Funnel-shaped, low-frequency equatorial waves

Funnel-shaped, low-frequency radiation, as observed in frequency time spectrograms, is frequently found at the earth's magnetic equator which extends from the proton-cyclotron frequency up to the lower hybrid frequency. Ray-tracing calculations can qualitatively reproduce the observed frequency-time characteristics of these emissions if the waves are propagating in the fast magnetosonic mode starting with wave normal angles of about 88 deg at the magnetic equator. The funnel-shaped emissions are consistent with generation by protons with a ring-type velocity space distribution. A ring-shaped region of positive slope in the velocity space density distribution of protons is observed near the Alfven velocity, indicating that the ring protons strongly interact with the waves. Ray-tracing calculations show that for similar equatorial wave normal angles lower-frequency fast magnetosonic waves are more closely confined to the magnetic equator than higher-frequency fast magnetosonic waves. For waves refracted back toward the equator at similar magnetic latitudes, the lower-frequency waves experience stronger damping in the vicinity of the equator than higher-frequency waves. Also, wave growth is restricted to higher frequencies at larger magnetic latitudes. Wave damping at the equator and wave growth off the equator favors equatorial wave normal angle distributions which lead to the funnel-shaped frequency time characteristic.