Critical Density Of Negative Ions Research Articles

Observation of hole Peregrine soliton in a multicomponent plasma with critical density of negative ions

AbstractThe evolution of hole Peregrine soliton (appearing as a deep trough between two crests) from ion‐acoustic perturbations excited in a multicomponent plasma with critical density of negative ions has been observed. The observed soliton is described by the rational solution of the cubic nonlinear Schrödinger equation, which can appear as an isolated high peak or a deep hole depending on the phase of the underlying carrier wave relative to the envelope. The measured amplitude of the hole Peregrine soliton (depth from crest to trough) is found to be more than twice the background wave height. The experimental observations are compared with the theoretical results obtained from the solution of the cubic nonlinear Schrödinger equation. The frequency spectrum of the Peregrine soliton is analyzed and found to be triangular in shape.

Highlights from the Asia Pacific Region

It is well known that multicomponent plasma with negative ions supports a number of wave modes such as ion-acoustic solitons described by the Kortewege-de Vries (KdV) equation, modified KdV solitons at critical density of negative ions and ion-acoustic envelop solitons described by nonlinear Schrödinger equation (NLSE). The NLSE which is equivalent to the mKdV equation is applicable in describing evolution of ion-acoustic wave in plasma at critical density of negative ions which becomes modulationaly unstable when the nonlinear co-efficient is negative.

Reflection of Solitons at Critical Density of Negative Ions: Contribution of Thermal and Gyratory Motions of Ions

On the basis of appropriate modified Korteweg-deVries (mKdV) equation derived for three cases of nn0 ne0 together with nn0 ne0.

Soliton propagation in an inhomogeneous plasma at critical density of negative ions: Effects of gyratory and thermal motions of ions

The effects of gyratory and thermal motions of ions on soliton propagation in an inhomogeneous plasma that contains positive ions, negative ions, and electrons are studied at a critical density of negative ions. Since at this critical negative ion density the nonlinear term of the relevant Korteweg–deVries (KdV) equation vanishes, a higher order of nonlinearity is considered by retaining higher-order perturbation terms in the expansion of dependent quantities together with the appropriate set of stretched coordinates. Under this situation, time-dependent perturbation leads to the evolution of modified KdV solitons, which are governed by a modified form of the KdV equation that has an additional term due to the density gradient present in the plasma. On the basis of the solution of this equation and obliquely applied magnetic field, the effects of gyratory and thermal motions of ions are analyzed on the soliton propagation for three cases, nn0<ne0, nn0=ne0, and nn0>ne0, together with nn0 (ne0) as the density of negative ions (electrons). The role of the negative ions in the evolution of the modes and the solitons is also discussed. Under the limiting cases, our calculations reduce to the ones obtained by other investigators in the past. This substantiates the generality of the present analysis.

Reflection of nonlinear solitary waves (mKdV solitons) at critical density of negative ions in a magnetized cold plasma

The reflection of ion acoustic solitons in a magnetized inhomogeneous plasma having positive ions, negative ions and electrons is studied theoretically at the critical density of negative ions, where both compressive and rarefactive solitons are found to exist. Relevant modified Korteweg–deVries (mKdV) equations corresponding to two oppositely moving solitons are coupled to obtain a variable coefficient coupled mKdV equation, which is further solved to obtain the expression of amplitude and width of the reflected solitons. The effect of magnetic field B0, its obliqueness θ (angle between the directions of magnetic field and wave propagation) and negative to positive ion density ratio d0 on the amplitude and width of the reflected solitons together with the reflection coefficient are investigated. A comparison is made between the incident and reflected solitons and it is found that the compressive (rarefactive) solitons are downshifted (upshifted) after the reflection.

Modified Korteweg-deVries soliton evolution at critical density of negative ions in an inhomogeneous magnetized cold plasma

Soliton propagation at critical density of negative ions is studied for weakly inhomogeneous magnetized cold plasma having positive ions, negative ions, and electrons. A general phase velocity relation is obtained and possible modes are studied for different cases involving different constituents of the plasma. Two types of modes (fast and slow) are found to propagate for the equal mass of the positive and negative ions. However, a limit on the obliqueness of magnetic field is obtained for the propagation of slow mode. For both types of modes, a variable coefficient modified Korteweg-deVries equation with an additional term arisen due to the density gradient is realized, which admits solutions for compressive solitons and rarefactive solitons of the same amplitudes at critical negative ion density. The propagation characteristics of these solitons are studied under the effect of densities of ions, magnetic field, and its obliqueness. The amplitudes of fast and slow wave solitons show their opposite behavior with the negative ion concentration, which is consistent with the variation of phase velocities with the negative ion density.

