TeV electron-positron collisions with luminosities of 1034cm-2 s-1 using the CERN tunnels for the damping rings

The fundamental equations of linear electron-positron colliders are used to obtain a new expression of the beam invariant emittance which depends upon very few parameters and which is valid for all acceleration methods. Since we look for upper limits, emittance growth during acceleration and chromatic effects in the low-β focusing system are neglected. Even with these optimistic assumptions, for luminosities of the order of 1034 cm-2 s-1 at few TeV of center of mass energy, the required emittances are very small and many kilometers of damping rings are needed to damp the positron (and electron) bunches. It is suggested that few rings having a large circumference are better suited than a very large number of small rings. (orig.)