A self-consistent model of the magnetosphere with centrifugal wind,I

Under the purely centrifugal approximation (gravity and pressure force are neglected), stellar magnetospheres are classified into three main types of different physical properties in the two-dimensional parameter space. They are characterized essentially by the strength of the magnetic field and the plasma density, at the base of the magnetosphere. Among the three types, the type II magnetosphere has moderate surface densities for a given field strength, and is expected to possess a centrifugal wind blowing across the magnetic field lines without affecting them appreciably. Such a situation may be realized through a modification of the electric field from that under the ideal-MHD condition, owing to the inertia of a plasma. In order to illustrate this mechanism, the type II magnetosphere is taken up for a numerical simulation. The effect of artificial viscosity is avoided by integrating the characteristic equations for both components of the plasma, instead of solving the fluid equations directly. Our model reproduces a disk-like outflow of the centrifugal wind across the magnetic field lines which are closed through the equatorial plane.     

Ballooning modes in the inner magnetosphere of the Earth

In this paper the low-frequency ideal MHD (magnetohydrodynamical) perturbations in the inner magnetosphere of the Earth are studied. The set of partial differential equations obtained from the MHD equations in the ballooning approximation and the dipole model of the geomagnetic field is used for this purpose. These equations describe both small-scale and large-scale perturbations in the magnetospheric plasmas. In the “cold” plasma approximation the obtained equations describe poloidal and toroidal standing Alfvén modes. The account of plasma pressure leads to the appearance of an additional type of oscillations—the slow magnetosonic modes. The stability of the magnetospheric plasma with respect to the ballooning perturbations was analyzed. We describe the ballooning perturbations taking into account a coupling between the poloidal Alfvén modes and the slow magnetosonic modes.     

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.     

Fluid description of a collisionless plasma and electric current systems in cosmic plasmas

The large-scale structure of a collisonless, two-component plasma with a typical Larmor radius of ions ? and scale-lengthL is discussed using Maxwell transport equations. Special attention is paid to the situations in which the usual one-fluid model of plasma based on the expansion of the transport equations in the powers of the ratio ?/L is not a satisfactory approximation. The one-fluid model fails if the magnetic-field-aligned component of the mass velocity or the magnetic-field-aligned component of the typical random velocity of particles is much larger than the other components of the mass and random velocities. The model also fails if the component of the typical random velocity of particles, which is perpendicular to the field lines, substantially exceeds the mass velocity of particles across the field lines. A quasi-static plasma is discussed as an example of plasmas on which the expansion in the powers of ?/L is not applicable. The relation between the electric current flowing in a quasi-static plasma (or in a hot plasma streaming along the field lines) and the topology of the magnetic lines of force is analysed. There are two distinguishable currents of different origin in such a plasma. Magnetic field generated by the currents acquires a geometry in which one current flows in the surfaces perpendicular to the binormals to the field lines while the other current flows along the binormals.     

Gravitational stability of finitely conducting two-component plasma through porous medium

The gravitational stability of magnetized self-gravitating two-component plasma of finite conductivity flowing through porous medium is studied. Effect of magnetic field, porosity, viscosity, finite conductivity, and neutral gas friction is considered on the stability of the system. Dispersion relations are derived from linearized equations using normal mode analysis. Longitudinal and transverse wave propagations are discussed. On the basis of Hurwitz criterion, the stability of the system is discussed. It is found that Jeans's criterion determines the stability of the system. Jeans's expression depends on the sonic speeds in both the components. For transverse wave propagation in perfectly conducting plasma. Jeans's expression is modified due to magnetic field and porosity but in case of finitely conducting plasma the Jeans's expression remains unaltered. Collisional frequency, viscosity, permeability of the porous medium have damping effect.     

The Hall effect as the producer of current sheets in astrophysical plasmas

Our solution of the MHD equations with the Hall effect shows that this effect can produce thin current sheets in stellar atmospheres at heights where the plasma is tenuous and the Hall effect can profoundly influence the magnetic field variations. The current in the sheets is directed oppositely to the local plasma density gradient. In partiuclar, such a phenomenon is possible on the Sun near the base of the corona.     

X射线脉冲星周期的变化与吸积盘边界的K-H不稳定性

本文在中子星磁层与吸积盘之间引入了一个速度、密度、压强和磁场都连续变化的有限厚度的剪切层,以代替Anzer理论中的切向间断面,用磁流体力学方法讨论了中子星磁层与吸积盘交界处等离子体可压缩情况下平面波扰动的K-H不稳定性。结果表明,K-H不稳定性依然存在,径向波矢扰动成为不稳定的主要模式。文中特别讨论了剪切层厚度取值对中子星自转的影响,表明适当调节剪切层厚度就可解释X射线脉冲星周期的变化。将此模型应用到脉冲X射线源Her X-1上,得到较好的结果。     

