Fast Solitary Waves Research Articles

Charged space debris induced nonlinear magnetosonic waves using inertial magnetohydrodynamics

The excitations of nonlinear magnetosonic waves in the presence of charged space debris objects in the low Earth orbital (LEO) plasma region are investigated by taking into account the effects of electron inertia in the framework of classical magnetohydrodynamics (MHD); which is also referred to as inertial magnetohydrodynamics. The magnetosonic waves are found to be governed by a forced Kadomtsev–Petviashvili (KP) equation with the forcing term representing the effects of space debris objects. The dynamical behaviours of both slow and fast magnetosonic solitary waves are explored in detail. Exact pinned accelerated magnetosonic lump wave solutions are shown to be stable for the entire region in the parameter space of slow waves and a large region in the parameter space of fast waves. In a similar way, exact pinned curved magnetosonic solitary wave solutions become stable for a small region in the parameter space of fast waves. These exact solutions with special properties are derived for some specific choices of the forcing debris functions. These novel results can have potential applications in the scientific and technological aspects of the space debris detection and mitigation in the near-Earth space.

Theoretical studies of low and high frequency electrostatic solitary waves in the magnetopause associated with asymmetric magnetic reconnection

In a comprehensive analysis of Cluster data, Graham et al. (2015) have reported the existence of slow and fast electrostatic solitary waves (ESWs) associated with asymmetric magnetic reconnection arising from the merger of the magnetic fields, and mixing, of the hot tenuous magnetospheric plasma and the cooler dense magnetosheath plasma. Their analysis also reveals the presence of four electron species, two background Maxwellian distributions and a pair of counter-streaming electron beams. Using the measured plasma parameters and a plasma model consistent with the observations, together with an ion component for charge neutrality, we use fluid dynamic theory in an attempt to identify the plasma modes associated with the ESWs, as well as the polarity and admissible range in speed of the fast and slow structures. It can be inferred from the data sets in Figure 4 in Graham et al. (2015) obtained during the crossing of the Cluster satellites C3 and C4 of the separatrix near the ion diffusion region that the distributions of the two counterstreaming electron beams vary from having identical characteristics to showing small differences over the period during which the ESWs were observed. Accordingly, we align the theoretical parameters in our study with Cluster observations by considering the effect of identical and non-identical counterstreaming electron beam distributions on the existence of ESWs.

Collisions between solitary waves propagating in the two-dimensional hexagonal packing granular system

In this paper, we investigate head-on and overtaking collisions of two solitary waves propagating in two-dimensional (2D) hexagonal packing confined in a rectangular region, using the fifth-order Runge–Kutta numerical scheme. In the head-on collision, numerical results indicate that the velocity amplitude of the solitary waves and the second solitary waves is proportional to the impacting velocity of the solitary waves. The relationship between phase shift and impacting velocity satisfies the equation [Formula: see text]. For head-on collisions of the waves with an equal amplitude of velocity, this power exponent is [Formula: see text], which can be well predicted by the binary collision approximation theory. For the case of head-on collisions between the waves with unequal amplitudes of solitary waves, this power exponent becomes [Formula: see text]. During an overtaking collision, the fast solitary wave has a positive phase shift, and the slow solitary wave has a negative phase shift. The phase shift of the fast solitary wave also has a power exponential relationship with the impacting velocity. The two waves either form a single peak in transition, or remain separated throughout the encounter with a double-peak formation depending on the ratio of the impacting velocity of solitary waves. The critical condition between the two regimes is consistent with those obtained by the Korteweg–de Vries model.

