1. Introduction
Energy spectrum distributions of energetic particles are an essential indicator for understanding the underlying physics of magnetospheric particle dynamics. In general, it is well recognized that both electron and proton energy spectra in space plasmas follow a Kappa or Kappa-like profile having fluxes steeply falling with increasing energy (e.g., Freden, 1965; Pizzella et al., 1962; Summers et al., 2009). In contrast, a number of previous studies reported ‘reversed’ energy spectra of energetic particles that do not follow monotonically decrease profiles of fluxes with increasing energy but represent flux minima at lower energies and flux maxima at higher energies. Based on the Molniya 1 measurements, Vakulov et al. (1975) observed a flux maximum of the outer belt electron energy spectra at energy ~1- 2 MeV. West et al. (1981), using 60 keV to 3 MeV electron data from Ogo5, showed a flux maximum at ~1.5 MeV and a minimum at ~500 keV. By analyzing the ring current proton spectra (1 - 300 keV) observed by the Explorer 45, Williams et al. (1973) reported the flux minima of proton energy spectra at energies ~20 - 100 keV over L ~ 3.2 - 4.0, which they attributed to the ion-cyclotron instability. Based on the AMPET CCE measurements, Krimigis et al. (1985) observed the flux maxima at energies ~100 - 300 keV during both the main and recovery phases of a geomagnetic storm.
Along with the launch of the twin Van Allen Probes mission in August 2012 (Mauk et al., 2012), the long-term accumulation of unprecedented, high quality particle datasets with fine energy resolutions has fueled a resurgence in magnetospheric particle dynamics studies. By combining the MagEIS and REPT measurements, Zhao et al. (2019a) reported a reversed energy spectrum of radiation belt electrons, which is featured by the flux maximum ~1 – 2 MeV and flux minimum ~ 100’s keV and is reasonably accounted for energy-dependent electron losses induced by hiss wave (e.g., Ni et al., 2019; Fu et al., 2020). A following statistical analysis of Zhao et al. (2019b), on basis of the detailed analysis of reversed electron energy spectra, found that reversed energy spectra dominate inside the plasmasphere at L < 2.5.
Comparatively, there remains lacking the systematic information about the global distribution of the reversed energy spectra of ring current protons. The availability of Van Allen Probes RBSPICE data enables a comprehensive study in this regard. Therefore, this letter is dedicated to investigate the global distribution of reversed proton energy spectra based upon multi-year RBSPICE data from Van Allen Probes. By establishing an automatic identification criterion for the reversed proton energy spectra, we intend to perform a statistical analysis to explore the global distribution features of the reversed proton energy spectrum, its occurrence pattern, its dependence on geomagnetic activity, and its profile characteristics in terms of the energy range of local flux minimum and the ratio of local flux maximum to minimum.