Currents in the Jovian middle magnetosphere draw out magnetic field lines radially into a configuration which has high equatorial curvature and weak field strength. Charged particles spiral along field lines into this equatorial region, where depending on their energies, they may have gyroradii comparable to or larger than the scale length of the field Magnetic moment violation resulting in a stochastic change in pitch angle may thus occur locally at the equator. Using a linear approximation to the field variation and a mathematical technique for distorting the orbit integration into the complex gyrophase plane, we derive a formula for the nonadiabatic change Δ&mgr; in magnetic moment. Δ&mgr; varies as cos &Ugr;, where &Ugr;, is particle gyrophase at the equator, so that if a particle traverses the equator several times with different values of &Ugr;r it suffers randomly correlated values of Δ&mgr;. The algebraic formula for Δ&mgr; is in excellent agreement with previous numerical computerations. The phase space density, averaged over several bounce periods, satisfies a diffusion equation in pitch angle. The diffusion coefficient depends on particle energy, pitch angle, and the field line along which the particles are moving. Energetic sulfur ions (hundreds of keV and higher) are diffused in a few tens of bounce periods beyond 20 RJ, and the behavior of protons is not too dissimilar. Electrons, which at the same energy have much smaller gyroradii, become nonadiabatic and diffusive only near 28 RJ, where the magnetic model predicts a combination of especially weak field and large spatail variation. Pioneer and Voyager particle results are summarized in the light of this diffusion mechanism; while there is evidence for magnetic moment violation, an utter absence of pitch angle structure in the outer magnetodisc region (which should thus follow from the magnetic model) has not been confirmed (or looked for, to a large degree). Implications for other magnetospheric mechanisms are discussed. Finally, the possibility of a similar diffusion in the Saturnian ring current region is addressed, and it is found that only at much higher energies (>100-MeV protons) is this type of nonadiabatic behavior to be expected.