  We compute the production of cosmic rays in the dynamical superbubble
produced by a cluster of massive stars. Stellar winds, supernova remnants and
turbulence are found to accelerate particles so efficiently that the nonlinear
feedback of the particles must be taken into account in order to ensure that
the energy balance is not violated. High energy particles do not scatter
efficiently on the turbulence and escape quickly after each supernova
explosion, which makes both their intensity inside the bubble and injection in
the interstellar medium intermittent. On the other hand, the stochastic
acceleration of low energy particles hardens the spectra at GeV energies.
Because cosmic rays damp the turbulence cascade, this hardening is less
pronounced when nonlinearities are taken into account. Nevertheless, spectra
with hard components extending up to 1 to 10 GeV and normalised to an energy
density of 1 to 100 eV cm$^{-3}$ are found to be typical signatures of cosmic
rays produced in superbubbles. Efficient shock reacceleration within compact
clusters is further shown to produce hard, slightly concave spectra, while the
presence of a magnetised shell is shown to enhance the confinement of cosmic
rays in the bubble and therefore the collective plasma effects acting on them.
We eventually estimate the overall contribution of superbubbles to the galactic
cosmic ray content and show typical gamma-ray spectra expected from hadronic
interactions in superbuble shells. In both cases, a qualitative agreement with
observations is obtained.
