Magnetoacoustic Solitons Research Articles

Magnetoacoustic solitons in Alkali-fullerene plasmas

Nonlinear propagation of magnetoacoustic waves in magnetized, collisionless, warm bi-ion plasmas with positive and negative ions of different masses and charge states are investigated. The two-fluid model is used here. Using reductive perturbation technique, the Korteweg-de Vries equation is derived as nonlinear dispersion relation, and its solution for the magnetoacoustic solitons propagating in the direction perpendicular to the external magnetic field is obtained. Using experimental values for the plasma parameters, magnetoacoustic soliton structures for K-fullerene plasma are illustrated along with some other useful alkali-fullerene plasmas.

Head on interaction of magnetoacoustic solitons in a spin-1/2 dense plasma with geometrical effects

The head on interaction due to two magnetoacoustic solitons is studied in a dense electron-ion magnetoplasma with geometrical and electron spin effects. For this purpose, the extended Poincaré-Lighthill-Kuo (PLK) technique and quantum two fluid equations are utilized to derive a set of nonplanar Korteweg–de Vries equations. The PLK method incorporates the post collision trajectories and the phase shifts encountered by the magnetoacoustic solitons after collision. The interaction is numerically analyzed by choosing some typical plasma parameters from compact astrophysical objects. It is observed that the spin-1/2 effects, statistical pressure, displacement current and geometry of the system significantly modify the phase shifts encountered by the solitons. It is noticed that the enhancement in the number density reduces the phase shift of the colliding solitons. Furthermore, the cylindrical geometry is observed to decrease phase shift by comparison with the planar geometry. The present investigation provides a deeper insight of head on collision caused by the magnetoacoustic solitons in dense magnetoplasmas.

Magnetoacoustic cnoidal waves and solitons in multi-ions plasmas with application to ionospheric plasmas

The magnetoacoustic nonlinear periodic (cnoidal) wave and solitons in multi-ion plasmas are studied, and its Korteweg–de Vries (KdV) equation is derived by applying the reductive perturbation (RP) method with appropriate boundary conditions. The dynamics of all species in a multi-ion plasma, which consists of warm (light) ions, cold (heavy) ions, and hot electrons, are taken in the electromagnetic field. Two types of multi-ion plasmas, i.e., H+-O+-e (positive ion plasma) and H+-O2−-e (negative ion plasma), are chosen, which can exist in different layers of the ionosphere. It is found that for the H+-O+-e plasma case, the nonlinear structure forms compressive magnetoacoustic wave pulses (which move with the super-Alfvénic speed of light ions in the lab frame) and depends on plasma parameters such as the external magnetic field intensity and light ion temperature and density. It is also found that the rarefactive magnetoacoustic wave structures (move with the sub-Alfvénic speed of light ions in the lab frame) are also formed in H+-O+-e plasma if heavy and light ions' density ratio is increased beyond a certain limit. In the case of negative ion (i.e., H+-O2−-e) plasma, again, compressive magnetoacoustic cnoidal waves and soliton structures are formed at a comparatively lower value of heavy to light ions' density ratio (χ) with the positive ion plasma case. Again, these compressive magnetoacoustic structures switch to the rarefactive ones in negative ion plasma when density ratio χ is increased beyond a certain limit. The parametric analysis and numerical plots are illustrated, and the obtained theoretical results are found to be consistent with the Freja experimental observations in the upper ionosphere.

Magnetoacoustic solitons in pair-ion fullerene plasma

ABSTRACT The propagation of magnetoacoustic (fast magnetohydrodynamic) waves in pair-ion (PI) fullerene plasma is studied in the linear and nonlinear regimes. The pair-ion (PI) fullerene plasma is theorized as homogeneous, magnetized, warm and collisionless. Employing multi-fluid magnetohydrodynamic model, the dispersion relation is obtained and wave dispersion effects which appear through ion inertial length are discussed. Using reductive perturbation technique (RPT), the Korteweg–de Vries (KdV) equation is derived and its solution for small but finite amplitude magnetoacoustic solitons propagating in the direction perpendicular to the external magnetic field is presented. The compressive magnetoacoustic soliton (i.e. positive potential pulse) propagating with super Alfvénic speed is obtained in magnetized PI fullerene plasma. The variations in the amplitude and width of the magnetoacoustic soliton structures are also illustrated by using numerical values of the plasma parameters such as ions' density, temperature difference between fullerene ions and magnetic field intensity, which have been taken from the PI plasma experiments already published in the literature.

