Accelerator Diagnosis and Control Based on Low Energy Empirical Model

该提案旨在开发和验证一种创建在线加速器模型的新方法，并进一步将其建立为加速器诊断和控制在实际操作和调试环境中的应用的基础，特别是在TRIUMF的先进稀有同位素实验室（ARIEL）项目中。正确有效地建立加速器输运和束流动力学模型的能力对于任何实时在线诊断和控制任务的成功至关重要。在低能量的情况下更是如此，因为关键性能参数往往“冻结”，在高能量时改变为时已晚。不幸的是，对于低能量（低beta）建模，效率和正确性并不总是兼容的目标。在许多情况下，在线使用更快的分析算法来模拟低能量下的效果，从而产生不正确的物理。我们建议用稍后将描述的在线经验模型来弥合这一差距。低β束流输运分析模型的失效原因如下：•腔内的速度变化•非相对论动力学，naïve场刚性缩放和到达时间依赖性•RF波形细节与正弦近似相反，但在低能量下很重要•显著的纵向-横向动量传递•螺线管和腔内的高阶像差•由于大动量扩散而对色度产生强烈影响•其他元素边缘场内的元素•低能时增加了对空间电荷的需求•在非设计阶段处理时变元素的算法缺陷•基于s坐标的公式无法捕获元素边界的飞行时间•任何非常规元素都无法进行精确的分析处理（现在限于低β），而在高度相对论性的情况下，大多数分析加速器和光束建模工具都可以如果没有这些问题，在非相对论性的情况下，可以包括从0到0.999或更大的范围，速度和准确性之间的两难境地是非常真实的，通常会带来有害的影响。当前提案中提出的解决方案，因此被称为低能量（低beta）经验模型，试图通过采用一种有效的经验方法来缓解这一困境，这种方法独立于被建模的物理过程的性质和细节，只要存在一个专用的建模工具，可以正确地将感兴趣的过程建模为有限数量的控制和光束参数的函数。建模工具可以解释所有相关的物理细节，而不需要封闭形式的公式或近似物理过程。结果被渲染成有效的数值模型，可以快速准确地预测详细的机器和梁的行为。这个过程在概念上是简单的和可伸缩的，并且可以应用于任何组件的任何建模工具。扩展这种方法的可能方向有很多。基本上，基础物理的复杂性并不会给这种方法带来额外的概念难度。在当前提出的低能量经验模型范围内获得的经验和开发的基础设施可以作为更雄心勃勃的项目的基础，例如基于受控光束测量或统计积累的机器数据的真实数据的经验模型。这种发展可以导致确定和有效地控制加速器传统上最易挥发的部分的能力。

This proposal aims to develop and validate a new approach to creating online accelerator models, and to further establish it as the basis for accelerator diagnostic and control applications in realistic operation and commissioning environments, especially at the Advanced Rare Isotope Laboratory (ARIEL) project at TRIUMF. The ability to correctly and efficiently model accelerator transport and beam dynamics is critical to the success of any real-time online diagnosis and control task. This is even more so at low energy where key performance parameters are often “frozen in” and too late to change at higher energy. Unfortunately, efficiency and correctness are not always compatible objectives for low energy (low-beta) modeling. In many cases faster analytic algorithms are used online to model effects at low energy, producing incorrect physics. We propose to bridge this gap with an online empirical model to be described later. Failure of analytical models for low-beta beam transport arises from the following: • Velocity changes within cavities • Non-relativistic dynamics, naïve field-rigidity scaling, and arrival-time dependence • RF waveform detail defying sinusoidal approximation but important at low energy • Significant longitudinal-transverse momentum transfer • Higher order aberrations in solenoids and in cavities • Strong impact of chromaticity due to large momentum spread • Elements inside fringe fields of other elements • Increased need to account for space charge at low energy, possibly with subdivided elements • Nontrivial interplay between all phase space dimensions preventing reduction/decoupling of model • Algorithm deficiency to deal with time-varying elements at off-design phase • Inability of S-coordinate based formulation to capture time-of-flight at element boundaries • Any unconventional element defying accurate analytical treatment (now limited to low-beta) While in the highly relativistic regime most analytical accelerator and beam modeling tools can be free of these problems, toward the non-relativistic end, which can encompass range of beta from 0 up to 0.999 or beyond, this dilemma between speed and accuracy is very real, often with detrimental effects. The solution put forth in the current proposal, henceforth referred to as the low energy (low beta) empirical model, attempts to mitigate this dilemma by adopting an efficient empirical approach, independent of the nature and detail of the physical process being modeled as long as a dedicated modeling tool exists that correctly models the process of interest as functions of a limited number of control and beam parameters. The modeling tool can account for all pertinent physical details without need of closed-form formulation or approximation to physical processes. The outcome is rendered into efficient numerical models that can quickly and accurately predict detailed machine and beam behavior. This process is conceptually simple and scalable, and can be applied to any modeling tool for any component. Possible directions in which to extend this approach are many. Basically, complexity in underlying physics does not present additional levels of conceptual difficulty for this approach. Experience gained and infrastructure developed within the current proposed scope of low energy empirical model can serve as the basis for more ambitious projects such as empirical model based on real data from controlled beam based measurements or statistically accumulated machine data. Such development can lead to the capability of deterministically and efficiently controlling the traditionally most volatile sections of an accelerator.