It is shown that corotation of charged particles in the azimuthally asymmetric magnetic field of the Jovian magnetosphere leads to a pitch-angle-dependent energy loss and gain of particles that drift from noon to midnight and midnight to noon, respectively. An isotropic pitch angle distribution at noon would become dumbbell-like at midnight. Nonadiabatic scattering relaxes the dumbbell distribution toward isotropy without changing the particle's energy. This scattering represents an increase of the first adiabatic invariant M. As the particles drift back toward noon at an increased value of M, they gain more energy than they lost during their drift from noon to midnight. The overall energy gain per rotation can be as large as a factor of 2, and in 10 rotations the total energy may be increased by several orders of magnitude. The model can account for the 10-hour modulation of spectral index and makes a number of testable predictions.