Estimating the Azimuthal Mode Structure of Ultra Low Frequency Waves and Its Effects on the Radial Diffusion of Radiation Belt Electrons

Characterizing the azimuthal mode number of Ultra Low Frequency (ULF) waves is critical to quantifying the radial diffusion of radiation belt electrons. A Wavelet cross-spectral technique is applied to the compressional ULF waves observed by multiple pairs of GOES and MMS satellites to estimate the mode structure of ULF waves. A more realistic distribution of mode numbers is achieved by inclusion of the modes corresponding to different wave propagation directions as well as at higher than fundamental mode number. For the event study of a geomagnetic storm using GOES data, ULF wave power is found to dominate at low mode numbers during high solar wind dynamic pressure. The change of sign in around noon was observed to be consistent with anti-sunward wave propagation due to solar wind. To reduce the 2 ambiguity in resolving , a cross-pair analysis is performed on GOES field measurements which is demonstrated to be effective in generating more reliable mode structure of ULF waves during high Auroral Electrojet (AE) periods. During another event with two consecutive interplanetary shocks compressing the dayside magnetopause, contribution of low versus high modes in the power of ULF pulsations and their frequency signatures are resolved using high-fidelity multi-probe MMS magnetometer data. The analysis clearly shows that shock onset corresponds to more in-phase magnetic fluctuations in the Pc4-5 regimes than what follows, and smaller spatial scale fluctuations are implied by the dominant high mode numbers observed after both shocks hit and passed the magnetosphere. At the shock impacts, the contribution of higher frequencies (e.g., \u3e7 mHz, corresponding to Pc-4) to the wave power is not negligible, while after the impacts, the power distributes significantly over lower frequencies (e.g.,pulsations). A threshold mode, th, is introduced to give an approximate range of the largest resolvable using ideal-MHD models. In addition, a first-principle calculation is introduced to address the long-lasting debate on the contribution of higher ULF wave azimuthal mode number (e.g., ||\u3e1) on the radial diffusion rates of energetic electrons. We showed that the simplified assumption of =+1 in ULF waves would overestimate the by more than 300%. Therefore, contrary to the previous assumptions in earlier work, inclusion of the negative as well as higher mode values are both important and must be considered in the estimations of radial diffusion of radiation belt electrons