Heat deposition by transient beam passage in spoilers

Future electron-positron linear colliders must produce bunches of tiny emittance grouped in short bunch trains in order to provide adequately large luminosities. A collimation system must be installed between the end of the main linac and the optical elements of the final focus to protect the detectors from errant beams. With ordinary values of the betatron functions, the transverse beam size is of a few microns. With such sizes, the local deposition of heat of even a single bunch train is so high that no material can survive such an event.The problem is solved by increasing the beam sizes at the location of the collimators. But the use of large betatron functions is costly and can induce strong optical errors. It is therefore important to compute precisely safe beam sizes which allow the survival of the collimators, in order to limit their increase to the minimum needed. The deposition of heat occurs both by ionisation along the path of the particles which traverse the material and by ohmic image current heating at the surface of the collimator, for that fraction of the beam which flies outside the collimator.With small bunches, heat diffusion is substantial even with short bunch trains and helps to reduce the excursion of temperature. The rise of temperature is computed by solving analytically the time-dependent heat equation in two spatial dimensions near an interface with vacuum. Numerical results are given for the CLIC study.