Electron beam brightness ($\beta$)

The electric current delivered per transverse probe area per solid angle. For a uniform circular probe of diameter $d$ and a small convergence semiangle $\alpha$, one convention is $\beta =4I/({\pi }^2{d}^2{\alpha }^2)$. State the accelerating voltage, angular convention and whether brightness is reduced by a voltage factor before comparing sources. A smaller aperture changes current as well as convergence; finite electron beam brightness prevents arbitrary current in an arbitrarily small probe.