Colliding crystalline beams

The understanding of crystalline beams has advanced to the point where one can now, with reasonable confidence, undertake an analysis of the luminosity of colliding crystalline beams. Such a study is reported here. It is necessary to observe the criteria, previously stated, for the creation and stability of crystalline beams. This requires, firstly, the proper design of a lattice. Secondly, a crystal must be formed, and this can usually be done at various densities. Thirdly, the crystals in a colliding-beam machine are brought into collision. The authors study all of these processes using the molecular dynamics (MD) method. The work parallels what was done previously, but the new part is to study the crystal-crystal interaction in collision. They initially study the zero-temperature situation. If the beam-beam force (or equivalent tune shift) is too large then overlapping crystals can not be created (rather two spatially separated crystals are formed). However, if the beam-beam force is less than but comparable to that of the space-charge forces between the particles, they find that overlapping crystals can be formed and the beam-beam tune shift can be of the order of unity. Operating at low but non-zero temperature can increase the luminosity by several orders of magnitude over that of a usual collider. The construction of an appropriate lattice, and the development of adequately strong cooling, although theoretically achievable, is a challenge in practice