Effect of a large Oth harmonic octupole on stable betatron oscillations Page: 3 of 9
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:
- 2 - C18! 73-6
asimthal distance, measured along the equilibrium orbit, K(s) is the gradient
forcing function (a =rs t: , 0(s) is the octupole forcing function, given by
0(s) - .(2.2)
gere, the iagnetic field is assued to be expanded in the series
3=-5 + 3x+' "xZ +'15"x3 . . , (2.3)
and p - op , (2.4)
with p the beading radius.
Our first assumption is the stability of the linear betatroa system. Ve
thus transform to betatron coordinates1:
1i -= , (2.5)
# = (2.6)
1 d ' (2.7)
where C is the circumference of the equilibrium orbit. Equation (2.1) is thea
li + v 1i - , p3oi9 , (2.g)
where differentiation is with respect to the angle variable, *.
The smooth approximation consists of replacing p(s) in this equation by
some average value,
_ ... ...r...,.
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.
Month, M. Effect of a large Oth harmonic octupole on stable betatron oscillations, report, September 20, 1973; Upton, New York. (digital.library.unt.edu/ark:/67531/metadc1022442/m1/3/: accessed November 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.