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Weakly nonlinear dust ion-acoustic shock waves in a dusty plasma with nonthermal electrons
Physics of Plasma
Abstract
Weakly nonlinear dust ion-acoustic (DIA) shock waves are investigated in a dusty plasma with nonthermal electrons. A modified Korteweg–de Vries equation with a cubic nonlinearity is derived. Due to the net negative dust charge μZd and electron nonthermality, the present plasma model can admit compressive and rarefactive weak DIA shock waves. The effect of increasing μZd is to lower the critical nonthermal parameter βc above which only rarefactive DIA shock waves are admitted. Our investigation may help to understand the nonlinear structures observed in the auroral acceleration regions.
The basic properties of dust acoustic (DA) waves in magnetized three component plasmas with fully non-linear mobile dust components and non-thermal ions and electrons is theoretically investigated. We have adopted the pseudopotential (Sagdeev potential) approach to establish the existence of parametric domain for solitons. High-amplitude subsonic rarefactive solitons are seen produced which are affected by the direction of magnetic field. Relatively higher value of and Mach number creates higher amplitude.
Starting from one dimensional Kappa distribution for electrons, we have systematically developed the combined Kappa-Cairns distribution. We have found the effective bounds of both nonthermal parameters and for the combined Kappa-Cairns distribution. This distribution can generate more highly energetic particles in comparison with both Kappa and Cairns distributions. We have investigated ion acoustic solitary structures in a collisionless magnetized plasma composed of negatively charged static dust grains, adiabatic warm ions and a population of highly energetic electrons generated from the combined Kappa-Cairns distribution. Sagdeev pseudo-potential technique has been considered to investigate the arbitrary amplitude steady state solitary structures including double layers and supersolitons. We have developed a computational scheme to draw the existence domains showing the nature of existence of different solitary structures. Different solitary structures of both positive and negative polarities have been observed for different values of and . We have seen two important transitions of solitary structures for negative polarity, viz., soliton before the formation of double layer → double layer → supersoliton → soliton after the formation of double layer, and soliton before the formation of supersoliton → supersoliton → soliton. For the second case, we have a supersoliton structure without the formation of double layer and this case is completely new one for magnetized plasma. Different solitary structures supported by the system have been investigated with the help of compositional parameter spaces and the phase portraits of the dynamical systems describing different solitary structures.
Arbitrary amplitude dust ion acoustic solitary structures have been investigated in an unmagnetized collisionless dusty plasma consisting of negatively charged static dust grains, adiabatic warm ions, nonthermal electrons and isothermal positrons. A computational scheme has been developed to draw the qualitatively different existence domains or compositional parameter spaces showing the nature of existence of different solitary structures with respect to any parameter of the present plasma system. The present system supports both positive and negative potential double layers, coexistence of solitary waves of both polarities and positive potential supersolitons.
Recent observations show the existence of high energy electrons in various astrophysical plasmas which their distribution functions are highly non thermal. The presence of dust ion acoustic localized waves in plasmas which contain non thermal electrons and ions with kinematic viscosity along with stationary charged dust is investigated. Solitary shock waves are derived as solutions of nonlinear wave equation of the medium using the reductive perturbation method by employing suitable stretching coordinates. Both rarefactive and compressive shock profiles are created in the medium according to the initial values of the medium parameters. We report that increasing the electron number density makes a growth in the amplitude of negative shock waves while it decreases the amplitude of positive shock profile. Some behavior of observed transience in the plasma waves can be explained using the presented results.
Sagdeev's pseudo potential method is employed to study dust ion-acoustic solitary waves in an unmagnetized plasma with non-thermal electrons. An exact analytical expression is obtained for the pseudo potential. The range of parameters for the existence of solitary waves and double layers using the analytical expression of the Sagdeev potential has been found. It is observed that, depending on the values of the plasma parameters like ion temperature ω, non-thermal electron parameter β and the value of the dust grain charge μZ d, both rarefactive and compressive solitary waves may exist. Critical values of these parameters, beyond which solitary waves would cease to exist, areobtained for some particular cases. Double layer solutions are also obtained for certain parametric values. Exact numerical results are obtained for arbitrary amplitude solitons and double layers.
Nonlinear quantum positron-acoustic (QPA) waves are investigated for the first time, within the
theoretical framework of the quantum hydrodynamic model. In the small but finite amplitude limit,
both deformed Korteweg-de Vries and generalized Korteweg-de Vries equations governing, respectively,
the dynamics of QPA solitary waves and double-layers are derived. Moreover, a full finite
amplitude analysis is undertaken, and a numerical integration of the obtained highly nonlinear
equations is carried out. The results complement our previously published results on this problem.
