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# 物理代写|高能物理代写High Energy Physics代考|PY751 Multi-level triggers

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## 物理代写|高能物理代写High Energy Physics代考|Multi-level triggers

A sophisticated trigger system should be able to reduce the input rate from background processes in an efficient way without losing good events. In order to improve the quality of an experiment using fast processors one has a specific aspect of quality in mind, i.e. the statistical significance or the number of good events recorded per time unit.

To reduce dead time and to include complex decisions in the trigger, several trigger levels are required. At each trigger level more information is available to perform better filtering. Assuming that the cross section is so high that the experiment is limited by the tape speed, one can only record events with a rate of $7 \mathrm{~Hz}$. In this case one can use three trigger levels.

1. Trigger 1 acts on the prompt information that is available in scintillation counters, proportional chambers or drift chambers with small gaps. Hardwired processors and fast electronics select a rough trigger, which should not run above $10 \mathrm{kHz}$.
2. The input rate at level 2 is $100 \mu \mathrm{s}$ per event $(10 \mathrm{kHz})$. Within this time data can be digitized by ADCs. Special processors like digital signal processors (see Subsection 1.7.1) or special processors with Content Addressable Memories (CAMs) can do a better track or energy cluster search or vertex fitting. Depending on the readout time of the entire event the output rate should be below $20-100 \mathrm{~Hz}$.
3. At level three the complete event information and digitizations are available. The track filtering can be improved and correlations between various detector elements can be utilized to reduce the data rate to $7 \mathrm{~Hz}$, which matches the tape speed. At this level clusters of fast standard processors can be used to finish their task in $100 \mathrm{~ms}$. If $100 \mathrm{~ms}$ are not enough the events can be handed over to several parallel processors. But one must take care when designing a high speed bus. Between each trigger level the events must be buffered. This decouples the different processor speeds and the statistical arrival of the data. The optimal buffer length will be given in Subsection 1.3.1.

## 物理代写|高能物理代写High Energy Physics代考|Queuing theory

The results of queuing theory can be used to answer the following questions which are illustrated by Fig. $1.8$ (Morse 1958; Allen 1978; Margenau and Murphey 1964). The events occur independently of each other and enter the system with a rate of $\lambda=5$ events per second. These events are handled by processors with different rates and different buffer lengths.

1. What is the dead time of a system with an input rate $\lambda$ and a processing rate $\mu=\lambda$ ?
2. What is the dead time of a system as before with five event buffers in front of the processor?
3. How fast must a processor with a single buffer be to get the same dead time as in (2)?

Fig. 1.7. Gain factor obtained by using a second level trigger: $t_{\mathrm{e}}$ is the average waiting time for an event, $t_{\mathrm{R}}$ is the recording time $(\approx 0.1 \mathrm{~s}), t_{p}$ is the processing time for the second-stage trigger (here $t_{\mathrm{p}} / t_{\mathrm{R}}=0.1, t_{\mathrm{p}} \approx 0.01 \mathrm{~s}$ ). Parts (a)-(d) indicate in which way the number of processed events increases for rejection factors $K=1$ to 9 . In (e) $\kappa$ is the rejection rate of the second stage trigger. If events occur at a rate of $t_{\mathrm{e}}=0.001 \mathrm{~s}\left(t_{\mathrm{R}} / t_{\mathrm{e}}=100\right)$ and if $90 \%$ of the triggers are rejected by the second level processor the gain factor is 5 .

## 物理代写|高能物理代写High Energy Physics代考|Multi-level triggers

1. 触发器 1 作用于闪烁计数器、比例室或小间隙漂移室中可用的提示信息。硬连线处理器和快速电子设备选择一个粗略的触发器，它不应该在上面运行10千赫.
2. 第 2 级的输入速率为100米s每个事件(10千赫). 在这段时间内，数据可以通过 ADC 进行数字化。特殊处理器，如数字信号处理器（参见第 1.7.1 小节）或具有内容可寻址存储器 (CAM) 的特殊处理器，可以进行更好的轨道或能量簇搜索或顶点拟合。根据整个事件的读出时间，输出速率应低于20−100 赫兹.
3. 在第三级，完整的事件信息和数字化是可用的。可以改进跟踪过滤，并且可以利用各种检测器元件之间的相关性来降低数据速率7 赫兹，它与磁带速度相匹配。在这个级别，可以使用快速标准处理器集群来完成它们的任务100 小姐. 如果100 小姐还不够，事件可以移交给多个并行处理器。但是在设计高速总线时必须小心。在每个触发级别之间，必须缓冲事件。这将不同的处理器速度和数据的统计到达解耦。最佳缓冲区长度将在 1.3.1 小节中给出。

## 物理代写|高能物理代写High Energy Physics代考|Queuing theory

1. 具有输入速率的系统的死区时间是多少l和处理率米=l ?
2. 与以前一样，处理器前面有五个事件缓冲区的系统的死区时间是多少？
3. 具有单个缓冲区的处理器必须多快才能获得与 (2) 中相同的死区时间？

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。