 Geometric emittance

For a centered beam, the displayed rms area in $(z,z^{\prime })$ coordinates. A matched beam has $⟨z^2⟩=ϵ\beta$, where $\beta$ is one of the Courant-Snyder parameters. Under ideal acceleration, adiabatic damping of geometric emittance decreases this area even when the canonical phase-space area is preserved.