  Work within this thesis advances optimal control algorithms for application
to magnetic resonance systems. Specifically, presenting a quadratically
convergent version of the gradient ascent pulse engineering method. The work is
formulated in a superoperator representation of the Liouville-von Neumann
equation.
  A Newton-grape method is developed using efficient calculation of analytical
second directional derivatives. The method is developed to scale with the same
complexity as methods that use only first directional derivatives.
  Algorithms to ensure a well-conditioned and positive definite matrix of
second directional derivatives are used so the sufficient conditions of
gradient-based numerical optimisation are met.
  A number of applications of optimal control in magnetic resonance are
investigated: solid-state nuclear magnetic resonance, magnetisation-to-singlet
pulses, and electron spin resonance experiments.
