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

TL;DR

This paper uses optimal control theory to design minimal energy pulses for Bloch equations under dominant transverse relaxation, providing analytical formulas for pulse energy and duration.

Contribution

It introduces a novel application of Pontryagin's Maximum Principle to derive explicit optimal pulses in a specific relaxation regime.

Findings

Derived analytical expressions for pulse energy and duration.

Established an optimal feedback law for pulse design.

Focused on the case where transverse relaxation dominates.

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.