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It's a common question to ask what are the rates that the accelerator can generate.  The table below lists the rates that are natural for the accelerator.  These are the periodic rates that repeat exactly at the ~0.98 second period of the timing/MPS system.  Of course, we can generate other rates as well that aren't exactly periodic by doing the sort of thing you described - dropping shots or irregular sequences.  This has been useful for the OPCPA laser development in deciding the exact frequencies they will support.

Matt provides this example of how you can determine if various trigger rates overlap: 16kHz (16581 in the table) has factors (2,2,2,7).  102Hz has factors (2,2,5,5,7,13).  It's missing one factor of 2, so it only overlaps 1/2 of the time.  51Hz has (2,2,2,5,5,7,13), so it contains all the factors from 16kHz and thus overlaps 100%.

If a base accelerator rate is chosen (e.g. 33kHz) then other rates having the same prime factors as the accelerator rate are allowed, according to this table:

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