Electromagnetic circularly-polarised modes in plasmas with electron-streaming along the applied magnetic field

The effect of the electron-streaming along the applied magnetic field on the electromagnetic circularly-polarised modes in a Vlasov plasma propagating along the applied magnetic field is studied. It is found that the growth or decay of the circularly-polarised modes is affected by the electron-streaming in the presence of the thermal effects, unlike the case with the thermal effects absent.     

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.     

Attenuation of small-amplitude oscillations in a prominence–corona model with a transverse magnetic field

Observations show that small-amplitude prominence oscillations are usually damped after a few periods. This phenomenon has been theoretically investigated in terms of non-ideal magnetoacoustic waves, non-adiabatic effects being the best candidates to explain the damping in the case of slow modes. We study the attenuation of non-adiabatic magnetoacoustic waves in a slab prominence embedded in the coronal medium. We assume an equilibrium configuration with a transverse magnetic field to the slab axis and investigate wave damping by thermal conduction and radiative losses. The magnetohydrodynamic equations are considered in their linearised form and terms representing thermal conduction, radiation and heating are included in the energy equation. The differential equations that govern linear slow and fast modes are numerically solved to obtain the complex oscillatory frequency and the corresponding eigenfunctions. We find that coronal thermal conduction and radiative losses from the prominence plasma reveal as the most relevant damping mechanisms. Both mechanisms govern together the attenuation of hybrid modes, whereas prominence radiation is responsible for the damping of internal modes and coronal conduction essentially dominates the attenuation of external modes. In addition, the energy transfer between the prominence and the corona caused by thermal conduction has a noticeable effect on the wave stability, radiative losses from the prominence plasma being of paramount importance for the thermal stability of fast modes. We conclude that slow modes are efficiently damped, with damping times compatible with observations. On the contrary, fast modes are less attenuated by non-adiabatic effects and their damping times are several orders of magnitude larger than those observed. The presence of the corona causes a decrease of the damping times with respect to those of an isolated prominence slab, but its effect is still insufficient to obtain damping times of the order of the period in the case of fast modes.     

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.     

Small-Amplitude Disturbances in a Radiating and ScatteringGrey MediumI. Solutions of Given Real Frequency ω

We reanalyze the propagation of one-dimensional small-amplitude disturbances of given real frequency ω in a radiating and scattering grey medium using the Eddington approximation, which has been studied previously by us (Kaneko et al., 1976). Numerical results reveals three frequency regimes to be distinguished, and two wave modes always appear in each frequency regime. The governing equations and analytic solutions are derived for all wave modes using Whitham's method modified into quadratic form and approximate methods based on radiation thermodynamics. In the high-frequency regime appear the radiation-wave and adiabatic sound modes, which are damped by opacity and radiative cooling, respectively. Wave patterns in the intermediate-frequency and low-frequency regimes depend critically on the importance of radiation, for which the criterion is given in terms of the ratio of total specific heats at constant pressure and constant volume. When the radition overwhelms the matter (radiation-dominated case), the radiative mode in the intermediate-frequency regime is the constant-volume diffusion mode. When the matter overwhelms the radiation (matter-dominated case), damped radiation-wave and damped radiation-diffusion modes newly appear between the radiation-wave and constant-volume diffusion modes. The acoustic mode in the intermediate-frequency regime is the isothermal sound mode,which is damped by radiative cooling at higher frequencies and by radiation-thermal drag force at lower frequencies. Two modes appearing in the low-frequency regime are the isentropic radiation-acoustic and constant-pressure diffusion modes. The absorption coefficient derived for the former is shown to be a radiation-thermodynamic extension of that of Landau and Lifshitz (1987). The transition frequencies between all adjacent two modes are also derived to discuss the implications of them. This revised version was published online in July 2006 with corrections to the Cover Date.     

The effect of a poloidal magnetic field on the linear and adiabatic oscillations of a polytropen=3

The frequencies of the linear and adiabatic oscillations of a gaseous polytrope with a poloidal magnetic field are determined with the aid of a perturbation method. The influence of the poloidal magnetic field on the different types of spheroidal oscillation modes is discussed. The poloidal magnetic field generally strengthens the stability of the oscillation modes and this effect is the largest in the case of the non-radialp-modes.     

