STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
STUDIES OF ENERGY RECOVERY LINACS AT ... - CASA
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4.3 BBU Simulation Codes: Particle Tracking<br />
In the previous section an analytic expression for the threshold current of sta-<br />
bility for a cavity containing a single HOM was derived. While this is helpful for<br />
studying simple cases and understanding the parametric dependence of the thresh-<br />
old current, investigating BBU in an accelerator with several cavities and many<br />
HOMs per cavity and/or with coupled transverse optics requires computer simula-<br />
tion codes.<br />
4.3.1 Generic Algorithm<br />
The two particle tracking codes developed at Jefferson Laboratory are TDBBU<br />
(Two Dimensional Beam Breakup) discussed in Section 4.3.2 and ERLBBU (Energy<br />
Recovering Linac Beam Breakup) discussed in Section 4.3.3. The basic algorithm<br />
that is common to all particle tracking BBU codes is described by the following steps<br />
(for the sake of simplicity assume that only a single cavity with a single vertically<br />
polarized HOM is being simulated):<br />
1. The initially empty machine is filled with (PL/h) + 1 bunches (truncated to the<br />
nearest integer), where PL is the recirculation path length in terms of RF wave-<br />
lengths and h is the beam repetition subharmonic. For the typical 74.85 MHz<br />
repetition rate used in the FEL Upgrade and with the 1497 MHz CEBAF<br />
cavities, h = 20.<br />
2. An injected bunch propagates through the entire linac for the first time. Beam<br />
bunches up to a specified time are given an initial displacement and/or an init-<br />
ial angle to excite the HOM. During its passage, the bunch excites the HOM<br />
voltage according to<br />
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