Beam Intensity Limitations in Future Multi-Bend Achromat Light Sources

We show that emittance of fourth-generation 6 GeV machines such as PETRA IV is close to what is theoretically achievable due to beam intensity limitations from space charge and intra-beam scattering. Investigating these limitations, in particular their scaling with the bare lattice emittance and the beam energy, we argue that achieving further significant emittance reduction and increase in radiation brightness is only possible by increasing the beam energy. We outline the design and technological challenges on the way to such improvement.