Generation of short-lived large-amplitude magnetohydrodynamic pulses by dispersive focusing

Large-amplitude MHD waves are routinely observed in space plasmas. We suggest that dispersive focusing, previously proposed for the excitation of freak waves in the ocean, can be also responsible for the excitation of short-lived large-amplitude MHD waves in space plasmas. The DNLS equation describes MHD waves propagating in plasmas at moderate angles with respect to the equilibrium magnetic field. We obtained an analytical solution of the linearised DNLS equation governing the generation of large-amplitude MHD waves from small-amplitude wave trains due to the dispersive focusing. Our numerical solutions of the full DNLS equation confirm this result.     

Plasma-maser interaction of langmuir wave with kinetic Alfvén wave turbulence

A theoretical study is made on the generation mechanism of Langmuir mode wave in the presence of kinetic Alfvén wave turbulence in a magnetized plasma on the basis of plasma-maser interaction. It is shown that a test high frequency Langmuir mode wave is unstable in the presence of low frequency kinetic Alfvén wave turbulence. The growth of the Langmuir wave occurs due to direct and polarization coupling terms. Because of the universal existence of the kinetic Alfvén waves in large scale plasmas, the results have potential importance in space and astrophysical radiation processes.     

The Stability of the Relativistic Alfvén Waves

Within the framework of the special relativity, the system of reference comoving with Alfvén wave is defined and the form of the perturbations with respect to this system are deduced. The system of equations corresponding to the interaction of the waves, in the case when the relativistic Alfvén wave can generate new Alfvén waves and magnetosonic waves, is obtained in the most general form. In the one-dimensional case the time dependent perturbation method is used for obtain the dispersion equation for the relativistic coupled waves (decay processes). Finally, by solving numerically the dimensionless dispersion equation, the instability domains of the Alfvén waves are obtained. It is shown that there are possible decay processes and modulational instabilities.     

Nonlinear interaction between three kinetic Alfvén waves

Using Hall-MHD theory, we focus on the resonant interaction between three kinetic Alfvén waves. We thus derive three coupled equations which govern this process. It turns out that these equations contain the same coupling coefficient, directly showing that they satisfy the Manley–Rowe relations. The coupling coefficient can be written in a comparatively very simple form, that has not been deduced before. The decay rate, when a pump kinetic Alfvén wave decays into two similar Alfvén waves, is therefore easily estimated for plasmas of astrophysical interest.     

Generation of gravitational radiation in dusty plasmas and supernovae

We present a novel nonlinear mechanism for exciting a gravitational radiation pulse (or a gravitational wave) by dust magnetohydrodynamic (DMHD) waves in dusty astrophysical plasmas. We derive the relevant equations governing the dynamics of nonlinearly coupled DMHD waves and a gravitational wave (GW). The system of equations is used to investigate the generation of a GW by compressional Alfvén waves in a type II supernova. The growth rate of our nonlinear process is estimated, and the results are discussed in the context of the gravitational radiation accompanying supernova explosions.     

On kinetic Alfvén waves in a dusty plasma

The dispersion and damping of a dust-modified kinetic Alfvén wave, and a lower frequency dust kinetic Alfvén wave, is investigated in a dusty plasma comprising electrons, ions, and negative dust. It is found that, when dust dynamics is neglected, the presence of cold dust modifies the usual kinetic Alfvén wave dispersion and damping owing to the inequality of the electron and ion densities. The dispersion relation of the dust kinetic Alfvén wave, with frequency below the dust cyclotron frequency, depends on the density and temperature parameters of all three species, and the wave damping is due to both electrons and ions.     

Ion pickup by the intrinsic low-frequency Alfvén waves with a spectrum

Ion pickup by a monochromatic low-frequency Alfvén wave, which propagates along the background magnetic field, has recently been investigated in a low beta plasma (Lu and Li 2007 Phys. Plasmas 14 042303). In this paper, the monochromatic Alfvén wave is generalized to a spectrum of Alfvén waves with random phase. It finds that the process of ion pickup can be divided into two stages. First, ions are picked up in the transverse direction, and then phase difference (randomization) between ions due to their different parallel thermal motions leads to heating of the ions. The heating is dominant in the direction perpendicular to the background magnetic field. The temperatures of the ions at the asymptotic stage do not depend on individual waves in the spectrum, but are determined by the total amplitude of the waves. The effect of the initial ion bulk flow in the parallel direction on the heating is also considered in this paper.     

