Effects of two-temperature electrons, external oblique magnetic field, concentration of charged dust grains and higher-order nonlinearity on dust ion-acoustic solitary waves in Saturn's E-ring

The purpose of the present work is to investigate some nonlinear properties of the dust ion-acoustic (DIA) solitary waves in a four-component hot-magnetized dusty plasma consisting of charged dust grains, positively charged ions and two-temperature isothermal electrons. Applying a reductive perturbation theory, a nonlinear Korteweg-de Vries (KdV) equation for the first-order perturbed potential and a linear inhomogeneous KdV-type equation for the second-order perturbed potentials are derived. Stationary solutions of these coupled equations are obtained using a renormalization method. A method based on energy consideration is used to obtain a condition for stable solitons. The effects of two different types of isothermal electrons, external oblique magnetic field, concentration of negatively (positively) charged dust grains and higher-order nonlinearity on the nature of the DIA solitary waves are discussed. The numerical results are applied to Saturn's E-ring.     

Transient Evolution of Nonlinear Localized Coherent Structures of Kinetic Alfvén Waves

We present numerical simulations of kinetic Alfvén waves (KAWs) and inertial Alfvén waves (IAWs) applicable to the solar wind, the solar corona, and the auroral regions, respectively, leading to the formation of coherent magnetic structures when the nonlinearity arises from ponderomotive effects and Joule heating. The nonlinear dynamical equation satisfies the modified nonlinear Schrödinger equation. The effect of nonlinear coupling between the main KAW/IAW and the perturbation, producing filamentary structures of the magnetic field, has been studied. Scalings in the spectral index of the power spectrum at different times have been calculated. These filamentary structures can act as a source for particle acceleration by wave?–?particle interaction because the KAWs/IAWs are mixed modes and Landau damping is possible.     

Viscous damping of nonlinear magneto-acoustic waves

The motivation for the present work is discussed, and in Section 2 the nonlinear Burger's equation is derived for wave propagation in a compressible unstratified viscous fluid permeated by a magnetic field (initially constant), using the reductive perturbation method of Taniuti and Wei (1968). An analytic solution of the equation is given (after Sakai, 1972) and the angular behaviour is shown for certain parameters describing the nonlinearity and damping of the system, for both fast- and slow-mode disturbances.     

Rayleigh-Taylor instability of a two-fluid layer under a general rotation field and a horizontal magnetic field

In this paper the Rayleigh-Taylor instability (RTI) of a two-fluid layer system under the simultaneous action of a general rotation field and a horizontal magnetic field is presented. An approximate and an exact solution of the eigenvalue equation are calculated. These solutions are important not only to understand more deeply the physical problem but also to determine the correct numerical solutions. Numerical calculations are done for an unstable density stratification in the cases of horizontal magnetic field parallel and perpendicular to the horizontal component of the angular velocity. For an adverse density stratification, it is shown that in comparison to previous works, the horizontal magnetic field creates new angular areas (of the angle of propagation of the perturbation) at which the perturbation is stable and propagates as traveling waves. It is also shown that the vertical component of the angular velocity has a destabilizing effect because it works to eliminate the stable angular areas.     

Effects of two-temperature electrons, external oblique magnetic field, and higher-order nonlinearity on dust acoustic solitary waves in a dusty plasma with vortex-like ion distribution

Nonlinear properties of the dust acoustic (DA) solitary waves in a dusty plasma consisting of negatively variable-charged dust particles, vortex-like distributed ions and two-temperature isothermal electrons are reported. A reductive perturbation theory has been used to derive a modified Korteweg-de Vries (mKdV) equation for the first-order perturbed potential and a linear inhomogeneous mKdV-type equation for the second-order perturbed potential. The renormalization method is used to obtain stationary solutions of these coupled equations. The modifications in the amplitude and width of the solitary wave structure due to the inclusion of two different types of isothermal electrons, external oblique magnetic field, higher-order nonlinearity, and vortex-like distributed ions are investigated. Also a method based on energy consideration was used to obtain the stability condition. Moreover, the numerical results are applied to investigate some nonlinear characteristics of the DA solitary waves.     

Nonlinear stability of an infinite cylinder in the presence of a uniform axial magnetic field

The effect of a uniform axial magenetic field on the nonlinear instability of a self-gravitating infinite cylinder is examined. Using the method of multiple scales, it is found that while the nonlinear (modulational) instability cannot be completely suppressed, the presence of a magnetic field does increase the range of stable wave numbers. The evolution of the amplitude is governed by a non-linear Schrödinger equation which gives the criterion for modulational instability.Department of Chemical Engineering and Technology.Department of Mathematics.     

MHD studies on the free convection and hall effects on waves in a semi-infinite plasma

In this paper, analytical MHD studies are made on the propagation of oscillatory waves in a semi-infinite plasma which is exposed to an applied magnetic field. The oscillatory wave is introduced into the plasma environment by temperature perturbation.The phase speeds of the resultant disturbance are discussed in terms Grashof, Prandtl, and Eckert numbers (free-convection parameters), Hall parameter, Alfvén parameter, and frequences. Expansion about small Eckert number is made to solve the very nonlinear coupled partial differential equations for the field variables. The appearance of steady streaming at all times in the first order expansion is mentioned.     

