There are recent considerations to increase the photomultiplier density in the IceCube detector array beyond that of DeepCore, which will lead to a lower detector energy threshold and a relatively huge fiducial mass for the neutrino detection. This initiative is known as "Precision IceCube Next Generation Upgrade" (PINGU). We discuss the possibility to send a neutrino beam from one of the major accelerator laboratories in the Northern hemisphere to such a detector. Such an experiment would be unique in the sense that it would be the only neutrino beam where the baseline crosses the Earth's outer core. We study the detector requirements for a beta beam, a neutrino factory beam, and a superbeam, where we consider the cases of both small θ 13 and large θ 13 , as suggested by the recent T2K and Double Chooz results. We illustrate that a flavor-clean beta beam best suits the requirements of such a detector, in particular, that PINGU may replace a magic baseline detector for small values of θ 13 -even in the absence of any energy resolution capability. For large θ 13 , however, a single-baseline beta beam experiment cannot compete if it is constrained by the CERN-SPS. For a neutrino factory, because of the missing charge identification possibility in the detector, a very good energy resolution is required. If this can be achieved, especially a low energy neutrino factory, which does not suffer from the tau contamination, may be an interesting option for large θ 13 . For the superbeam, where we consider the LBNE beam as a reference, electron neutrino flavor identification and statistics are two of the primary limitations. Finally, we demonstrate that in principle the neutrino factory and superbeam options may measure the density of the Earth's core at a sub percent level for sin 2 2θ 13 0.01. a this work if the large increase of statistics by this relatively huge detector mass may compensate for the loss of statistics from the long baseline. More specifically, consider a beta beam, neutrino factory beam, and a superbeam, and establish the detector requirements for each of these beam classes for small and large θ 13 . Sec. 4 discusses our detector parameterization. These requirements may serve as guidance for the optimization of the detector, if it were intended to receive a neutrino beam. Our primary focus is the optimization with respect to the most often used performance indicators, including the θ 13 , mass hierarchy (MH), and CP violation (CPV) discovery reaches as a function of (true) θ 13 and δ CP . Note that the neutrino oscillation physics using such a long core-crossing baseline is quite unique because of the "parametric enhancement" [22, 23] of the oscillation probability; for a detailed discussion, see Sec. 2. Conversely, the density of the Earth's core can be probed with such a neutrino beam [24], which we study in Sec. 7. Earlier works studying a neutrino beam to the South Pole include Refs. [25,26].As far as the different beam classes are concerned, we distinguish setups for small θ 13 , where only an uppe...