Coupled spatially homogeneous quasilinear kinetic equations are derived which describe the evolution of the energetic ion omnidirectional distribution function and the intensities of magnetohydrodynamic waves propagating parallel and antiparallel to the ambient magnetic field. The energetic ions are assumed to be nearly isotropic and possess speeds much greater than the Alfv¿n speed. For application to pickup ions the equations may also include an energetic ion injection rate and wave excitation or damping caused by isotropization of the newborn ions. The wave kinetic equations may be integrated to yield explicit expressions for the wave intensities, which may be substituted into the ion kinetic equations to yield a single self-consistent energy diffusion equation for the energetic ions. The theory represents the first treatment of stochastic (second-order Fermi) acceleration in which the back reaction of the ions on the turbulence is included self-consistently. Numerical solutions of the kinetic equations are presented for four cases of pickup ions in the solar wind which illustrate the essential features of the evolution: (1) interstellar pickup helium near a heliocentric radial distance of 1 AU; (2) interstellar pickup hydrogen near 10 AU; (3) water group pickup ions downstream of the bow wave of Comet Giacobini-Zinner for parameters observed during the International Cometary Explorer flyby; (4) water group pickup ions downstream of the bow wave of Comet Halley for parameters observed during the Giotto flyby.

The helium calculation reveals some modification of the solar wind wave spectrum and energy diffusion of the ions; although adiabatic deceleration is not included, acceleration rates are qualitatively consistent with the observed spectrum at 1 AU (M¿bius et al., 1985). The hydrogen calculation shows extreme damping of the solar wind wave spectrum in the cyclotron-resonant frequency range and a reduction in the acceleration rate of most of the ions. It is suggested that this behavior is responsible for an underabundance of hydrogen relative to the minor ions in the anomalous cosmic ray component, which is thought to originate from pickup ions accelerated at the solar wind termination shock. Wave damping is small at comet G-Z, and the calculated energy spectra do not appear to be in quantitative agreement with the observed spectra (Richardson et al., 1987). At Comet Halley, on the other hand, wave damping is substantial and the calculated spectra appear to be in general agreement with the observations (McKenna-Lawlor et al., 1989). ¿American Geophysical Union 1991