and a hot (suprathermal) non-Maxwellian component. A large scale positive radial gradient in electron temperature is observed, increasing from less than 1 eV in the inner magnetosphere to as high as 800 eV in the outer magnetosphere. Three fundamentally different plasma regimes were identified from the measurements: (1) the hot outer magnetosphere, (2) the extended plasma sheet, and (3) the inner plasma torus. Previously announced in STAR as N83-34872
Khurshed Alam, “Shock waves in a dusty plasma with dust of opposite polarities
- A Rahman
- A A Mamun