We describe a model for the acceleration of energetic protons and relativistic electrons in the Jovian magnetosphere, employing a four-step process in which ionospheric particles are (1) accelerated outward along field lines by the centrifugal force of corotation, (2) energized by magnetic field annihilation in the Jovian magnetospheric tail, (3) convected inward from the tail, thus experiencing adiabatic compression, and (4) diffused radially inward to form the Jovian trapped radiation belt. Steps 2--4 are analogous to the processes in the earth's magnetosphere that are thought to be responsible for the terrestrial radiation belts. There are three essential differences: the primary source of particles is assumed to be the ionosphere rather than the solar wind; steps 2 and 3 are not continuous but occur with the 10-hour period of Jupiter's rotation; and the energy source for the acceleration is the rotational energy of the planet rather than the solar wind. The periodicity is caused by a diurnal variation of the nightside distance to the last closed field line. The proposed model accounts for the 10-hour modulations in the energetic particle flux observed both outside and inside the Jovian magnetosphere by Pioneer 10 and Pioneer 11. We find that an additional mechanism is required in order to transfer some of the proton energy to the electrons (possibly through a wave instability of the two-stream type). Such an energy transfer mechanism appears also to be required in the terrestrial plasma sheet.