This presentation reviews the results of the Author's ongoing systematic study [1,2,3] concerned with the effects of magnetic field instabilities on various types of NMR signals and on derived NMR data. Despite the pronounced practical impact of this topic, its mathematical aspects have been so far somewhat neglected.
Magnetic field noise arises in practice from many sources, including the magnet system (materials, current generators and stabilizers, field stabilizer, NMR lock system), the NMR instrument (power wiring, transformers) and the enviromental (site-dependent!) magnetic noise (electric wiring, motors, transformers, mains stabilizers, air-conditioning, etc.). Some of the field-noise components are nearly a-periodic (white noise), while others are characterized by frequencies which are multiples of the mains frequency. Quasi-periodic field fluctuations also need to be taken into account (consider, for example, the techniques employing sample rotation).
It is important to understand that a noiseless field is a theoretical chimera which, like unicorns, does not exist in Nature!
As a stochastic phenomenon, field noise can be characterized by its auto-correlation function - an approach which unifies the treatement of its stochastic and periodic components. The essence of this study is finding out the correspondence between the field-noise autocorrelation function and the way it affects various NMR signals.
Even in the simplest case of plain FID's, the presence of field noise leads to a multitude of observable effects with well defined features. One can analyse statistics for the effects of field noise on single-scan features (such as spectral-band positions, heights and shapes) as well as those on accumulated data. The latter turn out to be equivalent to multiplying the FID by a well-defined, though definitely non-trivial, weighing function.
Very interesting is the effect of field noise on spin echos. This part of the work is directly pertinent to all multi-pulse NMR techniques which employ refocusing pulse sequence intervals (all 2D and 3D spectroscopy techniques and most MRI methods). Particularly dramatic may be the effects of periodic field fluctuations on data acquired using long, periodic trains of pulses (such as CPMG). In these cases one can occasionally witness disastrous resonance artifacts  whose complex nature is now finally well understood.
We shall also discuss the t1-noise artifacts in multi-dimensional NMR spectroscopies. In practice, t1-noise is almost totally due to the magnetic field noise and the present theory explains all its characteristic properties.
- S. Sykora, Field noise effects on NMR signals: FID's and 1D spectra, to be published.
- S. Sykora, Field noise effects on NMR signals: Hahn echos and CPMG, to be published.
- S. Sykora, Field noise effects on NMR signals: t1-noise in 2D spectra, to be published.
- A.Allerhand, Effect of Magnetic Field Fluctuations in Spin-Echo NMR Experiments, Rev.Sci.Instr. 41, 269 (1970).