Cosmic-Ray Spectrum Approximation Model: Experimental Results and Comparison with Other Models

We discuss a model which parameterizes the cosmic-ray (CR) spectrum at different physical conditions, which include the most important effects controlling the CR intensity, like convection–diffusion and energy losses. By a suitable choice of parameters the proposed model results in two approximations: one close to a “force–field” model (describing the energy losses of CRs in the inner heliosphere) and a “convection–diffusion” equation (giving the reduction of CR intensity in the outer heliosphere). The BESS (Balloon-borne Experiment with Superconducting Spectrometer) experimental spectra of galactic protons and helium nuclei are fitted by the model spectra. The calculation of the unknown parameters is performed using a constrained least squares method as an alternative to the standard chi-square minimization method, because the data contain not only random errors, but also systematic ones. The CR spectrum approximation (CRSA) model is compared to the Moscow State University (MSU) model and the Badhwar and O’Neill (Badhwar and O’Neill, Adv. Space. Res. 14, 749, 1994; Adv. Space Res. 17, 7, 1994) model; we show that depending on the choice of the model parameters it can be examined in the context of one of these two models. We derive a relation between the parameters of the CRSA and MSU models for rigidities above about 10 GV (drift effects are ignored) during periods of low to approximately average levels of solar activity. The drawbacks of the proposed approximation are that: i) the model parameters do not depend on rigidity and ii) the model does not take into account general trends in the variations of the heliospheric magnetic field; thus, the influence of the drift effects on the shape of the spectral curves for different magnetic field polarity swings is ignored.