Global orbit corrections Page: 3 of 7
This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to Digital Library by the UNT Libraries Government Documents Department.
The following text was automatically extracted from the image on this page using optical character recognition software:
In Reference , I will show how to solve the general problem when
the machine contains unknown magnet errors of known probability distribution, we
make measurements of known precision of the orbit displacements at a set of
points, and we wish to apply correcting bumps to minimize the weighted rms
orbit deviations. In this report, we will consider two simpler problems,
using similar methods. In Section II, we consider the case when we make M
beam position measurements per superperiod, and we wish to apply an equal
number M of orbit correcting bumps to reduce the measured position errors to
zero. In Section III, we consider the problem when the number of correcting
bumps is less than the number of measurements, and we wish to minimize the
weighted rms position errors. We will see that the latter problem involves
solving equations of a different form, but involving the same matrices as the
II. Reducing the Position Errors to Zero.
Let the beam position monitors be located at the points
s = sm + kS, m = 1,..., M, k = 0,...,N-1 , a (2.1)
where s is the distance measured along the reference orbit, sm are a set of M
points within a superperiod, k is the superperiod index and S is the length of
the reference orbit in a superperiod. Note that we assume the beam position
monitors are located at periodic points in all superperiods. Let the measured
orbit errors (horizontally, or vertically) be -Ykm. We wish to find a set of
orbit bumps Bz, which reduce the measured orbit deviations to zero. The bumps
are located at the points
Here’s what’s next.
This report can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Report.
Symon, K. Global orbit corrections, report, November 1, 1987; Illinois. (https://digital.library.unt.edu/ark:/67531/metadc676486/m1/3/: accessed April 26, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.