Investigation of Beam Instability Under the Effects of Long-Range Transverse Wake Fields in the Berkeley Future Light Source

An ultra-relativistic charged particle bunch moving through a resonator cavity leaves behind a wake field that will affect subsequent bunches (if the bunch is not ultra-relativistic, the wake field will not be exclusively behind it). If the initial bunch enters the cavity off-axis, it will produce a transverse wake field that can then kick later bunches off the axis. Thus, even bunches that were initially traveling on axis could be displaced and, in turn, produce their own transverse wake fields, affecting following bunches. The offsets obtained by bunches could increase along the bunch train, leading to the so-called multi-bunch beam break-up instability [1]. The purpose of our investigation is to see whether such instability will occur in the superconducting, 1.3 GHz, 2.5GeV linac (see Table 1) planned for the Berkeley future light source (BFLS). We assume an initial steady-state situation established for machine operation; i.e. a continuous process where every bunch follows the same trajectory through the linac, with only small deviations from the axis of the rf structures. We will look at a possible instability arising from a bunch having a small deviation from the established trajectory. Such a deviation would produce a wake field that is slightly different from the one produced by the bunches following the established trajectory. This could lead to subsequent bunches deviating further from the established trajectory. We will assume the deviations are small (at first) and so the difference in the wake field caused by a bunch not traveling along the established trajectory is well approximated by a long-range transverse dipole wake. We are concerned only with deviations from the established trajectory; thus, in our models, a transverse position of zero corresponds to the bunch traveling along the established trajectory. Under this assumption, only the additional long-range transverse dipole wake remains in our models