Investigation of Beam Instability Under the Effects of Long-Range Transverse Wake Fields in the Berkeley Future Light Source Page: 2 of 15
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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 . 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.
Type of Linac 1.3 GHz, 2.5 GeV
Charge per Bunch 800 pC
Bunch Frequency 1 MHz
Normalized Emittance 0.5pm
Eo 0.241 GeV
Efinal 2.183 GeV
Table 1: Beam and linac parameters for the Berkeley future light source
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Kur, Eugene & Zholents, Alexander A. Investigation of Beam Instability Under the Effects of Long-Range Transverse Wake Fields in the Berkeley Future Light Source, report, August 31, 2008; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc902934/m1/2/: accessed April 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.