We study the feasibility of a new generation axion helioscope, the most ambitious and promising detector of solar axions to date. We show that large improvements in magnetic field volume, x-ray focusing optics and detector backgrounds are possible beyond those achieved in the CERN Axion Solar Telescope (CAST). For hadronic models, a sensitivity to the axion-photon coupling of $gagammagtrsim {rm few} times 10^{-12}$ GeV$^{-1}$ is conceivable, 1--1.5 orders of magnitude beyond the CAST sensitivity. If axions also couple to electrons, the Sun produces a larger flux for the same value of the Peccei-Quinn scale, allowing one to probe a broader class of models. Except for the axion dark matter searches, this experiment will be the most sensitive axion search ever, reaching or surpassing the stringent bounds from SN1987A and possibly testing the axion interpretation of anomalous white-dwarf cooling that predicts $m_a$ of a few meV. Beyond axions, this new instrument will probe entirely unexplored ranges of parameters for a large variety of axion-like particles (ALPs) and other novel excitations at the low-energy frontier of elementary particle physics.