Geometric emittance
= Geometric emittance
{title2=$\epsilon=\sqrt{\langle z^2\rangle\langle z'^2\rangle-\langle zz'\rangle^2}$}
For a centered beam, the displayed rms area in $(z,z')$ coordinates. A matched beam has $\langle z^2\rangle=\epsilon\beta$, 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>[phase-space] area is preserved.