Sheets In Magnetic Fields Research Articles

Analysis of the Motion of Conducting Sheets in Magnetic Fields

Solution of the equation of motion for conductors in external magnetic fields requires the knowledge of the magnetic forces due to the induced eddy currents that, in turn, can be determined if the position and the velocity of the bodies are known. An iterative technique is adopted, where, at each time step, an initial value of the magnetic force is used to determine the position and the velocity of the body at the end of the time step and, then, the value of the force is corrected. To reduce the computational effort in the case of thin metallic sheets, it is proposed to use the surface integral equation of the induced eddy currents, with a supplementary term added to account for the motion. A sinusoidal with time variation of the excitation field is considered and a phasor representation of various physical quantities is employed. An average magnetic force over each period is used to solve the equation of motion.

Influence of the current density longitudinal distribution in current sheets on their magnetic field structure and formation dynamics. II: Formation dynamics of variously configured current sheets

The structure of Ampere forces responsible for the formation dynamics of classical and double-humped current sheets in magnetic fields with a null line is calculated numerically. Calculation data are compared with experimental data for the structure and dynamics of current sheets obtained using magnetic measurements and holographic interferometry.

Topological complexity and tangential discontinuity in magnetic fields

This is a study of the topological magnetostatic problem. A magnetic field embedded in a perfectly conducting fluid and rigidly anchored at its boundary has a specific topology invariant for all time. Subject to that topology, the force-free state of such a field generally requires the presence of tangential discontinuities (TDs). This property proposed and demonstrated by Parker [Spontaneous Current Sheets in Magnetic Fields (Oxford University Press, New York, 1994)] is explained in terms of (i) the overdetermined nature of the magnetostatic partial differential equations nonlinearly coupled to the integral equations imposing the field topology and (ii) the hyperbolic nature of the partial differential equation for the twist function α of the force-free field. The mathematical analysis elucidates a basic incompatibility between preserving a complex field topology and attaining equilibrium, if analyticity is assumed. Physics avoids this incompatibility via TD formation as a natural consequence of perfect conductivity. The study relates TD formation to topological complexity in two-dimensional and three-dimensional fields, as well as the topological connectivity and geometric shape of the field domain. Mathematical points made are given physical interpretations, but important topological concepts for understanding spontaneous TDs have remained incomplete. As an application, examples are presented to define twisted and untwisted potential fields found in simply and multiply connected domains, clarifying a confusion in several recent publications. Appendix A treats the expression of the frozen-in condition by a continuum of conserved, total generalized helicities. Appendix B reports briefly on concurrent developments showing that a published objection to the theory of spontaneous TDs is based upon a misunderstanding of the theory.

The Topological Nature of Boundary Value Problems for Force‐Free Magnetic Fields

The difficulties of constructing a three-dimensional, continuous force-free magnetic field in the solar corona are investigated through a boundary value problem posed for the unbounded domain external to a unit sphere. The normal field component Bn and the boundary value αb of the twist function α on the unit sphere, combined with the demand for a vanishing field at infinity, do constitute sufficient conditions for determining a solution if it exists, but Bn and αb cannot be prescribed independently. An exhaustive classification of the admissible (Bn,αb)-pairs is developed, using the topological properties of the α flux surfaces implied by their footprints described by the constant-αb curves on the unit sphere. The incompatibilities arising from boundary conditions contradicting the field equations are distinguished from the interesting one of (Bn,αb) being, in principle, admissible but requiring a weak solution describing a force-free field containing inevitable magnetic tangential discontinuities. This particular incompatibility relates the boundary value problem to the Parker theory of spontaneous current sheets in magnetic fields embedded in electrically perfectly conducting fluids. Our investigation strategically skirts around some important but formidable mathematical problems to arrive at physically definite conclusions and insights on the construction of force-free fields, both in the practical task of modeling coronal magnetic fields with magnetopolarimetric data and in the basic understanding of the Parker theory. Two specific demonstrations of (Bn,αb) are given to illustrate circumstances under which a continuous solution to the boundary value may or may not exist.

Magnetic structure of current sheets in magnetic fields with a singular X line

Direct measurements of magnetic fields in a plasma show that current sheets can form in magnetic configurations with an X line in the presence of a longitudinal magnetic field. It is found that, in a plane perpendicular to the X line and to the direction of the main current, the current sheet has two very different dimensions. The tangential and normal components of the magnetic field and current density in the sheet are determined. The influence of the initial conditions (such as the strength of the longitudinal magnetic field, the gradient of the transverse field, and the plasma ion mass) on the current sheet parameters is investigated.