Higher approximations in the theory of the average Hamiltonian

The canonical variant of the Krilov–Bogolyubov–Mitropolskii method of averaging is used to consider the higher approximations in the theory of the average Hamiltonian describing the evolution of a spin system under the influence of a pulse sequence. The use of the method of averaging in the resonance case is considered for the example of the pulse sequence $90_y-(\tau-\varphi_x-\tau)^n$. For spin systems with Suhl–Nakamura interaction, two cases are investigated when it is necessary to take into account the higher orders of the theory of the average Hamiltonian. The possibility of effective NMR line narrowing in such a situation is demonstrated.