We investigate the process of particle acceleration at the termination shock that develops in the bubble excavated by star clusters’ winds in the interstellar medium. We develop a theory of diffusive shock acceleration at such shock and we find that the maximum energy may reach the PeV region for very powerful clusters.
We show how the maximum energy is limited by two different processes: the particle escape from the bubble boundary and the drop of energy gain for particles able to diffuse up to the center of the cluster.
A crucial role in this problem is played by the dissipation of kinetic energy of the wind to magnetic perturbations. Under reasonable conditions the spectrum of the accelerated particles has a power law shape in momentum with a slope 4.0-4.3, in agreement with what is required based upon standard models of cosmic ray transport in the Galaxy.