Higher-order inertial Alfvén wave dressed solitons,quasiperiodic structures,and chaos in plasmas

The higher-order, low-amplitude inertial Alfvén wave (IAW) dressed soliton and chaos are investigated in a magnetized plasma. In the linear limit, the dispersion relation for propagation of IAWs in plasmas is also obtained in the presence of electron thermal effects and illustrated numerically. It is found that the electron inertial length plays an important role for wave dispersion effects and its phase speed is increased on including the electron temperature in the model. The reductive perturbation method is employed to obtain the first-order IAW Korteweg–de Vries (KdV) soliton and second-order dressed soliton solutions analytically, which gives electron density dip (or rarefactive) structure and moves with super Alfvénic speed in plasmas. The numerical illustrations of the KdV and dressed IAW solitons are also presented by using the laboratory and space plasma parameters given in the literature. Furthermore, a numerical study of quasi-periodicity and chaotic behaviour of IAWs in the presence of external periodic force is also discussed in detail. The effects of plasma beta (which depends on plasma density, electron temperature, and magnetic field intensity) and obliqueness of the wave propagation on the formation of nonlinear Alfvénic wave structures have also been presented.     

An exact nonlinear Alfvén wave solution in a toroidal magnetic field

The propagation of Alfvén waves along a non-uniform toroidal magnetic field in a highly conducting incompressible fluid rotating uniformly is studied. It is shown that there is an exact Alfvén wave solution with large but restricted form.     

Scattering of an Alfvén wave by an inhomogeneity in the solar wind density

The interaction between a nonlinear Alfvén wave and intense inhomogeneities in the density of interplanetary plasma is considered in the magnetohydrodynamic (MHD) approximation. The cold-plasma approximation was used to carry out a more correct study of the interaction since the thermal pressure can introduce pronounced changes into the shape of specified inhomogeneities in the plasma density. Results of numerical solution of the well-known MHD equations are presented in the form of three films demonstrating different scenarios of development of the nonlinear dynamics. The films allow us to observe the dynamic evolution of the form of an Alfvén perturbation and the changes in the density inhomogeneities. For small-amplitude Alfvén waves this corresponds to the process of linear transformation by the density inhomogeneities, which does not lend itself to comprehensive analytical study. Numerical simulation reveals the phenomena of reflection from regions of sharp density variation, which are very sensitive to the spatial scales of the interacting objects. The same method is used to investigate the scattering of strong waves. After reversible changes in shape in a high-density region (where oscillations of the shock-wave front are attenuated), a moderate-amplitude Alfvén wave is recovered in a more rarefied medium. A strong scattered Alfvén wave brings about irreversible changes in the shape of the density inhomogeneity. The results obtained illustrate the process of interaction between Alfvén waves and strong density perturbations related to piston or explosive shock waves in the solar wind. State Pedagogikal University, Nizhny Novgorod, Russia; Radiophysical Research Institute, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 2, pp. 152–163, February, 1998.     

Transformation of alfvén into slow magnetosonic disturbances in the magnetosphere due to reflection from magnetically conjugate ionospheric regions

We perform numerical and analytical studies of MHD phenomena within the framework of a one-dimensional model of the magnetosphere bounded by conjugate reflection surfaces. Specific features of the nonlinear transformation of an Alfvén wave into a slow magnetosonic one upon propagation along the magnetic fieldB ₀ are considered. Effects of reflection of a nonlinear magnetospheric wave from magnetically conjugate ionospheres are analyzed in detail. It is shown that the main effect for the case of a nonlinear Alfvén wave in a low-temperature plasma is the plasma sweeping off the volumes close to the reflecting boundaries. Numerical results which demonstrate the generation dynamics of the slow magnetosonic wave and plasma sweeping upon reflection of a powerful Alfvén wave from the ionosphere are in qualitative agreement with the analytical estimates. In a cold plasma, the effect is so significant that it requires a numerical study even if the initial Alfvén wave is linear. The key role of the ratio between the Alfvén and sound velocities for the value of the density disturbance is revealed. Pedagogical University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 4, pp. 285–295, April, 2000.     

On the kinetic Alfvén waves in nonrelativistic spin quantum plasmas

We have studied the effect of electron spin on the kinetic Alfvén waves in the presence of uniform static magnetic field in an electron–ion plasma. We deduce that the usual kinetic Alfvén waves are modified via spin quantum effects of electrons. The dimensionless parameters that determine the relative importance of the electron spin become prominent at higher densities. It is found that the kinetic Alfvén wave frequency decreases due to the electron spin contribution in the kinetic limit while in the inertial limit they are almost unaffected in a hot magnetized plasma.     