Contribution of Higher-Order Nonlinearity to obliquely electron-acoustic solitary waves in a magnetized auroral zone plasma

Using the Viking Satellite observations data in the dayside auroral zone, a theoretical investigation is carried out for contribution of the higher-order nonlinearity to nonlinear obliquely electron-acoustic solitary waves (EASWs) in a magnetized collisionless plasma consisting of a cold electron fluid and non-thermal hot electrons obeying a non-thermal distribution, and stationary ions. A Zakharov–Kuznetsov (ZK) equation that contains the lowest-order nonlinearity and dispersion is derived from the lowest order of perturbation and a linear inhomogeneous (ZK-type) equation that accounts for the higher-order nonlinearity and dispersion is obtained. A stationary solution for equations resulting from higher-order perturbation theory has been found using the renormalization method. The effects of the external magnetic field and the obliqueness are found to significantly change the higher-order properties (viz. the amplitude, width, electric field and energy) of the EASWs. The effect of higher-order nonlinearity on the amplitude and width of the soliton are also discussed. A comparison with the Viking Satellite observations in the dayside auroral zone are taken into account.     

Nonlinear standing waves on the surface of a self-gravitating cylinder

The weakly nonlinear standing waves on the surface of a self-gravitating incompressible fluid column are investigated in the presence of, a uniform axial-magnetic field. By use of the method of multiple scales, we have shown that near the critical wave number, the amplitude modulation of a standing wave can be described by a nonlinear Schrödinger equation with the roles of time and space variable interchanged. It is demonstrated that in presence of a magnetic field, the system is always stable near the critical wave number.Department of Chemical Engineering, and TechnologyDepartment of Mathematics     

Dust-ion-acoustic solitary waves and their multi-dimensional instability in a magnetized nonthermal dusty electronegative plasma

A rigorous theoretical investigation has been made on multi-dimensional instability of obliquely propagating electrostatic dust-ion-acoustic (DIA) solitary structures in a magnetized dusty electronegative plasma which consists of Boltzmann electrons, nonthermal negative ions, cold mobile positive ions, and arbitrarily charged stationary dust. The Zakharov-Kuznetsov (ZK) equation is derived by the reductive perturbation method, and its solitary wave solution is analyzed for the study of the DIA solitary structures, which are found to exist in such a dusty plasma. The multi-dimensional instability of these solitary structures is also studied by the small-k (long wave-length plane wave) perturbation expansion technique. The combined effects of the external magnetic field, obliqueness, and nonthermal distribution of negative ions, which are found to significantly modify the basic properties of small but finite-amplitude DIA solitary waves, are examined. The external magnetic field and the propagation directions of both the nonlinear waves and their perturbation modes are found to play a very important role in changing the instability criterion and the growth rate of the unstable DIA solitary waves. The basic features (viz. speed, amplitude, width, instability, etc.) and the underlying physics of the DIA solitary waves, which are relevant to many astrophysical situations (especially, auroral plasma, Saturn’s E-ring and F-ring, Halley’s comet, etc.) and laboratory dusty plasma situations, are briefly discussed.     

Obliquely propagating nonlinear structures in dense dissipative electron positron ion magnetoplasmas

Nonlinear electrostatic waves in dense dissipative magnetized electron-positron-ion (e-p-i) plasmas are investigated employing the quantum hydrodynamic model. In this regard, Zakharov Kuznetsov Burgers (ZKB) equation is derived in dense plasmas using the small amplitude perturbation expansion method. It is observed that obliqueness, positron concentration, kinematic viscosity, and the ambient magnetic field significantly alter the structure of nonlinear quantum ion acoustic waves in dense dissipative e-p-i magnetoplasmas. The present study may be useful to understand the nonlinear propagation characteristics of electrostatic shock structures in dense astrophysical systems where the quantum effects are expected to dominate.     

Obliquely propagating electrostatistic solitary structures in a hot magnetized dusty plasma with vortex-like electron distribution

The nonlinear properties of solitary waves structure in a hot magnetized dusty plasma consisting of a negatively charged, extremely massive hot dust fluid, positively charged hot ion fluid and vortex-like distributed electrons, are reported. A modified Korteweg de Vries equation (mKdV) which admits a solitary wave solution for small but finite amplitude is derived using a reductive perturbation theory. The modifications in the amplitude and width of the solitary wave structures due to the inclusion of an external magnetic field and dust and ions temperature are investigated. This revised version was published online in July 2006 with corrections to the Cover Date.     