Nonlinear Periodic Wave Propagation of Fast and Slow Magnetosonic Waves in the Presence of Oblique Magnetic Field

Fast and slow magnetosonic cnoidal and solitary wave structures in electron-ion plasmas are studied in the presence of an oblique magnetic field. Under the low-frequency wave assumption, cold ions are taken to be dynamic, while inertialess electrons are assumed as isothermally heated. The two-fluid magnetohydrodynamic model is applied to present the basic set of dynamic equations for magnetosonic waves in the presence of oblique magnetic field. The linear analysis is performed for studying fast and slow modes of magnetosonic waves and also discussed its limiting cases with magnetic field angle. The nonlinear analysis is done via the reductive perturbation method, and the Korteweg-de Vries (KdV) equation is derived with appropriate periodic boundary condition. The cnoidal wave and soliton solutions for both fast and slow magnetosonic waves are presented. The effects of variations of magnetic field angle and plasma beta on both fast and slow magnetosonic cnoidal and soliton wave structures are discussed using the space plasma parameters that exist in the literature.

Linear and nonlinear fluctuations of electron‐temperature‐gradient driven mode and electron acoustic mode in a two‐electron temperature nonthermal magnetized plasma

AbstractNonlinear vortical structures and soliton formation are investigated for electron temperature gradient instability in a two‐electron temperature non‐Maxwellian magnetoplasma. The inhomogeneity in magnetic field is also considered. A new set of nonlinear equations, using transport equations of Braginskii”s model, are formulated to study the nonlinear structures. A modified linear dispersion relation of coupled electron temperature gradient (ETG) mode and electron acoustic wave is derived. The ETG instability is found to increase with increase in ηec value that increases with sharp density gradients. The results are applied to auroral region of earth's magnetosphere and the calculated values of the nonlinear electric field of fast solitary waves are found to be in agreement with the Viking satellite observations.

Large amplitude ion-acoustic solitary waves in a warm negative ion plasma with superthermal electrons: The fast mode revisited

Large amplitude ion-acoustic fast mode solitary waves in a negative ion plasma with kappa electrons are revisited, using the Sagdeev pseudopotential approach. As is well known, this plasma supports the propagation of both compressive and rarefactive solitons, and there exist a range of parameter values in which the two types of structures coexist. This is confirmed by the present study, which is based on well-established soliton existence domains. After investigating the existence of solitons in terms of the lower and upper Mach number limits for broader regions in the parameter space, we have found that as a result of the ion thermal effects, the range of the allowed Mach numbers is reduced and only small amplitude rarefactive solitons propagate in this plasma, an effect that is enhanced by the superthermal behavior of the electrons. Rearranging our analytical work so as to get a two-positive ion plasma, our results show the presence of stopbands in the soliton existence domains, as reported by Nsengiyumva et al. [Phys. Plasmas 21, 102301 (2014)], despite the use of different normalization and different parameter space. This suggests that the observed stopbands are a real phenomenon, which needs consideration when studying plasma waves.

Solitary Wave Dynamics Governed by the Modified FitzHugh–Nagumo Equation

Abstract The paper deals with the studies of the nonlinear wave solutions supported by the modified FitzHugh–Nagumo (mFHN) system. It was proved in our previous work that the model, under certain conditions, possesses a set of soliton-like traveling wave (TW) solutions. In this paper, we show that the model has two solutions of the soliton type differing in propagation velocity. Their location in parametric space, and stability properties are considered in more details. Numerical results accompanied by the application of the Evans function technique prove the stability of fast solitary waves and instability of slow ones. A possible way of formation and annihilation of localized regimes in question is studied therein too.

Failed self-reformation of a sub-critical fast magnetosonic shock in collisionless plasma

We study with a 1D particle-in-cell (PIC) simulation the evolution of a subcritical perpendicular fast magnetosonic shock. The shock propagates at 1.5 times the fast magnetosonic speed. Some upstream protons are reflected by the shock’s electric potential. They form a beam which carries less energy than those that are reflected magnetically by super-critical shocks. The beam triggers the growth of a fast magnetosonic solitary wave upstream of the shock, which reflects the beam protons back to the shock. Extracting the momentum and energy of this beam allows the solitary wave to grow into a proto-shock that is trailed by a short downstream region. Protons from the shock-reflected proton beam increase the density of the plasma between the shock and the proto-shock reducing its potential difference relative to both surrounding structures. Bulk protons, which cross the proto-shock, react to the decreased potential jump. The plasma behind the proto-shock accelerates and so does the shock. The trailing end of the proto-shock speeds up in order to continue reflecting the beam protons and eventually it catches up with its front; the proto-shock collapses and the self-reformation fails. A more energetic proton beam could decrease the potential jump across the shock, let it collapse and replace it with the proto-shock.

