The physics model of a next-generation spallation-driven high-current ultracold neutron (UCN) source capable of delivering an extracted UCN rate of around an-order-of-magnitude higher than the strongest proposed sources, and around three-orders-of-magnitude higher than existing sources, is presented. This UCN-current-optimized source would dramatically improve cutting-edge UCN measurements that are currently statistically limited. A novel Inverse Geometry design is used with 40 L of superfluid $^4$He (He-II), which acts as a converter of cold neutrons (CNs) to UCNs, cooled with state-of-the-art sub-cooled cryogenic technology to $sim$1.6 K. Our design is optimized for a 100 W maximum heat load constraint on the He-II and its vessel. In our geometry, the spallation target is wrapped symmetrically around the UCN converter to permit raster scanning the proton beam over a relatively large volume of tungsten spallation target to reduce the demand on the cooling requirements, which makes it reasonable to assume that water edge-cooling only is sufficient. Our design is refined in several steps to reach $P_{UCN}=2.1times10^9,/$s under our other restriction of 1 MW maximum available proton beam power. We then study effects of the He-II scattering kernel as well as reductions in $P_{UCN}$ due to pressurization to reach $P_{UCN}=1.8times10^9,/$s. Finally, we provide a design for the UCN extraction system that takes into account the required He-II heat transport properties and implementation of a He-II containment foil that allows UCN transmission. We estimate a total useful UCN current from our source of $R_{use}=5times10^8,/$s from a 18 cm diameter guide 5 m from the source. Under a conservative no return approximation, this rate can produce an extracted density of $>1times10^4,/$cm$^3$ in $<$1000~L external experimental volumes with a $^{58}$Ni (335 neV) cut-off potential.
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