LHC upgrade IR optics options
[LHC upgrade Phase I layouts]
[MADX utilities for the LHC upgrade]
In a common bore design the mechanical aperture (A) is defined as the aperture needed by the beams plus
twice the orbit tolerance:
A = (Beam) + 2(Orbit)
The aperture needed by the beam is given by:
(Beam) = 1.1(18σ + 9.5σ)
where we assume a beta-beating of 20%, a distance to the wall of 9σ
and a beam-beam separation of 9.5σ. The required beam separation at each IR magnet should be further refined by tracking with parasitic beam-beam encounters as a function of the luminosity reach, and depends on beam intensity: it is 6.7σ at Q2 for the nominal LHC. The beam-beam separation could be relaxed by realigning the IR magnets in order to best use the available aperture (this approach needs further study).
In the two-bore designs there is no need to account for beam separation.
The r.m.s. beam size σ is defined as:
σ = (βε + D2σδ2)1/2
where β is the beta function, ε is the beam emittance (3.75e-6/7461 m for LHC at top energy),
D is the dispersion (in the vertical plane there can be residual dispersion due to vertical crossing of the beams)
and σδ is the momentum spread (0.113e-3 for LHC at top energy).
The orbit tolerance consists of three items:
(Orbit) = (Peak) + (Dispersion) + (Alignment)
The (Peak) is assumed as 3 mm, (Alignment) tolerances are 1.6 mm.
The 2nd item, the spurious dispersion is typically estimated from the maximum dispersion
and betas in the arcs [see paper],
with δ=0.86e-3, βx(arc)≈200m and Darc≈2m. In the case of the vertical crossing a deterministic vertical dispersion is propagated trough the ring. It is assumed to estimate this vertical dispersion as 50% of the maximum possible (since it depends on phase advance between IRs).
The coil aperture is therefore defined as the sum of the total mechanical aperture plus
twice the thickness of the beam pipe, the width of the He channel and the beam screen:
(Coil) = A + 2((BeamPipe) + (HeChannel) + (BeamScreen))
T. Sen has attributed the following values to these new quantities: 3, 4.5 and 1 mm, respectively.
But, of course these numbers depend on particular magnet design.