Session KP01 - Poster Session III.
POSTER session, Tuesday afternoon, March 23
Exhibit Hall, GWCC
Under certain conditions related to the frequency, the linearized equations of ideal magnetohydrodynamics have singular solutions in space that are signatures of a continuous spectrum. An important issue concerns the mathematical nature of the spatial singularities. The specific form of the singularity depends on the geometry of the plasma configuration and the plasma variables. A self-consistent expansion scheme that can be used to identify the singularity is presented. The expansion scheme is based on power series representations about magnetic surfaces \psi(\bfr) = const. The well-known logarithmic singularity \ln|\psi-\psi_0| coupled with the 1/(\psi-\psi_0) singularity is found if the plasma is compressible and the geometry is either planar or cylindrical. New results appear for axisymmetric toroidal geometry. It has been found that an essential singularity (\psi-\psi_0)^i\tau coupled with (\psi-\psi_0)^i\tau-1, where \tau is a real constant, is the general rule. This contradicts previous results of other authors. The logarithmic singularity appears only under special circumstances. An important toroidal configuration with the \ln|\psi-\psi_0| and 1/(\psi-\psi_0) singularities is a pressureless plasma with a purely poloidal magnetic field. Extension of the results to nonaxisymmetric toroidal geometry is discussed.