Tracking Studies in the LHeC Lattice

The Large Hadron Electron Collider (LHeC) is a proposed upgrade of the LHC to provide electron-proton collisions and explore a new regime of energy and luminosity for nucleon-lepton scattering. A nominal design has previously been presented, featuring a lattice and optical configuration to focus one of the proton beams of the LHC (reaching a value of β*=10 cm) and to collide it head-on with an electron beam to produce collisions with the desired luminosity of L=10³³ cm⁻² s⁻¹. The proton beam optics is achieved with the aid of a new inner triplet of quadrupoles at L*=10 m from the interaction point and the extension of the Achromatic Telescopic Squeezing (ATS) Scheme used for the High Luminosity-LHC project. The flexibility of this design has been studied in terms of minimising β* and increasing L*. In this work, particle tracking is performed in a thin lens approximation of the LHeC proton lattice to compute the dynamic aperture and perform frequency map analysis for different types of chromatic correction schemes, in order to find the one who will provide the most beam stability and to study the effects of non linearities.