“…In radiation belt models, when assessing the relative contribution of ULF waves to electron dynamics, ULF wave power is typically assumed to be broadband (e.g., Ali et al, ; Brautigam & Albert, ; Brautigam et al, ; Ozeke et al, ) and the value of m is assumed to be both positive and low for all frequencies. This is in despite of evidence for discrete wave power (e.g., Claudepierre et al, ; Mann et al, ; Rae et al, ), and both high (e.g., Le et al, ) and low (e.g., Sarris et al, ), and positive (Sarris et al, ) and negative (Le et al, ) azimuthal wave numbers within the outer radiation belt. In general, these assumptions are made for three fundamental reasons.…”