Dynamics of the Time Dependent Bloch NMR Equations For Complex rF B1(t) Magnetic Field

Abstract

This study examines the dynamical changes produced by a complex time-dependent rF B1(t) magnetic field in an initially unperturbed magnetic resonance system. The analysis uses the Green's function algorithm as a tool to solve the transverse component of the time-dependent Bloch NMR equations with complex rF B1(t) field. The time development of the system is studied in the Hersenberg picture in which the operators are subject to unitary transformation as the applied rF B1(t) field changes the state of the NMR system from its initial ground state into another coherent state. The detailed features of the rF B1(t) field essentially affect the evolution of the state during its application. The state of the system after the complete cessation of the radio-frequency field is determined exclusively by a Fourier component which is in resonance with the NMR system. The unitary operator allows us to determine all the physically relevant information about the system in terms of a NMR relaxation parameter.