Electromagnetic radiation from line sources interacting with a moving uniaxial dielectric or plasma half-space

The problem of electromagnetic radiation from electric and magnetic line sources interacting with a moving uniaxially anisotropic dielectric or plasma half-space is treated. The anisotropy of the plasma is due to an infinitely strong magnetizing field impressedparallel to the motion of plasma. The line source is oriented normal to the direction of medium motion. TheE and theH modes are excited independently in the medium by the magnetic and the electric line sources, respectively. Invoking the saddle-point method of integration, the far-zone radiation field and the radiation pattern are obtained for both line sources. It is found that the radiation from an electric line source is not affected by the anisotropy of the moving medium and that a magnetic line source invacuum has finite components of radiation in directions which are parallel and antiparallel to the direction of motion, for the case of a uniaxial plasma in contrast to the results for a uniaxial dielectric. Numerical results for the far-zone radiation pattern, referring to a magnetic line source, are presented for several values of parameters characterizing the non-dimensional velocity, the anisotropy of the medium, the electron-plasma density and the location of the line source.     

Magnetic field strength estimation in synchrotron radiation sources

In this paper a method of estimating the magnetic field strength,B, in a homogeneous microwave burst source with simplified expressions for the synchrotron radiation is presented. An approximate formula of the magnetic field is obtained using the method. Once the magnetic field is estimated the total number of energetic electrons along the line of sightN L can be estimated also. The errors ofB andN L have been given. It is found that this method is useful for semiquantitative investigations of models of radio burst sources.     

On the existence of the continuous spectrum of ideal MHD in a 2D magnetostatic equilibrium

The continuous spectrum of a 2D magnetostatic equilibrium with y-invariance is derived. It is shown that the continuous spectrum is given by an eigenvalue problem on each magnetic surface and is related to the different behaviour of the equilibrium quantities in different magnetic surfaces. The special case of a uniform poloidal magnetic field in a 1D equilibrium that is stratified with height, has been considered in detail and it is found that there is no continuous spectrum. It is shown that this result relies completely on the artificial property that the behaviour of the equilibrium quantities along a magnetic field line is independent of the field line considered. As a consequence the non-existence of a continuous spectrum in a 1D equilibrium with a uniform magnetic field cannot be used to argue that the continuous spectrum has no physical relevance.Research Assistant of the Belgian National Fund for Scientific Research.     

Spatial dispersion of Faraday rotation and its connexion with mode coupling

It is shown that the lack of linear polarization in the microwave radiation of solar bursts (reported in a earlier paper) may be explained by spatial dispersion of Faraday rotation. The maximum source diameter s without noticeable destruction of linear polarization is determined by the electron density and the magnetic field strength in the volume, where the linear polarization is generated. In the case where linear polarization is produced by the radiation source, s is smaller than only 20 km. In the other case where linear polarization is produced by mode coupling in a quasi-transverse magnetic field in the corona, the s-values are found to range from 10 to 6000 km, which is still much smaller than the generally adopted sizes of microwave burst sources. The second case has been investigated for several models of magnetic fields.     

Relativistic dispersion effects on SS433 jets

We here investigate the dispersion properties of radiation in the SS433 relativistic jets. We assume that the jet is composed of cold electron-proton plasma immersed in a predominantly parallel magnetic field to the jet axis. We find that for the mildly relativistic source SS433 (for which 〈ψ〉≃79°), the bulk velocity is too small (v≃0.26c) to produce significant changes in the dispersion properties of the medium. Nonetheless, in the rarefied outer regions of the jets, where radio emission dominates, even a weak magnetic field has some influence on the dispersion properties and there appear two different electromagnetic branches that are slightly sensitive to the bulk relativistic motion. In the inner, X-ray region, the magnetic field is much stronger, but in this region the high electron density preserves the isotropic character of the local plasma and no branch separation occurs. In the region of the jet where the IR and optical emission dominates, the cold plasma may be also considered isotropic, i.e., neither the magnetic field nor the bulk velocity is able to affect the propagation of the radiation. Finally, we find that the Doppler line displacement in SS433 is affected by plasma dispersion only in a narrow frequency range in the far IR. As a consequence, although the shift (z) modulation due to precession of the SS433 jets is well described by previous work, it has to be corrected by plasma dispersion effects in the far-IR range.     

Padé approximant calculations for the number of scattering during particle diffusion

The mean number of particle scattering in a semi-infinite and finite slab for arbitrary energy sources are calculated by Padé approximants. Uniform source distribution is considered for the finite slab. For the semi-infinite medium we calculatethe number of particles due external radiation and at a particular point in the medium. Numerical calculations and comparisons were performed.     

