Ion-acoustic Solitons In Plasma Research Articles

Universal reductions and solitary waves of weakly nonlocal defocusing nonlinear Schrödinger equations

We study asymptotic reductions and solitary waves of a weakly nonlocal defocusing nonlinear Schrödinger (NLS) model. The hydrodynamic form of the latter is analyzed by means of multiscale expansion methods. To the leading-order of approximation (where only the first of the moments of the response function is present), we show that solitary waves, in the form of dark solitons, are governed by an effective Boussinesq/Benney–Luke (BBL) equation, which describes bidirectional waves in shallow water. Then, for long times, we reduce the BBL equation to a pair of Korteweg–de Vries (KdV) equations for right- and left-going waves, and show that the BBL solitary wave transforms into a KdV soliton. In addition, to the next order of approximation (where both the first and second moment of the response function are present), we find that dark solitons are governed by a higher-order perturbed KdV (pKdV) equation, which has been used to describe ion-acoustic solitons in plasmas and water waves in the presence of higher-order effects. The pKdV equation is approximated by a higher-order integrable system and, as a result, only insubstantial changes in the soliton shape and velocity are found, while no radiation tails (in this effective KdV picture) are produced.

Particle acceleration by ion-acoustic solitons in plasma

We propose a new acceleration mechanism for charged particles by using cylindrical or spherical non-linear acoustic waves propagating in ion-electron plasma. The acoustic wave, which is described by the cylindrical or spherical Kortweg-de Vries equation, grows in its wave height as the wave shrinks to the center. Charged particles confined by the electric potential accompanied with the shrinking wave get energy by repetition of reflections. We obtain power law spectrums of energy for accelerated particles. As an application, we discuss briefly that high energy particles coming from the Sun are produced by the present mechanism.

Ion-acoustic solitons in plasma: an application to Saturn’s magnetosphere

Soliton formation in plasma is addressed. Nonlinear acoustic waves in plasma where the combined effects of bounded spherical geometry and the transverse perturbation are dealt with, in two-temperature electron plasma are studied. Using the perturbation method, a spherical Kadomtsev-Petviashvili equation (SKP) that describes the ion acoustic waves is derived. The plasma is modeled by a kappa distribution function for both electrons components as found in Saturn’s magnetosphere. It is found that parameters taken into account have significant effects on the properties of nonlinear waves. The model is applied to Saturn’s magnetosphere, where two temperature superthermal electrons are present. Hence, ion acoustic waves are deduced for three regions, namely, the inner, the intermediate and the outer Saturn’s magnetosphere. We point out, that this work has been motivated by recent observations of Saturn’s magnetosphere.

Dust ion acoustic solitons in a plasma with kappa-distributed electrons

Dust ion acoustic solitons in an unmagnetized dusty plasma comprising cold dust particles, adiabatic fluid ions, and electrons satisfying a κ distribution are investigated using both small amplitude and arbitrary amplitude techniques. Their existence domain is discussed in the parameter space of Mach number M and electron density fraction f over a wide range of values of κ. For all κ>3/2, including the Maxwellian distribution, negative dust supports solitons of both polarities over a range in f. In that region of parameter space solitary structures of finite amplitude can be obtained even at the lowest Mach number, the acoustic speed, for all κ. These cannot be found from small amplitude theories. This surprising behavior is investigated, and it is shown that fc, the value of f at which the KdV coefficient A vanishes, plays a critical role. In the presence of positive dust, only positive potential solitons are found.

Ion-acoustic solitons in plasmas with two adiabatic constituents

AbstractLarge amplitude ion-acoustic solitons are treated by a Sagdeev pseudopotential analysis, in a plasma with two adiabatic constituents, with the full inclusion of inertial and pressure effects for both. The sign of the supersonic species determines the polarity of the solitons, which are compressive in both constituents. Emphasis is placed on the determination of the soliton existence domains in compositional parameter space, allowing correct Sagdeev pseudopotential graphs to be easily generated, and offering insight into why limitations occur. Soliton velocities are bounded from below by the true acoustic velocity in the plasma model, and from above by the breakdown of the description when the supersonic ions reach their sonic point. Increases in the mass density ratio and the soliton velocity or decreases in the temperature ratio lead to increases in soliton amplitudes and decreases of the widths. Applications include hydrogen and electron–positron plasmas, and various kinds of dusty plasmas.

Ion-acoustic solitons in plasmas with two-temperature ions

This paper discusses the existence of ion-acoustic solitons in a plasma consisting of hot and cool ions, and hot electrons, where the words “hot” and “cool” reflect the ratio of thermal effects to inertial effects. For the hot species general polytropic pressure relations are considered, as well as the isothermal limit, γ=1 (Boltzmann distribution). It is shown that negative potential solitons are not supported. Existence domains in parameter space (effective soliton Mach number and fractional cool ion density) for positive potential solitons are found, the limits being imposed by physical effects such as vanishing densities. Numerical results are given for a typical value of γ>1 and for γ=1, for three representative values of the hot ion to electron temperature ratio.

