Transverse emittance blow - up due to injection errors

The tight transverse emittance budget for the LHC beam imposes severe constraints on the blow-up produced by injection errors. The modifications to the beam distributions and their possible parameterisation in terms of blow-up factors are discussed for betatron and dispersion mismatch as well as for injection offsets. The cases of initial uniform or gaussian distributions are considered in detail and analytical formulas derived. As already shown in previous papers [1-3 and references therein] the blow-up factor after filamentation seems the most adequate approximation to evaluate the blow-up due to injection errors as compared to the geometrical blow-up, normally quoted. The latter is more adequate for aperture considerations in the transfer lines and in the circular accelerators.