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

TRIUMF-CERN在大型强子对撞机(HL-LHC)高光度升级方面的合作*专注于研究束-束相互作用及其对光束质量和最大可达到光度的影响。*接下来描述由CERN制定并在2016年*TRIUMF-CERN谅解备忘录中确认的研究课题。下面的大多数项目都处于非常先进的阶段，有几个结果*被报道了。*对大型强子对撞环周围的质子的长期(数百万圈)跟踪被用来估计动态*光圈(DA)--稳定粒子轨迹的区域。最大光度是任何对撞机的主要特征。它定义在能量顶端和存在束-束碰撞的情况下，即当两个*碰撞的光束在几个相互作用点(IP)附近相遇时，例如*大型强子对撞机中的Atlas和CMS。在跟踪中，通常应用弱-强模型，其中假设一束*不变，而另一束(弱)的粒子被跟踪以计算DA。DA*发生部分退化，因为这些弱束粒子在强束场处受到偏转*，既有以激电穿越其核心时的偏转，也有数百次不可避免的“远距离”相遇。*后者是限制光度的主要因素。*跟踪主要在BOINC-LHC用于分布式计算的六轨平台上执行，*连接全球*数千台计算机。欧洲核子研究中心提供对HL-LHC数据库和两个主要计算程序*MadX和Six-Track的访问。TRIUMF在设置*LHC点阵、提交作业、处理等方面拥有丰富的经验。*各种机器设置和参数将在TRIUMF进行研究，与目前的LHC*(机器开发)及其未来的HL增强有关。重点介绍了调谐扫描(调谐空间中工作点的优化*)、非线性共振的解释以及在新的高梯度四极杆领域中具有*随机误差的机器建模。目前处于原型阶段，*计划在2023年左右安装。此外，我们还模拟了两种旨在提高对撞机效率的新型装置：用于倾斜束团的蟹形腔和长程束流-束流相互作用的“线补偿”。*我们还基于解析的*理论，利用李代数技术建立了非线性泰勒映射。目标是解释观察到的*共振并得出混沌运动的早期指标。*为学生设想的主题是：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和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