Ion-acoustic Rogue Waves Research Articles

Surface engineering by rogue wave induced by energetic carbon clusters

Swift heavy ions are effective in nanostructuring material surfaces. The irradiation of lanthanum fluoride with 30 MeV C60 leads to the creation of surface nanohillocks of size larger than the ones produced by monoatomic heavy ions. The generation of the observed nano-sized hillocks is described here by a new approach that is based on ion-induced intensive electronic excitations that create localized rogue waves. Consequently, the induced nonlinear ion-acoustic rogue waves are considered a hallmark of nanohillock formation. Plasma hydrodynamic equations produce a relationship between normalised electron number density and crystal lattice spacing. Similarities to the hillock profile suggest the crucial primary role of electron density in the fabrication of surface nanostructures.

Ion-acoustic rogue waves in a multi-component plasma medium

The nonlinear propagation of ion-acoustic (IA) waves (IAWs) in a four component plasma medium (FCPM) containing inertial warm positive ions, and inertialess isothermal cold electrons as well as non-extensive (q-distributed) hot electrons and positrons is theoretically investigated. A nonlinear Schrödinger equation (NLSE) is derived by using the reductive perturbation method, and it is observed that the FCPM under consideration supports both modulationally stable and unstable parametric regimes which are determined by the sign of the dispersive and nonlinear coefficients of NLSE. The numerical analysis has shown that the maximum value of the growth rate decreases with the increase in q (q>1), and the modulationally unstable parametric regime allows to generate highly energetic IA rogue waves (IARWs), and the amplitude and width of the IARWs increase with an increase in the value of hot electron number density while decrease with an increase in the value of cold electron number density. The applications of our investigation in understanding the basic features of nonlinear electrostatic perturbations in many space plasma environments and laboratory devices are briefly discussed.

Characteristic behaviour of N-order ion acoustic rogue waves solution in electron-positron-ion plasmas

The characteristic behaviour of breathers as well as N-order Rogue wave (RW) solution in homogeneous unmagnetized electron-positron-ion plasmas (consisting of cold ions, and isothermal Maxwellian electrons and positrons) has been studied theoretically. Nonlinear Schrödinger (NLS) equation is derived employing Krylov-Bogoliubov-Mitropolosky (KBM) perturbation technique in solving the concerned problems. The analytical solution of the NLS equation in the forms of breathers such as Akhmediev breather (AB), Kuznetsov-Ma breather (KM) solitons, as well as first-, second-, third-, and fourth-order RWs solution are obtained. The characteristic behaviour of breathers’ and their dependency on the relevant physical parameters are examined. The different orders of RWs are analyzed to obtain the region of existence of ion acoustic (IA) rogue waves (IARWs) with respect to unstable region. The potential profiles concerning different orders of RWs depend on the ratio of positron to electron concentrations () and wave number (). Analysis reveals that the spatial difference between the two adjacent peaks of AB profiles are increasing with the enhancement of transformer physical parameter (), while the temporal evolution between the two neighboring peaks of KM profiles decreases with increasing and the amplitudes become large as well. The amplitudes of first-, second-, and third-order RWs profiles are decreasing with increasing while the amplitude of fourth-order RWs profile is increasing. The results obtained in this study may be useful in understanding the propagation of nonlinear waves in optical fibers, Bose-Einstein condensates, plasma physics and atmospheric physics.

