Estimates of the power per mode number of broadband ULF waves at geosynchronous orbit

In studies of radial diffusion processes in the magnetosphere it is well known that ultralow frequency (ULF) waves of frequency mωd can resonantly interact with particles of drift frequency ωd, where m is the waves\textquoteright azimuthal mode number. Due to difficulties in estimating m, an oversimplifying assumption is often made in simulations, namely that all ULF wave power is located at a single mode number. In this paper a technique is presented for extracting information on the distribution of ULF power in a range of azimuthal mode numbers. As a first step, the cross power and phase differences between time series from azimuthally aligned magnetometers are calculated. Subsequently, through integrating the ULF power at particular ranges of phase differences that correspond to particular mode numbers, estimates of the fraction of the total power at each phase difference range or mode number are provided. Albeit entwined with many ambiguities, this technique offers critical information that is currently missing when estimating radial diffusion of energetic particles. As proof-of-concept, the technique is first tested successfully for a well-studied case of narrowband ULF Field Line Resonances (FLR) for which the mode number was calculated simultaneously through ground-based and space measurements. Subsequently, the technique is demonstrated for the broadband ULF waves that accompanied the 2003 \textquotedblleftHalloween\textquotedblright magnetospheric storms. The temporal evolution of power at each mode number gives insight into the evolution of ULF waves during a storm as well as more accurate characterization of broadband ULF waves that can be used in radial diffusion simulations.