The azimuthal wavenumber m of ultra lowfrequency (ULF) waves in the magnetosphere is a required parameter in the calculations of the diffusion rates of energetic electrons and protons in the magnetosphere, as electrons and protons of drift frequency ! d have been shown to radially diffuse due to resonant interaction with ULF waves of frequency omega=m omega(d) . However, there are difficulties in estimating m, due to lack of multipoint measurements. In this paper we use magnetic field measurements at geosynchronous orbit to calculate the cross- spectrogram power and phase differences between time series from magnetometer pairs. Subsequently, assuming that ULF waves of a certain frequency and m would be observed with a certain phase difference between two azimuthally aligned magnetometers, the fraction of the total power in each phase difference range is calculated. As part of the analysis, both quiet-time and storm-time distributions of power per m number are calculated, and it is shown that during active times, a smaller fraction of total power is confined to lower m than during quiet times. It is also shown that in the dayside region, power is distributed mostly to the lowest azimuthal wavenumbers m = 1 and 2, whereas on the nightside it is more equally distributed to all m that can be resolved by the azimuthal separation between two spacecraft.
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Sarris, Theodore E. and Li, Xinlin, "Geomagnetic activity and local time dependence of the distribution of ultra low-frequency wave power in azimuthal wavenumbers, m" (2017). Laboratory for Atmospheric & Space Physics Faculty Contributions. 6.