Beam break up analysis for the Berkeley Recirculating Linac Light Source
We describe here a study of a single bunch Beam Break Up (BBU) instability for a proposed Berkeley fast x-ray facility based on a recirculating linac [1]. The recirculating linac employs a 600 MeV superconducting RF linear accelerator and the electron beam energy of {approx} 2.5 GeV is reached over four beam passes through the linac. A 120 MeV superconducting RF linear accelerator is used as an injector to the recirculating linac. The machine parameters are listed in Appendix A. The equation describing the transverse displacement x(s,z) of the electrons in an accelerated bunch, as a function of their longitudinal position within the bunch z, can be written in the form [2]: d/ds[{gamma}(s) dx/ds] + k{sup 2}(s){gamma}(s)x(s,z) = r{sub 0}{integral}{sub z}{sup {infinity}}{rho}(z')W{sub {perpendicular}}(z'-z)x(s,z')dz' (1) where {gamma} is the relativistic factor, k the focusing strength, r{sub 0} the classical electron radius, {rho} the bunch density, W{sub {perpendicular}} the transverse wake function per unit length and s indicates the position along the linac. We assume infinitesimally small transverse beam dimensions (a good approximation, when the bunch dimensions are much less than the size of the beam pipe), so that x has to be interpreted as the displacement of the centre of a bunch slice. We also assume a bunch length much less than the betatron wavelength, therefore the displacement in the RHS of Eq.(1) is not retarded and, finally, we use an average transverse wake function obtained averaging the calculated short range wake of a single cavity [2] over the linac length. At first we consider the effect associated with a displacement of the electron bunch at the injection into the perfectly aligned linac. Later we extend the analysis to the case of misalignments of the linac RF cavities and cryomodules. Throughout the paper we compare the results obtained to the output of a simple tracking code, written as a Mathematical notebook. In order to keep the analytical expressions reasonably simple, we model the linac length as entirely filled with RF cavities (thus neglecting all the drift spaces, accounting for as much as one third of the total length). This causes the wakefield intensity used in the analysis to be bigger than the actual value and the average accelerating gradient to be smaller. It is shown in the paper that this corresponds to a conservative estimate of the BBU growth.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE Director, Office of Science (US)
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 840444
- Report Number(s):
- LBNL-49483; CBP Tech Note 411; R&D Project: Z3FSCB; TRN: US0502035
- Resource Relation:
- Other Information: PBD: 20 Jan 2002
- Country of Publication:
- United States
- Language:
- English
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