  The use of liquid metal batteries is considered as one promising option for
electric grid stabilisation. While large versions of such batteries are
preferred in view of the economies of scale, they are susceptible to various
magnetohydrodynamic instabilities which imply a risk of short-circuiting the
battery due to the triggered fluid flow. Here we focus on the current driven
Tayler instability and give critical electrical currents for its onset as well
as numerical estimates for the appearing flow structures and speeds. Scaling
laws for different materials, battery sizes and geometries are found. We
further discuss and compare various means for preventing the instability.
