Luminosity and tune shift in e+e- storage rings

Luminosity and tune shift have been the subject of numerous papers and talks since the invention of electron-positron storage rings. This paper derives an equation for luminosity and one for the linear tune shift based upon two simple assumptions. The first assumption is that the storage ring be designed such that the linear tune shifts in the two transverse planes, x and y, are equal; i.e., that Δnu/sub x/ = Δnu/sub y/. The second assumption is that the maximum acceptable disruption angle, θ/sub D/, of the colliding beams is approximately equal to the ''natural'' beam spread, θ/sub B/, of the stored colliding beams at the interaction point. First derived is the results for round beams having transverse gaussian distribution functions and then extend the derivation to beams having elliptical cross sections. Then compared are theoretical results with the observed results in several operating machines and with the ''design'' parameters of three new machines; namely KEK, BEPC, and LEP