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We implement adaptive mesh refinement (AMR) simulations of global topological strings using the public code, GRChombo. We perform a quantitative investigation of massive radiation from single sinusoidally displaced string configurations, studying a range of string widths defined by the coupling parameter $λ$ over two orders of magnitude, effectively varying the mass of radiated particles $m_H \sim \sqrtλ$. We perform an in-depth investigation into the effects of AMR on massive radiation emission, including radiation trapping and the refinement required to resolve high frequency modes. We use quantitative diagnostic tools to determine the eigenmode decomposition, showing a complex superposition of high frequency propagating modes with different phase and group velocities. We conclude that massive radiation is generally strongly suppressed relative to the preferred massless channel, with suppression increasing at lower amplitudes and higher $λ$. Only in extreme nonlinear regimes (e.g.\ with relative amplitude $\varepsilon \sim 1.5$ and $λ< 1$) do we observe massive and massless radiation to be emitted at comparable magnitude. We find that massive radiation is emitted in distinct high harmonics of the fundamental frequency of the string, and we demonstrate that, for the sinusoidal configurations studied, massive radiation is exponentially suppressed with $\sqrtλ$ (i.e. the particle mass). Finally, we place these results in the context of axions and gravitational waves produced by cosmological cosmic string networks, and note that AMR provides a significant opportunity to explore higher $λ$ (thin string) regimes whilst using fewer computational resources.