Interaction and resonance of fast magnetoacoustic solitary waves in cylindrical geometry for dense astrophysical plasmas

The cylindrical Kadomtsev-Petviashvili (CKP) equation, also known as Johnson's equation, is derived for dense electron ion plasmas in the small amplitude limit to study the interaction and resonance of two magnetoacoustic solitons in cylindrical geometry. The exact analytical solutions of the CKP equation are derived using Hirota's direct method and a novel gauge transformation. It is observed that cylindrical geometry transforms the line solitons to the horseshoe-like solitary structures. For multi-solitons, it is shown that the interaction parameter for the CKP solitary wave depends upon the plasma parameters of the system. For the present investigation, plasma parameters are chosen that are customarily found in the white dwarf stars. The interaction of magnetoacoustic solitons are shown to change their trajectory and introduce a phase shift. The resonance condition is developed for the CKP equation which shows that the amplitude of resultant solitons becomes four times the amplitude of initial solitons.

Cylindrical fast magnetosonic solitary waves in quantum degenerate electron-positron-ion plasma

The nonlinear properties of fast magnetosonic solitary waves in a quantum degenerate electron-positron (e-p) plasma in the presence of stationary ions for neutralizing the plasma background of bounded cylindrical geometry were studied. By employing the standard reductive perturbation technique and the quantum hydrodynamic model for the e-p fluid, the cylindrical Kadomtsev-Petviashvili (CKP) equation was derived for small, but finite, amplitude waves and was given the solitary wave solution for the parameters relevant to dense astrophysical objects such as white dwarf stars. By a suitable coordinate transformation, the CKP equation can be solved analytically. An analytical solution for magnetosonic solitons and periodic waves is presented. The numerical results reveal that the Bohm potential has a main effect on the periodic and solitary wave structures. By increasing the values of the plasma parameters, the amplitude of the solitary wave will be increased. The present study may be helpful in the understanding of nonlinear electromagnetic soliton waves propagating in both laboratory and astrophysical plasmas, and can help in providing good agreement between theoretical results and laboratory plasma experiments.

Fast and Slow Mode Solitary Waves in a Five-Component Plasma

We have investigated fast- and slow-mode solitary profiles in a five-component plasma consisting of positively and negatively charged pair ions, hydrogen ions, and hotter and colder electrons. Of these, the heavier ions and colder photoelectrons are of cometary origin while the other components are of solar origin; the electrons are described by kappa distributions. The Zakharov-Kuznetsov (ZK) equation is derived, and solutions for fast- and slow-mode solitary structures are plotted for parameters relevant to comet Halley. We found that the presence of hydrogen ions determines the polarity of the fast- and slow-mode solitary structures. Also, variations of equilibrium number density of hydrogen ions and charge numbers on the heavier pair ions act differently on the fast- and slow-mode solitary structures. The addition of hydrogen ions significantly affects the amplitude of the solitary structures for the fast mode. Further, the cyclotron frequency of the lighter and heavier ions has a noticeable effect on the width of the solitary waves.

Arbitrary amplitude fast electron-acoustic solitons in three-electron component space plasmas

We examine the characteristics of fast electron-acoustic solitons in a four-component unmagnetised plasma model consisting of cool, warm, and hot electrons, and cool ions. We retain the inertia and pressure for all the plasma species by assuming adiabatic fluid behaviour for all the species. By using the Sagdeev pseudo-potential technique, the allowable Mach number ranges for fast electron-acoustic solitary waves are explored and discussed. It is found that the cool and warm electron number densities determine the polarity switch of the fast electron-acoustic solitons which are limited by either the occurrence of fast electron-acoustic double layers or warm and hot electron number density becoming unreal. For the first time in the study of solitons, we report on the coexistence of fast electron-acoustic solitons, in addition to the regular fast electron-acoustic solitons and double layers in our multi-species plasma model. Our results are applied to the generation of broadband electrostatic noise in the dayside auroral region.

