“…This gives rise to a specific signature in satellite observations characterized by modulations in particle flux at the wave frequency, with a 180 • phase shift across the resonant energy (for which the unperturbed drift speed matches the azimuthal phase speed of the wave; Southwood & Kivelson, 1981). In cases of both electrons and ions, such signatures have been found in a number of event studies Dai et al, 2013;Hao et al, 2017;Hartinger et al, 2018;Mann et al, 2013;Zong et al, 2009Zong et al, , 2012. Further refinements to the theory and modeling incorporate the effects of day/night asymmetry, azimuthal localization and spectral bandwidth of the wave amplitude, and nonlinear effects on particle dynamics Degeling et al, 2007Degeling et al, , 2011Li et al, 2017Li et al, , 2018Zhou et al, 2016).…”