Rarefaction Solitons Research Articles

Solitary fast magnetosonic waves propagating obliquely to the magnetic field in cold collisionless plasma

Solutions describing solitary fast magnetosonic (FMS) waves (FMS solitons) in cold magnetized plasma are obtained by numerically solving two-fluid hydrodynamic equations. The parameter domain within which steady-state solitary waves can propagate is determined. It is established that the Mach number for rarefaction FMS solitons is always less than unity. The restriction on the propagation velocity leads to the limitation on the amplitudes of the magnetic field components of rarefaction solitons. It is shown that, as the soliton propagates in plasma, the transverse component of its magnetic field rotates and makes a complete turn around the axis along which the soliton propagates.

Rarefaction solitons initiated by sheath instability

The instability of the cathode sheath initiated by the cold energetic electron beam is studied by the one-dimensional fluid model. Numerical simulations show the generation of travelling rarefaction solitons at the cathode. It is obtained that the parameters of these solitons strongly depend on the parameters of electron beam. The “stretched” variables are derived using the small-amplitude analysis. These variables are used in order to obtain the Korteweg-de Vries equation describing the propagation of the rarefaction solitons through the plasma with cold energetic electron beam.

Large-amplitude solitons in gravitationally balanced quantum plasmas

Using the quantum fluid model for self-gravitating quantum plasmas with the Bernoulli pseudopotential method and taking into account the relativistic degeneracy effect, it is shown that gravity-induced large-amplitude density rarefaction solitons can exist in gravitationally balanced quantum plasmas. These nonlinear solitons are generated due to the force imbalance between the gravity and the quantum fluid pressure via local density perturbations, similar to that on shallow waters. It is found that both the fluid mass-density and the atomic-number of the constituent ions have significant effect on the amplitude and width of these solitonic profiles. Existence of a large-scale gravity-induced solitonic activities on neutron-star surface, for instance, can be a possible explanation for the recently proposed resonant shattering mechanism [D. Tsang et al., Phys. Rev. Lett. 108, 011102 (2012)] causing the intense short gamma ray burst phenomenon, in which release of ≃1046–1047 ergs would be possible from the surface. The resonant shattering of the crust in a neutron star has been previously attributed to the crust-core interface mode and the tidal surface tensions. We believe that current model can be a more natural explanation for the energy liberation by solitonic activities on the neutron star surfaces, without a requirement for external mergers like other neutron stars or black holes for the crustal shatter.

Soliton and multiphonon microdynamics of thermal conductivity of plutonium and uranium in the temperature range of martensitic phase transitions

The microdynamics of nonlinear crystal lattice vibrations of Pu and U at temperatures of martensitic phase transitions has been studied. Using the Lenard-Jones potential, the dynamic equations are solved when the energy is transferred by solitons. The synchronism of solitons and the energy flux peaks demonstrates the staccato-effect. The temperature dependences of the thermal conductivity have maxima at the phase transitions. A spectral analysis shows that the main heat transfer is provided by rarefaction solitons. Upon the martensitic transition, the spectral density is transformed with “ignition” of the high-frequency region. The spectral density demonstrates maxima of the quasi-biphonon type.

Soliton microdynamics of heat conduction in plutonium and uranium in the temperature range of martensitic phase transitions

The microdynamics of large-amplitude nonlinear lattice vibrations of plutonium and uranium has been investigated at high reactor temperatures in the ranges of martensitic phase transitions. Solutions of nonlinear dynamic equations have been obtained using the Lennard-Jones interatomic potential for the soliton generation and the energy transfer by solitons between the crystal boundaries in the shells. The synchronism of the soliton trajectories and peaks of energy fluxes demonstrates an analog of the shot effect. The temperature dependences of thermal conductivity coefficients are consistent with the experiment and exhibit local maxima in the ranges of phase transitions. A spectral analysis has revealed that the dominant heat transfer is provided by rarefaction solitons. The martensitic phase transitions are accompanied by a reorganization of the spectral density in the phase plane with a sharp increase in the high-frequency range. The spectral density has maxima of the quasi-biphonon type. The obtained data in dimensionless form, apart from plutonium and uranium, can be used for other monatomic crystals. The specific features of the thermal conductivity and microdynamics of the formation of vacancies and pores in crystals without shells have been discussed.

