On the existence of transverse MHD oscillations in an inhomogeneous magnetoplasma
Abstract
In a cold plasma with no compressional field perturbation the equations governing the two perpendicular components of magneticfield perturbation decouple. These two equations depend only upon spatial derivatives along the background magnetic field, and give the impression of independent fieldline motion in the two transverse directions. However, the perturbation magnetic field b must be divergencefree. It is not meaningful to ask if the field perturbation on an individual background line of force satisfies . b = 0. To decide whether b is divergencefree, we need to know about its spatial variation, i.e. what the state of the neighbouring field lines is. In this paper we investigate two classes of solutions: first we allow the perturbation magnetic flux to satisfy . b = 0 by threading across the background lines of force; the second solution closes b by allowing the perturbation flux to encircle the background field lines (torsional Alfvén waves). For both of these solutions we study the relationship between neighbouring field lines, and are able to derive a set of criteria that the background medium must satisfy. For both classes we find restrictions upon the background magneticfield geometry  the first class also has a constraint upon the plasma density. The introduction of perfectly conducting massive boundaries is also considered, and a relation given that they must satisfy if the field perturbation is to remain transverse. The criteria are presented in such a manner that it is easy to test if a given medium will be able to support the solutions described above. For example, a threedimensional dipolo geometry is able to carry oscillatory toroidal fields; but not purely poloidal ones or a torsional Alfvén wave.
 Publication:

Journal of Plasma Physics
 Pub Date:
 February 1990
 DOI:
 10.1017/S002237780001463X
 Bibcode:
 1990JPlPh..43...83W
 Keywords:

 Cold Plasmas;
 Magnetic Field Configurations;
 Magnetohydrodynamic Waves;
 Nonuniform Plasmas;
 Plasma Oscillations;
 Wave Packets;
 Field Aligned Currents;
 Transverse Waves;
 Wave Equations;
 Plasma Physics