Nonlinear propagation of ultra-low-frequency electromagnetic modes in a magnetized dusty plasma

A theoretical investigation has been made of nonlinear propagation of ultra-low-frequency electromagnetic waves in a magnetized two fluid (negatively charged dust and positively charged ion fluids) dusty plasma. These are modified Alfvén waves for small value of and are modified magnetosonic waves for large , where is the angle between the directions of the external magnetic field and the wave propagation. A nonlinear evolution equation for the wave magnetic field, which is known as Korteweg de Vries (K-dV) equation and which admits a stationary solitary wave solution, is derived by the reductive perturbation method. The effects of external magnetic field and dust characteristics on the amplitude and the width of these solitary structures are examined. The implications of these results to some space and astrophysical plasma systems, especially to planetary ring-systems, are briefly mentioned. Received 8 July 1999 and Received in final form 11 October 1999     

[Russian Text Ignored].

Using the drift kinetic equation the influence of the ballooning component of the perturbed transit ion pressure on the low-frequency Alfvéen waves in a toroidal plasma is considered. It is shown that this contribution to the plasma pressure leads in a relatively cold plasma (plasma edge) to a stabilization of the Alfvéen modes. Taking into account drift effects the modified Alfvéen wave becomes unstable if the temperature gradient is large enough. All the perturbations are strongly localized around the corresponding rational magnetic surface.     

Rogue internal waves in the ocean: Long wave model

Rogue waves can be categorized as unexpectedly large waves, which are temporally and spatially localized. They have recently received much attention in the water wave context, and also been found in nonlinear optical fibers. In this paper, we examine the issue of whether rogue internal waves can be found in the ocean. Because large-amplitude internal waves are commonly observed in the coastal ocean, and are often modeled by weakly nonlinear long wave equations of the Korteweg-de Vries type, we focus our attention on this shallow-water context. Specifically, we examine the occurrence of rogue waves in the Gardner equation, which is an extended version of the Korteweg-de Vries equation with quadratic and cubic nonlinearity, and is commonly used for the modelling of internal solitary waves in the ocean. Importantly, we choose that version of the Gardner equation for which the coefficient of the cubic nonlinear term and the coefficient of the linear dispersive term have the same sign, as this allows for modulational instability. From numerical simulations of the evolution of a modulated narrow-band initial wave field, we identify several scenarios where rogue waves occur.     

Kinetic Alfvén waves in turbulent plasmas

The anomalous damping of a coherent kinetic Alfvén wave in turbulent plasmas is investigated.     

Induced scattering and two-photon absorption of Alfvén waves with arbitrary propagation angles

An equation for the spectral energy density of collisionless Alfvén waves, propagating at arbitrary angles to the average magnetic field, is derived on the basis of the theory of weak turbulence. The main nonlinear processes for the case studied are induced scattering and two-photon absorption of Alfvén waves by thermal ions. An equation is derived for thermal particles which describes particle diffusion, accompanying these processes, in momentum space. The results are qualitatively different from previous results obtained by other authors for Alfvén waves propagating along the average magnetic field.     

Mode mixing of Alfvén waves in bismuth

We have investigated the propagation of Alfvén waves in bismuth at 4.2 K using a microwave interferometer at 34.45 GHz and applying magnetic fields up to 1 Tesla. At certain angles between the external magnetic field and the direction of propagation of the Alfvén waves in the crystal, we have observed intense oscillations of the amplitude and the phase of the interferometer curves. We explain these oscillations as due to a superposition of the two Alfvén wave modes. The phase velocities of the two modes are calculated from the measurements. Comparing them with a general dispersion relation we find good agreement between the theoretical phase velocities and the experimental values.     

Formation of convective cells by modulational instability of drift Alfvén waves

A model equation describing drift Alfvén wave with E × B nonlinearity is derived. For a special ordering a nonlinear Schrödinger equation is derived, which governs modulational instability of the drift Alfvén wave. Translational invariance is assumed along the magnetic field. The relation between the characteristic scale lengths parallel and perpendicular to the drift flow for the onset of cell formation has been found. The influence of perpendicular ion viscosity is also discussed.     

Ion acoustic parametric decay instability in a plasma with β > 1

It is found that in a plasma with β > 1 a finite amplitude ion acoustic wave is unstable and decays into two shear Alfvén waves propagating in opposite directions. The threshold and growth rate of the instability are determined.