Adiabatic damping of geometric emittance
= Adiabatic damping of geometric emittance
{title2=$\epsilon\propto p_s^{-1}$}
For slowly accelerated paraxial motion, $z'\simeq p_z/p_s$ decreases as longitudinal <momentum> grows while transverse canonical <phase space>[phase-space] area is conserved. The <normalized emittance> stays constant in the ideal limit, so the <geometric emittance> scales inversely with longitudinal <momentum>. This is kinematic damping rather than dissipation of canonical area.