The effect of the lower ionosphere on hydromagnetic modes in the plasmasphere

Dimensionless resonant frequencies of hydromagnetic modes have been calculated for a simple model plasmasphere including a lower ionosphere. Results for the Alfvén mode are broadly consistent with those obtained by Hughes and Southwood [1976]. It is further concluded that the lower ionosphere, despite its strong damping effect for part of the day, does not provide much dissipative coupling between adjacent magnetic field shells in the Alfvén mode. The fast mode is found to be only slightly damped for horizontal wavelengths of global extent.     

Models of magnetic field generation in partly stable planetary cores: Applications to Mercury and Saturn

A substantial part of Mercury's iron core may be stably stratified because the temperature gradient is subadiabatic. A dynamo would operate only in a deep sublayer. We show that such a situation arises for a wide range of values for the heat flow and the sulfur content in the core. In Saturn the upper part of the metallic hydrogen core could be stably stratified because of helium depletion. The magnetic field is unusually weak in the case of Mercury and unusually axisymmetric at Saturn. We study numerical dynamo models in rotating spherical shells with a stable outer region. The control parameters are chosen such that the magnetic Reynolds number is in the range of expected Mercury values. Because of its slow rotation, Mercury may be in a regime where the dipole contribution to the internal magnetic field is weak. Most of our models are in this regime, where the dynamo field consists mainly of rapidly varying higher multipole components. They can hardly pass the stable conducting layer because of the skin effect. The weak low-degree components vary more slowly and control the structure of the field outside the core, whose strength matches the observed field strength at Mercury. In some models the axial dipole dominates at the planet's surface and in others the axial quadrupole is dominant. Differential rotation in the stable layer, representing a thermal wind, is important for attenuating non-axisymmetric components in the exterior field. In some models that we relate to Saturn the axial dipole is intrinsically strong inside the dynamo. The surface field strength is much larger than in the other cases, but the stable layer eliminates non-axisymmetric modes. The Messenger and Bepi Colombo space missions can test our predictions that Mercury's field is large-scaled, fairly axisymmetric, and shows no secular variations on the decadal time scale.     

MAGNETO-ATMOSPHERIC OSCILLATIONS IN A MODEL UMBRA

The behaviour of magneto-acoustic-gravity oscillations in a model umbra is investigated by means of a normal mode analysis. The normal modes are evaluated for different types of boundary conditions holding at various levels in the model atmosphere and for a range of magnetic field strengths and horizontal wave numbers. For certain boundary conditions complex eigenfrequencies are present. For atmospheric cavities whose lower boundary is located at the bottom of the photosphere or in the upper convective region, the coupling between horizontal and vertical motions leads to spectra which are sensitive to the value of the horizontal wave number, k, and the strength of the vertical magnetic field, B0. For cavities located above the temperature minimum, the eigenfrequencies are independent of both k and B0, supporting the conclusions of ugda, Locns, and Staude (1987) that the motion is longitudinal along the magnetic field lines. The frequencies evaluated from the normal mode analysis correspond closely to the observed 2–3-minute band found in sunspot umbrae.     

Viscous Damping of Non-Adiabatic MHD Waves in an Unbounded Solar Coronal Plasma

The damping of MHD waves in solar coronal magnetic field is studied taking into account thermal conduction and compressive viscosity as dissipative mechanisms. We consider viscous homogeneous unbounded solar coronal plasma permeated by a uniform magnetic field. A general fifth-order dispersion relation for MHD waves has been derived and solved numerically for different solar coronal regimes. The dispersion relation results three wave modes: slow, fast, and thermal modes. Damping time and damping per periods for slow- and fast-mode waves determined from dispersion relation show that the slow-mode waves are heavily damped in comparison with fast-mode waves in prominences, prominence–corona transition regions (PCTR), and corona. In PCTRs and coronal active regions, wave instabilities appear for considered heating mechanisms. For same heating mechanisms in different prominences the behavior of damping time and damping per period changes significantly from small to large wavenumbers. In all PCTRs and corona, damping time always decreases linearly with increase in wavenumber indicate sharp damping of slow- and fast-mode waves.     

