title: Restricted diffusion in grossly inhomogeneous fields.
abstract: We analyze the effects of geometrical restriction on the nuclear magnetization of spins diffusing in grossly inhomogeneous fields where radio-frequency (RF) pulses are weak relative to the total field inhomogeneity, making the rotation angle space-dependent and thus exciting multiple coherence pathways. We show how to separate the effects of restricted diffusion from the effects of the pulses in the case when the change in the field experienced by a diffusing spin in the course of the experiment is small compared to the RF magnitude. We then derive explicit formulas for the contribution of individual coherence pathways to the total magnetization in arbitrary pulse sequences. We find that, for long diffusion times, restriction can dramatically alter the spectrum and the shape of a particular echo, while for short times, the correction will be proportional to the pore space surface-to-volume ratio. We demonstrate these results on the example of the early echoes of the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence.
authors.affiliation: Schlumberger-Doll Research, 36 Old Quarry Road, Ridgefield, CT 06877-4108, USA. lzielinski@ridgefield.oilfield.slb.com
authors.forename: Lukasz J
authors.initials: LJ
authors.lastname: Zielinski
authors.forename: Pabitra N
authors.initials: PN
authors.lastname: Sen