CME's,filament eruptions,and sheared low-lying magnetic loops in multipolar magnetic configuration

The finite element method was used to solve a partial differential equation (magnetostatic equation) for multipolar magnetic regions. It is found that the height of magnetic field lines above the magnetic neutral line of a central strong bipolar magnetic field decreases as the field lines' footpoints approach the neutral line and also with increased magnetic shear. Both the electric current density and plasma pressure in the sheared low-lying loops are high. We suggest that the sheared low-lying loops may store the energies of large coronal mass ejections (CMEs) and filament eruptions. In addition, it is found that a lower pressure area exists above the low-lying loops and that it is similar in morphology to a coronal cavity. Above the lower pressure area there is a higher pressure area, which may be the source of CMEs. In this area magnetic shear leads to magnetic reconnection, which may be the cause of high coronal temperature.     

Application of the sine-Poisson equation in solar magnetostatics

Solutions of the sine-Poisson equation are used to construct a class of isothermal magnetostatic atmospheres, with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry. The distributed current in the model j is directed along the x-axis, where x is the horizontal ignorable coordinate. The current j varies as the sine of the magnetostatic potential and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. We investigate in detail solutions for the magnetostatic potential A corresponding to the one-soliton, two soliton, and breather solutions of the sine-Gordon equation. Depending on the values of the free parameters in the soliton solutions, horizontally, periodic magnetostatic structures are obtained possessing either (a) a single X-type neutral point, (b) multiple neutral X-points, or (c) solutions without X-points. The solution cases (b) and (c) contain two families of intersecting current sheets, in which the line of intersection forms flux concentration points (or singularities) for the magnetic field. The solutions illustrate the contribution of the anisotropic J × B force (B, magnetic field induction), the gravitational force, and the gas pressure gradient to the force balance.     

One more explanation of superluminal motion

The occurrence of superluminal motion in extragalactic radio sources is believed to be quite common. Among others, the geometrical scattering of radio radiation can also cause superluminal expansion and or motion and halo formation, In this paper, the effectiveness of the stimulated Raman scattering in producing these features is investigated. The scattering medium is a plasma whose position, density and temperature decide the rate and angle of scattering. When the radiation from a stationary and constant source gets scattered from a stationary plasma, a halo is formed around the source. However, the scattering of a rotating radiation beam does produce superluminal motion of the virtual source. It is found that the plasma should have the characteristics of the emission-line regions and the intercloud medium in order to Raman scatter the radiation. Since the scattering is polarization dependent, it is possible to estimate the rotation of the electric vector along the direction of the apparent motion of a radio source.     

Coherent Synchrotron Radiation of Gamma-Ray Bursts

By now there is no doubt that the gamma-ray bursts (GRB) have a cosmological origin. This allows to regard GRB as the most powerful known energy sources, ε∼ 10⁵⁴ erg (with a total number of gamma quanta N_γ∼ 10⁶⁰). A plausible mechanism of coherent synchrotron radiation (CSR) of relativistic electrons driven by a local magnetic field is studied in this paper. We consider relativistic electrons arising in the Compton scattering of a GRB in directions close to that of the ray from the source to a ground-based observer. The synchrotron pulses from Compton electrons located at different points on the line between the GRB source and the observer arrive at the observation point simultaneously. This simultaneity ensures the coherence of the detected radiation. Both molecular clouds in the host galaxy of the GRB and our own Galaxy, as well as the Earth atmosphere are assumed to be scatterers of the GRB radiation. Signals of each scatterer reach the Earth surface, and can be detected at radio wavelengths. We estimate the characteristics of this radiation. The comparison of GRB data with the corresponding information on CSR pulses offers a way to determine some global characteristics of the medium between the Earth and the GRB source.     

Observations of magnetic fields in the Milky Way and in nearby galaxies with a Square Kilometre Array

