The stability of tokamaks and astrophysical objects like accretion disks about black holes or galactic plasmas can be described from one point of view, namely magneto-hydrodynamics (MHD). This stunning fact is due to the scale independence of the MHD equations, which thus provides an extremely powerful tool to deal with the abundant presence of plasma in the Universe.

Not surprisingly though, the different origins of the two kinds of confined plasmas result in very different physical systems. Tokamaks are engineered to eventually yield fusion power, with the plasma held together by magnetic forces that are balanced by mechanical forces on the induction coils that have to be firmly fixed to the building. On the other hand, in accretion disks, the birth places of stars and stellar systems, the plasmas are held together against centrifugal acceleration by the gravitational pull of the central compact object.

I will demonstrate how ‘intuition’ on stability obtained from tokamaks and blindly applied to astrophysical systems leads to paradoxes that are only resolved, and thus provide for a fruitful interaction between the two research communities, when the different effects of magnetic fields, rotation and gravity on plasma confinement are accounted for.