Simulation of nuclear magnetic resonance spin echoes using the Bloch equation: Influence of magnetic field inhomogeneities

There are a number of low cost nuclear magnetic resonance (NMR) applications that are based on measurements of spin-spin (T2) and spin-lattice (T1) relaxation times. Pulsed rf magnetic fields are typically used to flip the nuclear spins in these measurements. The ability to perform these measurements in relatively nonuniform magnetic fields is a factor in minimizing costs. In this work, we explore the limitations of field inhomogeneity on spin echo techniques for measuring relaxation times. Using a computer model that was developed for this study, we numerically integrate the Bloch equation to simulate spin echo peaks for CPMG and other pulse sequences. We quantify how higher intensity rf pulses result in increased amplitudes of spin echo peaks in an inhomogeneous static magnetic field. An rf amplitude which is five times the maximum inhomogeneity in the static field results in less than 0.5% attenuation between even numbered peaks in a CPMG sequence.