Formation of ion acoustic rogue waves in warm dense matter

Formation of ion acoustic rogue waves in warm dense matter

Three-Dimensional Rogue Waves in Earth’s Ionosphere

The modulational instability of ion-acoustic waves (IAWs) in a four-component magneto-plasma system consisting of positive–negative ions fluids and non-Maxwellian (r,q) distributed electrons and positrons, is investigated. The basic system of fluid equations is reduced to a three-dimensional (3D) nonlinear Schrödinger Equation (NLS). The domains of the IAWs stability are determined and are found to be strongly affected by electrons and positrons spectral parameters r and q and temperature ratio Tp/Te (Tp and Te are positrons and electrons temperatures, respectively). The existence domains, where we can observe the ion-acoustic rogue waves (IARWs) are determined. The basic features of IARWs are analyzed numerically against the distribution parameters and the other system physical parameters as Tp/Te and the external magnetic field strength. Moreover, a comparison between the first- and second-order rogue waves solution is presented. Our results show that the nonlinearity of the system increases by increasing the values of the non-Maxwellian parameters and the physical parameters of the system. This means that the system gains more energy by increasing r, q, Tp, and the external magnetic field through the cyclotron frequency ωci. Finally, our theoretical model displays the effect of the non-Maxwellian particles on the MI of the IAWs and RWs and its importance in D–F regions of Earth’s ionosphere through (H+,O2−) and (H+,H−) electronegative plasmas.

Nonlinear Dynamics of Ion Acoustic Solitary and Rogue Waves in Dense Quantum Plasmas

Nonlinear Dynamics of Ion Acoustic Solitary and Rogue Waves in Dense Quantum Plasmas

Ion-Acoustic Rogue Waves in Double Pair Plasma Having Non-Extensive Particles

The modulational instability (MI) of ion-acoustic (IA) waves (IAWs) and associated IA rogue waves (IARWs) are studied in double-pair plasma containing inertial positive and negative ions, inertialess non-extensive electrons and iso-thermal positrons. A standard nonlinear Schrödinger equation (NLSE) is derived by employing reductive perturbation method. It can be seen from the numerical analysis that the plasma system supports both modulationally stable (unstable) parametric regime in which the dispersive and nonlinear coefficients of the NLSE have opposite (same) sign. It is also found that the basic features of IAWs (viz., MI criteria of IAWs, amplitude, and width of the IARWs, etc.) are rigorously changed by the plasma parameters such as mass, charge state, and number density of the plasma species. The outcomes of our present investigation should be useful in understanding the propagation of nonlinear electrostatic IAWs and associated IARWs in astrophysical and laboratory plasmas.

Head-on collision of ion-acoustic multi-solitons and study of rogue waves in electron-beam superthermal plasma

In this investigation, head-on collision of ion-acoustic (IA) multi-solitons and study of characteristics of ion acoustic rogue waves in an unmagnetized plasma which includes ion fluid, superthermal hot electrons, and penetrated by electron beam have been presented. The Korteweg-de Vries equation have been derived by employing the extended Poincaré-Lighthill-Kuo (PLK) method. Further, multi-solitons of different KdV equations have also been determined by following the Hirota bilinear method. The combined effects of electron beam parameters and variation of different physical parameters on the characteristics of IA solitons and phase shifts of multi-solitons have been analyzed. It is remarked that electron beam components and other plasma parameters significantly influence the phase shifts and other properties of ion-acoustic solitons (IASs). Furthermore, the nonlinear Schrodinger equation (NLSE) has been derived from the KdV equation by using appropriate transformation. The characteristics of different orders rogue waves have also been studied from the different solutions of NLSE. The results of this study may be of great importance to understand the characteristics properties of various kinds of nonlinear solitary structures in different kinds of plasma systems.

Nonlinear ion acoustic rogue waves in a superthermal electron–positron–ion plasma

In this paper, the nonlinear ion acoustic rogue waves (IARWs) are investigated in an unmagnetized, collisionless plasma which consist of positive ions, superthermal electrons and positrons, respectively. A nonlinear Schrodinger equation (NLSE) of IAW packets has been obtained by using the reductive perturbation technique. Furthermore, the effects of superthermal electrons and positrons on the nonlinear dispersion relation, the group velocity and the modulational instability of nonlinear ion acoustic wave (IAW) packets have been studied in detail. At the same time, the characteristics of first- and second-order IARW also have been discussed. It seems that there is some significant influence of superthermal electrons and positrons on the nonlinear ion acoustic waves. Meanwhile, it is also found that the first- and second-order IARW consisting of Peregrine breathers can be excited by using the modulational instability in this system.

