Large Amplitude Solitary Waves Research Articles

Arbitrary amplitude solitary waves in plasmas with dust grains of opposite polarity and non-thermal ions

AbstractThe existence of large amplitude solitary waves in a plasma comprised of a cold negative dust fluid, adiabatic positive dust fluid, Boltzmann electrons and non-thermal ions is theoretically investigated. Different regions in parameter space that correspond to different values of the ratio of the charge-to-mass ratios of the positive and negative dust grains have been identified where either negative or positive potential solitary wave structures occur and a region where coexistence of negative and positive potential solitary waves is supported.

Effect of ion temperature on localized ion-acoustic waves with flat-topped electron distribution

The effect of ion temperature on the propagation of arbitrary amplitude ion-acoustic solitary waves is studied in an unmagnetized plasma which consists of a positively charged, warm ion fluid and hot electrons obeying a flat-topped distribution. A flat distribution for trapped particles is considered corresponding to the nonlinear interaction between electrons and electrostatic wave potential during its evolution. The basic properties of large amplitude solitary waves are studied by deriving an energy integral equation involving the Sagdeev potential. It is shown that the effects of such electron behavior and ion temperature change the regions of existence of arbitrary amplitude compressive solitary waves. By expanding the Sagdeev potential to include higher order nonlinearities of the electric potential, an exact steady state solution is also obtained, which confirms the possibility of ion-acoustic solitary waves in the small amplitude limit. Furthermore, two asymptotic cases of the stationary solution are found which are related to the contribution of flat-trapped electrons.

Role of trapped electrons on the propagation of localized dust ion-acoustic waves

The nonlinear propagation of arbitrary amplitude of dust ion-acoustic (DIA) waves in an unmagnetized dusty plasma composed of a cold ion fluid, stationary dust grains and hot electrons obeying a trapped distribution, is investigated. The trapped particles are included in this model as a result of the nonlinear resonant interaction of the localized electrostatic wave potential with electrons during its evolution. The properties of large amplitude solitary waves are studied by deriving an energy integral equation involving the Sagdeev potential, whereas those of small but finite amplitude DIA solitary waves are investigated by means of the reductive perturbation method. The new parametric regimes for the existence of solitary structures are found, and the effects of trapped electrons along with static dust particles on these profiles are discussed.

Solitary wave generation dynamics at Luzon Strait

A high resolution modeling study is undertaken, with a 2.5-dimensional nonhydrostatic model, of the generation of internal waves induced by tidal motion over the ridges in Luzon Strait. The model is forced by the barotropic tidal components K1, M2, and O1. These tidal components, along with the initial density field, were extracted from data and models. As the barotropic tide moves over the Luzon Strait sills, there is a conversion of barotropic tidal energy into baroclinic tidal energy. Depressions are generated that propagate towards the Asian Seas International Acoustics Experiment (ASIAEX) test site on the Chinese continental shelf. Nonlinear effects steepen the depressions, frequency and amplitude dispersion set in, and disintegration into large amplitude solitary waves occurs. The effects of varying the initial density field, tidal component magnitudes, as well as adding a steady background current to represent the occasional excursions of the Kuroshio Current into the strait, are considered. Depressions are generated at each of the two sills in Luzon Strait which radiate away, steepening and evolving into internal solitary wave trains. Baroclinic fluxes of available potential energy, kinetic energy and linear are calculated for various parameter combinations. The solitary wave trains produced in the simulations generally consist of large amplitude wave trains alternating with small amplitude wave trains. During strong tidal flow, Kelvin–Helmholtz type instabilities can develop over the taller double-humped sill. The solitary waves propagating towards the ASIAEX test site have been observed to reach amplitudes of 120–250 m, depending on the tidal strength. ASIAEX observations indicate amplitudes up to 150 m and the Windy Island Experiment (WISE) measurements contain magnitudes over 200 m. The model results yield solitary wave amplitudes of 70–300 m and half widths of 0.60–3.25 km, depending on parameter values. These are in the range of observations. Measurements by Klymak et al. (2006), in the South China Sea, exhibit amplitudes of 170 m, half widths of 3 km and phase speeds of 2.9 m s −1. Model predictions indicate that the solitary waves making up the wave packet each experience different background currents with strong near surface shear. The energy in the leading soliton of the large amplitude wave trains ranges between 1.8 and 9.0 GJ m −1. The smaller value, produced using barotropic tidal currents based on the Oregon State University data base, is the same as the energy estimated to be in a solitary wave observed by Klymak et al. (2006). Estimates of the conversion of barotropic tidal energy into radiating internal wave energy yield conversion rates ranging between 3.6% and 8.3%.

