Finite lifetimes of ideal poloidal Alfvén waves

Abstract

Standing second harmonic poloidal Alfvén waves can be excited by drift‐bounce resonance with energetic particle populations in the Earth's magnetosphere. Using a cold, ideal, MHD model, we study the temporal evolution of the resulting poloidal Alfvén waves. Imposing an azimuthal dependence of exp (iλy) in a “box” model of the magnetosphere, we describe poloidal waves, using a large azimuthal wavenumber λ. In homogeneous media, poloidally polarized waves simply oscillate in time. However, if these waves are excited in a nonuniform medium, we find that their polarization rotates from poloidal to toroidal in time. This polarization change is driven by magnetic field gradients which develop as the poloidal wave fields phase mix in time. Asymptotically, all the initial poloidal wave energy is ultimately transferred to a toroidal polarization. On the basis of this phase mixing we define a poloidal lifetime as the time taken for the poloidal and toroidal amplitudes to become equal. We find that the lifetime is given by τ = λ/ (dωA/dx). The irreversible change from a poloidal to a toroidal polarization is in agreement with early studies [Radoski, 1974] but contrary to a recent report [Ding et al., 1995]. Our results support the findings of Radoski. Consequently, poloidal Alfvén waves in the Earth's magnetosphere may have a finite poloidally polarized lifetime, after which they become dominantly toroidal, determined by their azimuthal wavenumber and the local natural Alfvén frequency gradient.