Toroidal Component Of Magnetic Field Research Articles

Magnetohydrodynamic equilibrium conditions for a plasma in the presence of a rapidly rotating magnetic field

The ideal magnetohydrodynamic equations are used to investigate the equilibrium configurations of a plasma when it is subjected to an external rotating magnetic field. It is shown that the rigid rotor model for the steady toroidal current is an exact solution of the equations provided that there are no oscillating secondary currents within the plasma and that there is no toroidal component of the steady magnetic field. Experimental observations of rotamak plasmas indicate that these conditions are often not satisfied. The rigid rotor model may therefore not be applicable to these plasmas. A perturbation method is used to generalise the theory to include the effects of small oscillating secondary currents and small toroidal magnetic fields.

On the decay of the toroidal component of a large-scale stellar magnetic field

On the decay of the toroidal component of a large-scale stellar magnetic field

The effect of a magnetic field on solar luminosity

A simple model of the sun in the presence of different interior magnetic field configurations (purely poloidal field, a general magnetic field having both poloidal and toroidal components, and a toroidal field) has been computed. The effects of these three types of magnetic field on the luminosity, radius, and effective temperature have been calculated. It is found that, although there is a change in luminosity of the configuration, the change in effective solar temperature depends mainly on the change in radius. Further, it is found that it is the toroidal magnetic field component that tends to reduce the effective temperature of the Sun. The possible effect of changes in the magnetic field profile during the period of presolar activity and postsolar activity is discussed.

The compact torus

The objective of the compact torus approach is to provide toroidal magnetic-field configurations that are based primarily on plasma currents and can be freed from closely surrounding mechanical structures. Some familiar examples are the current-carrying plasma rings of reversed-field theta pinches and relativistic-electron ’’smoke ring’’ experiments. The spheromak concept adds an internal toroidal magnetic field component, in order to enhance MHD stability. In recent experiments, three different approaches have been used to generate spheromak plasmas: (1) the reversed-field theta pinch; (2) the coaxial plasma gun; (3) a new quasi-static method, based on the initial formation of a toroidal plasma sleeve around a mechanical ring that generates poloidal and toroidal fluxes, followed by field-line reconnection to form a detached spheromak plasma. The theoretical and experimental MHD stability results for the spheromak configuration are found to have common features.

Comment on ‘average photospheric poloidal and toroidal magnetic field components near solar minimum’ by Duvall et al.

We discuss the dynamical interpretation of evidence for an azimuthal tilt of the global magnetic field from the radial direction at the photosphere. We point out that the Reynolds stresses of supergranular convective motions might produce the required small tilt of intense flux tubes, without implying an unacceptably large momentum flux across the photospheric surface into the solar wind. Our calculations lead us to conclude that there is little reason, at present, to infer (Duvall et al., 1979) a separate low intensity constituent of the global magnetic field, from the observational evidence for an azimuthal tilt. More precise measurements of the vertical component of supergranular motions would be useful in determining the actual torque exerted by the Reynolds stresses on the magnetic field.

Average photospheric poloidal and toroidal magnetic field components near solar minimum

Average (over longitude and time) photospheric magnetic field components are derived from 3′ Stanford magnetograms made near the solar minimum of cycle 21. The average magnetograph signal is found to behave as the projection of a vector for measurements made across the disk. The poloidal field exhibits the familiar dipolar structure near the poles, with a measured signal in the line Fe i λ 5250 A of ≈ 1 G. At low latitudes the poloidal field has the polarity of the poles, but is of reduced magnitude (≈ 0.1 G). A net photospheric toroidal field with a broad latitudinal extent is found. The polarity of the toroidal field is opposite in the nothern and southern hemispheres and has the same sense as subsurface flux tubes giving rise to active regions of solar cycle 21.

