ONCE MORE - THE CONTINUOUS-SPECTRUM OF IDEAL MAGNETOHYDRODYNAMICS

A controversy on the existence of continuous spectra of ideal magnetoh ydrodynamics in addition to the well-known Alfven and slow continua, d ating back to a conjecture by Grad [Proc. Natl. Acad. Sci. USA 70, 337 7 (1973)] and revived by Lashmore-Davies, Thyagaraja, and Cairns [Phys . Plasmas 4, 3243 (1997)], is once more resolved by demonstrating that the resolvent operator is bounded in the relevant domain: There are n o additional continua. In addition, the solution of the initial value problem is constructed in terms of the three-dimensional Green's dyadi c, which is free of apparent singularities and clearly exhibits the cl assical continua as delta functions on the diagonal. This construction provides the connection with the proper and improper normal modes and shows that the local dynamics on the magnetic surfaces is described b y the classical continua. (C) 1998 American Institute of Physics. [S10 70-664X(98)03609-X].