  We present a complete and consistent theory of vector radially
self-accelerating beams (RSABs). We use this theory as a model for describing
the properties of focussed RSABs, and to show, in particular, that only
circular polarised RSABs maintain their self-accelerating character upon
focussing. Moreover, we also calculate the linear and angular momentum for
paraxial vector RSABs, and discuss both their global and local properties.
