A new set of quasi-linear kinetic equations is presented for transverse waves propagating along an axisymmetric magnetic field configuration. A WKB expansion is used to include effects of nonhomogeneity and nonplanarity of the waves. The equations allow simultaneous calculation of the spatial (and temporal) evolution of wave power spectra and the spatial (and temporal) evolution of particle distribution functions, including for the first time important wave-particle interactions which depend explicitly on the nonplanarity of the waves and the nonhomogeneity of the plasma and fields. The usefulness of the equations is demonstrated for a cold plasma, where a number of new results for wave propagation and acceleration of the plasma have been obtained. Along the way, a new quasi-linear separation of the average distribution function has been introduced, the usefulness of which is demonstrated by comparison with fluid theory. The principal new results are briefly summarized in section 6 of the paper.