Stabilization of magnetohydrodynamic instabilities by force-free magnetic fields. III: Shearless magnetic fields.
Abstract
The marginal-stability analysis, as given in two previous papers, is further elaborated for magnetic fields of constant direction in the plane case and for magnetic fields of constant pitch in the cylindrical case. For these shearless magnetic fields discontinuities arise in the stability criteria. The physical significance of these discontinuities is discussed. From the marginal-stability analysis the principle of exchange of stabilities is derived. This theory is applied to constant-pitch magnetic fields, which are shown to be necessarily unstable. Growth rates of the instabilities of these fields are calculated, correcting earlier results of Ware. Simple modifications of some constant-pitch models, namely Van der Laan's model of a constant-pitch force-free field and Alfvén's model of a constant-pitch field with parabolic pressure profile, prove to yield completely stable pinch configurations of a sharp or diffuse kind. An appendix is devoted to toroidal effects.
- Publication:
-
Physica
- Pub Date:
- 1971
- DOI:
- 10.1016/0031-8914(71)90114-5
- Bibcode:
- 1971Phy....53..535G