Figure 1.

(a) Coil geometry of a typical 3.2  $\mathrm{mm}$ Bruker MAS probe. The position within the sample space is indicated by the cylindrical coordinates $r$ , $z$ , and $\mathit{\vartheta }$ . (b) Spatial rf field distributions for typical probe designs with MAS rotors of 3.2, 1.9, and 1.3  $\mathrm{mm}$ outer diameter at a frequency of 600  $\mathrm{MHz}$ . Relative rf amplitudes ${\mathit{\omega }}_{\mathrm{rel}}$ and phases ${\mathit{\varphi }}_{\mathrm{rel}}$ are shown as a function of the position within the active sample volume for $\mathit{\vartheta }=\mathrm{90}{}^{\circ }$ . The length and position of the solenoid coil is indicated by dashed lines. (c) Parameters of coil geometries of the 3.2, 1.9, and 1.3  $\mathrm{mm}$ MAS probes considered in this work. The $z$ values were sampled in steps of 0.05  $\mathrm{mm}$ for all three probes. The $r$ values were sampled in steps of 0.05  $\mathrm{mm}$ for the 3.2 and the 1.9  $\mathrm{mm}$ probes and in steps of 0.025  $\mathrm{mm}$ for the 1.3  $\mathrm{mm}$ probe. The sample volume considered in the numerical simulations and Floquet analyses presented in Sect.  was restricted to the length of the coil.