Higher-order contributions to ion-acoustic solitary waves in a warm multicomponent plasma with an electron beam

Higher-order contributions in reductive perturbation theory are studied for small- but finite-amplitude ion-acoustic solitary waves in a warm plasma with negative-ion, positron and electron constituents traversed by a warm electron beam (with different temperatures and pressures). The basic set of fluid equations are reduced to a Korteweg–de Vries (KdV) equation for the first-order perturbed potential and a linear inhomogeneous KdV-type equation for the second-order perturbed potential. At the critical negative-ion density, the coefficient of the nonlinear term in the KdV equation vanishes. A new set of stretched coordinates is then used to derive a modified KdV equation and a linear inhomogeneous modified KdV-type equation at the critical density of negative ions for the second-order perturbed potential. Stationary solutions of the coupled equations, for both cases, are obtained using a renormalization method.

Ion-acoustic solitons and shocks in negative ion-beam relativistic plasma

We have analyzed the formation of solitons in a beam plasma system consisting of warm relativistic negative ions. The subsequent destruction of the nonlinearity of Korteweg-deVries equation near the critical density of negative ions and evolution of the shock wave are discussed in detail. The physical attributes of the ion-acoustic solitary wave and shocks are depicted graphically for the plasmas having (H/sup +/, Cl/sup -/) ions, (H/sup +/, O/sup -/) ions, (H/sup +/, SF/sub 5//sup -/) ions, (He/sup +/, Cl/sup -/) ions. It is found that mass ratio of negative ions and positive ions, relativistic effect and negative ion concentration have important contribution on the formation of solitons and shocks in the plasma.

Ion-acoustic solitons in a warm plasma including negative ions in the vicinity of critical density

Ion-acoustic solitons in a warm plasma with different adiabatic ion constituents (with the same temperature) and isothermal electrons in the vicinity of critical negative ion density are studied by use of the reductive perturbation theory. The basic set of equations is reduced to an evolution equation which includes quadratic and cubic nonlinearities. The effective potential of this equation agress exactly, for small wave amplitudes, with the Sagdeev potential obtained from the exact stationary solution of the original fluid equations. This implies that the evolution equation holds not only in the vicinity of the critical ion density, but also in the whole range of the negative ions under the condition of small wave amplitude.

Cylindrical and Spherical Solitons at the Critical Density of Negative Ions in a Generalised Multicomponent Plasma

Propagation of nonlinear ion-acoustic waves in generalised multicomponent plasmas bounded by cylindrical and spherical geometries is investigated. At the critical density of negative ions where the nonlinearity of the Korteweg-deVries (K-dV) equation vanishes, the ion-acoustic solitary wave is described by a modified K-dV (mK-dV) equation. It is also emphasised that near the critical density neither the K-dV nor mK-dV equation is sufficient to describe fully the ion-acoustic waves and thus there is a need to derive a further mK-dV (fmK-dV) equation in the vicinity of this critical density. Furthermore, the amplitude variations of the K-dV and mK-dV solitons depending on the limitations of geometrical effects are also discussed, emphasising that the results could be of interest for diagnosing the soliton properties of laboratory plasmas.

Thermal Effects on K-dV Solitons Existing at the Critical Density of Negative Ions in Ion-Beam Plasmas

Ion-acoustic solitons in a generalized multicomponent plasma are studied through the derivation of Korteweg-de Vries (K-dV) equation. The negative ions and ion-beams play quantitatively various roles on the existence of solitons in the plasma. Especially, the critical density introduced by the negative ions exhibits the existence of a large amplitude soliton in plasmas and due to which a derivation of a modified K-dV (mK-dV) equation is needed. By taking the higher order nonlinearity in the plasma, the transition of the K-dV equation to the mK-dV equation is also shown. Moreover, various models of the plasma due to the non-isothermality are also considered in the discussions. Further study closely related to the stability of the soliton is made and yields the salient features of the solitons.

Soliton Characteristics at the Critical Density of Negative Ions in Ion-beam Plasmas

By using the reductive perturbation technique, ion-acoustic waves are studied in a generalised multicomponent plasma. The multiple ions modify drastically the characteristics of the solitary waves. In particular, the negative ions have a critical density at which the nonlinearity of the Korteweg-deVries (K-dV) equation vanishes and the ion-acoustic solitary wave is seen to be described by a modified K-dV (mK-dV) equation. Using higher order nonlinearities, the non-uniform transition of the K-dV equation to the mK-dV equation along with the conservation of the Sagdeev potential is described. Theoretical observations on the existence of the solitary waves, as expected, could be of interest in laboratory plasmas

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.