Сборник с доклади от XXXIV Международен симпозиум | Page 289

In the next interval, Ea < E < 200 MeV / nucleon, ionization losses and spectrum intensities begin to decrease. This decreasing trend in ionization losses continues into interval 3, 200 < E < 850 MeV / nucleon, but with a shallower slope that reflects the physical nature of the energy loss process.

The subsequent intervals, interval 4, 850 < E < 5000 MeV / nucleon, and interval 5, E > 5000 MeV / nucleon, involve relativistic particles whose energies increase significantly. Beyond interval 5 lies the " knee " of the CR spectrum at E ∼ 3 − 4 × 1015 eV. Cosmic ray energies can reach E > 1018 eV for Ultra High Energy Cosmic Rays( UHECRs) and E > 1020 eV for Extremely High Energy Cosmic Rays( EHECRs) [ 7 ].

Now, we introduce the energy intervals and subintervals used in the ionization rate models CORIMIA and CORSIMA:

( 4) kT � E ��� � 0.15 �E �. ��, � ∗ �E � �E �, � � 200 �E ���, � � 850 �E ���, � � 5000 �E ����, � � ∞

This sequence of inequalities defines the subintervals with the corresponding energy bounds, reflecting the physical characteristics of particles in each interval. These intermediary bounds characterize the CORIMIA and CORSIMA models, and depend on the particle ' s path through the atmosphere, as considered in the relevant formulas.

We will now demonstrate the mathematical expression for calculating the ionization rate when the effective rigidity of particle penetration falls within interval 1 from equation( 1), and does not exceed the upper boundary:

q�h� � ρ�h� Q

� �

�. ��

� �. ��, ����

�� D�E� �dE dh � dE � � � D�E� � dE

� ��� dh � dE � �

�. ��

� �, ����

� �

( 5) � � D�E� � �� � dE �� � � � D�E� � ��

� � dE �. ��, � ��

� �

���

� ���, ����

� � D�E� � dE dh � dE � � � D�E� � dE

� �, � dh � dE � � …

���

Here, Q = 35 eV is the energy required to form one electron-proton pair [ 15 ], [ 13 ]. The integral bounds are determined by formulas( 1) and( 14), as well as reference [ 1 ]. The ionization loss function without boundary crossings is calculated in equations( 6),( 7), and( 8) for terms I, II, and III of equation( 5). The ionization loss function with boundary crossings is calculated in equations( 9) and( 10) for terms II, IV, and VI of equation( 4). The integration bounds of term VI are further explained in [ 1 ].

Table 1: Subtracted differential spectra for Helium observed by several telescopes( LET1, red and HET B, blue) of the ISOIS instrument onboard Parker Solar Probe( PSP) [ 14, Fig. 10a ]. Here are the source data for the calculations of Fig. 2.

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