3. Observations and Statistical Results
Figure 1 displays the observations of proton fluxes during 16 - 30 March, 2015. The solar wind parameters and geomagnetic indices obtained from the OMNIweb are plotted in Figures 1a-b. On 17 March 2015 when an intense geomagnetic storm occurred, the solar wind speed jumped from ~400 to ~600 km/s and the interplanetary magnetic field (IMF) Bz turned quickly from northward (~15 nT) to southward (~-15 nT). The Dst index dropped from ~30 to ~-220 nT with the AE index increasing significantly from ~100 to 1500 nT. At the same time, the RBSPICE onboard the Van Allen Probe B observed evident proton flux increases at energies of 44.7 and 81.6 keV (Figures 1c-d). However, the enhancements of 268.9 keV proton fluxes did not occur until 18 March. The black solid lines in Figures 1c-e indicate the plasmapause location calculated using Liu et al., (2015) model. In Figures 1c-d, the proton fluxes outside the plasmasphere are higher than those inside the plasmasphere during quiet times. During the recovery phase after 18 March, 44.7 and 81.6 keV proton fluxes at lower L (~2 – 4) gradually decreased while the 268.9 keV proton fluxes increased and then remained relatively stable. Figures 1f-h further show the proton energy spectra at the indicated time intervals. As shown in Figure 1f, the proton fluxes generally decreased monotonically with increasing energy over L ~3.0 – 5.6. However, several days later (Figures 1g-h), the proton energy spectra at L < ~5.2 exhibited “reversed” structures with fluxes decay more significantly at low energies < ~200 keV, leading to flux minima at energies ~80 keV. These flux minima reduced with decreasing L shells.
Figure 2 illustrates some key parameters of the reversed proton energy spectra. This representative example occurred at 02:04:47 on 29 March 2015at L = 3.15. In this example, proton energy spectrum has a clear flux minimum (f min) at Emin~82 keV and a flux maximum (f max) at Emax ~221 keV with the ratio of flux maximum to minimum reaching ~60. To automatically identify the reversed proton energy spectra, we adopted three criteria: (1) proton energy spectra show the existence of the maximum and minimum, and the corresponding energy of flux maximum (Emax) is greater than that of flux minimum (Emin), (2)\(\frac{f_{\max}}{f_{\min}}>3\), and (3) there must be at least one energy channel between the Emax and Eminto avoid the misclassification.
To further investigate the relation between the geomagnetic activities and the reversed proton spectra in a long period, we present the geomagnetic indices and proton fluxes with three energy channels (44.7, 81.6 and 268.9 keV) during 2015 in Figures 3a-d with the white solid lines representing plasmapause locations. When the Dst index suddenly decreased and the AE index increased, the locations of plasmapause were reduced to lower L (~2 – 3). For 44.7 and 81.6 keV protons, the fluxes outside the plasmasphere are ~1 order of the magnitude higher than those inside the plasmasphere in most cases, yet this is opposite to the fluxes of 268.9 keV protons. While inside the plasmasphere, the proton fluxes at energies 44.7 and 268.9 keV are generally 1~2 orders higher than those at energies 81.6 keV. With increasing energy, the proton energy spectra are going to show the decreasing and then increasing trend which is the reversed feature depicted in Figure 2. Figures 3e-h demonstrate the key parameters of automatically selected reversed proton energy spectra. The occurrence rate of the reversed proton energy spectra is calculated with the grids of 0.1 L and one day. The locations of plasmapauses match well with the upper boundaries of the region with the occurrence rate > 90%. During quiet times, the plasmapauses usually locate at L > 4.5 so that the reversed proton energy spectra locate at L ~2 – 4. We find that the proton reversed energy spectra are likely to be observed under active geomagnetic conditions (Dst > -50 nT and the AE > 1000 nT). As shown in Figures 3f-h, the proton energies of flux maxima mostly lie in the range of ~82-400 keV, decreasing with increasing L shells. Similarly, the proton energies of flux minima for reversed energy spectra are tens of keV. Note that there still are a few events which distribute outside the plasmasphere at L > ~4.5 with Emax > 328 keV and Emin > 100 keV. Figure 3f reveals that the flux maxima are ~10 to 30 times greater than the flux minima at L < 4, while the ratios decrease from ~10 to 3 with increasing L shells at L > 4.
Figure 4 shows the global distributions of reversed proton energy spectra as a function of L shell and MLT for three indicated geomagnetic conditions (Dst>-30 nT, -50 nT<Dst<-30 nT and Dst<-50 nT) from January 2013 to December 2016. From top to bottom, each row presents the number of total samples, occurrence rate, the corresponding energies of flux maximum and minimum, and the ratio of flux maximum to minimum. The region of our interest has been divided into smaller bins with the resolution of 0.5 L × 1 MLT, and the blank bins means the observational samples are less than 50. Both the Emax, Emin, and the ratio of flux maximum to minimum in Figures 4g-o are valued by averaging the cases in one bin. Most samples are observed during quiet times (Dst > -30 nT) at L ~2.5 - 4.5 (Figure 4a). The reversed proton spectra almost persistently exist over L ~ 2 – 4 during quiet times, with occurrence rates >90%. Besides, the occurrence rates decrease with increasing L shells, which is consistent with the observations shown in Figure 1, and decreases under more active geomagnetic activities. The upper boundary of higher occurrence rate (>90%) regions shift from higher to lower L shells. Regarding to the MLT dependence, we find that the occurrence rates on the dayside are slightly higher than those of nightside, especially during the geomagnetically active periods (Dst < -50 nT). In Figures 4g-l, the statistical distributions of the Emax and Emin demonstrate that the proton fluxes mostly reach the peaks at energies ~200 - 400 keV and drop to the valleys at energies ~50 - 100 keV. Both Emax and Emin decrease first as the L shell increases to ~5, while they suddenly increase on two MLT sectors (15-19, 22-05) at L>5 with relatively small samples. In addition, the statistics of Emax and Emin show a less geomagnetic activity dependence. The ratios decrease with the increasing L shells, which are smaller under the more active geomagnetic conditions (Figures 4m-o).