  I extend and update earlier work, summarised in [1], whereby the invariant
polarisation-tensor field (ITF) for deuterons in storage rings was introduced
to complement the invariant spin field (ISF). Taken together, the ITF and the
ISF provide a definition of the equilibrium spin density-matrix field which, in
turn, offers a clean framework for describing equilibrium spin-1 ensembles in
storage rings. I show how to construct the ITF by stroboscopic averaging, I
give examples, I discuss adiabatic invariance and I introduce a formalism for
describing the effect of noise and damping.
