Analysis and Simulation of the Propagation of Cosmic Rays in the Fractal and Homogeneous Galactic Medium

The energy spectrum of cosmic rays exhibits a power-law distribution, meaning there are more particles at lower energies and fewer particles at higher energies. There is a feature known as the knee at about 3×1015eV in the energy spectrum of cosmic rays, and there is another feature called the ankle at about 1018eV. There are several models to explain the knee and ankle features in the energy spectrum of cosmic rays, such as, shock acceleration model, which suggests that the knee may be arise from the maximum energy that can be achieved through shock waves produced by supernova explosions, extragalactic sources model, which suggests that the ankle may be arise from the extremely energetic astrophysical sources outside our galaxy, and the propagation models, that we focus on in this research. Cosmic ray propagation has usually been assumed to be in a form of normal diffusion, which is a diffusion process with a linear relationship to time. But, in anomalous diffusion, the mean squared displacement of a particle has a non-linear relationship to time. In this research, we investigate the propagation of cosmic rays in the galactic medium. First, we simulate the trajectory of cosmic rays with the energy of 1017eV from the galactic center in two models of diffusion to show the differences between propagation in the homogeneous and fractal galactic medium. Simulations show that cosmic ray propagation in the galactic medium gives a greater galactic residence time and energy density for normal diffusion particles compared to anomalous diffusion particles. Here, the program, that is applied in this research, presents the results of a simulation using a model of the galactic magnetic field appropriate to the related medium. It uses the technique described in Clay et al. (2000) and Clay (2002). Normal cosmic ray diffusion assumes very simple properties of the structure of cosmic magnetic fields. A better approximation is to assume that the magnetic structure has fractal properties when modelling the propagation. Later, residence times of cosmic rays on a wide range of energy spectrum in the anomalous diffusion model are found. Results can correspond to Lagutin’s point of view saying that the “knee” in the cosmic ray spectrum is the consequence of anomalous diffusion of the particles in the fractal galactic medium (Lagutin et al., 2001b). In other words, the “knee” may be caused by the extensive distances that cosmic ray particles can travel between inhomogeneities of magnetic fields and from the fact that a particle stays in a magnetic trap for a long time. Our study is useful for understanding the possibility that some spectral features (the knee and the ankle) of the spectrum of cosmic rays observed at Earth are induced by the fractal nature of the galactic medium.