Interaction of fast magnetoacoustic solitons in dense plasmas

One dimensional propagation of fast magnetoacoustic solitary waves in dense plasmas with degenerate electrons is investigated in this paper in the small amplitude limit. In this regard, Korteweg deVries equation is derived and discussed using the plasma parameters that are typically found in white dwarf stars. The interaction of fast magnetoacoustic solitons is explored by using the Hirota bilinear formalism, which admits multi soliton solutions. It is observed that the values of the propagation vectors determine the interaction of solitary waves. It is further noted that the amplitude of the respective solitary waves remain unchanged after the interaction; however, they do experience a phase shift.

Reflection of ion acoustic solitary waves in a dusty plasma with variable charge dust

An inhomogeneous plasma comprising ions, two temperature electrons and dust grains with variable charge is explored for its unperturbed state for ions’ drift due to density gradient and perturbed state for the evolution of ion acoustic solitary waves and their reflection under the effect of an external magnetic field. The ion drift velocity is found to depend on the plasma parameters and magnetic field. The perturbed state of plasma supports two types of ion acoustic waves, which evolve into fast and slow compressive solitary structures under certain conditions. However, only the fast solitary wave is observed to be reflected and acquired opposite polarity to that of the incident solitary wave. The solitary waves are found to be downshifted after their reflection. The reflection coefficient acquires higher values in the case of dust grains of fixed charge in comparison with the case of fluctuating charge on the dust grains. It means the reflection becomes stronger when the charge on the dust grains does not fluctuate and remains fixed. The effect of dust grain density is to enhance the amplitude of solitary waves but to weaken their reflection. The amplitudes of both the incident and reflected solitons remain higher for the case of fluctuating charge on the dust grains in comparison with the case of fixed charge. The effective temperature of the plasma is also found to alter the solitary structures significantly in the case of dust grains having fluctuating charge.

Propagation of two dimensional cylindrical fast magnetoacoustic solitary waves in a warm dust plasma

A set of multi-fluid equations and Maxwell’s equations are carried out to investigate the properties of nonlinear fast magnetoacoustic solitary waves with the combined effects of dusty plasma pressure and transverse perturbation in the bounded cylindrical geometry. The reductive perturbation method has been applied to the dynamical system causeway and the derived two dimensional cylindrical Kadomtsev–Petviashvili equation (CKP) predicts different natures of solitons in complex plasma. Under a suitable coordinate transformation the CKP equation can be solved analytically. The change in the soliton structure due to mass of dust, ion temperature, ion density, and dust temperature is studied by numerical calculation of the CKP equation. It is noted that the dust cylindrical fast magnetoacoustic solitary waves in warm plasmas may disappear slowly because of an increase in dust mass. The present analysis could be helpful for understanding the nonlinear ion-acoustic solitary waves propagating in interstellar medium and pulsar wind,which contain an excess of superthermal particles.

Solitary waves excited by relativistic positron showers of astrophysical naturally doped superthermal plasmas

The longitudinal fast solitary waves induced by weakly relativistic positron showers of astrophysical origin are studied in a plasma system contaminated with some massive impurities in presence of superthermal effects. The superthermal effects are due to the high energy electrons. The impurities are dust corpuscles with positive and negative charges. It is noticed that increase in the kappa parameter of electrons and relativistic streaming factor of weakly relativistic positron shower, negative dust concentration invoke an enhancement in the strength of solitary wave. On the other hand increase in the shower’s temperature as well as positive dust concentration diminish the solitary hump strength. It is worth to mention that only hump type compressive fast solitary waves are predicted by our model, for the given set of plasma parameters, because the convective coefficient of the nonlinear governing equation for solitary wave remains positive in considered regime of interaction for plasma and positron shower. Our calculations in linear regime predict both the fast and slow positron shower induced longitudinal, electrostatic perturbations. Our results may be of importance in understanding the nonlinear propagation of waves in doped astrophysical superthermal plasmas with relativistic positron showers.