Dissipation of Standing Slow Magnetoacoustic Waves in Hot Coronal Loops

The damping of standing slow waves in hot (T>6 MK) coronal loops of semicircular shape is revisited in both the linear and nonlinear regimes. Dissipation by thermal conduction, compressive viscosity, radiative cooling, and heating are examined for nonstratified and stratified loops. We find that for typical conditions of hot SUMER loops, thermal conduction increases the period of damped oscillations over the sound-crossing time, whereas the decay times are mostly shaped by compressive viscosity. Damping from optically thin radiation is negligible. We also find that thermal conduction alone results in slower damping of the density and velocity waves compared to the observations. Only when compressive viscosity is added do these waves damp out at the same rate as the observed rapidly decaying modes of hot SUMER loop oscillations, in contrast to most current work, which has pointed to thermal conduction as the dominant mechanism. We compare the linear predictions with numerical hydrodynamic calculations. Under the effects of gravity, nonlinear viscous dissipation leads to a reduction of the decay time compared to the homogeneous case. In contrast, the linear results predict that the damping rates are barely affected by gravity.     

Magnetic and boundary effects on thermal instabilities in solar magnetic fields: Localized modes in a slab geometry

The coupling of thermal and ideal MHD effects in a sheared magnetic field is investigated. A slab geometry is considered so that the Alfvén mode can be decoupled from the system. With the total perturbed pressure approximately zero, the fast mode is eliminated and a system of linearized equations describing magnetic effects on the slow mode and thermal mode is derived. These modes evolve independently on individual fieldlines. One of the main features of this approach is that the influence of the dense photosphere can be included. A variety of different conditions that simulate the photospheric boundary are presented and the different results are discussed. A choice of field geometry and boundary conditions is made which removes mode rational surfaces so that there are no regions in which parallel thermal conduction can be neglected. This provides a stabilizing mechanism for the thermal mode. Growth rates are reduced by 30–40% and there is complete stabilization for sufficiently short fieldlines. The influence of dynamic and thermal boundary conditions on the formation of prominences is discussed.     

Analytical Estimation of the Scale of Earth-Like Planetary Magnetic Fields

In this paper we analytically estimate the magnetic field scale of planets with physical core conditions similar to that of Earth from a statistical physics point of view. We evaluate the magnetic field on the basis of the physical parameters of the center of the planet, such as density, temperature, and core size. We look at the contribution of the Seebeck effect on the magnetic field, showing that a thermally induced electrical current can exist in a rotating fluid sphere. We apply our calculations to Earth, where the currents would be driven by the temperature difference at the outer-inner core boundary, Jupiter and the Jupiter’s satellite Ganymede. In each case we show that the thermal generation of currents leads to a magnetic field scale comparable to the observed fields of the considered celestial bodies.     

中子星的热演化和磁衰减

本文研究了中子星的热演化、自转演化和磁场演化的相互影响．考虑了一个自洽模型：中子星因磁偶极辐射而自转减慢，在内部产生某些加热过程，中子星磁场通过壳层的欧姆耗散来衰减．结果表明，磁场衰减提高了加热过程的重要性；相反，加热效应减慢了磁衰减．因此可以得出，中子星的热、自转和磁场也许不是独立演化的．不仅如此，这些演化与初始条件有关，因此，人们也许可以从射电和Ｘ射线观测对脉冲星年龄、初始磁场和周期给出某些限制．     

Perturbative analysis of two-temperature radiative shocks with multiple cooling processes

The structure of the hot downstream region below a radiative accretion shock, such as that of an accreting compact object, may oscillate because of a global thermal instability. The oscillatory behaviour depends on the functional forms of the cooling processes, the energy exchanges of electrons and ions in the shock-heated matter, and the boundary conditions. We analyse the stability of a shock with unequal electron and ion temperatures, where the cooling consists of thermal bremsstrahlung radiation which promotes instability, plus a competing process which tends to stabilize the shock. The effect of transverse perturbations is considered also. As an illustration, we study the special case in which the stabilizing cooling process is of order 3/20 in density and 5/2 in temperature, which is an approximation for the effects of cyclotron cooling in magnetic cataclysmic variables. We vary the efficiency of the second cooling process, the strength of the electron–ion exchange and the ratio of electron and ion pressures at the shock, to examine particular effects on the stability properties and frequencies of oscillation modes.     

