A theory of long-period magnetic pulsations (Pc 3 to Pc 5) is presented as an initial value problem to explain impulse-excited pulsations. By using a one-dimensional model a wave equation that shows a coupling between a surface wave and a shear Alfvén wave is derived. By solving this equation on the basis of initial value approach we conclude that there is a continuous spectrum with damping proportional to inverse power of time and that there are weakly damped discrete eigenmodes (surface eigenmodes) due to sharp variations in the plasma parameters. The frequency ωr and the damping rate γ of the surface eigenmode are given approximately by ωr = k∥(BI² + BII²)/μ0(ρI + ρII)1/2 and γ/ωr = |k⊥/▽(ln υA²)| respectively, where υA(=B/(μ0ρ)1/2) is the Alfén speed, k∥ and k⊥ are wave numbers parallel and perpendicular to the magnetic field, and subscripts I and II refer to quantities associated with each side of the surface. The result is used to explain recent observations of plasmapause-associated magnetic pulsations as well as magnetic pulsations excited by sudden commencements and sudden impulses near the magnetopause.
Chen et al. (1974) studied this question.