Most studies of GeV Galactic Cosmic Rays (GCR) nuclei assume a steady
state/continuous distribution for the sources of cosmic rays, but this
distribution is actually discrete in time and in space. The current progress in
our understanding of cosmic ray physics (acceleration, propagation), the
required consistency in explaining several GCRs manifestation (nuclei,
γ,...) as well as the precision of present and future space missions
(e.g. INTEGRAL, AMS, AGILE, GLAST) point towards the necessity to go beyond
this approximation. A steady state semi-analytical model that describes well
many nuclei data has been developed in the past years based on this
approximation, as well as others. We wish to extend it to a time dependent
version, including discrete sources. As a first step, the validity of several
approximations of the model we use are checked to validate the approach: i) the
effect of the radial variation of the interstellar gas density is inspected and
ii) the effect of a specific modeling for the galactic wind (linear vs
constant) is discussed. In a second step, the approximation of using continuous
sources in space is considered. This is completed by a study of time
discreteness through the time-dependent version of the propagation equation. A
new analytical solution of this equation for instantaneous point-like sources,
including the effect of escape, galactic wind and spallation, is presented.
Application of time and space discretness to definite propagation conditions
and realistic distributions of sources will be presented in a future paper.Comment: final version, 8 figures, accepted in ApJ. A misprint in fig 8 labels
has been correcte