The effect of finite electrical conductivity on compressible magnetoconvection

The stability of a polytropic fluid layer in the presence of a uniform vertical magnetic field is studied under the combined influence of thermal and magnetic diffusion. The main objective of the present investigation is to examine the effect of finite electrical conductivity of the medium on the stability of hydromagnetic modes which are believed to be important in the sunspot phenomena. It is shown that the inclusion of finite electrical conductivity has destabilizing effect on convective modes and small-scale convection can occur in the presence of strong magnetic field, provided the magnetic diffusivity is larger than the thermal diffusivity. The magnetic diffusivity, however, has a tendency to stabilize the fast, slow, and Alfvén-modes.     

Non-Axisymmetric Oscillations of Thin Prominence Fibrils

We study non-axisymmetric oscillations of thin prominence fibrils. A fibril is modeled by a straight thin magnetic tube with the ends frozen in dense plasmas. The density inside and outside the tube varies only along the tube and it is discontinuous at the tube boundary. Making a viable assumption that the tube radius is much smaller than its length, we show that the squares of the frequencies of non-axisymmetric tube oscillations are given by the eigenvalues of the Sturm–Liouville problem for a second-order ordinary differential equation on a finite interval with the zero boundary conditions. For an equilibrium density that is constant outside the tube and piecewise constant inside we derived a simple dispersion equation determining the frequencies of non-axisymmetric oscillations. We carry out a parametric study of this equation both analytically and numerically, restricting our analysis to the first even mode and the first odd mode. In particular, we obtained a criterion that allows to find out if each of these modes is a normal or leaky mode.     

Sausage MHD Waves in Incompressible Flux Tubes with Twisted Magnetic Fields

Twisted magnetic flux tubes are of considerable interest because of their natural occurrence from the Sun’s interior, throughout the solar atmosphere and interplanetary space up to a wide range of applicabilities to astrophysical plasmas. The aim of the present work is to obtain analytically a dispersion equation of linear wave propagation in twisted incompressible cylindrical magnetic waveguides and find appropriate solutions for surface, body and pseudobody sausage modes (i.e. m = 0) of a twisted magnetic flux tube embedded in an incompressible but also magnetically twisted plasma. Asymptotic solutions are derived in long- and short-wavelength approximations. General solutions of the dispersion equation for intermediate wavelengths are obtained numerically. We found, that in case of a constant, but non-zero azimuthal component of the equilibrium magnetic field outside the flux tube the index ν of Bessel functions in the dispersion relation is not integer any more in general. This gives rise to a rich mode-structure of degenerated magneto-acoustic waves in solar flux tubes. In a particular case of a uniform magnetic twist the total pressure is found to be constant across the boundary of the flux tube. Finally, the effect of magnetic twist on oscillation periods is estimated under solar atmospheric conditions. It was found that a magnetic twist will increase, in general, the periods of waves approximately by a few percent when compared to their untwisted counterparts.     

On the quasi-periodic oscillations in magnetars

We study torsional Alfvén oscillations of magnetars, that is neutron stars with a strong magnetic field. We consider the poloidal and toroidal components of the magnetic field and a wide range of equilibrium stellar models. We use a new coordinate system  ( X , Y )  , where     and     and a ₁ is the radial component of the magnetic field. In this coordinate system, the one+two-dimensional evolution equation describing the quasi-periodic oscillations (QPOs), see Sotani et al., is reduced to a one+one-dimensional equation where the perturbations propagate only along the y -axis. We solve the one+one-dimensional equation for different boundary conditions and the open magnetic field lines, that is magnetic field lines that reach the surface and there match up with the exterior dipole magnetic field as well as closed magnetic lines, i.e. magnetic lines that never reach the stellar surface. For the open field lines, we find two families of QPO frequencies: a family of 'lower' QPO frequencies which is located near the x -axis and a family of 'upper' frequencies located near the y -axis. According to Levin, the fundamental frequencies of these two families can be interpreted as the turning point of the continuous spectrum. We find that the upper frequencies are multiples of the lower ones by a constant equalling  2 n + 1  . For the closed lines, the corresponding factor is   n + 1  . By using these relations, we can explain both the lower and the higher observed frequencies in SGR 1806−20 and SGR 1900+14.