Interaction of magnetoacoustic solitons in electron-positron plasmas

The interaction between two, four and six magnetoacoustic solitons in electron-positron plasmas are investigated. The extended Poincaré–Lighthill–Kuo (PLK) perturbation method is employed to derived two KdV equations for magnetoacoustic solitons moving towards each other and studied the head-on collision between them and their phase shifts. The Hirota bilinear method is used to have multi-soliton solutions of already derived two KdV equations for right and left moving solitons. The four and six magnetoacoustic solitons solutions of the two KdV equations are obtained to discuss their interaction and phase shifts. It is found that only compressive magnetoacoustic solitons structures are formed in electron-positron plasma. The present study may be useful to understand the collective phenomena related to head-on and overtaking magnetoacoustic solitons interaction in electron-positron plasmas that may occur in a pulsar magnetosphere.

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.

Interaction of magnetoacoustic solitons in plasmas with dispersion effects through electron inertia

The head‐on collision between two magnetoacoustic solitons is investigated in a magnetized plasma containing inertial cold ions and warm electrons. A two‐fluid magnetohydrodynamic (MHD) model is used to study the magnetoacoustic solitons interaction in plasmas. The magnetoacoustic wave dispersion effects appearing through electron inertial length (skin depth) are also included in the model. By using the extended Poincaré–Lighthill–Kuo (PLK) method, the Korteweg–de Vries (KdV) equations are derived for the low amplitude left and right moving magnetoacoustic solitons, their trajectories, and corresponding phase shifts after their elastic collisions are obtained analytically and examined numerically as well. It is found that only positive polarity (compressive) soliton structures of magnetoacoustic waves are formed. The profiles of head‐on collision and the time evolution of two compressive interacting magnetoacoustic solitons are also presented for illustration. The effect of plasma beta, which depends on plasma density, electron temperature, and magnetic field intensity, on the phase shift of the interacting magnetoacoustic solitons is also examined.

Fast magnetohydrodynamic cnoidal waves and solitons in electron-positron plasma

Linear and nonlinear propagation of fast magnetohydrodynamic waves (or magnetoacoustic waves) are studied in homogeneous, magnetized and warm collisionless electron-positron (e-p) plasma by using two fluid magnetohydrodynamic model. In the linear limit, the wave dispersion relation is obtained and wave dispersion effect which appears through inertial length in e-p plasma system is also discussed. Using reductive perturbation method, the Korteweg-de Vries (KdV) equation for small but finite wave amplitude of magnetoacoustic waves is derived with appropriate boundary conditions. The cnoidal wave and soliton solutions are obtained using well known Sagdeev potential approach for magnetoacoustic waves in e-p plasmas propagating in the direction perpendicular to the external magnetic field. The phase portrait analysis and numerical illustration of magnetoacoustic cnoidal waves and solitons is also presented by using the parameters such as magnetic field intensity, plasma density and temperature of electron and positron fluids for astrophysical plasma situations exist in the literature.

Modulational instability of ion-acoustic waves in magnetoplasma with pressure of relativistic electrons

In this research, the modulation of a weakly three-dimensional electrostatic ion-acoustic wave (IAW) is studied in dense magnetoplasma consisting of relativistic degenerate inertialess electrons and nondegenerate inertial thermal ions. It is assumed that the degeneracy pressure law for electrons follows the Chandrasekhar equation of state. The standard reductive perturbation theory has been applied to obtain the corresponding three-dimensional nonlinear Schrodinger equation, where the nonlinearity is in balance with the dispersive terms. This equation governs the dynamics and shows the slow modulation of the IAWs. This equation also been influenced not only by the external magnetic field but also by the usual plasma parameters. The numerical results indicate that new instability regimes arise when we consider the relativistic parameter ( μe), the ion to electron temperature ratio (σi), and the normalized ion cyclotron frequency (ωci) which though cannot be observed in the unmagnetized case can considerably modify the profiles of the envelope magneto acoustic solitons. Also, some significant explicit critical frequencies are obtained, which permit us to consider new regimes different from the usual unmagnetized plasma for propagation of IAWs in the magnetoplasma, which may exist in space or astrophysics.