The effect of non-uniform magnetic field on the slow mode oscillations

In this paper, the slow MHD mode oscillations of the coronal plasma are studied. The aim is to identify the effect of structuring (such as magnetic field, temperature, density, and pressure) on the frequencies of oscillations. We modelled the coronal medium as a low-β plasma with longitudinally density and pressure stratifications and a weakly inhomogeneous magnetic field varied slowly with height and radial directions. The linearized ideal MHD equations reduced to a single Klein–Gordon differential equation for square of oscillatory frequencies. The eigenfunctions and analytical dispersion relations are derived. The dispersion relations were solved numerically. In the case of uniform magnetic field, the previous studies verified. Our numerical results show that, the frequencies and their ratios are very sensitive functions of pressure scale height, and slightly varying functions of inhomogeneity parameter of magnetic field. By changing the magnetic field strength between the apex and footpoints of the loop about 50%, the frequencies ratio are changed about 5%. We concluded that, the pressure scale height and temperature gradient are first order effects and inhomogeneity of magnetic field is a second order effect on the slow mode oscillations.     

Magnetic field aligned modeling for the upper F region and for the plasmasphere

Existing empirical models, e.g., the IRI and the PRIME model, have shortcomings for the upper-most F region and usually have no realistic formulation for the plasmasphere. These shortcomings can be overcome by replacing purely height oriented modeling by magnetic field aligned approaches.A magnetic field approximation is presented which uses dipole field lines with apexes above the dip equator. Modeling along these field lines can be based on diffusive equilibrium. For a single ion plasma (e.g., an H+ plasma) the integrations which are necessary to model along the field lines in a realistic way can be carried out by means of series expansions. For a multiple ion plasma and in case of arbitrary dependence of electron and ion temperatures on the coordinates one has to apply numerical integration.The principles of joining a field aligned model to a height oriented one are discussed including a method to cross the dip equator in a consistent way.A practical example is presented with a plasmasphere model added to the global model NeUoG which was developed at the University of Graz. The future development aims at replacing all of the topside F region of the model by a magnetic field aligned approach.     

Maximum mass of magnetic white dwarfs

We revisit the problem of the maximum masses of magnetized white dwarfs(WDs).The impact of a strong magnetic field on the structure equations is addressed.The pressures become anisotropic due to the presence of the magnetic field and split into parallel and perpendicular components.We first construct stable solutions of the Tolman-Oppenheimer-Volkoff equations for parallel pressures and find that physical solutions vanish for the perpendicular pressure when B(?) 10~(13) G.This fact establishes an upper bound for a magnetic field and the stability of the configurations in the(quasi) spherical approximation.Our findings also indicate that it is not possible to obtain stable magnetized WDs with super-Chandrasekhar masses because the values of the magnetic field needed for them are higher than this bound.To proceed into the anisotropic regime,we can apply results for structure equations appropriate for a cylindrical metric with anisotropic pressures that were derived in our previous work.From the solutions of the structure equations in cylindrical symmetry we have confirmed the same bound for B ~ 10~(13) G,since beyond this value no physical solutions are possible.Our tentative conclusion is that massive WDs with masses well beyond the Chandrasekhar limit do not constitute stable solutions and should not exist.     

The effect of magnetic shear on the MHD stability of a prominence model

The Hood-Anzer prominence model (Hood and Anzer, 1990) is modified to include magnetic shear. The stability properties of the model are then assessed to see if significant magnetic shear can stabilize ideal MHD disturbances. It is shown that a strong shear gradient in the magnetic field near the base of the prominence provides a stabilizing effect and realistic prominence heights are indeed possible.     

How To Use Magnetic Field Information For Coronal Loop Identification

The structure of the solar corona is dominated by the magnetic field because the magnetic pressure is about four orders of magnitude higher than the plasma pressure. Due to the high conductivity the emitting coronal plasma (visible, e.g., in SOHO/EIT) outlines the magnetic field lines. The gradient of the emitting plasma structures is significantly lower parallel to the magnetic field lines than in the perpendicular direction. Consequently information regarding the coronal magnetic field can be used for the interpretation of coronal plasma structures. We extrapolate the coronal magnetic field from photospheric magnetic field measurements into the corona. The extrapolation method depends on assumptions regarding coronal currents, e.g., potential fields (current-free) or force-free fields (current parallel to magnetic field). As a next step we project the reconstructed 3D magnetic field lines on an EIT-image and compare with the emitting plasma structures. Coronal loops are identified as closed magnetic field lines with a high emissivity in EIT and a small gradient of the emissivity along the magnetic field.     

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.     

Thermosolutal instability of a partially-ionized plasma

The thermosolutal instability of a partially-ionized plasma in the presence of a horizontal magnetic field is considered to include the frictional effect of collisions of ionized with neutrals. The sufficient conditions for non-existence of overstability are derived. The solute gradient and magnetic field introduce oscillatory modes in thermosolutal convection which were non-existent in their absence. The magnetic field and stable solute gradient are found to have stabilizing effects whereas collisional effect of ionized with neutrals is found to have destabilizing effect on thermosolutal instability of a partially ionized plasma.     

