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

大型强子对撞机（HL-LHC）高亮度升级项目的研究重点是研究束流相互作用及其对束流质量和最大可达到亮度的影响。接下来将描述由CERN制定并在2016年TRIUMF-CERN谅解备忘录中确认的调查主题。下面的大多数项目都处于良好的后期阶段，并报告了几个结果。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）——稳定粒子轨迹的领域。最大亮度是任何对撞机的主要特征。它的定义是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，如大型强子对撞机中的Atlas和CMS。在跟踪中，通常采用弱-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的部分退化发生了，因为这些弱光束粒子在穿越IP的核心时，以及在数百次不可避免的“远程”遭遇时，都会受到强光束场的偏转。后者是限制光度的主要因素。跟踪主要在BOINC-LHC六轨平台上执行，用于分布式计算，连接全球数千台计算机。欧洲核子研究中心提供了HL-LHC数据库和两个主要计算代码MadX和Six-Track的访问权限。TRIUMF在设置LHC晶格，提交作业，处理等方面有丰富的经验。各种机器设置和参数将在TRIUMF上进行研究，这与当前的LHC（机器开发）和未来的HL增强有关。这些是：交叉角，发射度，束数，圆形或平坦的碰撞波束选择在IP等。重点介绍了新型高梯度四极场中音调扫描（音调空间中工作点的优化）、非线性共振的解释和随机误差机器的建模。目前处于原型阶段，计划在2023年左右安装。此外，还对两种旨在提高对撞机效率的新型装置进行了建模：用于在IP处倾斜束束的蟹状空腔，以及用于远程束-束相互作用的“线补偿”。我们也继续研究基于解析理论的光束相互作用的理论方面，使用李-代数技术来建立非线性泰勒映射。目的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，重点是非线性效应和哈密顿系统的稳定性，熟悉CERN代码和我们的泰勒映射工具，并最终获得独立执行HL-LHC跟踪的能力。

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.