Interactions between magnetic fields advected by matter play a fundamental role in the Universe at all possible scales. A crucial role these interactions play is in making turbulent fields highly anisotropic, leading to observed ordered fields. These in turn, are important evolutionary factors for all the systems within and around. Despite scant evidence, due to the difficulty in measuring even near-Earth events, the magnetic field compression factor in these interactions, measured at very varied scales, is limited to a few. However, compressing matter in which a magnetic field is embedded, results in compression up to several thousands. Here we show, using laboratory experiments and matching three-dimensional hybrid simulations, that there is indeed a very effective saturation of the compression when two independent magnetic fields are advected by plasmas encounter. We found that the observed saturation is linked to a build-up of the magnetic pressure at the inflows encounter point, which decelerates them and thereby stops further compression. Moreover, the growth of an electric field, induced by the incoming flows and the magnetic field, acts in redirecting the inflows transversely, further hampering field compression.
