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Unformatted text preview: 25. Accelerator physics of colliders 1 25. ACCELERATOR PHYSICS OF COLLIDERS Revised July 2009 by D.A. Edwards (DESY) and M.J. Syphers (FNAL). 25.1. Luminosity This article provides background for the High-Energy Collider Parameter Tables that follow. Of prime importance in a collider run is the integrated luminosity ; the ratio of yield to cross section. Integrated luminosity is the integral over time of the instantaneous luminosity denoted here by L . Today’s colliders all employ bunched beams. If two bunches containing n 1 and n 2 particles collide head-on with frequency f , the luminosity is L = f n 1 n 2 4 πσ x σ y (25 . 1) where σ x and σ y characterize the transverse beam profiles in the horizontal (bend) and vertical directions. In this form it is assumed that the bunches are identical in transverse profile, that the profiles are independent of position along the bunch, and the particle distributions are not altered during bunch passage. Whatever the distribution at the source, by the time the beam reaches high energy, the normal form is a useful approximation as suggested by the σ-notation. In the case of an electron storage ring, synchrotron radiation leads to a Gaussian distribution in equilibrium, but even in the absence of radiation the central limit theorem of probability and the diminished importance of space charge effects produces a similar result. The n ’s and σ ’s in Eq. (25 . 1) may change with time during a “store”, and control of that time variation is a major factor in integrated luminosity. The integral achieved over a period such as a week is a measure of overall systems performance, as it will include such inﬂuences as turn-around time for refill. The formula needs a variety of modifications depending on the type of collider; for example, the angular distribution of particle velocities in a bunch may cause a significant variation in transverse beam size through the collision overlap region. This effect and others specific to collider type will be discussed in later sections. In the Tables, luminosity is stated in units of cm − 2 s − 1 . Integrated luminosity, on the other hand, is usually quoted as the inverse of the standard measures of cross section such as femtobarns and, recently, attobarns. Subsequent sections in this report enlarge brieﬂy on the dynamics behind collider design, comment on the realization of collider performance in a selection of today’s facilities, and end with some remarks on future possibilities. 25.2. Single Particle Dynamics Today’s operating HEP colliders are all alternating-gradient synchrotrons [1,2], and the material of this section reﬂects that circumstance. The single particle transverse motion in this focusing structure is not a simple sinusoid; rather it may be expressed in the form x ( s ) = A p β ( s ) cos[ ψ ( s ) + δ ] , (25 . 2) C. Amsler et al. , PL B667 , 1 (2008) and 2009 partial update for the 2010 edition (http://pdg.lbl.gov) January 28, 2010 12:02 2...
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