If Neptune has a large magnetic moment, a weak supply of plasma for its magnetosphere, and a magnetic moment that is in near alignment with the planetary spin axis, we argue that, except for a region near the magnetopause, the Neptunian magnetosphere is almost completely quiescent. Because the inner portion of a magnetosphere tends to be shielded from solar-wind influences, a large magnetosphere would have all latitudes shielded except for a small polar region. If, for example, the equatorial magnetic field at cloudtop levels B0 were as large as, say, Jupiter's (4.2 Gauss), and if plasma pressure within the magnetosphere were negligible, the nominal nose distance Rm of the magnetosphere would be 74 RN. The sheilded region could extend out to 25 RN, which corresponds to a magnetic latitude of nearly 80¿. Nm varies as B01/3, so the size of the magnetosphere is not very sensitive to the strength of the planetary magnetic field. Also, typical variations in solar-wind ram pressure do not cause large changes in the size of such a magnetosphere because Rm varie as the 6th root of the ram pressure. Standard magnetospheric theory promises that Neptune is a rotationally dominated magnetosphere, so the solar wind is not an effective power source. Zonal wind can contribute to energization of trapped radiation if the dipole is tilted relative to the spin axis. If Neptune's ionosphere and Triton's atmosphere together do not supply more than about 1 kg/sec to the magnetosphere, then, with a spin-axis-aligned dipole, the internal power sources for the magnetosphere would be less than 109 Watts (less than 1% of the average power utilized by the Earth's magnetosphere). This is consistent with this thus far observed lack of radio and auroral UV emissions. In such a magnetosphere, because they would enjoy a long residence time, non-relativistic particles could collect to form a substantial radiation belt. ¿ American Geophysical Union 1989