Effect of excavated trapped electron distributions on ion-acoustic solitary structures in an electron–positron–ion plasma

Fully nonlinear propagation of ion-acoustic solitary waves in an unmagnetized electron–positron–ion plasma is investigated. A more realistic situation is considered in which electrons interact with the wave potential during its evolution and, follow the vortex-like excavated trapped distribution. The basic properties of large amplitude solitary waves are studied by deriving an energy integral equation involving Sagdeev potential. It is shown that effects of such electron behavior and positron concentration change the maximum values of the Mach number and amplitude for which solitary waves can exist. The small amplitude limit is also investigated by expanding the Sagdeev potential to include third-order nonlinearity of electric potential. In this case, exact analytical solution is obtained which is related to the contribution of the resonant electron to the electron density. It is shown from both highly and weakly nonlinear analysis that the plasma system under consideration supports only compressive solitary waves.

Nonlinear electrostatic modes in astrophysical plasmas with charged dust distributions

Context. Most theoretical investigations of wave phenomena in dusty plasmas have treated charged dust as additional heavy negative ions in standard multispecies models. Many dusty plasma experiments use monodisperse grains, but charged (and neutral) grains in space environments come in a whole range of sizes and compositions, hence in masses and charges. Dust density distributions having a power-law decay with size are often observed in planetary rings. Aims. There is a need to investigate larger solitary structures, since wave descriptions involving charged dust distributions have usually been limited to linear or weakly nonlinear modes. Methods. Sagdeev pseudopotential methods describe large-amplitude solitary waves in a co-moving reference frame and are adapted to include dust distributions, using mass and charge, or alternatively size, as additional variables. Observed power-law distributions lead to descriptions involving hypergeometric functions. Results. Lower limits for possible solitary wave velocities follow from requiring that the Sagdeev pseudopotentials have a local maximum for the undisturbed conditions, whereas upper limits come from ensuring that dust densities remain real. Nonlinear amplitudes increase with solitary wave velocities and relative electron temperature. Under similar plasma conditions, dust size distributions admit slower solitary wave solutions, with correspondingly smaller amplitudes than given by monodisperse dust models. For typical planetary ring conditions, the difference can be quite appreciable.

Effect of deviations from isothermality of ions on the propagation of localized dust-acoustic waves

The effect of deviations from isothermality of ions on arbitrary amplitude dust-acoustic solitary structures is studied in an unmagnetized dusty plasma which consists of a negative charged dust fluid, free electrons and hot ions obeying a trapped distribution. For the finite deviation from isothermality of ions, the basic properties of large amplitude solitary waves are studied by employing pseudo-potential approach. It is shown that the effect of such ion behavior changes the maximum values of the Mach number and the amplitude for which solitary wave can exist. For the case that the deviation from isothermality due to nonlinear resonant particle effects is small, calculations by reductive perturbation method leads to a generalized Korteweg–de Vries equation with mixed nonlinearity. The latter admits a stationary dust-acoustic solitary solution with similar width and qualitatively different amplitude in comparison to the case that deviations from isothermality are finite. Furthermore, effects of the equilibrium free electron density and such trapped ions on the amplitude of solitary structures imply a non-uniform transition from the Boltzmann ion distribution to the trapped ion one.

Effect of ion temperature on arbitrary amplitude ion acoustic solitary waves in quantum electron-ion plasmas

Using Sagdeev’s pseudopotential technique, the effect of ion temperature on the arbitrary amplitude ion acoustic solitary waves in quantum electron-ion plasma is studied. In addition, the effect of ion temperature on the region of existence, as well as on the shape of the solitary waves, is also investigated extensively. It is shown that for large amplitude solitary wave, quantum parameter H does not play any role in determining the region of existence and on the amplitude of the solitary waves. However, H has a significant effect on the width of the solitary wave. It is worth noting that our results are in agreement with previous investigations when the effect of ion temperature is neglected.

