  We present the results of a field theory simulation of networks of strings in
the Abelian Higgs model. Starting from a random initial configuration we show
that the resulting vortex tangle approaches a self-similar regime in which the
length density of lines of zeros of $\phi$ reduces as $t^{-2}$. We demonstrate
that the network loses energy directly into scalar and gauge radiation. These
results support a recent claim that particle production, and not gravitational
radiation, is the dominant energy loss mechanism for cosmic strings. This means
that cosmic strings in Grand Unified Theories are severely constrained by high
energy cosmic ray fluxes: either they are ruled out, or an implausibly small
fraction of their energy ends up in quarks and leptons.
