Classical Tearing Mode Research Articles

Local effect of equilibrium current on tearing mode stability in the collisional regime. I

The local effect of the equilibrium current on the linear stability of low poloidal number tearing modes in the collisional regime is investigated analytically. The set of eigenmode equations describing the relevant mode dynamics inside the tearing layer, including the local effect of the equilibrium current, is solved variationally to derive the dispersion relations for the m≥2 and m=1 tearing modes. The local effect of the equilibrium current is found to increase the well-known FKR growth rate for the classical tearing mode, to enhance stabilization for the m≥2 drift-tearing mode, and to slightly increase the growth rate for the m=1 mode.

Dissipative instabilities of magnetic neutral layers with velocity shear

We consider, in the framework of dissipative MHD, the general problem of instability of magnetic neutral sheets in the presence of velocity shear. Both resistivity and viscosity are included in the treatment. We show that velocity shear and/or viscosity introduce different orderings with respect to resistive tearing modes and that the classical tearing modes represent a singular case. Possible orderings for growth rates are discussed and a specific example containing the effect of velocity shear is treated in detail.

On reconnexion experiments and their interpertation

A number of reconnexion concepts and experiments are briefly reviewed in order to re-examine the present interpretation of these experiments. In particular, we offer explanations as to why some experiments appear to develop Petschek modes, tearing modes, or netural current sheets. The explanations require an understanding of the proper role of magnetic Reynolds numbers, the limits of the frozen-in concept, and the importance of natural importance of natural boundary conditions. We find that netural current sheets usually from in experiments with highly symmetrical (and therefore unnatural) boundary conditions. The classical tearing mode develops from perturbations of a neutral current sheet. In less constrained geometries multiple neutral points may appear but the classical tearing mode theory needs modification to explain these cases rigorously. A Petschek mode develops in even less constrained systems although the theoretical description is highly idealized. We offer explanations as to why some experimenters appear to find neutral current sheets in quadrupole fields and examine the usefulness of concepts derived from neutral current sheet theory.

Kinetic theory of tearing instability

The guiding-center kinetic equation with Fokker-Planck collision term is used to study, in cylindrical geometry, a class of dissipative instabilities of which the classical tearing mode is an archetype. Variational solution of the kinetic equation obviates the use of an approximate Ohm’s law or adiabatic assumption, as used in previous studies, and it provides a dispersive relation which is uniformly valid for any ratio of wave frequency to collision frequency. One result of using the rigorous collision operator is the prediction of a new instability. This instability, driven by the electron temperature gradient, is predicted to occur under the long mean-free path conditions of present tokamak experiments, and has significant features in common with the kink-like oscillations observed in such experiments.