Damping of geomagnetic pulsations by the ionosphere

A significant sink of geomagnetic pulsation energy is due to Joule dissipation in the ionosphere. To investigate this we have computed the damping experienced by standing Alfvén waves in a dipole magnetic field. Both the uncoupled poloidal and toroidal modes are considered with Joule dissipation being introduced through a boundary condition which relates the electric and magnetic field strengths at the ionosphere, viz: $\text{4πΣ}{}_{\mathrm{p}}\text{E}\text{c}\text{= b,}\text{where}\text{Σ}{}_{\mathrm{p}}$ is the height integrated Pederson conductivity. The damping rates are strongly dependent on the ionospheric conductivity and we find that typically the normalized damping rate, $\text{γ}\text{ω}\text{,}\text{is}\text{～0.1}$ for nightside values of conductivity and ～0.01 for the dayside. This would account for the observed scale of bandwidths in pulsation signals. Away from regions of extreme damping we find γ ∝ L^?1Σ_p^?1.