Final focus systems for linear colliders Page: 2 of 40
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1. INTRODUCTION
The final focus system of a linear collider must perform two primary functions: it must focus
the two opposing beams so that their transverse dimensions at the interaction point are small
enough to yield acceptable luminosity, and it must steer the beams together to maintain collisions.
In addition, the final focus system muBt transport the outgoing disrupted beams to a location
where they can be recycled or safely dumped. Ab of this writing, the only full-scale collider final
focusing system actually constructed is that of the SLAC Linear Collider, better known simply
as the SLC.
The SLC is designed to collide 50 GeV beams of electrons and positrons at an initial luminosity
of about 10“ cm-2 sec-1 and ultimately to reach a luminosity of 6 x 10s0 cm-2 sec-1 when several
planned improvements are completed.1 White this luminosity is appropriate for the SLC energy
range, a linear collider built for a much higher energy will need much greater luminosity. This is
because the cross sections for interesting physics, described by point-like fundamental processes,
drop with increasing center-of-mass energy as 1/jE2^. The cross section for producing new quark-
antiquark states, for example, is expected to be roughly
oQq * 10-S7 E& [TeV-2] cm* . (l)
Thus, the luminosity appropriate for a machine with energy ECJDM is about
L = 1082 El^ [TeV2] cm“2 sec"1 . (2)
At this luminosity, roughly 100 QQ states would be produced per day if they exist at all at that
energy. The event rate for interesting physics processes is expected to be about the same for all
machines satisfying this relationship.3
Luminosity is given by the expression
1_ f N+ JV-
4x Ox0y
(3)
where N+ and N~ are the numbers of positrons and electrons per bunch, and / is the frequency of
^<fjji^|ns. ffx and ov are the RMS radii of the bunches in the horizontal and vertical dimensions,
2
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Erickson, R.A. Final focus systems for linear colliders, article, November 1, 1987; Menlo Park, California. (https://digital.library.unt.edu/ark:/67531/metadc1093183/m1/2/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.