Upper limits in the toroidal component of force-free magnetic fields in stellar atmospheres in the context of solar and stellar flares

Doing numerical calculations of axially symmetric force-free fields, Milsom and Wright (1976) have noticed that there seem to be no solutions if the toroidal component of the field exceeds a certain limit. In the present paper this problem is reexamined in the approximation of a plane stellar surface using a very simple analytic approximation. The results of Milsom and Wright (1976) are confirmed but, in contrast to their interpretation, it is shown that these limitations do not indicate the possibility of sudden changes of the topology of the magnetic field. This is because in a stellar atmosphere the toroidal component of the surface magnetic field is no independent quantity but is produced by shearing motions in the star which will prevent the toroidal magnetic field from exceeding its maximum value. To study the possibility of sudden changes in the magnetic field, which could cause stellar flares, the calculations are re-done prescribing the motion of the magnetic footpoints (shear in the stellar surface) instead of the toroidal component of the surface field. Using the same mathematical formalism it is found that no sudden changes can occur for configurations where all field lines connect to the stellar surface but that sudden changes may be possible for a more complicated field topology.

Models of Upper Main Sequence Stars Containing a Toroidal Component of Magnetic Field

Models of Upper Main Sequence Stars Containing a Toroidal Component of Magnetic Field

Nonaxisymmetric equilibria in tokamaks and Ohmically heated stellarators

An asymptotic expansion scheme is set up, which is appropriate to deal with the deviations from axisymmetry occurring in tokamaks and Ohmically heated stellarators. Solutions of the magnetohydrostatic equations are sought to all orders in the expansion parameter, which is related both to the magnitude of the deviations from axisymmetry and to the ratio of poloidal vs toroidal components of current and magnetic field. Arguments are presented for the existence of the solution to any finite order, the pressure and current profiles across the plasma column, in general, being determined by the nonaxisymmetric part of the external magnetic field. If the latter, however, has certain symmetries, then a degeneracy occurs, and the pressure and current profiles can again be given with some degree of arbitrariness. It is shown that for tokamaks and stellarators of standard design, viz., including the perturbations associated with the ’’ripples’’ in the toroidal field, the ’’gaps’’ in the copper shell, and the helical windings, the degree of arbitrariness in the pressure and current profiles is the same as in the axisymmetric theory. Thus, in such machines the above profiles are expected to be governed entirely by transport effects, a conclustion which is borne out by the experiments.

An External Ring System for Magnetic Plasma Confinement

A new scheme for steady-state magnetic plasma confinement is suggested, consisting of a superposition of two poloidal magnetic field components. The first arises from the unidirectional currents flowing in a number of ring-shaped external conductors. The second is produced by an oppositely directed azimuthal current in the plasma. Whenever being necessary, an additional toroidal magnetic field component can be introduced. The scheme differs from those having passive guard conductors surrounding the plasma, in the sense that given currents are fed into the rings from external sources. This scheme provides a closed axisymmetric magnetic bottle with closed guiding-centre drift orbits of the plasma particles, as well as possibilities of "bootstrap" operation. The problems are considered of stabilizing electrostatic modes by means of minimum-average-B geometry, and of stabilizing electromagnetic modes by means of the mutual forces between the currents in the plasma and those in the external conductors.

Force-Free Magnetic-Field Structures and Their Role in Solar Activity

view Abstract Citations (177) References (12) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Force-Free Magnetic-Field Structures and Their Role in Solar Activity Barnes, C. W. ; Sturrock, P. A. Abstract Magnetic-field structures in solar active regions are expected to be substantially force-free. A method is proposed for calculating such structures by numencal methods. The method is applied to the study of the magnetic-field pattern associated with a sunspot of one polarity surrounded by a magnetic region of opposite polarity when the sunspot rotates with respect to the surrounding region. Rotation introduces a toroidal component of magnetic field, and the associated pressure leads to inflation of the magnetic-field pattern. If the differential rotation exceeds about 1S0 , the force-free magnetic field has energy greater than that of an open magnetic-field configuration with the same photospheric boundary conditions. It is concluded that, beyond this point, the force-free field structure is metastable and can be converted into an open field structure by an explosive MHD instability. The resulting field pattern is then of the form previously proposed as the site of high-energy solar flares. Publication: The Astrophysical Journal Pub Date: June 1972 DOI: 10.1086/151527 Bibcode: 1972ApJ...174..659B full text sources ADS |