Amplitude modulation and relaxation due to diffusion in NMR experiments with a rotating sample

The simultaneous effects of diffusion and coherent averaging by magic angle sample spinning (MASS) are investigated both theoretically and experimentally for spins diffusing in a spatially varying susceptibility field. The diffusion introduces a periodic modulation and a relaxation of the magnetization amplitude. The attenuation exponent for the nth echo at an early time is given by D0γ2g2πn/(4ωr3), where ωr is the rotor frequency, D0 the diffusion coefficient, γ is the gyromagnetic factor, and a factor g2 which is related to, but different from, the volume average of the gradient squared.