  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.
