Optimizing Sudden Passage in the Earth's-Field NMR Technique

Abstract

The equation of motiondM/dt= γM × B(t) is solved numerically for the case B(t) = jB_p(t) + kB_e. The fieldB_eis a small static field, typically the earth's field. The fieldB_p(t) is a damped oscillation having frequency greater than, or on the order of, the precession frequency in fieldB_e. Such oscillation inevitably occurs at the end of the rapid cutoff of the coil current used to polarize the sample. It is assumed thatB_p(t) is initially large compared toB_e, and that magnetization M is initially along the resultant field B. This is the usual situation in the earth's-field NMR technique when the polarizing field is produced by a coil of moderate to high impedance. It is shown that, when properly damped, the transient can be used to restore the magnetization to thex–yplane, thereby maximizing the amplitude of the subsequent free precession signal. The damping required is close to critical damping, so that the problem of circuit ringing when the coil is switched to receiver mode is also eliminated.