Phase-mixing poloidal alfvén wave polarisations

Standing poloidal Alfvén waves are believed to be excited by drift-bounce resonance with energetic particle populations in the Earth's magnetosphere. Using a fully compressible ideal MHD model, in a cartesian geometry, we investigate the temporal evolution of localised poloidal Alfvén waves evolving in radially inhomogeneous magnetoplasmas. We find that the polarisation of these waves rotates from being poloidal to toroidal in time. This polarisation rotation is driven by the magnetic field gradients which develop as the wave fields phase mix in time. Asymptotically, in an ideal plasma, all the wave energy is deposited in the toroidal polarisation. We define the time taken for the toroidal and poloidal amplitudes to become equal as the ideal poloidal lifetime, tau = lambda(domega_A/dx)^-1 and verify the result numerically (where lambda is the azimuthal wavenumber, and x represents the radial direction). Further, by using the method of multiple timescales, we analytically determine the time dependent wave solutions and find excellent agreement with our numerical work. The finite lifetime of ideal poloidal Alfvén waves is important if the spatial and temporal features of both in-situ satellite and ground-based observations are to be fully understood.