The role of magnetic fields in the dynamical evolution of galaxies and of the interstellar medium (ISM) is not well understood, mainly because such fields are difficult to directly observe. Radio astronomy provides the best tools to measure magnetic fields: synchrotron radiation traces fields illuminated by cosmic-ray electrons, while Faraday rotation and Zeeman splitting allow us to detect fields in all kinds of astronomical plasmas, from lowest to highest densities. Here, we describe how fundamental new advances in studying magnetic fields, both in our own Milky Way and in other nearby galaxies, can be made through observations with the proposed Square Kilometre Array. Underpinning much of what we propose is an all-sky survey of Faraday rotation, in which we will accumulate tens of millions of rotation measure measurements toward background radio sources. This will provide a unique database for studying magnetic fields in individual Galactic supernova remnants and Hii regions, for characterizing the overall magnetic geometry of our Galaxy’s disk and halo, and for understanding the structure and evolution of magnetic fields in galaxies. Also of considerable interest will be the mapping of diffuse polarized emission from the Milky Way in many narrow bands over a wide frequency range. This will allow us to carry out Faraday tomography of the Galaxy, yielding a high-resolution three-dimensional picture of the magnetic field within a few kpc of the Sun, and allowing us to understand its coupling to the other components of the ISM. Finally, direct synchrotron imaging of a large number of nearby galaxies, combined with Faraday rotation data, will allow us to determine the magnetic field structure in these sources, and to test both the dynamo and primordial field theories for field origin and amplification.     

A self-consistent model of a thermally balanced quiescent prominence in magnetostatic equilibrium in a uniform gravitational field

We present a theoretical model of quiescent prominences in the form of an infinite vertical sheet. Self-consistent solutions are obtained by integrating simultaneously the set of nonlinear equations of magnetostatic equilibrium and thermal balance. The basic features of the models are: (1) The prominence matter is confined to a sheet and supported against gravity by a bowed magnetic field. (2) The thermal flux is channelled along magnetic field lines. (3) The thermal flux is everywhere balanced by Low's (1975b) hypothetical heat sink which is proportional to the local density. (4) A constant component of the magnetic field along the length of the prominence shields the cool plasma from the hot surrounding. We assume that the prominence plasma emits more radiation than it absorbs from the radiation fields of the photosphere, chromosphere and corona, and we interpret the above hypothetical heat sink to represent the amount of radiative loss that must be balanced by a nonradiative energy input. Using a central density and temperature of 10¹¹ particles cm^–3 and 5000 K respectively, a magnetic field strength between 2 to 10 gauss and a thermal conductivity that varies linearly with temperature, we discuss the physical properties implied by the model. The analytic treatment can also be carried out for a class of more complex thermal conductivities. These models provide a useful starting point for investigating the combined requirements of magnetostatic equilibrium and thermal balance in the quiescent prominence.     

Study of Ribbon Separation and Magnetic Reconnection Rates in a Two-Ribbon Flare

In this paper, we present a study of the correlation between the speed of flare ribbon separation and the magnetic flux density during the 10 April 2001 solar flare. The study includes the section of the neutral line containing the flare core and its peripheral area. This event shows clear two-ribbon structure and inhomogeneous magnetic fields along the ribbons, so the spatial correlation and distribution of the flare and magnetic parameters can be studied. A weak negative correlation is found between the ribbon separation speed (V _r) and the longitudinal magnetic flux density (B _z ). This correlation is the weakest around the peak of the flare. Spatially, the correlation is also weakest at the positions of the hard X-ray (HXR) sources. In addition, we estimate the magnetic reconnection rate (electric field strength in the reconnection region E _rec) by combining the speed of flare ribbons and the longitudinal magnetic flux density. During flare evolution, the time profiles of the magnetic reconnection rate are similar to that of the ribbon separation speed, and the speeds of ribbon separation are relatively slow in the strong magnetic fields (i.e., V _r is negatively correlated with B _z ). However, along the flare ribbons, E _rec fluctuates in a small range except near the HXR source. A localized enhancement of the reconnection rate corresponds to the position of the HXR source.     

Line formation in a magnetic field

The effect of noncoherent scattering is examined for an absorption line formed in a uniform magnetic field. It is shown that the Stokes parameters of the line radiation may be computed by using the line source function in the absence of a magnetic field as a first approximation for that in the presence of a magnetic field.     

Rotational circulation-preserving magnetogeostrophic flows

It has been shown that the only steady, inviscid, magnetogeostrophic rotational circulation-preverving motion whose magnetic field line pattern is that of the irrotational motion is a complex-lamellar motion whose magnetic field magnitude bears a constant value on a magnetic field line.     

