  We consider the persistent currents induced by an artificial gauge field
applied to interacting ultra-cold bosonic atoms in a tight ring trap. Using
both analytical and numerical methods, we study the scaling of the persistent
current amplitude with the size of the ring. In the strongly interacting regime
we find a power-law scaling, in good agreement with the predictions of the
Luttinger-liquid theory. By exploring all interaction regimes we find that the
scaling is optimal, i.e. the current amplitude decreases slower with the system
size, at intermediate interactions.
