Résumé
In this work we investigate the shape of the spectrum of cosmic ray (CR) protons produced inside superbubbles (SB), by the means of a simple semi-analytical model of CR production and transport embedded inside Monte-Carlo simulations of OB associations timelines. We consider regular acceleration (Fermi I process) at the shock front of supernova remnants (SNRs), as well as stochastic re-acceleration (Fermi II process) and escape controlled by magnetic turbulence inside the SB. In this first attempt we limit ourselves to linear acceleration by strong shocks and neglect protons energy losses. We observe that CR spectra, although strongly intermittent, get a distinctive shape resulting from a competition between acceleration and escape: they are harder at the lowest energies (slope s < 4) and softer at the highest energies (s > 4). The momentum at which this spectral break occurs depends critically on the various SB parameters - but interestingly all their effects can be summarized by a single dimensionless parameter. For reasonable values of SB parameters, and especially for highly magnetized and turbulent SBs, very hard spectra can be obtained over an important range of CR. energies, which has important implications on the high-energy emission from these objects.