The propagation of dust ion-acoustic shock waves (DIASHWs) in an unmagnetized dissipative dusty plasma system consisting of inertial ions, non-inertial, non-extensive q-distributed electrons, and negatively charged stationary dust is investigated in bounded non-planar (cylindrical and spherical) geometry. A modified Burgers equation is derived and its numerical solution is obtained. It is found that the basic features of DIASHWs are significantly modified by the effects of electron non-extensivity and ion kinematic viscosity in bounded geometry. It is also shown that the propagation characteristics of non-planar DIASHWs in a non-extensive plasma are qualitatively different from those of planar ones.
The linear and nonlinear dust-ion-acoustic (DIA) wave propagating obliquely with respect to an external magnetic field is studied in a magnetized complex plasma which consists of a cold ion fluid, superthermal electrons, and static dust particles. The propagation properties of two possible modes (in the linear regime) are investigated. It is found that the electron suprathermality and the electron population decrease the phase velocities of both modes, while obliqueness leads to increase of separation between two modes. An energy-like equation derived to describe the nonlinear evolution of DIA solitary waves. The influences of electron suprathermality, obliqueness, and electron population on the existence domain of solitary waves and the soliton characteristics are examined. It is shown that the existence domain of the DIA soliton and its profile are significantly depending on the deviation of electrons from thermodynamic equilibrium, electrons population, and obliqueness. It is also found that the suprathermal plasma supports the DIA solitons with larger amplitude.
The effects of dust charge fluctuations and deviations from isothermality of electrons are incorporated in the study of nonlinear
dust ion-acoustic waves. Deviations from isothermality of electrons are included in this model as a result of nonlinear resonant
interaction of the electrostatic wave potential with electrons during its evolution. The basic properties of stationary structures
are studied by employing the reductive perturbation method, and conditions for the formation of small but finite amplitude
dust ion-acoustic solitary waves in the space dusty plasma situations are clearly explained. It is shown that a more depletion
of the background free electrons owing to the attachment of these electrons to the surface of the dust grains during the charging
process can lead to the formation of solitary waves with smaller amplitude. Furthermore, effects of the dust charge fluctuation
and deviations from isothermality of electrons show a non-uniform behavior for the amplitude of solitary waves in transition
from the Boltzmann electron distribution to a trapped electron one. It is also found that the dust charge fluctuation caused
by trapped as well as free electrons is a source of dissipation, and is responsible for the formation of the dust ion-acoustic
shock waves.
KeywordsDeviations from isothermality–Dust charge fluctuations–Solitary waves–Shock waves
For an unmagnetized multicomponent dusty plasma, the effects of non-thermal electron distribution, ion temperature and two
oppositely charged dust grains are incorporated in the study of arbitrary amplitude solitary waves. An energy-like integral
equation involving Sagdeev potential is derived, and the existence, formation and basic properties of solitons are studied.
It is also found a definite interval for the Mach number for which solitary waves exist and depends sensitively upon the population
of fast or non-thermal electrons present. Our results should be useful to understand the properties of localized electrostatic
disturbances that may occur in space dusty plasma.
KeywordsNon-thermal distribution–Negative (positive) dust concentration–Ion temperature–Solitary waves
Dust ion acoustic solitary structures have been investigated in an
unmagnetized nonthermal plasma consisting of negatively charged dust grains,
adiabatic positive ions and nonthermal electrons. For isothermal electrons, the
present plasma system does not support any double layer solution, whereas for
nonthermal electrons, negative potential double layer starts to occur whenever
the nonthermal parameter exceeds a critical value. However this double layer
solution is unable to restrict the occurrence of all negative potential
solitary waves of the present system. As a result, two different types of
negative potential solitary waves have been observed, in which occurrence of
first type of solitary wave is restricted by M_c<M M_D, where M_c is the lower bound of Mach number
M and M_D(>M_c) is the Mach number corresponding to a negative potential double
layer. A finite jump between the amplitudes of negative potential of solitary
waves at M=M_D-\epsilon_1 and at M=M_D+\epsilon_2 has been observed, where
0<\epsilon_1<M_D-M_c and \epsilon_2>0. An analytical theory for the existence
of double layer has been presented. A numerical scheme has also been provided
to find the value of Mach number at which double layer solution exists and also
the amplitude of that double layer. Although the occurrence of coexistence of
solitary structures of both polarities is restricted by M_c<M <= M_max, only
negative potential solitary wave still exists for all M>M_max, where M_max is
the upper bound of M for the existence of positive potential solitary waves
only. Qualitatively different compositional parameter spaces showing the nature
of existing solitary structures of the energy integral have been found. These
solution spaces are capable of producing new results and physical ideas for the
formation of solitary structures.
