Physics of auroral phenomena : proceedings of the 36th Annual seminar, Apatity, 26 February – 01 March, 2013 / [ed. board: A. G. Yahnin, A. A. Mochalov]. - Апатиты : Издательство Кольского научного центра РАН, 2013. - 215 с. : ил., табл.

Yu. V. Balabin el al. AN( J0, у, А Г, c, A,(p) = Y ■■З Д '1A(R) •G(W У•? ) ) 'M 20 Л=1 The discrepancy function, which must be minimized in the space of six parameters, is 0 ( J o,r,A/,c,A,<p) = ]T[ANL •( J 0, y ,Ay , c ,A,<p) -AM L]2 (4) (5) where index L is the stations number, ДМ is actually observed increase at the station. The calculation of the minimum value of Ф provides the RSP flux parameters. More information about this technique can be found in [3, 4, 5]. a v и ь W 30 a) / I A " v . ” 10' 2 и 40 Г V , ВшппЬнгц A u : J w 4 J .1..!..1 ...... ! t 3.0 A л 2 3.4 3.4 З.И 4.0 Tiiic Buy T 1 N 3.0 3.2 3.4 3.4 3.8 4.0 Tim e.I'T Fig. 1 GLE70. a) Increase profiles, experimental (solid lines) and derived (dots), of SCR at some stations, b) Derived spectra o f SCR. Function Ф in (5) is the baseline. In some cases the analysis of the profiles for events of increase using the data from the global network of stations, along with the interplanetary environment data indicates the presence of loop structures in the interplanetary magnetic field and the presence of the reverse (to the Sun) flux of RSP. Sometimes a detailed analysis o f the amplitude distribution of increases in the global network of NM shows the intensity gap at pitch angles close to 90 degrees. In such cases the basic pitch angle distribution appears too coarse and the resulting solution has too big discrepancy. For such cases the function G(0) was taken in the form considering features of RSP flux: bidirectional or with a depression at pitch angles close to 90 degrees. More about this see in [6].We note especially that in all these cases the modified form of function G(0) for certain values of parameters converges monotonically to (3). This is done in order to minimize the error associated with a priori settings for solving the inverse problem. Results Totally about 50 events from GLE05 to GLE71 have been processed. The energy parameters of differential spectra are shown in the Table 1. While solving the inverse problem we used the rigidity values, and then translated results into the energy values in GeV. For all events shown in Table 1 calculation of the spectra was carried out at 5 minutes intervals. Thus it is possible to trace the dynamics o f the spectra during the event. There are only three events for which there is no a five-minute data and the calculation of the spectra were done on hourly data. For short GLE (no longer than 3-4 hours) spectra were obtained from start to finish, for a long GLE spectra were calculated on the growth phase, the maximum and the start of the decreasing. The table demonstrates typical spectra of the growth/maximum phase and decrease phase for each event. For most events there are two components in the spectrum: prompt and delayed. Differential spectrum of the prompt component has an exponential form 1(E) = J 0 •exp ( - E / E 0) (6) where J0 is an intensity, proton/(m2-s-sr-GeV); E0 is a characteristic energy, GeV. The spectrum of the delayed component has a power law form 1(E) = J x E -r (7) where J! is an intensity at 1 GeV energy proton/(m2-s-sr-GeV); g is a spectral index. Most of the spectra calculated by our technique are in good agreement with direct measurements in the stratosphere (80-400 MeV) and on spacecrafts (80-700 MeV). 107