Performance of the cross-polarization experiment in conditions of radiofrequency field inhomogeneity and slow to ultrafast magic angle spinning (MAS).

In this paper, we provide an analytical description of the performance of the cross-polarization (CP) experiment, including linear ramps and adiabatic tangential sweeps, using effective Hamiltonians and simple rotations in 3D space. It is shown that radiofrequency field inhomogeneity induces a reduction in the transfer efficiency at increasing magic angle spinning (MAS) frequencies for both the ramp and the adiabatic CP experiments. The effect depends on the ratio of the dipolar coupling constant and the sample rotation frequency. In particular, our simulations show that for small dipolar couplings (1 $\mathrm{kHz}$) and ultrafast MAS (above 100 $\mathrm{kHz}$) the transfer efficiency is below 40 % when extended contact times up to 20 $\mathrm{ms}$ are used and relaxation losses are ignored. New recoupling and magnetization transfer techniques that are designed explicitly to account for inhomogeneous radiofrequency fields are needed.