The potential role of magnetic fields and cosmic ray propagation for feedback processes in the early Universe can be probed by studies of local starburst counterparts with an equivalent star-formation rate. In order to study the cosmic ray propagation and determine the magnetic field strength and dominant loss processes in the nearby prototypical starbursting galaxy M82, a multi-frequency analysis at four radio wavelengths is presented. We find that the radio emission from the core region is dominated by very dense H-regions and supernova remnants, while the surrounding medium is filled with hot X-ray and neutral gas. Cosmic rays radiating at frequencies higher than 1.4 GHZ suffer from high synchrotron and inverse Compton losses in the core region and are not able to reach the halo. These findings, together with the strong correlation between H alpha ionised polycyclic aromatic hydrocarbons (PAHsup +), and our radio continuum data, suggest a magnetic field which is frozen into the ionised medium and driven out of the galaxy kinematically.