Normalized emittance (${ϵ}_n={\beta }_{\mathrm{rel}}{\gamma }_{\mathrm{rel}}ϵ$)

The geometric emittance multiplied by the relativistic velocity and Lorentz factor. For paraxial acceleration without dilution, this is proportional to transverse canonical phase-space area and remains constant. Thus geometric emittance decreases approximately as inverse beam momentum.