The magnetostatic mode (MSM) spectrum of a 300$mu$m diameter single crystalline sphere of yttrium iron garnet is investigated using broadband ferromagnetic resonance (FMR). The individual MSMs are identified via their characteristic dispersion relations and the corresponding mode number tuples $(nmr)$ are assigned. Taking FMR data over a broad frequency and magnetic field range allows to analyze both the Gilbert damping parameter~$alpha$ and the inhomogeneous line broadening contribution to the total linewidth of the MSMs separately. The linewidth analysis shows that all MSMs share the same Gilbert damping parameter $alpha=2.7(5) times 10^{-5}$ irrespective of their mode index. In contrast, the inhomogeneous line broadening shows a pronounced mode dependence. This observation is modeled in terms of two-magnon scattering processes of the MSMs into the spin-wave manifold, mediated by surface and volume defects.
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