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.     

Wave beams in the magnetoelastic crust of pulsars

The propagation of axially symmetric magnetoelastic waves near the equatorial plane of the crust of a neutron star embedded in a transverse magnetic field is examined. The crust is treated as a solid-state plasma and waves are excited in it in the form of a transverse magnetic field applied to the inner boundary of the star’s crust. The time dependent equation is solved in a linear approximation assuming that the perturbing magnetic field is small compared to the unperturbed field. A simple, exact solution in the form of linear gaussian beams is obtained without additional conditions being imposed on the dissipation, dispersion, and narrowness of the beam, provided only that the velocity c_n of these waves depends weakly on position. This last condition is satisfied for the plasma in the crust of a neutron star. As it propagates to the star’s surface, the radius of the beam remains constant. The electric currents generated by the wave beam on the star’s surface are also calculated. __________ Translated from Astrofizika, Vol. 50, No. 4, pp. 547–556 (November 2007).     

Alfvén waves in the solar atmosphere

The nonlinear propagation of Alfvén waves on open solar magnetic flux tubes is considered. The flux tubes are taken to be vertical and axisymmetric, and they are initially untwisted. The Alfvén waves are time-dependent axisymmetric twists. Their propagation into the chromosphere and corona is investigated by solving numerically a set of nonlinear time-dependent equations, which couple the Alfvén waves into motions parallel to the initial magnetic field (motion in the third coordinate direction is artificially suppressed). The principal conclusions are: (1) Alfvén waves can steepen into fast shocks in the chromosphere. These shocks can pass through the transition region into the corona, and heat the corona. (2) As the fast shocks pass through the transition region, they produce large-velocity pulses in the direction transverse to B _o. The pulses typically have amplitudes of 60 km s^–1 or so and durations of a few tens of seconds. Such features may have been observed, suggesting that the corona is in fact heated by fast shocks. (3) Alfvén waves exhibit a strong tendency to drive upward flows, with many of the properties of spicules. Spicules, and the observed corrugated nature of the transition region, may therefore be by-products of magnetic heating of the corona. (4) It is qualitatively suggested that Alfvén waves may heat the upper chromosphere indirectly by exerting time-dependent forces on the plasma, rather than by directly depositing heat into the plasma.     

Magneto-atmospheric waves from a localized source

A technique developed by Lighthill for finding the asymptotic solution of an inhomogeneous wave equation with constant coefficients is applied to the study of wave propagation in magneto-atmospheres. The geometry of the wave number surface plays an important role in determining the generation and propagation of various types of magneto-atmospheric waves from a localized forcing region. Examples of these wavenumber surfaces are exhibited for various magnetic field strengths and wave frequencies. The asymptotic far field is tabulated for a time-harmonic, spatially gaussian, localized forcing term.     

Stokes Diagnostics of Magneto-Acoustic Wave Propagation in the Magnetic Network on the Sun

The solar atmosphere is magnetically structured and highly dynamic. Owing to the dynamic nature of the regions in which the magnetic structures exist, waves can be excited in them. Numerical investigations of wave propagation in small-scale magnetic flux concentrations in the magnetic network on the Sun have shown that the nature of the excited modes depends on the value of plasma β (the ratio of gas to magnetic pressure) where the driving motion occurs. Considering that these waves should give rise to observable characteristic signatures, we have attempted a study of synthesised emergent spectra from numerical simulations of magneto-acoustic wave propagation. We find that the signatures of wave propagation in a magnetic element can be detected when the spatial resolution is sufficiently high to clearly resolve it, enabling observations in different regions within the flux concentration. The possibility to probe various lines of sight around the flux concentration bears the potential to reveal different modes of the magnetohydrodynamic waves and mode conversion. We highlight the feasibility of using the Stokes-V asymmetries as a diagnostic tool to study the wave propagation within magnetic flux concentrations. These quantities can possibly be compared with existing and new observations in order to place constraints on different wave excitation mechanisms.     

Driven waves in a two-fluid plasma

We study the physics of wave propagation in a weakly ionized plasma, as it applies to the formation of multifluid, magnetohydrodynamics (MHD) shock waves. We model the plasma as separate charged and neutral fluids which are coupled by ion–neutral friction. At times much less than the ion–neutral drag time, the fluids are decoupled and so evolve independently. At later times, the evolution is determined by the large inertial mismatch between the charged and neutral particles. The neutral flow continues to evolve independently; the charged flow is driven by and slaved to the neutral flow by friction. We calculate this driven flow analytically by considering the special but realistic case where the charged fluid obeys linearized equations of motion. We carry out an extensive analysis of linear, driven, MHD waves. The physics of driven MHD waves is embodied in certain Green functions which describe wave propagation on short time-scales, ambipolar diffusion on long time-scales and transitional behaviour at intermediate times. By way of illustration, we give an approximate solution for the formation of a multifluid shock during the collision of two identical interstellar clouds. The collision produces forward and reverse J shocks in the neutral fluid and a transient in the charged fluid. The latter rapidly evolves into a pair of magnetic precursors on the J shocks, wherein the ions undergo force-free motion and the magnetic field grows monotonically with time. The flow appears to be self-similar at the time when linear analysis ceases to be valid.     