Three-dimensional dissipative ion-acoustic rogue waves in magnetized plasma with adiabatic ions and nonextensive electrons

ABSTRACT The modulational instability of ion-acoustic rogue waves in a three-dimensional magnetized, dissipative plasma consisting of inertial warm positive ions and nonextensive electrons has been theoretically investigated. Using the well-known reductive perturbation method, the (3+1)-dimensional modified nonlinear Schrödinger equation (mNLSE), i.e. the standard NLSE in addition to the dissipative term has been derived and then solved to obtained instability criteria, as well as first- and second-order rogue wave solutions. It is found that increasing viscosity results in dissipation of energy which makes the IARW shorter and thinner as was reported in the literature. Furthermore effects of relevant parameters such as nonextensive parameter, and magnetic field on growth rate and rogue waves solutions were discussed in detail. The results of the present investigation may be useful in understanding and predicting the nonlinear excitations that occur in space and laboratory dissipative plasma systems.

Heavy ion–acoustic rogue waves in magnetized electron–positron multi‐ion plasmas

AbstractNon‐linear heavy ion‐acoustic waves (HIAWs) are studied in a homogeneous magnetized four‐component multi‐ion plasma composed of inertial heavy negative ions, light positive ions, and inertia‐less non‐extensive electrons and positrons. The non‐linear Schrödinger equation is derived in this model using the perturbation method. The criteria for modulational instability of HIAWs and the basic features of finite‐amplitude heavy ion acoustic rogue waves (HIARWs) are investigated. The presence of the magnetic field was found to reduce the amplitude of HIARWs and enhances the stability. It is interesting to note that increasing positive ion mass causes decreases in the amplitude and width of rogue waves, which is opposite behaviour to that demonstrated in the previous study of these waves in an unmagnetized plasma. Furthermore, it is also shown that striking parameters, such as the non‐extensive parameter, the positron number density, the electron number density, the electron temperature, and the magnetic field parameter, play an undeniable role on the stability of waves packets. The findings of the present investigation may be of wide relevance to some plasma environments, such as active galactic nuclei, pulsar magnetospheres, and other magnetic confinement systems.

Three-dimensional Nonlinear Structures in Magnetized Complex Plasmas

A three-dimensional multi-component magneto-plasma system consisting of hybrid nonextensive-nonthermal-distributed electrons, positive ions, and immobile negatively charged dust grains is considered to examine the modulational instability (MI) of dust ion-acoustic waves (DIAWs). The reductive perturbation method, which is valid for small but finite amplitude DIAWs, is employed to derive the (3 + 1)-dimensional nonlinear Schrodinger equation (NLSE). The NLSE leads to the MI of DIAWs as well as the formation of dust ion-acoustic rogue waves (DIARWs), which are formed due to the effects of nonlinearity in the propagation of DIAWs. It is found that the basic features (viz. amplitude and width) of the DIAWs and DIARWs (which is formed in the unstable region) are significantly modified by the various plasma parameters such as non-extensive (non-thermal) parameter q(α), number densities of plasma species, threshold modulational obliqueness ($${{\theta }_{c}}$$), etc. The application of the results in space and laboratory magneto-plasma system is briefly discussed.

Head-on Collision of Ion-Acoustic Solitary Waves with Two Negative Ion Species in Electron–Positron–Ion Plasmas and Production of Rogue Waves