Solitary electrostatic structures involving density depletions have been observed in the upper ionosphere by the Freja satellite [Dovner et al., 1994]. If these are interpreted as ion sound solitons, the difficulty arises that the standard Korteweg-de Vries description predicts structures with enhanced rather than depleted density. Here we show that the presence of non-thermal electrons may change the nature of ion sound solitary structures and allow the existence of structures very like those observed.
A kinetic analysis of the excitation of dust
BGK(Bernstein-Greene-Kruskal) modes in a collisional dusty plasma is
presented. It is found that in the case where all the electrons are
attached to the dust particles, consequent modifications in the
nonlinear electrostatic potential structure can significantly influence
the existence and properties of the nonlinear BGK modes. The derivation
goes parallel to that done in standard kinetic analysis.
The effect of nonthermal ions and variable dust charge on small-amplitude nonlinear dust-acoustic (DA) waves is investigated. It is found that both compressive and rarefactive solitons exist and depend on the nonthermal parameter a. Using a reductive perturbation theory, a Zakharov-Kuznetsov (ZK) equation is derived. At critical value of a, a{sub c}, a modified ZK equation with third- and fourth-order nonlinearities, is obtained. Depending on a, the solution of the evolution equation reveals whether there is coexistence of both compressive and rarefactive solitary waves or double layers (DLs) with the possibility of their two kinds. In addition, for certain plasma parameters, the solitary wave disappears and a DL is expected. The variation of dust charge number, wave velocity, and soliton amplitude and its width against system parameters is investigated for the DA solitary waves. It is shown that the incorporation of both the adiabatic dust-charge variation and the nonthermal distributed ions modifies significantly the nature of DA solitary waves and DA DLs. The findings of this investigation may be useful in understanding the ion acceleration mechanisms close to the Moon and also enhances our knowledge on pickup ions around unmagnetized bodies, such as comets, Mars, and Venus.
We report observations of “fast solitary waves” that are ubiquitous in downward current regions of the mid-altitude auroral zone. The single-period structures have large amplitudes (up to 2.5 V/m), travel much faster than the ion acoustic speed, carry substantial potentials (up to ∼100 Volts), and are associated with strong modulations of energetic electron fluxes. The amplitude and speed of the structures distinguishes them from ion-acoustic solitary waves or weak double layers. The electromagnetic signature appears to be that of an positive charge (electron hole) traveling anti-earthward. We present evidence that the structures are in or near regions of magnetic-field-aligned electric fields and propose that these nonlinear structures play a key role in supporting parallel electric fields in the downward current region of the auroral zone.
Propagation of small but finite amplitude ion acoustic solitons and double layers are investigated in electron–positron–ion
plasmas in presence of highly negatively charged impurities or dust. The presence of negatively charged dust particulates
can result in existence of two critical concentrations of ion–electron density ratio α. One of them α
D
decides the existence of double layers, whereas the other one α
R
decides the nature of the solitons and double layers. The system supports both compressive and rarefactive solitons as well
as double layers. The parameter regimes of transitions from compressive to rarefactive solitons and double layers are also
specified.
Simultaneous observations of polar mesosphere
summer echoes (PMSE) have been carried out during summer 1994 in northern Norway
using three radars on different frequencies: the ALOMAR SOUSY radar at Andenes
on 53.5 MHz, the EISCAT VHF radar at Tromsø on 224 MHz and the MF radar at
Tromsø on 2.78 MHz. During the common measuring period in July/August 1994,
PMSE could be detected at 224 and 53.5 MHz, and there are strong hints that PMSE
also occur at 2.78 MHz. Reliable correlations between hourly backscattered power
values indicate that the PMSE structures have zonal extensions of more than 130
km and can be detected at very different scales (half wavelength) between 0.67 (EISCAT
VHF radar) and 54 m (MF radar). Using the wind values derived by the MF radar it
can be shown that the mesospheric wind field influences the structure of PMSE.
The diurnal variation of PMSE is strongly connected with tidal-wind components,
whereas spatial differences of PMSE can partly be explained by the mean wind
field.
Bipolar wave structures and nonthermal particle distributions measured by the FAST satellite in regions of downward current are interpreted in terms of the nonlinear evolution of a two-stream instability. The instability results in holes, both in the electron distribution in phase space and in the electron density in real space. The wave potential energy, which traps the electrons, has a single minimum, and the associated electric field is bipolar. The early bipolar structures are coherent over hundreds of Debye lengths in the direction perpendicular to the magnetic field. After thousands of plasma periods the perpendicular coherence is lost, the structures break up, and electrostatic whistlers begin to dominate. Simulations and preliminary analysis of this breakup and emission process are presented.