Evolution of electron holes in two electron population plasmas

Formations and existence conditions of electron holes from one-dimensional Vlasov simulations in a collisionless unmagnetized two component plasma are presented. Kinetic simulation results quantitatively confirm the Fast Auroral SnapshoT (FAST) observations of large amplitude (up to 500mV∕m) solitary waves at the edge of the auroral kilometric radiation (AKR) source region.

Effect of electron inertia on large amplitude solitary waves in presence of kinematic viscosity in dusty plasma

Nonlinear dust acoustic solitary waves in a dusty plasma are studied for nonzero kinematic viscosity. Sagdeev’s potential can be obtain upto any order in ϕ. The existence of soliton solution is determined by pseudopotential approach. It is seen that the electron inertia has a significant effect on the existence of solitary waves in presence of kinematic viscosity.

Large Amplitude Solitary Waves in a Four-Component Dusty Plasma with Nonthermal Ions

Dust acoustic solitary waves are studied in a four-component dusty plasma. Positively and negatively charged mobile dust and Boltzmann-distributed electrons are considered. The ion distribution is taken as nonthermal. The existence of a soliton solution is determined by the pseudo-potential approach. It is shown that in small amplitude approximation our result obtained from the Sagdeev potential technique reproduce the result obtained by Sayed and Mamun [Phys. Plasmas 14, 014501 (2007)] provided one cosiders the nonthermal distribution for ions.

Large-amplitude dust-acoustic solitary waves in an electron-depleted hot dusty plasma with trapped ions

A theoretical model is presented to show the existence, formation, and possible realization of large-amplitude dust-acoustic solitary potentials in electron-depleted hot dusty plasma with trapped ions. These nonlinear localized structures are self-consistent solutions of the Vlasov equation in which the ion response is non-Maxwellian due to the ion trapping in the large-amplitude plasma potentials. Emphasis is given to the role of the grain temperature. Interestingly, one finds that the effect of increasing the dust temperature is to restrict the domain of allowable Mach numbers. The latter enlarges when the relative amount of trapped ions is increased. Furthermore, the nonlinear potential shrinks and exhibits smaller depth and smaller width than the one involving cold dust grains. The strong localization of the dust particles becomes less pronounced when the dust temperature is increased. The results complement and provide new insights into previously published results on this problem and their relevance to space dusty plasmas is pointed out.PACS Nos.: 52.27.Lw; 52.35.Fp; 52.35.Sb; 52.35.Tc; 52.35.Mw

Comment on "Obliquely propagating large amplitude solitary waves in charge neutral plasmas" by F. Verheest, Nonlin. Processes Geophys., 14, 49–57, 2007

A similar argument can be made for Hall-MHD solitons in which the acceleration of the protons is 0(VAp), the length scale is VA/p yielding the fractional charge sep- aration n/n  2 /! 2 =V 2 A /c 2 , where VA andp are the Alfven speed based on the proton mass density and the pro- ton gyrofrequency, respectively, demanding that n/n is rel- ativistically small and divE6=0. This is the reason why the standard Hall-MHD equations do not require Poisson's equa- tion and do not impose any constraint on divE. The electric fields are derived from Faraday's law and the equations of the motion together with the condition divj=0. Poisson's equation provides us only with an estimate of the charge sep- aration ratio n/n as was shown above. In the classic nonlinear wave propagating transverse to the

Dispersive Nonlinear Waves in Two‐Layer Flows with Free Surface Part II. Large Amplitude Solitary Waves Embedded into the Continuous Spectrum

In this paper we study the dispersive model derived in Part I, for the description of long wave propagation in two‐layer flows with free surface. As in the case of the full water–wave problem, this model reproduces the resonance between short waves and long waves. The resulting wave is a generalized solitary wave, characterized by ripples in the far field in addition to the solitary pulse. In this work we focus on particular members of this family resulting from vanishing ripples. These are called embedded solitary waves and they correspond to true homoclinic orbits. Two wave regimes, characterized by elevation or depression of the interface between the layers, are presented. A critical depth ratio separates these two regimes. It is shown how this relates to a change of the global properties for the potential of the Hamiltonian system derived for traveling waves. In oceanic conditions, solitary waves are presented and their broadening is observed as the wave speed increases. We have observed that, for such waves to exist, their speed cannot exceed a certain limit value depending on the density ratio and thickness of each fluid. Finally, other sets of parameters were considered for which multihumped solitons exist, showing the richness and complexity of the Hamiltonian system considered here.