Ion-acoustic solitons in dusty plasma

The dynamics of dust ion-acoustic solitons is analyzed in a wide range of dusty plasma parameters. The cases of both a positive dust grain charge arising due to the photoelectric effect caused by intense electromagnetic radiation and a negative grain charge established in the absence of electromagnetic radiation are considered. The ranges of plasma parameters and Mach numbers in which “conservative” (nondissipative) solitons can exist are determined. It is shown that, in dusty plasma with negatively charged dust grains, both compression and rarefaction solitons can propagate, whereas in plasma with positively charged dust grains, only compression solitons can exist. The evolution of soliton-like compression and rarefaction perturbations is studied by numerically solving the hydrodynamic equations for ions and dust grains, as well as the equation for dust grain charging. The main dissipation mechanisms, such as grain charging, ion absorption by dust grains, momentum exchange between ions and dust grains, and ion-neutral collisions are taken into account. It is shown that the amplitudes of soliton-like compression and rarefaction perturbations decrease in the course of their evolution and their velocities (the Mach numbers) decrease monotonically in time. At any instant of time, the shape of an evolving soliton-like perturbation coincides with the shape of a conservative soliton corresponding to the current value of the Mach number. It is shown that, after the interaction between any types of soliton-like perturbations, their velocities and shapes are restored (with a certain phase shift) to those of the corresponding perturbations propagating without interaction; i.e., they are in fact weakly dissipative solitons.

Soliton microdynamics of structural phase transitions in crystalline materials and phonons of a new type on phase interfaces

It is shown that the generation of nonlinear soliton, breather, and shock waves at high dynamic excitations leads to martensitic phase transformations in crystalline materials of the α-uranium type. Investigations have been performed by modeling the atomic microdynamics with the use of the modified interaction potential. It is shown that collisions of compression shock waves and rarefaction solitons lead to the generation of nuclei of new phases, which evolve according to the domino principle. The phonon spectra of systems with phase interfaces are investigated. A new effect of the total internal phonon reflection has been discovered. It is shown that surface phonons of radically a new type (different from the Rayleigh surface waves) are excited on interfaces. The results are adapted to materials of the α-uranium type, where solitons have been found at slow-neutron scattering.

Large-amplitude ion acoustic solitons in a bi-ion plasma

A gas-dynamic model is used to study the conditions for the existence of large-amplitude ion acoustic solitons in a plasma with negative ions. It is shown that the limiting Mach number—the upper boundary of the region of existence of compression solitons—depends nonmonotonically on the temperature of the positive ions. The result is that, for certain fixed densities of the negative ions, there are one or two temperature boundaries between the regions where solitons can and cannot exist. It is found that, for rarefaction solitons, it is fundamentally important to take into account electron inertia and that the Mach number of such solitary waves is restricted not by the complete decompression of electrons within the wave (as thought previously), but by the fact that the electrons at the center of the wave reach the acoustic speed, above which the thermal-pressure-induced action cannot be transferred back to the electron flow and smooth continuous solutions are impossible.

Ion-acoustic solitons in Bi-Ion dusty plasma

The propagation of ion-acoustic solitons in a warm dusty plasma containing two ion species is investigated theoretically. Using an approach based on the Korteveg de Vries equation, it is shown that the critical value of the negative ion density that separates the domains of existence of compression and rarefaction solitons depends continuously on the dust density. A modified Korteveg de Vries equation for the critical density is derived in the higher order of the expansion in the small parameter. It is found that the nonlinear coefficient of this equation is positive for any values of the dust density and the masses of positive and negative ions. For the case where the negative ion density is close to its critical value, a soliton solution is found that takes into account both the quadratic and cubic nonlinearities. The propagation of a solitary wave of arbitrary amplitude is investigated by the quasi-potential method. It is shown that the range of dust densities around the critical value within which solitary waves with positive and negative potentials can exist simultaneously is relatively wide.

Rarefaction waves, solitons, and holes in a pure electron plasma

The propagation of holes, solitons, and rarefaction waves along the axis of a magnetized pure electron plasma column is described. The time dependence of the radially averaged density perturbation produced by the nonlinear waves is measured at several locations along the plasma column for a wide range of plasma parameters. The rarefaction waves are studied by measuring the free expansion of the plasma into a vacuum. A new hydrodynamic theory is described that quantitatively predicts the free expansion measurements. The rarefaction is initially characterized by a self-similar plasma flow, resulting in a perturbed density and velocity without a characteristic length scale. The electron solitons show a small increase in propagation speed with increasing amplitude and exhibit electron bursts. The holes show a decrease in propagation speed with increasing amplitude. Collisions between holes and solitons show that these objects pass through each other undisturbed, except for a small offset.

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.

Rarefaction Ion Acoustic Solitons in Two-Electron-Temperature Plasma

This paper shows that rarefaction ion acoustic solitons appear in a two-electron-temperature plasma. And also it presents general conditions and physical mechanism for existence of the rarefaction solitons. It is found that finite amplitude rarefaction and compression solitons coexist in a plasma within a certain parameter region.