Abstract: A method of NMR (nuclear magnetic resonance) excitation of a sample having a magnetic moment, including, applying a longitudinal magnetic field to the sample; and changing the magnetic moment in a substantially continuous manner by moving an effective magnetic-field vector &ohgr;e more than 90°, wherein for all portions of the sample in which the moment is changed, the angular velocity of the effective field vector at at least one angle, 90°+&agr;, is different from the angular velocity at 90°−&agr;.

Abstract: New methods of generating optimal inversion pulses and adiabatic pulses in magnetic resonance imaging are disclosed. Trajectories, maximum sweep rates, and velocity profiles are used in defining an optimal pulse, over support regions. Adiabatic pulses are optimized by using the trajectory as a constraint of optimization, but selecting trajectories with velocity profiles, without using the adiabatic condition as a constraint for optimizing the velocity profile. A method or inverting MR spins substantially, independently of the pulse duration, by selecting a transition width between 1.4 and 1.9 and dividing that width by the pulse duration is disclosed; and A new method of inverting adiabatic, MR, amplitude modulated spins, with a trajectory defined by sin .alpha./cos .alpha., where .alpha.<0.9 and at least 50% of the trajectory is outside, in a z-x rotating frame of reference that rotates at the instantaneous frequency of the RF pulse is also taught.