Calculating luminosity for a coupled Tevatron lattice

The traditional formula for calculating luminosity assumes an uncoupled lattice and makes use of one-degree-of-freedom lattice functions, β_H and β_V, for relating transverse beam widths to emittances. Strong coupling requires changing this approach. It is simplest to employ directly the linear normal form coordinates of the one turn map. An equilibrium distribution in phase space is expressed as a function of the Jacobian´s eigenvectors and beam size parameters or emittances. Using the equilibrium distributions an expression for the luminosity was derived and applied to the Tevatron lattice, which was coupled due to a quadrupole roll