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polarization and (2) to determine if a global rotation is more robust in its ability to
increase the threshold current than a local reflector.
Before discussing the details of each case, a brief explanation of how the sim-
ulations were performed is required. Initially, all of the fourteen measured dipole
HOMs in each of the eight cavities of zone 3 were simulated for each of the three
machine optics. Dipole HOMs were then removed according to their impedance,
(R/Q)QL, the lowest impedance modes being removed first, so that for the case
of a single dipole HOM per cavity only the mode with the highest impedance is
simulated. Each dipole HOM is assumed to be comprised of two orthogonal polar-
izations. These polarizations are then rotated by an angle with standard deviations
of (0, 5, 10, 15, 20, 25, 30, 35, 40, 45) ◦ . A total of 140 simulations (14 dipole
modes × 10 rotation angles) were performed for each optics configuration with the
results presented by the two-dimensional surface plots shown in Figs. 6.12, 6.13 and
6.14 for the decoupled optics, local reflector and global rotation, respectively.
In the instance of decoupled optics, the threshold current remains relatively
insensitive to changes in the HOM polarizations. As the deviation of the mode
orientations from 0 ◦ and 90 ◦ increases, the threshold current also increases, albeit
only slightly, consistent with Eq. (4.21). Because the optics is decoupled and the
modes well separated in frequency, coupling between modes is negligible and the
current for stability can be determined by the threshold current due to the worst
individual mode.
The optics describing the local reflector were derived from machine all-save
values used for the measurements described in Section 6.3.1. From the arguments
of Section 6.3, the expected increase in the threshold current is observed. The point
of interest however, is that as the HOM rotation angle increases, the effectiveness
of the local reflector rapidly diminishes. Thus, unless it is known that dangerous
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HOMs are oriented very nearly to 0 ◦ or 90 ◦ , a reflection scheme may not adequately