A SIMPLE RELATIONSHIP BETWEEN TOTAL RF PULSE ENERGY AND MAGNETIZATIONRESPONSE - THE NONLINEAR GENERALIZATION OF PARSEVALS RELATION

A simple expression for the total energy of an RF pulse is given in te rms of the magnetization response of the pulse. It is shown to be a no nlinear generalization of Parseval's relation and is one of an infinit e number of conserved quantities, or integrals of the motion, found in the theory of nonlinear evolution equations. The simplicity of this e xpression enables the statement of a straightforward criterion for pul ses that must have their energy reduced. It also allows the proof of s ome important theorems in pulse theory, including the known result tha t minimum-phase pulses are minimum energy pulses, and the previously u nknown result that B-1-insensitive pulses must induce (possibly improp er) bound states. A comparison of the energy require ments of minimum- phase and self-refocused pulses is given. Further, ''Butteworth'' puls es are compared to ''Chebyshev I'' pulses and found to require more en ergy in general. (C) 1995 Academic Press, Inc.