Tinkering at the main-ring lattice Page: 3 of 21
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- 3 -
beam size = Ih h + [Xp (AP/p)] 2
where h is the horizontal beta function and 7c is the horizontal
beam emittance. If the particle distribution is Gaussian in the (x,x')
space and uniform within (Ap/p), some 92% of the beam will be inside
this beam size. If the distribution is Gaussian in (Ap/p) as well, the
percentage is of course higher. Assuming the entrance to the first
Lambertson to be at 2m downstream from F17, one finds for the ideal main
ring operated at vh =v 19.4,
h = 92.08m, Xp = 5.45m
beam size protons at 125 GeV/c: 11.7mm,
p's at 8.89 GeV/c: 13.6mm.
Note that, for protons, the momentum dispersion contributes more than
90% of the total beam size while it is practically all betatron ampli-
tude for p's. If we are to ease the situation here, the main ring lat-
tice must be modified such that both h and X decrease. There is an
additional feature in the C48-F17 arrangement which makes the situation
even worse. When the beam is moved inward at F17, it has a rather large
positive angle because of the strong horizontal focusing at F17. For the
shift of -40mm, the angle is +0.79mrad so that the kicked beam moves
outward by \8mm at the end of the downstream Lambertson. It has been
pointed out to me by Carlos Hojvat, who designed the system originally,
that any type of closed-orbit bump is of no help since both the kicked
beam and the circulating beam will be affected by it. Such a bump can
change the position and angle of both beams together relative to the
geometrical center line of aperture.* An obvious solution is to roll
the first (upstream) Lambertson to cancel the positive angle and make
the beam parallel to the circulating beam in the second (downstream)
Lambertson. Figs. lA and lB show schematically how two Lambertsons can
be arranged for the optimum beam clearance. Note that the dotted line
*
According to the design report, ref. 1 (p. 2, Chapter 3), four magnets
are already placed at F15, F17, F18 and F22 for this purpose.
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Ohnuma, S. Tinkering at the main-ring lattice, report, August 23, 1982; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc1052178/m1/3/: accessed April 23, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.