The interactions between ion acoustic solitary waves (IASWs) are investigated considering completely ionized electron–positron–ion (e–p–i) plasmas consisting of ions with positive and two negative species, nonthermal electrons, and positrons. Two-sided Korteweg–de Vries (KdV) and modified KdV (mKdV) equations are derived using extended Poincare–Lighthill–Kuo (ePLK) reductive perturbation method. To investigate the production of ion-acoustic rogue waves (IARWs), the rational solution of nonlinear Schrodinger equation (NLSE) is derived from the mKdV equation. Two types of plasmas containing $${\text{A}}{{{\text{r}}}^{ + }}$$ , $${{{\text{F}}}^{ - }}$$ , and $${\text{SF}}_{{\text{5}}}^{ - }$$ species, as well as $${\text{SF}}_{{\text{5}}}^{ + }$$ , $${{{\text{F}}}^{ - }}$$ , and $${\text{SF}}_{{\text{5}}}^{ - }$$ species, are taken into account to study their effects on the amplitudes and phase shifts after collision, as well as the production and properties of rogue waves (RWs). It is observed during collision that a high-amplitude wave is produced in the interaction region depending on the type and parameters of plasmas. The nonthermality of electrons and positrons, electron-to-positron temperature ratio, and the density of negative ions modify the phase shift and amplitude of the waves produced during the collision of the two solitons. The amplitude of the RW for the $${\text{A}}{{{\text{r}}}^{ + }}$$ , $${{{\text{F}}}^{ - }}$$ , and $${\text{SF}}_{{\text{5}}}^{ - }$$ plasmas is found to be larger than that for the $${\text{SF}}_{{\text{5}}}^{ + }$$ , $${{{\text{F}}}^{ - }}$$ , and $${\text{SF}}_{{\text{5}}}^{ - }$$ plasmas.

Ion-Acoustic Rogue Waves in Multi-ion Plasmas**Supported by the Bangladesh Ministry of Science and Technology Fellowship Award and the Alexander von Humboldt Foundation for a Postdoctoral Fellowship

The basic properties of nonlinear ion-acoustic (IA) waves (IAWs), particularly finite amplitude IA rogue waves (IARWs) in a plasma medium (containing pair ions, iso-thermal positrons, and non-thermal electrons) are theoretically investigated by deriving the nonlinear Schrödinger equation (NLSE). The criteria for the modulational instability of IAWs, and the basic features of finite amplitude IARWs are identified. The modulationally stable and unstable regions are determined by the sign of the ratio of the dispersive coefficient to the nonlinear coefficient of NLSE. The latter is analyzed to obtain the region for the existence of the IARWs, which corresponds to the unstable region. The shape of the profile of the rogue waves depends on the non-thermal parameter α and the ratio of electron temperature to positron temperature. It is found that the increase in the value of the non-thermal parameter enhances both the amplitude and width of IARWs, and that the enhancement of electron (positron) temperature reduces (enhances) the amplitude and width of IARWs. It is worth to mention that our present investigation may be useful for understanding the salient features of IARWs in space (viz., upper region of Titan’s atmosphere, cometary comae, and Earth’s ionosphere, etc.) and laboratory (viz., plasma processing reactor and neutral beam sources, etc.) plasmas.

Rogue waves in multi‐pair plasma medium

The non‐linear propagation of ion acoustic (IA) waves, which is governed by the non‐linear Schrödinger equation, in multi‐pair plasmas (MPPs) containing adiabatic positive and negative ion fluids as well as non‐extensive (q‐distributed) electrons and positrons is theoretically investigated. It is observed that the MPP under consideration supports two types of modes, namely fast and slow IA modes, and the modulationally stable and unstable parametric regimes for the fast and slow IA modes are determined by the sign of the ratio of the dispersive coefficient to the non‐linear one. It is also found that the modulationally unstable regime generates highly energetic IA rogue waves (IARWs), and the amplitude as well as the width of the IARWs decreases with increase in the value of q (for both q > 0 and q < 0 limits). These new striking features of the IARWs are found to be applicable in the space (i.e., D‐region [], and F‐region [H+, H−] of the Earth's ionosphere) and laboratory MPPs (i.e., fullerene [C+, C−]).

The characters of ion acoustic rogue waves in nonextensive plasma

Several well-known nonlinear waves in the rational solutions of the nonlinear Schrödinger equation are studied in two-component plasmas consisting of ions fluid and nonextensive electrons, such as Kuznetsov–Ma breather (K-M), bright soliton, rogue wave (RW), Akhmediev breather (AB) and dark soliton, and so on. In this paper, we have investigated the characteristics of K-M, AB, and RW's propagation in plasma with nonextensive electron distribution, and the dependence of amplitude and width for ion acoustic rogue waves in this system. It is found that K-M' triplet is appearance-disappearance-appearance-disappearance. AB solitons only appear once and RW is a single wave that appears from nowhere and then disappears. It is also noted that the wave number and nonextensive parameter of electrons have a significant influence on the maximum envelope amplitude, but, the influence of the width was not significant. At the same time, the effects of the small parameter, which represent the nonlinear strength, on the amplitude and width of ion acoustic rogue waves are also being highlighted.

