## 5 Results  
The differential, omnidirectional energy spectra of trapped protons along the four portions of orbits depicted in Figure 3, all generated by the AP9 model, are shown in Figure 4. As energy increases, the spectrum in each orbit decreases with a somewhat  
Figure 3: Representation of the four orbits chosen for the time-profile evaluation as a function of geographical latitude and longitude; orbit 1 appears to be more peripheral with respect to, for example, orbit 3. Figure 2: Geographical extension of the SAA for \(>\)1, \(>\)10, and \(>\)100 MeV protons (respectively, blue, red, and green curves in the panel), obtained from the AP9 model. different steepness, as expected. This is, in fact, due to the different aspects of the trapping mechanism, which is the resulting effects of cosmic ray albedo neutron decay (CRAND), solar proton injection, and radial diffusion [45]. The CRAND mechanism is the principal trapped proton source above \(\sim\)100 MeV, and the shape of the albedo neutron vertical spectrum above the geomagnetic cut-off is very similar to the one observed in trapped protons, i.e., the spectrum is decreasing as energy increases. On the contrary, the solar injection is more relevant below \(\sim\)100 MeV (and it is more important for L \(>\) 2), while the radial diffusion tends to redistribute trapped particles in different L, so its effects are more complex. As a result, the trapped proton flux is strongly anisotropic and the overall spectrum changes rapidly, heavily depending on the region (latitude, longitude, L, etc.) where it is estimated. The time profiles (5-s resolution) for the \(>\)10 MeV trapped protons along the orbits defined above are also shown in Figure 5. In each panel, the color palette relates to the different particle energy. Note that during each portion of the CSES-01 orbits, the spectra possess a different shape as a function of time. For example, during orbit 1, trapped fluxes tend to decrease very rapidly, while for the other orbits this decrease is slower. This is due to the fact that orbit 1 crosses the SAA region only in its peripheral section, so the trapped population is only encountered for a small amount of time. Furthermore, in each panel it seems that energetic protons are more concentrated in the internal sectors of the SAA, while low-energy protons are more widely distributed and spread over a larger area; this was inferred also from Figure 2, and it is another proof of the high variability of trapped fluxes inside the inner belt. Figure 4: Differential, omnidirectional energy spectra of \(>\)10 MeV trapped protons obtained with the AP9 model and averaged over each CSES-01 orbit (see title above each panel). In each orbit, the spectrum decreases as energy increases, as expected. To assess the level of agreement between the AP9 model and the experimental data, a preliminary analysis was conducted using omnidirectional \(\sim\)50 MeV calibrated proton data from HEPD, obtained following the same procedure used in [40]. As can be seen from the four panels in Figure 6, the agreement seems to be good, even if some small discrepancies are evident, mostly in the peripheral regions of the SAA; these are probably due to the different operational definition of South Atlantic Anomaly that was used to derive the data with HEPD (For the HEPD data analysis, we define the South Atlantic Anomaly as the region enclosed in a value of the magnetic field \(>\)20,000 nT.). Further studies are needed to verify the agreement even in a longer time period and with the extensive use of simulations. For the purposes of this preliminary analysis, the uncertainties of the AP9 model--related to measurement, gap-filling, or dynamic variations due to space-weather processes--are not taken into account. A future, more complete comparison with HEPD observations will require a precise assessment of the AP9 confidence levels, in order to better evaluate the match with experimental data.