LIGO Document T1300786-v6

LIGO III Quad Pendulum Conceptual Design Optimization

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T - Technical notes
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This technical note expands upon Madeleine Waller's work with Norna Robertson during the summer of 2012 on the LIGO III quadruple pendulum conceptual design. The document establishes some relatively simple but practical equations, based on some approximations and assumptions. These equations are used to optimize the longitudinal and vertical seismic isolation properties of the pendulum. This optimization is constrained by the payload limit of the BSC-ISI, the total length of the pendulum, and the desired test mass weight. The goal is to meet or beat the aLIGO quad performance.

It is shown that it is not possible to meet the aLIGO performance within the current constraints. 3 possible modifications to these constraints are proposed, which allow aLIGO performances to be met.

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Notes and Changes:
-v2: Corrected the accounting of the 4 fibers in the bounce mode derivation of appendix B. No results are impacted.
-v3: Fixed some typos
-v4: Added a figure and some text to Section 3 showing the longitudinal modes for all 3 solutions can be damped from the top mass.
-v5: Fixed a typo in the vertical bounce mode figure of the appendix.
-v6: Added appendix section A.3.3 to show that the longitudinal isolation is convex in m2 and m3. This proves that solving the m2 and m3 equations simultaneously by iteration, as was done, leads to the optimal solution for both.
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