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In a recent publication from UMRAM researchers, it is shown that simultaneous use of linear and nonlinear gradients provides better B1+ inhomogeneity correction than using only linear or only nonlinear gradients. In high field scanners (3T or above), perfectly spatially homogeneous radio frequency (RF) pulse cannot be achieved inside the body because wavelength becomes comparable with the object dimension. In literature, spoke excitation, which uses RF pulses together with the commercial linear gradient fields, can provide more homogeneous excitation by correcting the B1+ inhomogeneity. In this study, it is shown that when there are additional nonlinear gradient fields driven by independent amplifiers, degree of freedom in the excitations problem is increased. Formulations and design techniques are formulated in the study. In an example experiment, transmit inhomogeneity is decreased 46% while it can only be decreased 20% with the original hardware of the scanner in the same scenario.