We introduce a diagnostic for measuring the transverse phase space (TPS) and transverse second moments of a particle beam in a single shot. The diagnostic consists of a slit followed by a simple projection beam line to project the TPS onto an imaging screen. The beam line is composed of a skew quadrupole magnet followed by a normal quadrupole magnet with an imaging screen at the end. The skew quadrupole generates a coupling between the initial $x$ and the final $y$, while the normal quadrupole removes the correlation between the initial $x$ and the initial $x^{\prime }$. Thus, the initial $(x,x^{\prime })$ is mapped onto the final $(x,y)$. The slit is needed before the projection beam line to remove the initial $(y,y^{\prime })$ contribution from the final $(x,y)$ image on the screen. We present simulation studies and a demonstration of the diagnostic with an experiment performed at Argonne Wakefield Accelerator facility. We also discuss the method’s limitations.

中文翻译：

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使用投影法单次测量横向第二矩

我们介绍一种用于测量单次射束的横向相空间（TPS）和横向秒矩的诊断程序。诊断包括一个狭缝，然后是一条简单的投影光束线，以将TPS投影到成像屏幕上。光束线由偏斜四极磁体，然后是普通的四极磁体，末端带有成像屏幕。歪斜的四极杆在初始$X$ 最后 $ÿ$，而普通四极杆消除了初始 $X$ 和最初的 $X^{\prime }$。因此，最初$（X，X^{\prime }）$ 映射到最终 $（X，ÿ）$。在投影光束线之前需要缝隙以去除初始$（ÿ，{ÿ}^{\prime }）$ 决赛的贡献 $（X，ÿ）$屏幕上的图像。我们将在Argonne Wakefield Accelerator设施中进行的实验中提供模拟研究和诊断证明。我们还将讨论该方法的局限性。