Spin dynamics of Carr-Purcell-Meiboom-Gill-like sequences in grossly inhomogeneous B-0 and B-1 fields and application to NMR well logging

The spin dynamics for Carr-Purcell-Meiboom-Gill-like sequences is analyzed in grossly inhomogeneous B-0 and B-1 fields. This problem is important for many applications, especially when the bandwidth of the signal is excitatio n limited. Examples include stray-held NMR or inside-out NMR probes used in well logging. The amplitudes of the first few echoes exhibit a characteris tic transient behavior but quickly approach a smooth asymptotic behavior. F or simple Hamiltonians without scalar or dipolar couplings, the evolution o f a refocusing subcycle for a given isochromat is described by a rotation. Simple expressions for the signal of the Nth echo are derived in terms of t hese effective rotations that have a simple geometrical interpretation. It is shown that the asymptotic behavior is controlled by the direction of the axis of these effective rotations and the signal is dominated by magnetiza tion "spin-locked" to the rotation axis. The phase of the signal is indepen dent of the details of the held inhomogeneities. Relaxation in inhomogeneou s fields leads to a signal decay that is in general nonexponential with an initial decay rate that is a weighted sum of T-1(-1) and T-2(-1). At long t imes, the echo amplitudes decay to a finite value. Phase cycling eliminates this offset. The effect of diffusion is also studied. This analysis has be en applied to an inside-out NMR well logging apparatus. Good quantitative a greement is found between measurements and calculations that are based on t he measured B-0 and B-1 field maps. (C) 2000 Academic Press.