Analytical Approach to Calculate Quasi-thermal Noise Spectrum in Irregular Plasma

Basic properties of quasi-thermal noise spectrum in irregular plasma have been investigated using an analytical point of view. A simple formula for the plasma frequency splitting effect has been obtained for ionospheric conditions. A passive electric antenna, immersed in a stable plasma, detects the fluctuations of the electric potential due to thermal motion of the ambient particles. Properties of this quasi-thermal noise spectrum in homogeneous plasma are relatively well known and are effectively used for diagnostics of space plasma (Aksenov et al., 1978; Trakhtengerts and Chugunov, 1978; Kellog, 1981; Meyer-Vernet and Perche, 1989). Especially, in the Earth's ionosphere or solar wind plasma, random irregularities of electron density are always present. These irregularities may substantially change properties of these media through electromagnetic radiation and may also modify quasi-thermal noise spectrum, which depends on the effective dielectric permittivity tensor. This tensor is defined as the dielectric permittivity tensor of some imaginary `effective' regular medium in which the field of point source is the same as the mean field in the medium with random irregularities (Ryzhov, Tamoikin and Tatarskii, 1965; Ryzhov 1968). Since the correlation function of electric field fluctuations in random medium may be expressed through the effective dielectric constant tensor (Ryzhov, 1968), it may be used for direct calculation of quasi-thermal noise spectrum. In Zabotin et al. (2000), the Born approximation was used to calculate numerically the effective dielectric permittivity tensor and the modified noise spectrum while we analytically estimate herein the modified noise spectrum. This revised version was published online in July 2006 with corrections to the Cover Date.     

Nonlinear Force-Free Reconstruction of the Global Solar Magnetic Field: Methodology

We present a novel numerical method that allows the calculation of nonlinear force-free magnetostatic solutions above a boundary surface on which only the distribution of the normal magnetic field component is given. The method relies on the theory of force-free electrodynamics and applies directly to the reconstruction of the solar coronal magnetic field for a given distribution of the photospheric radial field component. The method works as follows: we start with any initial magnetostatic global field configuration (e.g. zero, dipole), and along the boundary surface we create an evolving distribution of tangential (horizontal) electric fields that, via Faraday’s equation, give rise to a respective normal-field distribution approaching asymptotically the target distribution. At the same time, these electric fields are used as boundary condition to numerically evolve the resulting electromagnetic field above the boundary surface, modeled as a thin ideal plasma with non-reflecting, perfectly absorbing outer boundaries. The simulation relaxes to a nonlinear force-free configuration that satisfies the given normal-field distribution on the boundary. This is different from existing methods relying on a fixed boundary condition – the boundary evolves toward the a priori given one, at the same time evolving the three-dimensional field solution above it. Moreover, this is the first time that a nonlinear force-free solution is reached by using only the normal field component on the boundary. This solution is not unique, but it depends on the initial magnetic field configuration and on the evolutionary course along the boundary surface. To our knowledge, this is the first time that the formalism of force-free electrodynamics, used very successfully in other astrophysical contexts, is applied to the global solar magnetic field.     

Steady magnetic reconnection in three dimensions

The concepts of magnetic reconnection that have been developed in two dimensions need to be generalised to three-dimensional configurations. Reconnection may be defined to occur when there is an electric field (E) parallel to field lines (known as potential singular lines) which are potential reconnection locations and near which the field has an X-type topology in a plane normal to that field line. In general there is a continuum of neighbouring potential singular lines, and which one supports reconnection depends on the imposed flow or electric field. For steady reconnection the nearby flow and electric field are severely constrained in the ideal region by the condition that E = 0 there. Potential singular lines may occur in twisted prominence fields or in the complex magnetic configuration above sources of mixed polarity of an active region or a supergranulation cell. When reconnection occurs there is dynamic MHD behaviour with current concentration and strong plasma jetting along the singular line and the singular surfaces which map onto them.     

A numerical study of the pre-ejection, magnetically-sheared corona as a free boundary problem

A class of magnetostatic equilibria with axial symmetry outside a unit sphere in the presence of plasma pressure and an r ^–2 gravitational field is constructed. The structure contains a localized current-carrying region confined by a background bipolar potential field, and the shape of the region changes subject to the variation of the electric current. The continuity requirement for the magnetic field and plasma pressures at the outer boundary of the cavity defines a free boundary problem, which is solved numerically using a spectral boundary scheme. The model is then used to study the expansion of the current-carrying region, caused by the buildup of magnetic shear, against the background confining field. The magnetic shear in our model is induced by the loading of an azimuthal field, accompanied by a depletion of plasma density.We show that due to the additional effect of confinement by the dense surrounding plasma, the energy of the magnetic field can exceed the energy of its associated open field, presumably a necessary condition for the onset of coronal mass ejections. (However, the plasma beta of the confining fluid is higher than that in the outer boundary of a realistic helmet-streamer structure.) Furthermore, under the assumption that coronal mass ejections are driven by magnetic buoyancy, the result from our model study lends further support to the notion of a suspended magnetic flux rope in the low-density cavity of a helmet-streamer as a promising pre-ejection configuration.The National Center for Atmospheric Research is sponsored by the National Science Foundation.