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

TRIUMF-CERN关于大型强子对撞机（HL-LHC）高亮度升级的合作 * 专注于研究光束间的相互作用及其对光束质量和最大 * 可实现亮度的影响。接下来描述了调查的主题，由CERN制定，并在2016年的TRIUMF-CERN谅解备忘录中得到确认。以下大多数项目已进入相当后期的阶段，并报告了若干成果 **。长期（数百万圈）跟踪LHC环周围的质子被用来估计动态 * 孔径（DA）-稳定粒子轨迹的域。最大亮度是任何对撞机的一个主要特征。它被定义在最高能量和存在束-束碰撞的情况下，即当两个 * 碰撞的束在几个相互作用点（IP）附近相遇时，例如 * LHC中的Atlas和CMS。在跟踪中，习惯上应用弱-强模型，其中一个射束假设 * 不变，而另一个（弱）的粒子被跟踪以计算DA。DA * 的部分退化发生，因为这些弱射束粒子遭受强射束的场的偏转，* 当在IP处穿过其核心时，但也有数百次不可避免的"长距离“遭遇。* 后者是限制光度的主要因素。**跟踪主要在BOINC-LHC六轨平台上进行，用于分布式计算，连接全球数千台计算机。访问HL-LHC数据库和两个主要的计算代码，*MadX和Six-Track，由CERN提供。TRIUMF在设置 *LHC晶格，提交作业，处理等方面具有丰富的经验。各种机器设置和参数将在TRIUMF进行研究，这些都与当前的LHC *（机器开发）及其未来的HL增强有关。这些是：交叉角，发射度，束 * 人口，圆形或平面碰撞光束在IP等选项的重点是设置在调谐扫描（优化 * 的工作点在调谐空间），非线性共振的解释和建模的机器与 * 随机误差在新的高梯度四极杆领域。 目前处于原型阶段，计划在2023年或前后安装。此外，两个新的装置，旨在提高对撞机 * 的效率进行了建模：螃蟹腔倾斜聚束在IP，和“线补偿”的 * 远程光束-光束相互作用。我们还继续我们的研究理论方面的梁-梁相互作用的基础上的分析 * 理论使用李代数技术建立的非线性泰勒映射。 目标是解释观察到的共振现象，并得出混沌运动的早期指标。学生的课程包括：学习加速器物理学，重点是非线性效应和哈密顿系统的稳定性，熟悉CERN&nbs

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