  Regarding the Skyrme-Faddeev model on $\mathbb R^3$ as a $\mathbb C \mathbb
P^1$ sigma model, we propose $\mathbb C \mathbb P^n$ sigma models on $\mathbb
R^{2n+1}$ as generalisations which may support finite energy Hopfion solutions
in these dimensions. The topological charge stabilising these field
configurations is the Chern-Simons charge, namely the volume integral of the
Chern-Simons density which has a local expression in terms of the composite
connection and curvature of the CP^n field. It turns out that subject to the
sigma model constraint, this density is a total divergence. We prove the
existence of a topological lower bound on the energy, which, as in the
Vakulenko-Kapitansky case in R^3, is a fractional power of the topological
charge, depending on $n$. The numerical construction of the simplest ring
shaped un-knot Hopfion on R^5 is also discussed.
