Tracking studies for the LHC optics version 4 at injection energy

Extensive tracking studies have been performed for a realistic model of the LHC at the injection energy of 450 GeV. The underlying model contains all static multipole magnet errors and linear imperfections. The imperfect machines are corrected using control room techniques. The paper gives estimates for the dynamic aperture for 60 different realizations of errors for the versions 4. To get a better picture of the dynamics the emittance ratios are varied to sample a large fraction of the phase space. Phase space averaged apertures are compared with averages over different imperfect machines for selected emittance ratios. Lastly it is checked if the reduced systematic a₄ and b₄ multipolar components of the main bending magnets remain an important aperture limitation