Modelling the magnetic field and differential rotation effects for the vicinity of the base of convective zone in the Sun

In this work, some numerical solutions of magnetohydrodynamics equations are investigated in the presence of differential rotation with the use of previously developed algorithm. This algorithm includes the thin shell approximation and a special separation of variables which were used to obtain the radial and latitudinal variations of physical parameters in spherical coordinates. The magnetic field profile is chosen to produce comparable magnetic fluxes found in previous works. The sphericity and density shape parameters relevant to model is determined by using two different known differential rotation profiles. It is found that the shape of variations in physical parameters is strongly dependent to magnetic field profile and there is a considerable change in density with respect to reference model. It is as well shown that the spherical symmetric distributions of physical parameters are broken for the region of study.     

Plasma and Magnetic Field Inside Magnetic Clouds: a Global Study

Data observed during spacecraft encounters with magnetic clouds have been extensively analyzed in the literature. Moreover, several models have been proposed for the magnetic topology of these events, and fitted to the observations. Although these interplanetary events present well-defined plasma features, none of those models have included a simultaneous analysis of magnetic field and plasma data. Using as a starting point a non-force-free model that we have developed previously, we present a global study of MCs that include both the magnetic field topology and the plasma pressure. In this paper we obtain the governing equations for both magnitudes inside a MC. The expressions deduced are fitted simultaneously to the measurements of plasma pressure and magnetic field vector. We perform an analysis of magnetic field and plasma WIND observations within several MCs from 1995 to 1998. The analysis is confined to four of these events that have high-quality data. Only in one fitting procedure we obtain the orientation of the magnetic cloud relative to the ecliptic plane and the current density of the plasma inside the cloud. We find that the equations proposed reproduce the experimental data quite well.     

On the formation of coronal cavities

We present a theoretical study of the formation of a coronal cavity and its relation to a quiescent prominence. We argue that the formation of a coronal cavity is initiated by the condensation of plasma which is trapped by the coronal magnetic field in a closed streamer and which then flows down to the chromosphere along the field lines due to lack of stable magnetic support against gravity. The existence of a coronal cavity depends on the coronal magnetic field strength; with low strength, the plasma density is not high enough for condensation to occur. Furthermore, we suggest that prominence and cavity material is supplied from the chromospheric level. Whether a coronal cavity and a prominence coexist depends on the magnetic field configuration; a prominence requires stable magnetic support.We initiate the study by considering the stability of condensation modes of a plasma in the coronal streamer model obtained by Steinolfson et al. (1982) using a 2-D, time dependent, ideal MHD computer simulation; they calculated the dynamic interaction between outward flowing solar wind plasma and a global coronal magnetic field. In the final steady state, they found a density enhancement in the closed field region with the enhancement increasing with increasing strength of the magnetic field. Our stability calculation shows that if the density enhancement is higher than a critical value, the plasma is unstable to condensation modes. We describe how, depending on the magnetic field configuration, the condensation may produce a coronal cavity and/or initiate the formation of a prominence.NRC Research Associate.     

Turbulent spectrum of Alfvén waves excited by a kinetic instability for explaining the modulations with multi-timescales in solar flares

A low-frequency wave is treated as a local oscillation to modulate the guiding center of electrons beam, which is considered as free energy to excite Alfvén waves by a kinetic plasma instability under low-frequency approximation. The nonlinearity of the model is shown by a critical value of the amplitude of the low-frequency wave, and Alfvén waves are growing in a broad turbulent spectrum with fractional harmonics, which strongly depend on the criterion. The instability is limited in the direction nearly perpendicular to the ambient magnetic field. The growth rates are very sensitive to the beam speed that perpendicular to the magnetic field, the propagational angle, and the magnetic field strength, but not sensitive to the beam speed parallel to the magnetic field. This model is used to explain the modulations with multiple timescales in the flare light curves at radio, hard X-ray and H-alpha bands.     

Natural MHD oscillations of a neutron star

Natural, low-frequency, hydromagnetic oscillations of an isolated, nonrotating neutron star, which are localized in the peripheral crust, the structure of which is determined by the electron-nuclear plasma (the Ae phase), are studied. The plasma medium of the outer crust is treated as a homogeneous, infinitely conducting, incompressible continuum, the motions of which are determined by the equations of magnetohydrodynamics. In the approximation of a constant magnetic field inside the crust (the magnetic field outside the star is assumed to have a dipole structure), the spectrum of normal poloidal and toroidal hydromagnetic oscillations, due to presumed residual fluctuations of flow and their associated fluctuations in magnetic field strength, is calculated. Numerical estimates given for the periods of MHD oscillations fall in the range of periods of radio pulsar emission, indicating a close connection between the residual hydromagnetic oscillations and the electromagnetic activity of neutron stars. Translated from Astrofizika, Vol. 40, No. 1, pp. 77–86, January–March, 1997.