Perturbation of the radial and non-radial oscillations of a star by a magnetic field

A generalization of the perturbation method is applied to the problem of the radial and the non-radial oscillations of a gaseous star which is distorted by a magnetic field. An expression is derived for the perturbation of the oscillation frequencies due to the presence of a weak magnetic field when the equilibrium configuration is a spheroid. The particular application to the homogeneous model with a purely poloidal field inside, due to a current distribution proportional to the distance from the axis of symmetry, and a dipole type field outside is considered in detail. The main result is that the magnetic field has a large and almost stabilizing effect on unstableg-modes, particularly on higher order modes. With the considered magnetic field the surface layers appear to have a large weight.     

Stellar oscillations and magnetic field perturbations of the boundary conditions

The effect of a weak magnetic field on the adiabatic radial and non-radial oscillations of a stellar configuration is studied by means of a perturbation method. Special attention is devoted to the perturbation of the oscillation frequencies resulting from the change of the boundary conditions caused by the magnetic field. This change is related to the fact that the introduction of a magnetic field removes the singularity at the surface of the equilibrium configuration. The perturbation method is applied to Ferraro's model and the influence of a magnetic field on the frequencies of the different types of oscillation modes is discussed.     

Nonlinear dynamics of Landau damped kinetic Alfvén waves

In the present paper we have studied the nonlinear dynamical equation of Landau damped kinetic Alfvén wave (KAW) to investigate the nonlinear evolution of KAW and the resulting turbulent spectra in solar wind plasmas. We have introduced a parameter g which governs the coupling between the amplitude of the pump KAW and the density perturbation. The numerical solution has been carried out to see the dependence on the parameter g in the nonlinear part of our equation. Our results reveal the formation of damped localized structures of KAW as well as steepening of the turbulent spectra by increasing g when damping is taken into account. The power spectra of magnetic field fluctuations indicate the redistribution of energy among the higher wave numbers. Each power spectrum with and without damping splits up into two different scaling ranges, Kolmogorov scaling followed by a steeper scaling. The steepening in the power spectra with Landau damping is more than without Landau damping case (for the same value of g). This type of steeper spectra has also been observed in the solar wind and is attributed to the Landau damping effects.     

New Boundary Integral Equation Representation for Finite Energy Force-Free Magnetic Fields in Open Space above the Sun

A boundary integral equation to describe a force-free magnetic field with finite energy content in the open space above the solar surface is found. This is a new representation for a 3-D nonlinear force-free field in terms of the boundary field and its normal gradient at the boundary. Therefore the magnetic field observed on the solar surface can be incorporated into the formulation directly and a standard numerical technique, the boundary element method, can be applied to solve the field. A numerical test case demonstrates the power of the method by recovering the analytical solution to the desired accuracy and its application to practical solar magnetic field problems is straightforward and promising.     

Painlevé Analysis and Nonlinear Periodic Solutions for Isothermal Magnetostatic Atmospheres

The equations of magnetohydrodynamic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic equation for the magnetic potential , known as the Grad–Shafranov equation. Specifying the arbitrary functions in the latter equation, one gets a nonlinear elliptic equation. Analytical solutions of the elliptic equation are obtained for the case of a nonlinear isothermal atmosphere in a uniform gravitational field. The solutions are obtained by using the Painlevé analysis, and are adequate for describing parallel filaments of diffuse, magnetized plasma suspended horizontally in equilibrium in a uniform gravitational field.     

Mean-field dynamo with cubic non-linearity

The turbulent mean-field dynamo of αω-type with a mean helicity quadratically dependent on the magnetic field is investigated. A nonlinear system of ordinary differential equation is derived for the amplitudes of the magnetic field expansion over the eigenvectors of the linear problem. In a one-mode approximation the non-linear supercritical solution is stable when dγ/d D > 0, where γ is the growth rate of the linear solution and D is the dynamo number. Non-linear interation between two modes of dipole and quadrupole symmetry is considered. The conditions are found for the synchronization and beats of these modes under the assumption that the quadrupole mode is weaker than the dipole one.     

Modulation of ion acoustic waves

The multiple scales perturbation theory is applied to a system of dispersive waves including plasma waves (ion-acoustic waves). Assuming the amplitudes of waves are slowly varying function of space and time, we find that long-time slow modulation of the complex amplitude can be described by the non-linear Schrödinger equation. This result agrees with that obtained by Shimizu and Ichikawa using the reductive perturbation theory, and agrees exactly with the nonrelativistic limit of the nonlinear Schrödinger equation obtained by Nejoh using the stretching method.     

Linear Wave Beams in the Crust of a Neutron Star

The propagation of axially symmetric wave beams near the equatorial plane of a neutron star is studied. These waves are excited by a spatially bounded perturbation in the form of a transverse magnetic field applied to the inner boundary of the crust of the star. For a small ratio of the perturbed to the unperturbed magnetic field, a linear theory can be employed to solve the evolution equation. This condition is satisfied in the crust plasma of a neutron star for typical radio luminosities of pulsars. The resulting simple, exact solution in the form of linear gaussian beams exists without additional conditions on the dissipation, dispersion, and narrowness of the beams, if the velocity c _n of these waves is constant. The latter requirement is well satisfied for the plasma in neutron star crusts. The width of the gaussian beam also depends weakly on position.