RESONANT ALFVEN-WAVE EXCITATION IN 2-DIMENSIONAL SYSTEMS - SINGULARITIES IN PARTIAL-DIFFERENTIAL EQUATIONS

The resonant excitation of Alfven waves is considered in a cold plasma embedded in a uniform magnetic field Bz. All wave fields are assumed to vary as exp[i(lambday - omegat)], and the background medium is invariant in y. The background density distribution rho0(x, z) is otherwise completely arbitrary. Regular and singular solutions for the waves are derived systematically in the vicinity of a resonance by considering a generalized Frobenius series, and we are able to recover many results found in earlier studies. Some new features of our work include a generalization of the overlap integral determining the efficiency with which any resonance may be excited, and the possibility that xi(y) is-proportional-to 1/x(N) (N = 1, 2, 3 . . .) at the resonance. Hitherto only the solution with N = 1 has been considered.