A Multiple-Narrow-Pulse Approximation for Restricted Diffusion in a Time-Varying Field Gradient

Abstract

Analytical expressions for the NMR signal of an ensemble of spins diffusing in a bounded medium in the presence of a magnetic field gradient exist only in the limit of gradient pulses so short that no diffusion takes place during them. The temporal behavior of any gradient pulse is approximated by a sum of impulses, each being in the narrow-gradient-pulse limit. This approximate, analytical solution for the echo attenuation due to restricted diffusion between two parallel plates with reflecting boundaries in the presence of nonnarrow gradient pulses agrees with that from numerical simulations by Blees [J. Magn. Reson. A109,203 (1994)].