Large-scale zonal flow and magnetic field generation due to drift-Alfven turbulence in ionosphere plasma

In the present work, the generation of large-scale zonal flows and magnetic field by short-scale collision-less electron skin depth order drift-Alfven turbulence in the ionosphere is investigated. The self-consistent system of two model nonlinear equations, describing the dynamics of wave structures with characteristic scales till to the skin value, is obtained. Evolution equations for the shear flows and the magnetic field is obtained by means of the averaging of model equations for the fast-high-frequency and small-scale fluctuations. It is shown that the large-scale disturbances of plasma motion and magnetic field are spontaneously generated by small-scale drift-Alfven wave turbulence through the nonlinear action of the stresses of Reynolds and Maxwell. Positive feedback in the system is achieved via modulation of the skin size drift-Alfven waves by the large-scale zonal flow and/or by the excited large-scale magnetic field. As a result, the propagation of small-scale wave packets in the ionospheric medium is accompanied by low-frequency, long-wave disturbances generated by parametric instability. Two regimes of this instability, resonance kinetic and hydrodynamic ones, are studied. The increments of the corresponding instabilities are also found. The conditions for the instability development and possibility of the generation of large-scale structures are determined. The nonlinear increment of this interaction substantially depends on the wave vector of Alfven pumping and on the characteristic scale of the generated zonal structures. This means that the instability pumps the energy of primarily small-scale Alfven waves into that of the large-scale zonal structures which is typical for an inverse turbulent cascade. The increment of energy pumping into the large-scale region noticeably depends also on the width of the pumping wave spectrum and with an increase of the width of the initial wave spectrum the instability can be suppressed. It is assumed that the investigated mechanism can refer directly to the generation of mean flow in the atmosphere of the rotating planets and the magnetized plasma.     

Kink mode <Emphasis Type="Italic">m</Emphasis> = 1 in a thin plasma filament with discontinuous vertical magnetic field

In this paper, we study the conditions of realization and stability of kink modes with azimuthal wave numbers m = ±1 in a cylindrical plasma filament with a twisted magnetic field and a homogeneous current along its axis. We assume that there are vertical constant magnetic fields inside and outside of the filament; the filament is surrounded by current-free plasma; and outside of its boundary, the azimuthal magnetic field decreases inversely in proportion to the distance from the filament’s border. The dispersion equations for stable and unstable modes are obtained in the approximation of “thin” plasma filament. The analysis of the equations for the case of discontinuous vertical magnetic field at the filament’s boundary is provided. The conditions of propagation of the wave modes have been defined. We have obtained that the unstable modes with m = ±1 cannot be realized. The results of this work can be applied to the interpretation of the solar magnetic flux tubes’ behavior using measurements provided by the spacecrafts.     

Damping of Longitudinal Magneto–Acoustic Oscillations in Slowly Varying Coronal Plasma

We investigate the propagation of MHD waves in a magnetised plasma in a weakly stratified atmosphere, representative of hot coronal loops. In most earlier studies, a time-independent equilibrium was considered. Here we abandon this restriction and allow the equilibrium to develop as a function of time. In particular, the background plasma is assumed to be cooling due to thermal conduction. The cooling is assumed to occur on a time scale greater than the characteristic travel times of the perturbations. We investigate the influence of cooling of the background plasma on the properties of magneto–acoustic waves. The MHD equations are reduced to a 1D system modelling magneto–acoustic modes propagating along a dynamically cooling coronal loop. A time-dependent dispersion relation that describes the propagation of the magneto–acoustic waves is derived using the WKB theory. An analytic solution for the time-dependent amplitude of waves is obtained, and the method of characteristics is used to find an approximate analytical solution. Numerical calculations of the analytically derived solutions are obtained to give further insight into the behaviour of the MHD waves in a system with a variable, time-dependent background. The results show that there is a strong damping of MHD waves and the damping also appears to be independent of the position along the loop. Studies of MHD wave behaviour in a time-dependent backgrounds seem to be a fundamental and very important next step in the development of MHD wave theory that is applicable to a wide range of situations in solar physics.     

Reflection Properties of Gravito-MHD Waves in an Inhomogeneous Horizontal Magnetic Field

We derive the dispersion equation for gravito-magnetohydrodynamical (MHD) waves in an isothermal, gravitationally stratified plasma with a horizontal inhomogeneous magnetic field. Sound and Alfvén speeds are constant. Under these conditions, it is possible to derive analytically the equations for gravito-MHD waves. The high values of the viscous and magnetic Reynolds numbers in the solar atmosphere imply that the dissipative terms in the MHD equations are negligible, except in layers around the positions where the frequency of the MHD wave equals the local Alfvén or slow wave frequency. Outside these layers the MHD waves are accurately described by the equations of ideal MHD. We consider waves that propagate energy upward in the atmosphere. For the plane boundary, z=0, between two isothermal plasma regions with horizontal but different magnetic fields, we discuss the boundary conditions and derive the equations for the reflection and transmission coefficients. In the simpler case of a gravitationally stratified plasma without magnetic field, these coefficients describe the reflection and transmission properties of gravito-acoustic waves.     

