We develop the first fully three dimensional model describing the diffusion of cosmic rays in the Milky Way, which considers that most cosmic ray acceleration takes place in the galactic spiral arms and that these spiral arms are dynamic. The model includes the nuclear spallation chain up to Oxygen. With the model, we study different cosmic ray properties, such as their age, grammage traversed, and the ratio between secondary cosmic rays produced along the way and primary cosmic rays accelerated at the sources (in particular, the B/C ratio).

We show that the effect of having dynamic spiral arms is to limit the age of cosmic rays at low energies. This is because the age at low energies is determined by the time since the last spiral arm passage and not by their diffusion time. Using this model, the observed spectral dependence of the secondary to primary ratio is recovered without requiring any further assumptions such as having a galactic wind, re-acceleration or ad hoc assumptions on the diffusivity. In particular, we obtain a secondary to primary ratio which increases with energy below about 1 GeV, and explain the previously obtained ``discrepancy" between the sub-Fe/Fe ratio and the B/C, which manifests itself as an apparent paucity in short paths in standard models.