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Swept-frequency pulses have found applications in a wide range of areasincluding spectroscopic techniques where efficient control of spins isrequired. For many of these applications, a good understanding of the evolutionof spin systems during these pulses plays a vital role, not only in describingthe mechanism of techniques, but also in enabling new methodologies. Inmagnetic resonance spectroscopy, broadband inversion, refocusing, andexcitation using these pulses are among the most used applications in NMR, ESR,MRI, and $in$ $vivo$ MRS. In the present survey, a general expression forchirped pulses will be introduced, and some numerical approaches to calculatethe spin dynamics during chirped pulses via solutions of the well-knownLiouville-von Neumann equation and the lesser-explored Wei-Norman Lie algebraalong with comprehensive examples are presented. In both cases, spin statetrajectories are calculated using the solution of differential equations.Additionally, applications of the proposed methods to study the spin dynamicsduring the PSYCHE pulse element for broadband homonuclear decoupling and theCHORUS sequence for broadband excitation will be presented.

Spin dynamics during chirped pulses: applications to homonuclear decoupling and broadband excitation