Radiation from Global Topological Strings using Adaptive Mesh
  Refinement: Methodology and Massless Modes
  We implement adaptive mesh refinement (AMR) simulations of global topological
strings using the public numerical relativity code, GRChombo. We perform a
quantitative investigation of the dynamics of single sinusoidally displaced
string configurations, studying a wide range of string energy densities $\mu
\propto \ln{\lambda}$, defined by the string width parameter $\lambda$ over two
orders of magnitude. We investigate the resulting massless (Goldstone boson or
axion) radiation signals, using quantitative diagnostic tools to determine the
eigenmode decomposition. Given analytic radiation predictions, we compare the
oscillating string trajectory with a backreaction model accounting for
radiation energy losses, finding excellent agreement. We establish that
backreaction decay is accurately characterised by the inverse square of the
amplitude being proportional to the inverse tension $\mu$ for $3\lesssim
\lambda \lesssim 100$. We conclude that analytic radiation modelling in the
thin-string (Nambu-Goto) limit provides the appropriate cosmological limit for
global strings. We contextualise these results with respect to axions and
gravitational waves produced by cosmic string networks.
