The invariant polarisation-tensor field for deuterons in storage rings and the Bloch equation for the polarisation-tensor density

TL;DR

This paper extends the concept of the invariant polarisation-tensor field for deuterons in storage rings, providing a comprehensive framework for equilibrium spin ensembles, including construction methods, examples, and effects of noise and damping.

Contribution

It introduces an updated formalism for the invariant polarisation-tensor field, complementing the invariant spin field, and discusses its construction, properties, and effects in storage rings.

Findings

Construction of the ITF via stroboscopic averaging

Examples illustrating the ITF in practice

Formalism for noise and damping effects

Abstract

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.