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I am curious about the Large Hadron Collider and whether the proton (anti-) beams are clumps of protons (grouped together) or are they roughly equally distributed around the circumference of the ring.

The motivation for my question comes from thinking about how the LHC protons are injected and the time (I read on order of 20 minutes) it takes for the protons to come to peak energy with speed approaching $c$. In thinking of this it seems that the protons would begin to gather closer together (although, I could be all wrong on this).

K7PEH
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From LHC Website

Each proton beam at full intensity will consist of 2808 bunches per beam. Each bunch will contain $1.15 \times 10^{11}$ protons per bunch at the start of nominal fill and is around 30 cm. long with transverse dimensions of the order a mm, but in a collider as small as possible at the collision point (LHC - 16 microns fully squeezed).

The particles in the LHC are ultra-relativistic and move at 0.999997828 times the speed of light at injection  and  0.999999991 the speed of light at top energy

Energy in beam.

Total beam energy at top energy, nominal beam, 362 MJ

$2808 \,\text{bunches} * 1.15\times 10^{11}$ protons @ 7 TeV each. = $2808*1.15*10^{11}*7*1012*1.602*10^{-19}$ Joules = 362 MJ per beam

The bunches are generally separated by about 7.5 m or 25 ns. (this is actually 10 RF buckets - with an RF frequency of around 400.8 MHz). However, there are some holes in the bunch structure. The biggest is the beam abort gap of 3 microseconds (900 m.) - this is there to give the beam dump kickers time to get up to full voltage. There are also other smaller gaps in the beam which arise from similar needs from the SPS and LHC injection kickers.

A rough idea of how the bunches are inserted.

enter image description here

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