Natural emittance (${\epsilon }_{x0}=C_q{\gamma }^2{I}_5/(J_x{I}_2)$)

The equilibrium horizontal beam emittance set by synchrotron-radiation excitation and damping in an uncoupled storage ring. The radiation-integral relation is ${\epsilon }_{x0}=C_q{\gamma }^2{I}_5/(J_x{I}_2)$; similar cell optics give a cubic dependence on bending angle.