Techniques previously known from solid state physics are used to look at linear and weak non‐linear wave propagation in dust lattices. These expansion techniques include only electrostatic interactions between neighbor particles in addition to assuming small vibrations in the dust lattice. As a simple model for the dust lattice, a one‐dimensional Bravais lattice is considered. For this particular lattice, expressions for the linear phase velocity are compared to a quasi‐particle simulation. The word quasi here means that only the dust particles are represented as diffuse objects, while the plasma is treated as a fluid. The simulation is also used to study the breakdown of the analytical theory and to investigate non‐linear dust lattice waves. A very good agreement is found between the analytical expressions and the particle simulations, for cases where the average dust separation a is of the order of or larger than the plasma Debye length λD. This is a condition which very often applies to dust crystal in laboratory experiments. Application of this wave theory is therefore discussed with respect to recent laboratory experiments where dust lattice waves are excited.
A numerical investigation is presented to show the existence, formation, and possible realization of large-amplitude dust acoustic (DA) solitary waves in a charge varying dusty plasma with nonthermal ions. These nonlinear localized structures are self-consistent solutions of the collisionless Vlasov equation with a population of fast particles. The spatial patterns of the variable charge DA solitary wave are significantly modified by the nonthermal effects. The results complement and provide new insights into previously published results on this problem.
Laboratory experiments on waves in dusty plasmas performed at the University of Iowa are described. All of the experiments deal with low-frequency electrostatic waves and include studies of (i) electrostatic dust ion cyclotron (EDIC) waves, (ii) dust ion acoustic (DIA) waves and (iii) dust acoustic (DA) waves.
DOI:https://doi.org/10.1103/PhysRevLett.17.996
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.
It is found that a two-electron temperature plasma with isothermal electrons and cold ions admits both compressive and rarefactive solitons, as well as compressive and rarefactive double layers (depending on the concentration of low-temperature electrons). In this paper, a Korteweg–de Vries (K-dV) equation and a K-dV-type equation with cubic and fourth-order nonlinearity at the critical density of the low-temperature isothermal electrons are derived to discuss the properties of ion-acoustic solitons in a two-electron temperature plasma. In the vicinity of the critical electron density of low-temperature isothermal electrons, we have derived a K-dV-type equation with mixed nonlinearity, and the solution of this equation will have both compressive and rarefactive double layers for those values of critical electron density of low-temperature electrons for which ion-acoustic solitons do not exist. By using quasipotential analysis, critical Mach numbers M1c and M2c are obtained such that compressive ion-acoustic solitons exist when 1<M<M1c and rarefactive ion-acoustic solitons exist when 1<M<M2c. © 2000 American Institute of Physics.
Theoretical and experimental studies of low-frequency electrostatic waves in plasmas containing negatively charged dust grains are described. The presence of charged dust is shown to modify the properties of ion-acoustic waves and electrostatic ion-cyclotron waves through the quasineutrality condition even though the dust grains do not participate in the wave dynamics. If the dust dynamics is included in the analysis, new “dust modes” appear—dust acoustic and dust cyclotron modes. The results of laboratory experiments dealing with dust ion acoustic (DIA) waves and electrostatic dust ion cyclotron (EDIC) waves are shown. These modes are more easily excited in a plasma containing negatively charged dust. Finally, observations of dust acoustic (DA) waves are presented and measurements of the dispersion relation are compared with one obtained from fluid theory. © 1998 American Institute of Physics.
The effects of nonthermal ions with excess of fast (energetic) ions on
linear dust acoustic (DA) wave propagation has been investigated
incorporating the dust charge variation and the isothermal dust pressure
variation. It is seen that due to the dust charge variations in the
presence of nonthermal ions, instead of the usual damping, there is a
growth of the DA wave if the ion nonthermality parameter
a>15(1+σi)/(8-72σi),
σi(=Ti/Te<<1),
Ti(Te) is the ion (electron) temperature, and
there may occur, under certain conditions, exponentially growing mode
with zero real frequency. It is also seen that in the absence of dust
charge variations there also occurs a zero real frequency, exponentially
growing mode if the ion nonthermality parameter a>1. In absence of
dust charge variations or in the presence of adiabatic dust charge
variations, finite dust temperature Td can stabilize the
instability. However, in the presence of nonadiabatic dust charge
variations Td cannot stabilize the instability.
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.
1. Introduction; 2. Linear waves and instabilities in infinite media; 3.
Convective and non-convective instabilities; group velocity in unstable
media; 4. A first look at surface waves and instabilities; 5. Model
equations for small amplitude waves and solitons; weakly nonlinear
theory; 6. Exact methods for fully nonlinear waves and solitons; 7.
Cartesian solitons in one and two space dimensions; 8. Evolution and
stability of initially one-dimensional waves and solitons; 9.
Cylindrical and spherical solitons in plasmas and other media; 10.
Soliton metamorphosis; 11. Non-coherent phenonemena; Appendices;
References.
DOI: 10.1029/98GL00636 ͑1998͒. 053701-5 Weakly nonlinear dust ion-acoustic shock waves… Phys
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