Time scale of the largest imaginable magnetic storm

The depression of the horizontal magnetic field at Earth's equator for the largest imaginable magnetic storm has been estimated (Vasyliūnas, 2011a) as Dst ~ 2500 nT, from the assumption that the total pressure in the magnetosphere (plasma plus magnetic field perturbation) is limited, in order of magnitude, by the minimum pressure of Earth's dipole field at the location of each flux tube. The obvious related question is how long it would take the solar wind to supply the energy content of this largest storm. The maximum rate of energy input from the solar wind to the magnetosphere can be evaluated on the basis either of magnetotail stress balance or of polar cap potential saturation, giving an estimate of the time required to build up the largest storm, which (for solar-wind and magnetospheric parameter values typical of observed superstorms) is roughly between ~2 and ~6 h.