Shimming systems are required to provide sufficient field homogeneity for high resolution nuclear magnetic resonance (NMR). In certain specialized applications, such as rotating-field NMR and mobile ex situ NMR, permanent magnet-based shimming systems can provide considerable advantages. We present a simple two-dimensional shimming method based on harmonic corrector rings which can provide arbitrary multipole order shimming corrections. Results demonstrate, for example, that quadrupolar order shimming improves the linewidth by up to an order of magnitude. An additional order of magnitude reduction is in principle achievable by utilizing this shimming method for z-gradient correction and higher order xy gradients.
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