Study of Long-range Collisions and Wire Compensation for Tevatron Run-II

This report summarizes studies of long-range collisions and their compensation by current carrying wires for the Tevatron Run-II, which were performed during a two-week stay at Fermilab, February 22 to March 8, 2004. The weak-strong code WSDIFF was significantly extended to simulate the actual long-range encounters at the Tevatron for different antiproton bunches in the train at injection and in collision. Tune footprints and diffusive apertures simulated by this code are presented for various cases, differing in the bunch position, the energy, the number of long-range and head-on collisions, the presence of additional compensating wires and the momentum deviation. It is confirmed that the solution of 4 wires for injection, previously found by B. Erdelyi, raises the dynamic aperture, by about 1.0-1.5sigma. For both injection and collision an ideal compensation of the 6 or 3 closest long-range encounters was modeled, by removing these collisions altogether. At collision, an improvement in the dynamic aperture of the order of 0.5-1.0sigma is found. The much more copious residual long-range collisions are shown to also strongly affect the diffusive aperture, however, which highlights a lack of correlation between dynamic aperture and tune footprints. The dynamic aperture widely varies with the bunch number, ranging from 5 to 8sigma; along the train, in collision for on-momentum particles. Analytical calculations of tune shift, coupling, chromaticity and chromatic coupling similarly reveal a large variation from bunch to bunch, amounting to 16 units in chromaticity and 4 or 5 units in chromatic coupling. Achieving compensation for all bunches in the train appears a nontrivial challenge for dc wires, in particular if off-energy is also to be corrected. In a machine study on March 1, the Tevatron electron lens was used to simulate a wire and the dependences of beam lifetime, tune, emittances and bunch length on the beam-TEL distance were explored. The results of this experiment are reported elsewhere [1].