Compressive and rarefactive ion-acoustic solitons in bi-ion plasmas

Nonlinear propagation of ion-acoustic solitary structures in plasmas with an admixture of heavy ions is studied in the wave frame, where they are stationary, using a recently developed gas-dynamic approach, as an alternative to the conventional Sagdeev pseudopotential method. This viewpoint brings out the gas-dynamic aspects, which then allow a characterization of the solitary wave structures in terms of the species’ sonic points, the global charge neutral points, and critical collective Mach numbers. It is shown that the concepts of a critical density in the Korteweg–de Vries (KdV) treatment, and of a changeover from compressive to rarefactive soliton character, correspond to the formation of a second charge neutral point (outside equilibrium) in the rarefactive regime, at which the electric stresses maximize. It is possible therefore that in certain regions of parameter space compressive and rarefactive solitons can co-exist. The compressive solitons are not predicted by a weakly nonlinear KdV treatment, except very close to the changeover region at sufficiently small enough amplitudes, as typified by the “modified” KdV (mKdV) equation. Their prediction requires a fully nonlinear treatment. Existence criteria are deduced and evaluated numerically in the parameter space of soliton Mach number and normalized density of the heavy species for compressive and rarefactive ion-acoustic solitons in a plasma with negative ion admixture.

Ion-acoustic solitons in a plasma with a relativistic electron beam

Ion-acoustic solitons in a collisionless plasma consisting of warm ions, hot isothermal electrons, and a relativistic electron beam are studied by using the reductive perturbation method. The basic set of fluid equations is reduced to Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations. The effects of ion temperature and relativistic electron beam on ion-acoustic solitons are investigated. It has been shown that the four ion-acoustic modes can be propagated in this plasma system. The compressive and rarefactive ion-acoustic solitons satisfies the KdV equation for a given soliton velocity, beam density much smaller than the background electron density and the bulk ion temperature smaller than the background electron temperature for two modes. Also it has been illustrated that there exist mKdV solitons for some critical value of electron beam density in these cases. These critical values decrease as ion temperature increases for one of two modes and increase for the other one. Finally, it has been remarked that for another two modes only rarefactive KdV ion-acoustic solitons can be obtained. One of these modes exists for the electron beam density much smaller than the bulk electron density, and the other exists for almost all values of the beam density, even if it is greater than the background electron density.

Ion-acoustic solitons in multi-component plasmas including negative ions at critical densities

Ion-acoustic solitons in a plasma with different adiabatic ion constituents and isothermal electrons are studied via a reductive perturbation method. The basic fluid equations then give rise to KdV or modified KdV equations, depending upon the relative ion densities. At critical densities, rarefactive and compressive fast ion-acoustic solitons are possible. Explicit stationary solutions are discussed in the special case of cold ions, in a plasma containing two species of negative ions and one of positive ions. The inclusion of heavier ions, even at low densities, increases the amplitudes of the critical solitons.

Temperature effects on ion acoustic solitons in plasmas with near critical density of negative ions

The authors establish a Korteweg-de Vries type equation to describe ion acoustic solitons in a plasma made up of electrons, positive and negative ions near the critical density. It is shown that the amplitudes and widths of compressive and rarefactive solitons are dependent on the ion temperatures and that this dependence is strongly asymmetric when the positive and negative ion temperatures are unequal. As an application, they analyse results of an experiment.

Cylindrical Ion Acoustic Soliton in Plasma with Negative Ion

Cylindrical ion acoustic solitons are investigated theoretically and numerically in a plasma with negative ion. In a theoretical part, we derive a cylindrical Korteweg-de Vries equation for an ion acoustic wave. The sign of nonlinear coefficient depends on the negative ion density. At the critical density of the negative ion where the nonlinearity of the Korteweg-de Vries equation vanishes, the ion acoustic wave is described by a cylindrical modified Korteweg-de Vries equation, and in the vicinity of the critical density, it is described by a combined cylindrical equation of the Korteweg-de Vries and modified Korteweg-de Vries types. The change of a soliton amplitude due to the geometrical effect is analytically obtained in two limiting cases when the geometrical effect is much stronger or weaker than the nonlinear and dispersive effects. In the numerical calculation, the theoretical prediction for the change of the soliton amplitude is verified.

On Large Amplitude Ion Acoustic Solitons in Plasma with Negative Ions

This letter is concerned with existence conditions for ion acoustic solitons in a plasma with negative ions. It is shown that large Mach number potential-well solitons can be in existence in a certain parameter region.

Ion Acoustic Soliton in Plasma with Negative Ion

Ion acoustic solitons are investigated theoretically in a plasma composed of electron, positive ion and negative ion. Due to the presence of negative ion, the property of the ion acoustic soliton is drastically modified. At the critical density of the negative ion, the nonlinear coefficient of the Korteweg-de Vries equation vanishes and then the ion acoustic wave is described by the modified Korteweg-de Vries equation. The transition from the Korteweg-de Vries soliton to the modified Korteweg-de Vries soliton is also studied by means of an evolution equation with quadratic and cubic nonlinearities.

Observation of Ion-Acoustic Rarefaction Solitons in a Multicomponent Plasma with Negative Ions

The propagation of ion-acoustic solitons in a plasma with negative ions has been observed. For sufficiently large concentration of negative ions, applied rarefactive (negative) voltage pulses break up into solitons, whereas compressive pulses evolve into wave trains, with exactly the opposite behavior as that for a plasma composed only of positive ions. There is a critical value of the negative-ion concentration for which a finite-amplitude pulse propagates without steepening.