The ideal magnetohydrodynamic continuous spectrum in a cylindrical screw pinch: A question of completeness
The continuous spectrum of ideal magnetohydrodynamics in a cylindrical screw pinch is investigated. Contrary to many claims in the literature in the last twenty five years, it is rigorously proved that there are in fact four continua, the two new ones being those associated with the fast and slow magnetosonic waves, in addition to the previously described shear Alfvén and sound continua. Whereas the shear Alfvén and sound continua arise from the singularities of the Hain-Lüst equation, the magnetosonic continua result from the singularities of the resolvent operator associated with the non radial displacements. Two independent proofs of the existence theorem in question are given. The generalized eigenfunctions for all the four continua are constructed in terms of the fundamental Frobenius solutions of the Hain-Lüst equation and their singularity structures are highlighted. The two new, magnetosonic continua have potentially important consequences for plasma heating and turbulence. These are very briefly indicated, as are some generalizations of the approach adopted.
Bibliographic Reference: Report: EN (1998) 25pp.
Availability: Available from the Librarian, UKAEA, Culham Laboratory, Abingdon, Oxon, OX14 3DB (GB)
ISBN: ISBN 0853111928
Record Number: 199810438 / Last updated on: 1998-03-31
Original language: en
Available languages: en