Compendium of equations for the design of a very large hadron collider

摘要

In the following the authors give several relationships which are used for the211u001epreliminary design and to estimate the collider performance. They limit to the 211u001ecase of the performance during storage and colliding mode. Two of such relations 211u001eare the relation between bending field B, the bending radius (rho) and the proton 211u001emomentum p B (Tesla) (rho) (meter) = 3.3356 p (GeV/c) and the minimum requirement 211u001eof the collider luminosity L which scales with the beam energy E according to L = 211u001e(10(sup 33))cm(sup (minus)2) s(sup (minus)1) (E/20 TeV ). They assume that the 211u001ecollider is made of two identical intersecting rings where the two beams 211u001ecirculate in opposite directions otherwise with identical configuration, 211u001edimensions and intensity. Both beams are bunched. They also assume, for 211u001esimplicity, that the beams are round, that is they have the same betatron 211u001eemittance in the two transverse planes of oscillations, horizontal and vertical. 211u001eAlso the two beams are exactly round at the interaction point where the lattice 211u001efunctions (beta)* has also the same values in the two planes.