Characteristics of ion-acoustic solitary wave in a laboratory dusty plasma under the influence of ion-beam

We study the influence of ion beam and charged dust impurity on the propagation of dust ion-acoustic solitary wave in an unmagnetized plasma consisting of Boltzmann distributed electrons, positive ions, positive ion beam, and negatively charged immobile dusts in a double plasma device. On interacting with an ion beam, the solitary wave is bifurcated into a compressive fast and a rarefactive slow beam mode, and appears along with the primary wave. However, there exists a critical velocity of the beam beyond which the amplitude of the fast solitary wave starts diminishing and rarefactive slow beam mode propagates with growing amplitude. Whereas, the presence of charged dust impurity in the plasma reduces this critical beam velocity and a substantial modification in the phase velocity of the slow beam mode is observed with increasing dust density. Furthermore, the nonlinear wave velocity (Mach number) as well as the width of the compressive solitons are measured for different beam velocity and dust density, and are compared with those obtained from the K-dV equation. The experimental results are found in a well agreement with the theoretical predictions.

Dust-acoustic solitary waves in a strongly coupled inhomogeneous dusty plasma in the presence of polarization force and effective dust-temperature

The nonlinear propagation of the dust-acoustic waves is studied in a strongly coupled inhomogeneous dusty plasma which consists of the strongly correlated negatively charged dust grains and weakly correlated electrons and ions. The Korteweg-de Vries equation with variable coefficients and an additional term due to the density gradient is deduced, and its solution is found by appropriate transformations. The propagation of two possible modes (fast and slow) and their evolution are investigated. Only the fast rarefactive solitary waves are found to propagate in such plasma with parameter ranges corresponding to the experimental conditions. It is shown that the special patterns of nonlinear DA waves (e.g., amplitude and width) are significantly modified in a way that depends upon the effects of polarization force (which arises due to the interaction between thermal ions and highly negatively charged dust grains), effective dust-temperature (which arises from the electrostatic interactions among highly negatively charged dust and from the dust thermal pressure), equilibrium electron density, and ion temperature. The amplitude of solitary waves also decreases as the wave propagates in the direction of increasing dust concentration.

FAST SOLITONS ON STAR GRAPHS

We define the Schrödinger equation with focusing, cubic nonlinearity on one-vertex graphs. We prove global well-posedness in the energy domain and conservation laws for some self-adjoint boundary conditions at the vertex, i.e. Kirchhoff boundary condition and the so-called δ and δ′ boundary conditions. Moreover, in the same setting, we study the collision of a fast solitary wave with the vertex and we show that it splits in reflected and transmitted components. The outgoing waves preserve a soliton character over a time which depends on the logarithm of the velocity of the ingoing solitary wave. Over the same timescale, the reflection and transmission coefficients of the outgoing waves coincide with the corresponding coefficients of the linear problem. In the analysis of the problem, we follow ideas borrowed from the seminal paper [17] about scattering of fast solitons by a delta interaction on the line, by Holmer, Marzuola and Zworski. The present paper represents an extension of their work to the case of graphs and, as a byproduct, it shows how to extend the analysis of soliton scattering by other point interactions on the line, interpreted as a degenerate graph.

Two dimensional cylindrical fast magnetoacoustic solitary waves in a dust plasma

The nonlinear fast magnetoacoustic solitary waves in a dust plasma with the combined effects of bounded cylindrical geometry and transverse perturbation are investigated in a new equation. In this regard, cylindrical Kadomtsev–Petviashvili (CKP) equation is derived using the small amplitude perturbation expansion method. Under a suitable coordinate transformation, the CKP equation can be solved analytically. It is shown that the dust cylindrical fast magnetoacoustic solitary waves can exist in the CKP equation. The present investigation may have relevance in the study of nonlinear electromagnetic soliton waves both in laboratory and astrophysical plasmas.