Simulation study of planar and nonplanar super rogue waves in an electronegative plasma: Local discontinuous Galerkin method

Planar and nonplanar (cylindrical and spherical) ion-acoustic super rogue waves in an unmagnetized electronegative plasma are investigated, both analytically (for planar geometry) and numerically (for planar and nonplanar geometries). Using a reductive perturbation technique, the basic set of fluid equations is reduced to a nonplanar/modified nonlinear Schrödinger equation (NLSE), which describes a slow modulation of the nonlinear wave amplitude. The local modulational instability of the ion-acoustic structures governed by the planar and nonplanar NLSE is reported. Furthermore, the existence region of rogue waves is strictly defined. The parameters used in our calculations are from the lab observation data. The local discontinuous Galerkin (LDG) method is used to find rogue wave solutions of the planar and nonplanar NLSE and to prove L2 stability of this method. Also, it is found that the numerical simulations and the exact (analytical) solutions of the planar NLSE match remarkably well and numerical examples show that the convergence orders of the proposed LDG method are N + 1 when polynomials of degree N are used. Moreover, it is noted that the spherical rogue waves travel faster than their cylindrical counterpart. Also, the numerical solution showed that the spherical and cylindrical amplitudes of the localized pulses decrease with the increase in the time | τ |.

Ion-acoustic rogue waves in magnetized solar wind plasma with nonextensive electrons

Abstract Ion-acoustic rogue waves are investigated in a two-component magnetized solar wind plasma, composed of positively charged fluid ions, as well as nonextensive electrons. Typical solar wind plasmas parameters are used. It is shown that the wave number domain for the onset of ion-acoustic modulational instability enlarges as the electrons evolve towards their thermal equilibrium. Interestingly, we show that as the solar wind plasma expands far out from the sun, the wave amplitude increases and the IA rogue wave concentrates therefore a significant amount of energy. Our investigation may be of wide relevance to astronomers and space scientists working on the solar wind and interstellar plasmas.

Ion acoustic kinetic Alfvén rogue waves in two temperature electrons superthermal plasmas

The propagation properties of ion acoustic kinetic Alfven (IAKA) solitary and rogue waves have been investigated in two temperature electrons magnetized superthermal plasma in the presence of dust impurity. A nonlinear analysis is carried out to derive the Korteweg-de Vries (KdV) equation using the reductive perturbation method (RPM) describing the evolution of solitary waves. The effect of various plasma parameters on the characteristics of the IAKA solitary waves is studied. The dynamics of ion acoustic kinetic Alfven rogue waves (IAKARWs) are also studied by transforming the KdV equation into nonlinear Schrodinger (NLS) equation. The characteristics of rogue wave profile under the influence of various plasma parameters ( $\kappa_{c}$ , $\mu_{c}$ , $\sigma $ , $\theta$ ) are examined numerically by using the data of Saturn’s magnetosphere (Schippers et al. 2008; Sakai et al. 2013).

The impact of positrons beam on the propagation of super freak waves in electron-positron-ion plasmas

In this work, we examine the nonlinear propagation of planar ion-acoustic freak waves in an unmagnetized plasma consisting of cold positive ions and superthermal electrons subjected to cold positrons beam. For this purpose, the reductive perturbation method is used to derive a nonlinear Schrödinger equation (NLSE) for the evolution of electrostatic potential wave. We determine the domain of the plasma parameters where the rogue waves exist. The effect of the positron beam on the modulational instability of the ion-acoustic rogue waves is discussed. It is found that the region of the modulational stability is enhanced with the increase of positron beam speed and positron population. Second as positrons beam increases the nonlinearities of the plasma system, large amplitude ion acoustic rogue waves are pointed out. The present results will be helpful in providing a good fit between the theoretical analysis and real applications in future laboratory plasma experiments.