Magnetoacoustic nonlinear periodic (cnoidal) waves in plasmas

Magnetoacoustic nonlinear periodic (cnoidal) waves and solitons are studied in magnetized electron-ion plasmas with inertial cold ions and warm electrons. Using the two fluid model, the dispersion relation of the magnetoacoustic waves is obtained in the linear limit and the wave dispersive effects appear through the electron inertial length. The well known reductive perturbation method is employed to derive the Korteweg-de Vries equation for magnetoacoustic waves in plasmas. The Sagdeev potential approach is used, and the cnoidal wave solution of magnetoacoustic waves is obtained under periodic boundary conditions. The analytical solution for magnetoacoustic solitons is also presented. The phase plane portraits are also plotted for magnetoacoustic solitons shown as a separatrix, and the cnoidal wave structure always lies within the separatrix. It is found that plasma beta, which depends on the plasma density, electron temperature, and magnetic field intensity, has a significant effect on the amplitude and phase of the cnoidal waves, while it also affects the width and amplitude of the magnetoacoustic soliton in plasmas. The numerical results are plotted within the plasma parameters for laboratory and space plasmas for illustration. It is found that only compressive magnetoacoustic nonlinear periodic wave and soliton structures are formed in magnetized plasmas.

Modulationally stable envelope solitons in astrophysical magnetoplasmas with degenerate relativistic electrons

The formation and propagation characteristics of small-amplitude magnetoacoustic dark/grey solitons are investigated in a semi relativistic degenerate magnetoplasma whose constituents are electrons and singly ionized positive ions. For this purpose, the electrons are assumed to follow the degeneracy pressure law through the Chandrasekhar equation of state, while the inertial cold ions are taken as non-degenerate and magnetized. By solving the one-fluid quantum magnetohydrodynamic (QMHD) model with the aid of a reductive perturbation technique, a nonlinear Schrödinger (NLS) equation is derived for weakly nonlinear envelope magnetoacoustic solitons. The NLS equation admits the existence of stable excitations, e.g. dark and grey solitons for which the condition $P/Q<0$ holds. Numerical results reveal that the variation of plasma number density, magnetic field strength, relativistic parameter $({\it\eta}_{e0})$ and the quantum parameter $(H)$ significantly modify the profiles of the envelope magnetoacoustic solitons. The present results are important to understanding of the nonlinear dynamics of magnetoacoustic solitons in astrophysical dense magnetoplasmas (viz., white dwarfs, magnetars, neutron stars, etc.), where the relativistic degeneracy effects play a vital role in collective interactions.

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.

Phase shifts of magneto-acoustic solitons in spin-1/2 fermionic quantum plasma during head-on collision

AbstractThe head-on collision between two magneto-acoustic solitons in spin-1/2 fermionic quantum plasma is studied in the framework of the model proposed by Marklund et al. (Marklund, M., Eliasson, B. and Shukla, P. K. 2007 Phys. Rev. E. 76, 067401). The extended Poincare–Lighthill–Kuo method is used to obtain the phase shifts and the trajectories during the head-on collision of two solitons. The effect of the Zeeman energy for different speeds of the waves, the effect of the total mass density of the charged plasma particles for different strengths of magnetic field, the effect of the speed of the wave for different values of the Zeeman energy, and that of the ratio of the sound speed to Alfven speed for different values of Zeeman energ on the phase shift are studied. It is observed that the phase shifts are significantly affected in all the cases. The most interesting observation of this paper is that the phase shifts increase as well as decrease, and also they may be positive as well as negative depending upon the domain of the chosen parameters.

Propagation of nonlinear dust magnetoacoustic waves in cylindrical geometry

The cylindrical dust magnetoacoustic shocks in dissipative and solitons in non-dissipative dust-ion plasmas are studied. The dust particles are assumed to be fully negatively charged so that the density of electrons in comparison with dust and ions is negligible. The cylindrical Korteweg-de Vries Burgers and cylindrical Korteweg-de Vries equations are derived for dust magnetosonic waves by employing the reductive perturbation method. It is found that dust plasma parameters such as dust charge number, dust density, and ion temperature have strong influence on the profile of dust magnetoacoustic shocks and solitons. The results are also obtained numerically by using the data from laboratory experiments on dusty plasmas.

Dynamics of magnetoacoustic solitons in the case of transition radiation in an inhomogeneous magnetic field

A study is made of the change in the parameters of a magnetoacoustic soliton propagating in an inhomogeneous external magnetic field for both the case of abrupt change in the field and periodic variation of a small correction to a constant external field. It is shown that in the second case the width of the soliton and its velocity vary with a certain effective frequency.

Low-frequency radiation of magnetoacoustic solitons in an inhomogeneous magnetic field

Low-frequency radiation of magnetoacoustic solitons in an inhomogeneous magnetic field