A theoretical model and analysis of the acceleration of high-energy ~MeV/nuc ions in Jupiter's magnetosphere are presented. All measurements conducted in this energy range have consistently pointed to the probable occurrence of local nonadiabatic acceleration above that obtainable by radial diffusion alone. We consider first the creation of fast 75 km/s neutral sulfur and oxygen atoms in the Io torus by charge exchange. This process will eject upward of 2¿1028 neutrals per second which are recaptured in the magnetosphere by subsequent electron impact and charge exchange with the ambient plasma outside the torus as well as by solar UV photoionization. All processes together lead to an injection rate of greater than 4¿1025 heavy ions recaptured per second with a gyrospeed comparable to the local plasma flow speed. We show that subsequent adiabatic radial diffusion cannot produce the observed spectrum or high energies required by observations. We then consider the stochastic acceleration of this seed population by magnetohydrodynamic (MHD) waves. It is demonstrated how the properties of the observed particle spectrum are related to those of the power spectrum of MHD fluctuations measured by the magnetometer.