From: "Stephen Brooks" To: [...] Subject: Re: Cbeta parameter list Date: 2014 November 21; Friday 16:10 Sorry, I just had talk with Yue and we had this harmonic number business slightly wrong. If we want eRHIC analogue bunch spacing (within a "pyramid"), the best choice is 1.3GHz/3 = 433MHz (2.3ns). So the whole thing should be a multiple of 3 (not 4 as I had before). The number multiplied by three should be one away from a highly composite number C (divisible by many factors). The "one" being to allow a slip each time and the composite number so we have a choice of pyramid repetition rates. h = 3 * (C +/- 1) One good choice near our last one is h = 273 = 3*(90+1), where the bunches are injected every 270 RF periods but arrive 3 buckets later each turn. If the final turn is longer by half a wavelength, then the gap at the top is 3.5 RF wavelengths (2.7ns). 90 is divisible by 1,2,3,5,6,9,10,15,18,30,45,90. The eRHIC-like pyramid is 22 RF wavelengths long (about eight 433MHz units) so we can have up to 10 of these in the ring before they start to overlap. Of course, overlapping may work fine here up to the point of filling every 1.3GHz bucket. However, we can remove one or more of the 2,3,5,6,9, or 10 separate pyramids to make an ion clearing gap. The 2-pyramid situation is interesting because our ring revolution frequency at c is 1.3GHz/273 = 4.76MHz. Twice this is 9.52MHz, which is very close to the 9.38MHz between pyramids being used in eRHIC. You can use this to revise Figure 9 if you want. The vertical axis should be energies and each pass should show a range from entrance to exit of linac (for instance an upwards or downwards arrow for accelerating and decelerating passes). -Stephen