Wave-trains in the solar wind

The equations of motion of all relevant parameters of Alfvén waves propagating from the sun outwardly into the expanding interplanetary medium are discussed for the case of a quiet, ideal, isotropic, one-fluid solar wind plasma. It is found that the frequency of the wave reamains constant, while the wave vector and the amplitudes depend, in general, on the evolution of the background medium and on the angle between the wave vector and the interplanetary magnetic field. This latter dependence cancels approximately for the evolution of the amplitudes in the case of a pure, overall spiral magnetic field. It is shown that in this case the results of earlier discussions can be derived by less decisive restrictions.     

Stellar wind models with Alfvén waves

It is known that stellar winds from late type stars are of mixed thermal and magnetic origin. The stellar wind model presented in this work uses the hydrodynamic equations of mass and momentum conservation and closes the system of equations with a detailed energy equation. Both momentum and energy equations have terms due to the effects of Alfvén waves. A smooth transition between the two regimes for Alfvén wave propagation, the undamped and the damped modes, is achieved by considering the geometrical mean of both wave amplitudes. It will be shown that the initial push on the plasma is provided by the mechanical heating input, and that further out the Alfvén waves take over energetically.     

Field-aligned beams and reconnection in the jovian magnetotail

The release of plasma in the jovian magnetotail is observed in the form of plasmoids, travelling compression regions, field-aligned particle beams and flux-rope like events. We demonstrate that electrons propagate along the magnetic field lines in the plasma sheet boundary layer (PSBL), while close to the current sheet center the electron distribution is isotropic. The evidences of the counterstreaming electron beams in the PSBLs are also presented. Most of the field-aligned energetic ion beams are associated with the field-aligned electron beams and about half of them have the bipolar fluctuation of the meridional magnetic field component. Moreover they often show a normal velocity dispersion for the different species which fits well in the scenario of particle propagation from a single source. All features above are observed during jovian reconfiguration events which are typically bonded with plasma flow reversals. From all these characteristics, which are based on energetic particle and magnetic field measurements, we believe that the reconfiguration processes in the jovian magnetotail are associated with reconnection.     

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.     

射电喷流中相对论电子束激发的不稳定性

本文作者用相对论电子束在等离子体中运动时的色散关系讨论了纵向传播的波模的稳定性，发现静电Ｌａｎｇｍｕｉｒ波和Ａｌｆｖｅｎ波是不稳定的，并计算了其增长率，而高频电磁模和硝声模是稳定的。相对论电子束激发的Ｌａｎｇｍｕｉｒ波和Ａｌｆｖｅｎ波的不稳定性可用于解释射电喷流中相间的热斑、粒子再加速、辐射机制以及能量传输问题。     

Viscous damping of surface magnetohydrodynamic waves on magnetic interface in cold plasmas

Surface magnetohydrodynamic wave propagation on a magnetic interface in a cold plasma is studied. The anisotropic ion viscosity is taken into account. Only long waves damping weakly in a wave period are considered. The dispersion equation is obtained. This equation is shown always to have exactly one root if there is no viscosity. The dependences of phase velocity, penetration depth and damping decrement of waves on the parameters of undisturbed plasma and wave propagation direction are investigated. The resulting application for describing of surface wave damping in the solar corona is discussed.     

A formulation of non-ideal localized (or ballooning) modes in the solar corona

The stability equations for localized (or ballooning) modes in the solar atmosphere are formulated. Dissipation due to viscosity, resistivity, and thermal conduction are included using the general forms due to Braginskii (1965). In addition, the effect of gravity, plasma radiation, and coronal heating are included. The resulting equations are one-dimensional and only involve derivatives along the equilibrium magnetic field. Thus, the stabilising influence of photospheric line-tying, which is normally neglected in most numerical simulations, can be studied in a simple manner. Two applications to sound wave propagation and thermal instabilities in a low-beta plasma are considered with a view to determining realistic coronal boundary conditions that model the lower, denser levels of the solar atmosphere in a simple manner.Research Assistant of the Belgian National Fund for Scientific Research.     

Alfvén-magnetosonic waves interaction in the solar corona

The nonlinear propagation of the Alfvén and magnetosonic waves in the solar corona is investigated in terms of model equations. Due to viscous effects taken into account the propagation of the fast wave itself is governed by Burgers type equations possessing both expansion and compression shock solutions. Numerical simulations show that both parallely and perpendicularly propagating fast waves can steepen into shocks if their amplitudes are in excess of some sizeable fraction of the Alfvén velocity. However, if the magnetic field changes linearly in the perpendicular direction, then formation of perpendicular shocks can be hindered. The Alfvén waves exhibit a tendency to drive both the slow and fast magnetosonic waves whose propagation is described by linearized Boussinesq type equations with ponderomotive terms due to the Alfvén wave. The limits of the slow and fast waves are investigated.