Can photoinjectors reach the space-charge-limited brightness bound
In plain words
Theory gives a maximum brightness set by the field at the cathode and the electrons' sideways energy; real guns fall short by an amount that is not fully explained.
Precise statement
For short-pulse photoinjectors the maximal 4D normalized brightness of a pancake-shaped bunch is bounded by the cathode field $E_c$ and MTE (bound derived in 2009). Determine whether measured 4D or 5D brightness of DC, normal-conducting RF and superconducting RF guns can come within a factor 2 of this bound at bunch populations of $1\mathrm{e}8 \text{ to } 1\mathrm{e}9\,\mathrm{electrons}$, and which effects (image charge, nonuniform emission, imperfect emittance compensation, cathode roughness) cause the observed gap.
What would settle it
Measured slice brightness of one gun at several $E_{c}$ and MTE values compared with the bound and with a start-to-end model that accounts for the gap.