Limitations on anti p-p luminosity with direct injection and stacking of antiprotons

If protons of very high energy impinge on a target, a large part of the resulting antiprotons are sufficiently collimated to be injectible into a stacking and accelerating ring. They can then be stacked and injected into the main proton accelerator so as to produce anti p-p collisions without low energy antiproton cooling. A scheme is presented for the VBA, where 20 TeV protons produce 9 x 10-4 antiprotons per proton at 100 GeV, which are then stacked, accelerated to 1 TeV, and injected into the main ring. With 16 proton pulses of 1015 protons, one obtains a luminosity of the order of 1032 cm-2 sec-1 with a beam-beam tune shift of 10-3 per interaction region. The beams are bunched into 1000 bunches; the orbits are separated by means of relatively modest electostatic electrodes