Comment on ‘note on the stability of parallel magnetic fields’

It is shown that the conclusions arrived at regarding the instability of an incompressible fluid cylinder in the presence of the magnetic field and the streaming velocity in a recent communication easily follow from the study of propagation characteristics of Alfvén surface waves along cylindrical plasma columns made earlier.     

On the stability of twisted magnetic fields

The stability of helical magnetic fields is investigated when fluid motions are present along the lines of force. The general dispersion relation is obtained and some limiting cases are examined. It is established that the configuration can be unstable when the velocity field exceeds a certain critical value. This result is to be compared with the case when the helical fields confined by a rigid boundary are stable when the energy density in the velocity field is at least equal to that of the magnetic field.     

Note on the Helmholtz instability in stratified flows with magnetic fields

The nature of the neutral curves for the stability of a Helmholtz velocity profile in a stratified, Boussinesq fluid in the presence of a uniform magnetic field for the cases (1) an infinite fluid (2) a semi-infinite fluid with a rigid boundary is discussed.     

A note on the stability of helical velocity and magnetic fields

The stability of nonparallel helical velocity and magnetic fields in a plasma cylinder with free boundaries is examined. It is shown that, in case of weak helicity, the stability of the system remains unaffected.     

On the stability of helical velocity and magnetic fields

In this paper we study the stability of an infinitely conducting, incompressible, inviscid infinite cylinder with non-parallel helical velocity and magnetic field. It is shown that the system is stable if the energy in the -component of the velocity field is larger than that in the -component of the magnetic field.     

The structure and stability of coronal magnetic fields

Solar Physics - The high degree of symmetry often assumed in studies of the structure and stability of coronal magnetic field configurations is restrictive and can yield misleading results. We have...     

The structure and stability of coronal magnetic fields

The high degree of symmetry often assumed in studies of the structure and stability of coronal magnetic field configurations is restrictive and can yield misleading results. We have therefore developed fully three-dimensional numerical methods for constructing force-free equilibria and for examining their stability properties, which make no assumptions about symmetry. A test of the stability analysis has been performed by applying it to the Gold-Hoyle twisted flux tube, which is known to be kink-unstable if the helical field makes more than about one turn between the line-tying end-plates. Our preliminary result is that the critical number of turns is about 1.1, in good agreement with the previous best estimate. However, we find that the growth rate, which has not been discussed previously, is orders of magnitude smaller than expected, even when the flux tube is twisted far beyond the stability limit.     

Bounds on the ideal MHD stability of line-tied 2-D coronal magnetic fields

A tractable method for investigating the linear stability of line-tied 2-D coronal magnetic fields is introduced. It is based on the Bernstein et al. (1958) energy principle and can be applied to non-isothermal equilibria with gravity, having a translational invariance. The perturbed potential energy integral is manipulated to produce either necessary conditions for stability to localized modes or sufficient conditions for stability to global modes. Each condition only requires the solution of a set of ordinary differential equations, integrated along the magnetic field lines. The tests are employed to two different classes of equilibria. A linear force-free field is shown to be completely stable, regardless of the shear. The role of pressure gradients, footpoint displacements, line-tying and stratification on an isothermal magneto-hydrostatic equilibrium is assessed.     

The oscillations and the stability of rotating masses with magnetic fields

The existence of the point of bifurcation of rotating gaseous masses with toroidal magnetic fields is established from the first variations of the integral properties provided by the second-order virial relations. It is shown that the point of bifurcation, where the Jabcobi ellipsoids branch off from the Maclaurin spheroids, is unaffected by the presence of toroidal magnetic fields.     

The oscillations and the stability of rotating masses with magnetic fields

Using first variations of the integral properties of equilibrium second-order virial relations, the existence of the point of bifurcation of rotating gaseous masses with magnetic fields is substantiated. With the presence of a magnetic field component along the axis of rotation, it is shown that the point of bifurcation, where the Jacobi ellipsoids branch off from the Maclaurin spheroids, is altered, and in fact shifts to higher values of eccentricity compared to the one (namely,e=0.81267) obtained when there is no magnetic field.     

Photospheric line-tying conditions for the MHD stability of coronal magnetic fields

Using the localised, ballooning ordering, the effect of a density stratification on the ideal MHD stability of magnetic fields is investigated. It is found that, when the photospheric density is very much greater than the coronal value, the line tying conditons are best simulated by assuming that all coronal disturbances vanish at the photospheric boundary. This is commonly known as the rigid wall conditions.     

Simple tests for the ideal MHD stability of line-tied coronal magnetic fields

Methods for investigating the stability of line-tied, cylindrically-symmetric magnetic fields are presented. The energy method is used and the perturbed potential energy integral is manipulated to produce simple tests that predict either stability to general coronal disturbances or instability to localized modes, both satisfying photospheric line-tying. Using these tests the maximum amount of magnetic energy, that can be stored in the coronal magnetic field prior to an instability, can be estimated. The tests are applied to four different classes of equilibria and results are obtained for both arcade and loop geometries.     

