The momentum acceptance defines the maximum energy excursion that a particle can have before it is lost from the machine. The acceptance is given relative to the reference momentum. A typical optics with small ß* has an acceptance of 1% (LEP 0.7%). In general one has to consider the dynamic aperture which defines the limits for the stable particles in 6-D phase space (transverse and longitudinal).
The beam-beam parameter (or beam-beam tune shift) cannot be measured directly.
It can be inferred from the luminosity by inverting the relation between luminosity and beam-beam tune shift (usually for the vertical beam-beam tune shift).
It can also be calculated from the basic definition by plugging in the beam and optics parameters.
Beam charge compensation is an old idea to fight the beam-beam interaction by trying to neutralize each of the beam at the collision point. An extra e+ beam is merged at the collision point with the e- beam (moving the same direction), and extra e- beam is merged with the e+ beam. The idea is that a particle in one of the beams sees a net '0' electromagnetic field from the counter-rotating beam.
This idea was tried in an acceleration a long time ago, but the performance fell short by a factor 100 or so.
A circle of circumference L has a radius R = L / 2π. For example, a circle with a circumference of 100 km has a radius of 15.9 km.
A circular collider is in general not a perfect circle, but made of arc regions - meant at bending the beam with magnetic dipoles - and straigth sections, situated on both sides of the interaction points. This configuration is needed to protect the detectors placed around the interaction points from the synchrotron radiation [*] that would arise from bending the beams.
[*] Synchrotron radiation is the emission of photons from a charged particle moving in a magnetic field.