Beam-Beam Tracking Studies and Luminosity Optimzation for the High-Luminosity LHC Project

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The TRIUMF-CERN collaboration on High-Luminosity Upgrade of the Large Hadron Collider (HL-LHC) is ***focused on investigations of the beam-beam interaction and it's effects on beam quality and maximum ***achievable luminosity.******The topics for investigation are described next, as formulated by CERN and also confirmed in the ***TRIUMF-CERN MOU of 2016. Most items below are in a well advanced stage, with several results ***reported.******Long-term (millions of turns) tracking of protons around the LHC ring is used to estimate the dynamic ***aperture (DA) -- the domain of stable particle trajectories. The maximum luminosity is a main characteristic ***of any collider. It is defined at top energy and in the presence of beam-beam collisions, i.e. when the two ***colliding beams meet each other in the vicinity of several interaction points (IP) such as Atlas and CMS in ***the LHC. In tracking, it is customary to apply the weak--strong model where one beam is assumed ***unchanged, while particles of the other (weak) are tracked to compute the DA. A partial degradation of DA ***takes place since these weak--beam particles suffer deflections from the fields of the strong beam, ***both when traversing its core at an IP, but also as hundreds of unavoidable ``long--range'' encounters. ***The latter are the main factor limiting luminosity.******Tracking is predominantly performed on the BOINC-LHC Six-Track platform for distributed computing joining ***thousands of computers world-wide. Access to the HL-LHC database and two main computing codes, ***MadX and Six-Track, is provided by CERN. TRIUMF has an extended previous experience in setting ***LHC lattice, submission of jobs, processing etc.******Various machine-setups and parameters are to be studied at TRIUMF, related both to present LHC ***(machine development) and its future HL enhancement. Such are: crossing angle, emittance, bunch ***population, round or flat colliding beam options at the IP etc. Emphasis is set on tune-scans (optimization ***of the working point in tune space), explanation of nonlinear resonances and modeling the machine with ***random errors in the field of the new high-gradient quadrupoles. Currently at prototype stage, these are ***planned for installation in or around 2023. In addition, two novel devices intended to improve collider ***efficiency are modeled: crab cavities for tilting the bunch at the IP, and "wire compensation" of the*** long--range beam--beam interactions.******We also continue our studies on theoretical aspects of the beam-beam interaction based on an analytic ***theory using Lie-algebraic techniques to build the nonlinear Taylor map. The goal to explain the observed ***resonances and derive early indicators of chaotic motion.******Subjects envisaged for a student are: learning accelerator physics with emphasis on nonlinear effects and ***stability of Hamiltonian systems, becoming familiar with CERN&nbs