On the waves and instability in self-gravitating magnetic molecular clouds with ambipolar diffusion Part 1: Planar modal approach

It is well established that molecular clouds are the main sites of active star formation in our Galaxy. The interaction of the three major physical agents in molecular clouds, i.e. the self-gravity, magnetic fields, and ambipolar diffusion, in the form of waves and instability, governs the dynamics and evolution of molecular clouds. The present work is a new effort on this subject. This work consists of two parts. In Part 1, we complete the planar modal analysis by removing the restrictions on the direction of the velocity perturbation which were used in previous studies. Thus, the wave number vector k is allowed to take any direction with respect to the mean field B₀. The exact general dispersion relation is found to be a seventh-order equation and can be reduced to a quartic equation as the first approximation about the small parameter x_ρ = ρ_{i, 0}/ρ_n,0, the density ratio between ions and neutrals. The growth rate contour maps in the k plane are obtained for various values of the basic dimensionless parameters Λ and σ, where Λ = V_A,n/C_n is the ratio between the Alfvén speed and the sound speed in the neutrals, and the “coupling factor” σ = v_i/ω_g,n is the ratio between the average collision frequency of a neutral with ions and the self-gravitation response frequency. It is shown that, in all directions, magnetic field only reduces the growth rate but does not change the critical wave length for instability. The reduction of the growth rate depends on not only Λ, the dimensionless measure of the field strength, but also the direction of k as well as the coupling factor σ. The frequencies and the dissipation rates of the Alfvén waves and the fast and slow self-gravitating magnetosonic waves are calculated for all directions of k. The solutions of these waves are also given. Although the planar modal approach is important in understanding the basic mechanism of magnetic waves and instability, it does not take into account the three-dimensionality and the finite size of the cloud and is therefore only suitable to the local analysis. Thus, in order to discuss the global properties, we will develop a cylindrical modal approach in Part 2. There, we will also discuss certain nonlinear effects and show their importance in leading to a self-adjusting mechanism which slows down the global collapse at the early stage of cloud evolution and refreshes the outward propagating Alfvén and fast magnetosonic waves caused by star-forming or core-forming activities. In this way, a significant portion of the released gravitational energy during the global collapse is turned into the magnetic waves to support the cloud against the global collapse itself.     

Waves and instabilities in dark interstellar molecular clouds containing ferromagnetic dust grains

The propagation characteristics of magnetization waves, as well as the instabilities of sound waves in a self-gravitating dark interstellar molecular cloud containing ferromagnetic dust grains and baryonic gas clouds, have been theoretically investigated by including the dynamics of both ferromagnetic dust grains and baryonic gases. It has been shown that there exist two types of subsonic or supersonic (depending on the field strength of the magnetization) transverse magnetization waves, which can be regarded as counterparts of Alfvén waves (for the parallel propagation) and magnetosonic waves (for the perpendicular propagation) in a magnetoactive plasma. It has also been found that, in addition to the usual Jeans instability, the sound waves suffer a new type of instability, which is due to the combined effects of the baryonic gas dynamics and self-gravitational field in both weakly and highly collisional regimes.     

Decay of solitons in an isotropic collisionless quasineutral plasma with isothermal pressure

Soliton-type solutions of the complete unreduced system of transport equations describing the plane-parallel motions of an isotropic collisionless quasineutral plasma in a magnetic field with constant ion and electron temperatures are studied. The regions of the physical parameters for fast and slow magnetosonic branches, where solitons and generalized solitary waves—nonlocal soliton structures in the form of a soliton “core” with asymptotic behavior at infinity in the form of a periodic low-amplitude wave—exist, are determined. In the range of parameters where solitons are replaced by generalized solitary waves, soliton-like disturbances are subjected to decay whose mechanisms are qualitatively different for slow and fast magnetosonic waves. A specific feature of the decay of such disturbances for fast magnetosonic waves is that the energy of the disturbance decreases primarily as a result of the quasistationary emission of a resonant periodic wave of the same nature. Similar disturbances in the form of a soliton core of a slow magnetosonic generalized solitary wave essentially do not emit resonant modes on the Alfvén branch but they lose energy quite rapidly because of continuous emission of a slow magnetosonic wave. Possible types of shocks which are formed by two types of existing soliton solutions (solitons and generalized solitary waves) are examined in the context of such solutions.     

