Shear Alfven waves on stretched magnetic field lines near midnight in Earth's magnetosphere

The spectrum of toroidal standing shear Alfven waves (SAWs) is derived for a stretched magnetic field line geometry that is approximated by the Tsygan enko 96 magnetic field model. The model is applied to field lines near the midnight meridional plane. It is demonstrated that the fundamental mode fre quency for typical ambient parameters of Earth's magnetosphere is in the 1- 4 mHz range. This frequency is in agreement with the measured frequency of magnetospheric held line resonances, and is up to an order of magnitude sma ller than for a dipolar magnetic field. We conclude that stretching of Eart h's magnetic field offers a possible explanation for anomalously low freque ncy SAWs observed within diffuse auroral emission (H-beta) produced by ener getic proton precipitation in the inner plasma sheet.