  We report on the energy-momentum correlators obtained with recent numerical
simulations of the Abelian Higgs model, essential for the computation of cosmic
microwave background and matter perturbations of cosmic strings. Due to
significant improvements both in raw computing power and in our parallel
simulation framework, the dynamical range of the simulations has increased
four-fold both in space and time, and for the first time we are able to
simulate strings with a constant physical width in both the radiation and
matter eras. The new simulations improve the accuracy of the measurements of
the correlation functions at the horizon scale and confirm the shape around the
peak. The normalization is slightly higher in the high wave-number tails, due
to a small increase in the string density. We study for the first time the
behaviour of the correlators across cosmological transitions, and discover that
the correlation functions evolve adiabatically, ie the network adapts quickly
to changes in the expansion rate. We propose a new method for constructing
source functions for Einstein-Boltzmann integrators, comparing it with two
other methods previously used. The new method is more consistent, easier to
implement, and significantly more accurate.