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.     

Nonself-similar regimes of isothermal collapse of protostellar clouds

We consider the development of inhomogeneity in the isothermal collapse of protostellar clouds. The initial and boundary conditions correspond to the classical statement of the problem on the contraction of a homogeneous cloud from a given volume. A centered rarefaction wave is shown to propagate from the outer boundary of the cloud toward its center at the first collapse stage. Analysis reveals two possible regimes of isothermal collapse, depending on the relationship between the rarefaction wave focusing time t^* and the cloud free-fall collapse time t_ff. For cold clouds, t^*=t _ff and the rarefaction wave is not reflected. In this case, as time elapses, the cloud collapse becomes self-similar with the characteristic density profile ρ～r^?2. In hot clouds, t*<t _ff and the focusing can take place before the formation of an opaque core. Since the velocities of the rarefaction wave along and across magnetic field lines in a magnetized cloud are different, its front assumes a shape elongated along magnetic field lines. Depending on the initial conditions, based on analytical estimates, we investigate various possible scenarios for the collapse of magnetic protostellar clouds.     

Magnetosonic waves in antimony

A report is given on the observation of magnetosonic waves propagating through antimony in the Voigt-configuration. The waves were observed from a cut-off field and up to field of the order of 60 kG. The usual Alfvén-wave behavior as well as the influence of non-local effects were observed, the latter at the lower magnetic field values. The non-local effects are analysed in terms of the expressions given by Yokota and by Guthmann et al. It turns out, however, that these expressions are not able to account for the non-linear — in B^-1 — dispersion observed at the lower magnetic field values.     

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.     

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     

Parametric excitation by a pump magnetic field in a high temperature plasma

The parametric growth rates of Alfvén waves, fast compressional waves and ion acoustic waves excited by a time modulated magnetic field are calculated for the case of a high temperature plasma with anisotropic pressure. The plasma is described by the C.G.L. model.     

Model problem of wave refraction by a periodically nonuniform boundary of the solar plasma

The problem of the diffraction of Alfvén and magnetosonic waves by a boundary between two media in the form of a plane interface modulated by a running sinusoidal wave is considered in the linear approximation on the basis of the mathematical apparatus of integral equations of solar magnetohydrodynamics. The results obtained are analyzed and discussed.     

On the origin of solar wind. Alfvén waves induced jump of coronal temperature

Absorption of Alfvén waves is considered to be the main mechanism of heating in the solar corona. It is concluded that the sharp increase of the plasma temperature by two orders of magnitude is related to a self-induced opacity with respect to Alfvén waves. The maximal frequency for propagation of Alfvén waves is determined by the strongly temperature dependent kinematic viscosity. In such a way the temperature jump is due to absorption of high frequency Alfvén waves in a narrow layer above the solar surface. It is calculated the power per unit area dissipated in this layer due to damping of Alfvén waves that blows up the plasma and gives birth to the solar wind. A model short wave-length (WKB) evaluation takes into account the 1/f² frequency dependence of the transversal magnetic field and velocity spectral densities. Such spectral densities agree with old magnetometric data taken by Voyager 1 and recent theoretical calculations in the framework of Langevin-Burgers MHD. The presented theory predicts existence of intensive high frequency MHD Alfvén waves in the cold layer beneath the corona. It is briefly discussed how this statement can be checked experimentally. It is demonstrated that the magnitude of the Alfvén waves generating random noise and the solar wind velocity can be expressed only in terms of satellite experimental data. It is advocated that investigation of properties of the solar surface as a random driver by optical methods is an important task for future solar physics.     

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.     

Linear and nonlinear magnetohydrodynamic waves in twisted magnetic flux tubes

Dynamics of axisymmetric Alfvén and slow magnetoacoustic waves in weakly twisted magnetic flux tubes is considered. Linear dispersion relations for the waves are derived and analyzed in the presence of the twisting. The weakly nonlinear dynamics is shown to be governed by the Korteweg-de Vries equation. Nonlinear slow body waves appear as a narrowing of tube in a low β plasma and widening of tube, when β ⪢ 1. Nonlinear Alfvén torsional waves appear as a widening (β > 1) and narrowing (β < 1) of tube, accompanied by the local increase of the tube twisting.     