Effects of obliqueness and external magnetic field on the large amplitude solitary waves in a dusty plasma

The nonlinear excitation of large amplitude dust-acoustic (DA) solitary waves in a magnetized hot dusty plasma consisting of fast ions and charged dust grains is revisited to take into account the effects of embedding external magnetic field. The DA solitary wave is assumed to propagate obliquely to the magnetic field. Sagdeev's approach, which is valid for arbitrary amplitude solitary waves, is used. Both compressive and rarefactive solitary structures are shown to coexist by the effects of obliqueness and nonthermal or fast ions. It is found that as the percentage of fast particles ( β ) increases, the critical Mach number ( M c ) increases and the increase is more effective at the higher value of the direction cosine ( L z ). The solitary wave solutions for small amplitude DA waves exhibit distinct behaviors for different values of dust fluid temperature, β and L z .

Obliquely propagating large amplitude solitary waves in charge neutral plasmas

Abstract. This paper deals in a consistent way with the implications, for the existence of large amplitude stationary structures in general plasmas, of assuming strict charge neutrality between electrons and ions. With the limit of pair plasmas in mind, electron inertia is retained. Combining in a fluid dynamic treatment the conservation of mass, momentum and energy with strict charge neutrality has indicated that nonlinear solitary waves (as e.g. oscillitons) cannot exist in electron-ion plasmas, at no angle of propagation with respect to the static magnetic field. Specifically for oblique propagation, the proof has turned out to be more involved than for parallel or perpendicular modes. The only exception is pair plasmas that are able to support large charge neutral solitons, owing to the high degree of symmetry naturally inherent in such plasmas. The nonexistence, in particular, of oscillitons is attributed to the breakdown of the plasma approximation in dealing with Poisson's law, rather than to relativistic effects. It is hoped that future space observations will allow to discriminate between oscillitons and large wave packets, by focusing on the time variability (or not) of the phase, since the amplitude or envelope graphs look very similar.

Speed and shape of large-amplitude solitary waves in ion-beam plasma system

Large-amplitude solitary waves are investigated in ion-beam plasma system. The Sagdeev’s pseudopotential is determined in terms of the ion speedu. It is found that there exists a critical value ofu0, the value ofu at (u′)2 = 0, beyond which the solitary waves cease to exist. The critical value also depends on σ (the ion temperature) or σb (the ion beam temperature).

Nonlinear theory of large-amplitude stationary solitary waves in symmetric unmagnetized e − e + and C 60 − C 60 + plasmas

It is shown that large-amplitude stationary solitary electrostatic waves can exist in a symmetric plasma (e − e + or C 60 − C 60 + ), and the relevant parameter ranges (i.e., the range of the Mach numbers and the degree to which the plasma should be nonequilibrium) are determined. The basic requirement for the existence of such waves, specifically, that the symmetric plasma be in a nonequilibrium state, can easily be satisfied in low-density collisionless ideal plasmas under laboratory conditions.

Large amplitude dust acoustic solitary wave with positively charged dust grain

Large amplitude solitary waves are investigated in a dusty plasma containing electrons, positive ions, negative ions, and positively charged dust grains [N. D'Angelo, J. Phys. D 37, 860 (2004)] by the Sagdeev potential. Numerical investigations related to Q machine dusty plasma with a positive charge reveal that the nonlinear dust acoustic wave possesses only a supersonic compressive soliton. The range of Mach numbers where such solitary waves exist is also investigated.

Speed and shape of solitary waves in relativistic warm plasma

Large-amplitude solitary waves are investigated in a relativistic plasma with finite ion-temperature. The mass of electron is also considered. The Sagdeev’s pseudopotential is determined in terms ofu, the ion speed. It is found that there exists a critical value ofu0, the value ofu at which (u′)2=0, beyond which the solitary waves cease to exist. The critical value also depends on the parameters likeν, the soliton velocity;μ, the electronion mass ratio orσ, the temperature ratio of ion to electron. This result reproduces our previous result [Czech. J. Phys., Vol. 54 (2004), No. 4, 489–496] when the ion temperature is neglected.