Optimal Design of Minimum Energy Pulses for Bloch Equations in the case of Dominant Transverse Relaxation.

link: http://arxiv.org/abs/0908.3167
Abstract

In this report, we apply Optimal Control Theory to design minimum energy
$\pi/2$ and $\pi$ pulses for Bloch equations, in the case where transverse
relaxation rate is much larger than longitudinal so the later can be neglected.
Using Pontryagin's Maximum Principle, we derive an optimal feedback law and
subsequently use it to obtain analytical expressions for the energy and
duration of the optimal pulses.