ANALYTICAL TREATMENT OF ALFVEN RESONANCES AND SINGULARITIES IN NONUNIFORM MAGNETOPLASMAS

The linear resonant excitation of Alfven waves in a cold plasma permea ted by a nonuniform magnetic field is considered. The equilibrium magn etic field is irrotational and possesses an invariant coordinate perpe ndicular to the direction of the field. By solving for the coefficient s in a Generalized Frobenius Series the regular and singular solutions may be generated. The singular solution is logarithmic and produces a net absorption of energy at the resonant field line. The efficiency o f coupling between the fast mode and the resonant Alfven mode is deter mined by the following overlap integral along the resonant field line, integral (xi(betar)b(gamma0)/h(beta) d l; xi(betar) is the resonant e igenfunction, b(gamma0) is the compressional/parallel magnetic field p erturbation, and h(beta) is proportional to the separation of backgrou nd lines of force in the invariant direction. The amplitude of the sin gular solution is proportional to this integral, while the rate of ene rgy absorption at the resonance is proportional to its square. It is a lso shown how the analytical solution at the resonance may be used to avoid problems encountered in numerical solutions.