  Aims. We seek to understand convection in red supergiants and the mechanisms
that trigger the mass loss from cool evolved stars. Methods. Linear
spectropolarimetry of the atomic lines of the spectrum of $\mu$ Cep reveals
information well outside the wavelength range expected from previous models.
This is interpreted as structures in expansion that are visible in the front
hemisphere and sometimes also in the back hemisphere. We model the plasma
distribution together with its associated velocities through an inversion
algorithm to fit the observed linear polarization. Results. We find that
supposing the existence of plasma beyond the limb rising high enough to be
visible above it can explain the observed linear polarization signatures as
well as their evolution in time. From this we are able to infer the geometric
heights of the convective plumes and establish that this hot plasma rises to at
least 1.1 R*. Conclusions. $\mu$ Cep appears to be in an active phase in which
plasma rises often above 1.1 R* . We generalize this result to all red
supergiants in a similarly evolved stage, which at certain epochs may easily
send plasma to greater heights, as $\mu$ Cep appears to be doing at present.
Plasma rising to such heights can easily escape the stellar gravity.
