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### The 25 ns pumpkin teeth

If you looked at LHC page 1 in the last days, you may have noticed something interesting. They have been doing machine development (MD) for 25 nanosecond (ns) operation. In the lower left it says “25 ns MD Injecting 72 b trains”. This is an important development for the LHC and an important step toward operation at design. The “b” stands for “bunch” as explained below. The word “trains” refers to several such groups of 72 bunches hooked together.

Let us examine what 25 ns with 72 bunch trains means. Here is the layout of the CERN accelerator complex. The three main components that I am going to discuss here are the synchrotrons: the “proton synchrotron” (PS), the”super proton synchrotron” (SPS) and the LHC. A synchrotron is an accelerator with a circular ring of magnets that has some capability of accelerating the particles (in this case protons) and at the same time increasing the magnetic field in “sync” with the acceleration such that the bending radius stays fixed, i.e., the protons stay in the ring.

The relative sizes of the 3 synchrotrons are key to the injection scheme. The circumference of the SPS is 11 times that of the PS and the LHC is 27/7 that of the SPS. Now think of putting N proton bunches (with N an integer) into the PS with equal spacing. Then 11N bunches would fit into the SPS and (11N)(27/7) would fit into the LHC. If we want  things to come out even, then N must be divisible by 7. The value of N has been chosen to be 84 and the machine people refer to this as “harmonic 84”. By choosing harmonic 84, we have divided the LHC orbit into

(84) (11) (27/7) = 3564

parts. Since the orbit time for protons in the LHC is 88924 ns (26659 meters divided by the speed of the protons, very nearly the speed of light), and we have divided this orbit into 3564 pieces, each “bucket” as it is referred to corresponds to

(88924 ns) / 3564 = 24.95 ns .

Experimenters often speak of this number as 25 ns, after all what’s 50 picoseconds amongst friends?, but its precise value is important for the operation of the electronics.  So 25 ns is the time between collisions when the LHC is running at design. (Note: as of late the LHC has been running at 50 ns.) This inverse of this number is the collision frequency:

1 / (24.95 ns) = 40.079 MHz .

This is the clock frequency for LHC electronics. Note that MHz means million times per second, so the proton beams hit each other 40 million times per second. The protons pass through each other in a couple of ns and then nothing happens until the 25 ns later when the next bunches come along. Thus collisions occur every 25 ns. But wait! The beam structure is much, much richer than that!

When protons are injected into each of the synchrotrons, there is an injection kicker rise time. This is the time needed for the magnets that transport the protons between synchrotron rings to turn on. So of the 84 time slots in the PS, only the first 72 are filled and the last 12 are purposely left empty. Then fills of protons from the PS are injected into the SPS leaving an 8 bucket gap between them. This eight bucket gap is needed to “kick” the protons into the SPS. We do this 3 times after which we need to leave a larger gap of 38 buckets to kick the protons into the LHC. So far we have injected 3 groups of 72 bunches of protons from the PS into the SPS and into the LHC with the pattern:

72b  8e  72b  8e  72b 38e

where b stands for bunches of protons and e stands for buckets where there are no protons. Now let’s keep going with this to fill up the 3564 time slots. Notice that (11) (27/7) is about 42. We could fit 42 of these groups of protons into the LHC. But we want to leave a gap at the end as explained later, so we will only put in 39, in the form of 3 groups of 10 plus 9. To achieve this, first we do the same thing twice and then on the 3rd time we add a 4th bunch from the PS plus one extra empty bucket at the end. So now we have

72b  8e  72b  8e  72b 38e 72b  8e  72b  8e  72b 38e 72b  8e  72b  8e  72b 8e  72b 39e .

This is 10 trains. Now we repeat this 3 times. So far we have 30 trains

72b  8e  72b  8e  72b 38e 72b  8e  72b  8e  72b 38e 72b  8e  72b  8e  72b 8e  72b 39e 72b  8e  72b  8e  72b 38e 72b  8e  72b  8e  72b 38e 72b  8e  72b  8e  72b 8e  72b 39e 72b  8e  72b  8e  72b 38e 72b  8e  72b  8e  72b 38e 72b  8e  72b  8e  72b 8e  72b 39e .

For the last step we add 3 more shots from the SPS each containing 3 PS shots and at the end leave 119 missing buckets to add the last 9 trains (making 39 trains)

72b  8e  72b  8e  72b 38e 72b  8e  72b  8e  72b 38e 72b  8e  72b  8e  72b 8e  72b 39e 72b  8e  72b  8e  72b 38e 72b  8e  72b  8e  72b 38e 72b  8e  72b  8e  72b 8e  72b 39e 72b  8e  72b  8e  72b 38e 72b  8e  72b  8e  72b 38e 72b  8e  72b  8e  72b 8e  72b 39e 72b  8e  72b  8e  72b 38e 72b  8e  72b  8e  72b 38e 72b  8e  72b  8e  72b 119e .

Whew! We have filled up the 3564 time slots; 2808 (39 times 72) of them have protons and the rest are empty. But VERY important for the experimenters, the empty buckets occur in a known pattern. This pattern is used to synchronize the electronics. We can only get collisions in the 2808 buckets that contain protons and we know which buckets have the protons. The LHC bunch structure is like a “pumpkin tooth” pattern. For each part of the detector we line up these pumpkin teeth to adjust our clocks to the LHC machine.

Harmonic 84 injection scheme figure thanks to P. Collier.

The long string of 119 empty buckets adds up to 3 microseconds. This is referred to as the “abort gap” and it corresponds to the time needed to turn on the kicker magnets to dump the proton beams. This also turns out to be a blessing for the experiments because this time is used to do many things such as reset certain electronics and take calibration events.