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  codes and also our Taylor- map tools, and eventually gaining the ability to perform independently HL-LHC tracking.