CBN 95 - 5 1 Coherency of the Long Range Beam - Beam Interaction in CESR

Making more luminosity is the name of the game at CESR these days. Luminosity is proportional to the average beam current I, the vertical tuneshift parameter y, and inversely proportional to the vertical beta function at the interaction point y . The main thrust of our e orts is to increase the average beam current by adding more bunches, without losing ground on the other two parameters. This should work as long as the additional bunches can be kept from colliding with each other at the numerous crossing points in the arcs, and the machine hardware is capable of handling higher currents. The main limitation to the maximum number of bunches the ring can accommodate is due to the long range beambeam interaction that occurs when the bunches pass by each other in the arcs. Separation can be obtained at these points using electrostatically generated closed orbit distortions known as `pretzels'. However, the pretzel distortion is proportional to p x cos x and so good separation can be obtained over only the portions of the ring where the cosine term is not small. If crossing points are too close to pretzel nodes the long range beam-beam interaction causes a very short lifetime for the bunches which cross there. Roughly one can collide one train of closely spaced bunches for each integer of the horizontal tune and manage to avoid crossing points near the pretzel nodes. The total length of each train must limited to some fraction of half the minimum betatron wavelength. For illustration the actual pretzel in a portion of CESR is reproduced in gure 1 together with the beam envelopes and marks at the crossing points. Here we were running with nine trains consisting of two bunches separated by 28 ns. One may ask when does it actually make sense to increase the number of bunches, given the number and length of the trains is more or less xed? There are a few considerations: If the single bunch current is near or above the value for which y is saturated then luminosity will increase linearly with total beam current, independent of the number of bunches. In this case one may be able to avoid single bunch current limitations by adding more bunches. If the single bunch current is below the saturation value then it might be better to increase the single bunch current if possible, than to add more bunches, because the luminosity will go up faster than linear. For CESR, saturation