Dynamic interaction of plasma flow with the hot boundary layer of a geomagnetic trap

The study of the interaction between collisionless plasma flow and stagnant plasma revealed the presence of an outer boundary layer at the border of a geomagnetic trap, where the super-Alfvén subsonic laminar flow changes over to the dynamic regime characterized by the formation of accelerated magnetosonic jets and decelerated Alfvén flows with characteristic relaxation times of 10–20 min. The nonlinear interaction of fluctuations in the initial flow with the waves reflected from an obstacle explains the observed flow chaotization. The Cherenkov resonance of the magnetosonic jet with the fluctuation beats between the boundary layer and the incoming flow is the possible mechanism of its formation. In the flow reference system, the incoming particles are accelerated by the electric fields at the border of boundary layer that arise self-consistently as a result of the preceding wave-particle interactions; the inertial drift of the incoming ions in a transverse electric field increasing toward the border explains quantitatively the observed ion acceleration. The magnetosonic jets may carry away downstream up to a half of the unperturbed flow momentum, and their dynamic pressure is an order of magnitude higher than the magnetic pressure at the obstacle border. The appearance of nonequilibrium jets and the boundary-layer fluctuations are synchronized by the magnetosonic oscillations of the incoming flow at frequencies of 1–2 mHz.     

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.     

Strong space plasma magnetic barriers and Alfvénic collapse

High-magnitude magnetic barriers in space and solar plasma are proposed to be attributed to the pile up of magnetic field lines and their Alfvénic collapse for MHD flows. The analysis of experimental data from both the Interball and Cluster spacecrafts shows that high-magnitude magnetic structures found in the Earth magnetosheath and near the magnetopause are supported by a nearly thermal transverse plasma flow, with the minimum barrier width being on the order of the ion gyroradius. The collapse termination at such scales can be explained by the balance between the pile up of magnetic field lines and backward finite-gyroradius diffusion. Comparison between the theoretical, modeling, and experimental data shows that the Alfvénic collapse is, in general, a promising mechanism for magnetic field generation and plasma separation. The text was submitted by the authors in English.     

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.     

Excitation of Alfvén vortices in the ionosphere by the magnetospheric convection

We analyze conditions for excitation of ULF waves in the ionospheric Alfvén resonator (IAR), taking into account the altitude-inhomogeneous profile of the magnetospheric convection velocity. This profile is formed as a result of interaction of the convective flow with the neutral atmosphere at altitudes 90–150 km. ULF waves comprise oblique Alfvén waves, trapped into the IAR, and ionospheric drift waves, which are in resonance with them. These waves together form strongly anisotropic, closed current loops, whose scale along the magnetic field greatly exceeds their transverse scale, i.e., l_z ≫ l_⊥, and can be considered Alfvén vortices. Within the framework of the proposed model of the ionosphere, we study the instability threshold and the amplitude growth rate of the Alfvén vortices as functions of different parameters (wave vector k_22A5, angle between the wave vector and the convection velocity, ratio of the Alfvén-wave and Pedersen conductivities, etc.). Some estimates are given in application to the observed small-scale field-aligned currents in the auroral ionosphere. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 5, pp. 376–390, May 2008.     

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.     

Alfvén Waves in Non-Stationary and Non-Uniform Media: An Exactly Solvable Model

The modulation of Alfvén waves interacting with a non-uniform and non-stationary plasma is considered. The waveforms are allowed to change rapidly. We examine our phenomena by means of exact analytical solutions of the MHD equations in the presence of large amplitude disturbances of the magnetic field and plasma density. In contrast to the WKB approach, we do not have to use limiting assumptions regarding the variations of the background medium. We show that the large amplitude time and space disturbances lead to a new cut-off frequency for Alfvén wave propagation. A rapid reshaping of the Alfvén waveform can also obstruct the resonant interactions between the waves and the plasma particles.