The equilibrium and the stability of the Jeans spheroids with toroidal magnetic fields

We examine the effect of a toroidal magnetic field on the equilibrium and stability of homogeneous masses distorted by the tidal effects of a secondary (of massM at a distanceR). It is shown that if the toroidal magnetic field is assumed to be axisymmetric about the direction of the line joining the centres of mass of the primary and the secondary, then the equilibrium configuration is a prolate spheroid. Also determined are the characteristic frequencies of the various modes of oscillations belonging to the second harmonics. It is found that the magnetic field shifts these frequencies to higher values than the ones which prevail in the absence of a magnetic field.     

The effects of parallel and perpendicular viscosity on resistive ballooning modes in line-tied coronal magnetic fields

The study of resistive ballooning instabilities in line-tied coronal magnetic fields is extended by including viscosity in the stability analysis. The equations that govern the resistive ballooning instabilities are derived and the effects of parallel and perpendicular viscosity are included using Braginskii's stress tensor. Numerical solutions to these equations are obtained under the rigid wall boundary conditions for arcades with cylindrically-symmetric magnetic fields. It is found that viscosity has a stabilizing effect on the resistive ballooning instabilities with perpendicular viscosity being more important by far than parallel viscosity. The strong stabilizing effect of perpendicular viscosity can lead to complete stabilization for realistic values of the equilibrium quantities.Research Assistant at the Belgian Fund for Scientific Research.     

Force-free magnetic fields with singular current density surfaces and their stability

Starting from Bernstein's principle of magnetohydrodynamic energy, a general analysis is presented for the stability of a kind of 1-D force-free magnetic fields with singular current density surfaces and a single parameter in cylindrical coordinates. It is found that in the parameter space of this kind of force-free magnetic fields there simultaneously exist stable and unstable regions. Their stability is solely determined by the radial distribution of the magnetic pitch in the neighborhood of the cylinder axis, and is independent of the presence of singular current density surface at the boundary of the field.     

A note on the magnetic network of photospheric magnetic fields

It is suggested that the magnetic network in the unipolar region of the photosphere can be interpreted as the field of loop currents along the boundary of the supergranulation cells. The currents are generated by the dynamo process associated with the supergranulation.     

Imbalance of magnetic fields on the Sun

Differences of magnetic field flows of “+” and “?” polarities, i.e. the imbalance of magnetic fields for 26 years—from January 1, 1977, to September 30, 2003—are investigated,. The synoptic maps of the longitudinal vector of Sun’s magnetic field strength obtained at the Kitt Peak National Observatory (United States) and kindly given to us by Dr. J. Harvey have served as the initial material. The imbalance of magnetic fields’ cyclicity features and the deviations from the dipole structure of Sun’s magnetic field are determined. The contribution of latitude zones and fields of various strength into the general magnetic flux from the Sun is found. The latter characteristic was compared with the Sun’s mean magnetic field (MMF) obtained from the observations of the Sun as a star (Kotov et al., 2002; Kotov, 2008). The obtained results testify that the imbalance is one of physical characteristics of the Sun. The confirmations of this conclusion are the strict regularities of the Sun’s dipole structure changing; the complicated character of the imbalance cyclicity, i.e., the multiplicity of cycles; the solar nature of MMF changing; and the distinction between two classes of magnetic fields in the imbalance characteristics.     

The stability of force-free magnetic fields with cylindrical symmetry in the context of solar flares

The problem of the accumulation and storage of the energy released in solar flares is discussed; it is proposed that convective energy of the photosphere is transformed into magnetic energy of the chromosphere and corona. The consequences of a large ratio of magnetic pressure to gas pressure are investigated. In this case the field must be approximately force-free. The only suitable force-free fields which allow an analytical treatment are those of cylindrical symmetry. The stability of these fields is studied with the energy principle. It is shown that they are always unstable due to kink type instabilities. The shape of the unstable perturbations is described in detail and an upper limit for their amplitude is estimated. The consequences for the proposed mechanism of energy storage are briefly discussed.     

Structure of magnetic fields on the quiet sun

To obtain quantitative temporal and spatial information on the network magnetic fields, we applied auto- and cross-correlation techniques to the Big Bear videomagnetogram (VMG) data. The average size of the network magnetic elements derived from the auto-correlation curve is about 5700 km. The distance between the primary and secondary peak in the auto-correlation curve is about 17000 km, which is half of the size of the supergranule as determined from the velocity map. The correlation time is about 10 to 20 hours. The diffusion constant derived from the cross-correlation curve is 150 km² s^-1. We also found that in the quiet regions the total magnetic flux in a window 3 × 4 changes very little in nearly 10 hours. That means the emergence and the disappearance of magnetic flux are in balance. The cancelling features and the emergence of ephemeral regions are the major sources for the loss and replenishment of magnetic flux on the quiet Sun.