Résumé
Recent spectropolarimetric observations of the giant star Pollux have revealed that it possesses a weak global magnetic field of the order of a Gauss. Using 3-D nonlinear MHD simulations performed with the ASH code we study the source of this global magnetic field in this slowly rotating giant star (Omega*=Omega_sun/20). We find that the extended convective envelope is able to generate a multi-scales magnetic field reaching of the order of 10% of the kinetic energy contained in the envelope. This global field acts such as to suppress the strong differential rotation present in the purely hydrodynamical progenitor simulation. When filtering the large scale magnetic field components (dipole, quadrupole) we find magnetic field of the order of a few Gauss, hence in qualitative agreeement with observations. Our study confirms that such slowly rotating convective giants are likely to possess global magnetic field maintained through contemporaneous dynamo action and not as the vestige of their past main sequence activity.