Empirical model of cosmic ray spectrum in energy interval 1 MeV–100 GeV during 11-year solar cycle

Abstract

The galactic cosmic rays (GCR) are the main ionization source at altitude of ∼3–35 km in the atmosphere. For high latitude anomalous cosmic ray (ACR) component has also a significant influence on the atmospheric ionization. We propose an empirical model for differential spectra D( E) of galactic and anomalous cosmic rays in energy interval 1 MeV–100 GeV during solar cycle. In the model data are used which cover three solar cycles: 20, 22 and 23. The LEAP87, IMAX92, CAPRICE94, AMS98 and BESS experimental spectra for protons and alpha particles are fitted to the proposed empirical model. The modulated GCR differential spectra are compared with force-field approximation to the one-dimensional transport equation and with solutions of two-dimensional cosmic ray transport equation. For experimental spectra, the calculation of the model parameters is performed by Levenberg–Marquardt algorithm, applied to the special case of least squares. Algorithm that combines the rapid local convergence of Newton–Raphson method with globally convergent method for non-linear systems of equations is applied for theoretically obtained differential spectra. The described programmes are realized in algorithmic language C++. The proposed model gives practical possibility for investigation of experimental data from measurements of galactic cosmic rays and their anomalous component.