Lowest equilibrium emittance reachable in electron storage rings
In plain words
New diffraction-limited synchrotron rings shrink the beam until the x-rays are nearly coherent; collisions within the bunch and loss of stable orbits set a floor that is not yet known.
Precise statement
Multibend-achromat rings at $6\,\mathrm{GeV}$ operate with natural horizontal emittance eps_x of about 1.3e-8 to 1.4e-8 cm rad (ESRF-EBS, from 2020) and about 4e-9 cm rad (APS-U, from 2024). Determine the minimal equilibrium eps_x at $E = 6\,\mathrm{GeV}$ and circumference $1e5-2e5\,\mathrm{cm}$ with intrabeam scattering at full current, Touschek lifetime above $1\,\mathrm{h}$, and dynamic aperture adequate for on-axis or off-axis injection, and whether eps_x < 1e-9 cm rad (diffraction limit for $\sim 10\,\mathrm{keV}$ photons) is attainable.
What would settle it
A lattice optimization with these constraints giving $\mathrm{eps}_x$ versus circumference, checked against operating fourth-generation rings.