Luminosity Lifetime

In a symmetric or 'energy transparent' relativistic collider, the luminosity is given by L = N{sup 2}f{sub c}/4{pi}{sigma}*{sub x}{sigma}*{sub y} where N is the number of electrons or positrons per bunch, {sigma}*{sub x} ({sigma}*{sub y}) is the horizontal (vertical) rms beam size at the interaction point (IP), and f{sub c} is the collision frequency. If the beam sizes remain constant as the luminosity decreases, then the time dependence of luminosity is contained entirely in the time dependence of the beam currents, i.e., N O N(t), and we can rewrite the equation as L(t) = N{sup 2}(t)f{sub c}/4{pi}{sigma}*{sub x}{sigma}*{sub y}. There are two distinct categories for luminosity loss. In the first category are loss processes due to collisions between the two beams, that is, processes associated directly with the luminosity. In the second category (see below) are single-beam loss processes. The processes in the first category relevant to a high-energy collider are Bhabha scattering (e{sup +}e{sup -} O e{sup +}e{sup -}) and 'radiative' Bhabha scattering (e{sup +}e{sup -} O e{sup +}e{sup -}{gamma}). In the first process, a beam particle is lost if its angular deflection is beyond the ring's transverse acceptance; in the second process, loss occurs if the beam particle's momentum change is outside the longitudinal acceptance of the ring (typically determined by the RF bucket height)