  In this exposition, we propose a notion of rank and rigidity of locally
nilpotent derivations of affine fibrations. We show that the concept is
analogous to the perception of rank and rigidity of locally nilpotent
derivations of polynomial algebras. Our results characterize locally nilpotent
derivations of $\mathbb{A}^3$-fibrations having slice by classifying the fixed
point free locally nilpotent derivations in terms of their ranks.
