Errors in Measuring Transverse and Energy Jitter by Beam Position Monitors

TL;DR

This paper investigates errors caused by finite BPM resolution in measuring transverse and energy jitter, introducing a dynamic approach with virtual particles to better understand and optimize measurement system accuracy in accelerator physics.

Contribution

It presents a novel dynamic framework using virtual particles to analyze and improve BPM measurement accuracy, considering beam dynamics and error propagation.

Findings

Introduces a dynamic model for BPM error analysis.

Defines error emittances and energy spreads as properties of measurement systems.

Provides methods to optimize measurement accuracy by matching error betatron functions.

Abstract

The problem of errors, arising due to finite BPM resolution, in the difference orbit parameters, which are found as a least squares fit to the BPM data, is one of the standard and important problems of accelerator physics. Even so for the case of transversely uncoupled motion the covariance matrix of reconstruction errors can be calculated "by hand", the direct usage of obtained solution, as a tool for designing of a "good measurement system", does not look to be fairly straightforward. It seems that a better understanding of the nature of the problem is still desirable. We make a step in this direction introducing dynamic into this problem, which at the first glance seems to be static. We consider a virtual beam consisting of virtual particles obtained as a result of application of reconstruction procedure to "all possible values" of BPM reading errors. This beam propagates along the beam line according to the same rules as any real beam and has all beam dynamical characteristics, such as emittances, energy spread, dispersions, betatron functions and etc. All these values become the properties of the BPM measurement system. One can compare two BPM systems comparing their error emittances and rms error energy spreads, or, for a given measurement system, one can achieve needed balance between coordinate and momentum reconstruction errors by matching the error betatron functions in the point of interest to the desired values.