Numerical propagation of high energy cosmic rays in the Galaxy I: technical issues

We present the results of a numerical simulation of propagation of cosmic rays with energy above $10^{15}$ eV in a complex magnetic field, made in general of a large scale component and a turbulent component. Several configurations are investigated that may represent specific aspects of a realistic magnetic field of the Galaxy, though the main purpose of this investigation is not to achieve a realistic description of the propagation in the Galaxy, but rather to assess the role of several effects that define the complex problem of propagation. Our simulations of Cosmic Rays in the Galaxy will be presented in Paper II. We identified several effects that are difficult to interpret in a purely diffusive approach and that play a crucial role in the propagation of cosmic rays in the complex magnetic field of the Galaxy. We discuss at length the problem of the extrapolation of our results to much lower energies where data are available on the confinement time of cosmic rays in the Galaxy. The confinement time and its dependence on particles' rigidity are crucial ingredients for 1) relating the source spectrum to the observed cosmic ray spectrum; 2) quantifying the production of light elements by spallation; 3) predicting the anisotropy as a function of energy.