Third-order Corrections to the SLC Final Focus

The minimum p achievable at the interaction point @*> with the current design of the SLC final focus is limited to -5 mm by third order optical aberrations, most notably the Utzti and W3466 terms (using the notation of K. Brown). A new lattice is presented which effectively zeros these terms. The remaining third order terms which accrue from the interleaved sextupole pairs in the chromatic correction section (CCS) can be cancelled by the inclusion of five octupoles (two in the CCS, and three in tbe final telescope). The resulting final focus system is corrected to third order for any usable range of P*-(given the constraints on the beam divergence at the interaction point). The potential luminosity obtainable from such a system is also presented. .-I. It iRODUChON. The current design of the SLC final focus essentially follows the design proposed by Brown[l]. It consists of two tele. 7. scope sections, -separated by a chromatic correction section . (CCS) where two strong interleaved sextupole pairs (X and Y) are used to cancel the chromatic contribution to the beam size at the interaction point (IP)[2]. Although the design effectively cancels the second-order (chromatic) aberrations, the bandwidth of the system is limited by third-order effects. Analysis of these aberrations[3] has shown that they arise from two separate sources: (i) a small phase error between the sextupole pairs and the final triplet, and (ii) the interleaved X and Y sextupole pairs. The effect of the aberrations is to limit the minimum p* at the IP to approximately 5 mm in both planes; a smaller /3* leads to a larger beam size as the aberrations begin to dominate over the linear optics. With the typical beam emittances seen in the final focus during the 1992 physics run (600 by 400 prnpr in the horizontal and vertical planes respectively); the smallest possible p* was limited by SLD background considerations to give a beam divergence at the IP (t3*) of_-300 vr in both planes, corresponding to a p*, of -7 mm and a p*y of -5 mm, which compare well to.the optical optimum. For the current (1993) physics run, a “flat beam” is being used[4], where the vertical emittance in the final focus is of the order of 60 pnq.tr. The smallest vertical spot size (-0.8 pm) is now achieved with an IP beam divergence of approximately 100 pr, well below the SLD background limit. In order to increase the divergence (decrease the p*), it is first necessary to identify and correct those aberrations which lin& the beam l Work supported by Department of Energy contract DE-AC03-76SFOO515 size. In this paper, a third-order correction scheme is proposed which effectively minimizes the third-order contributions to the beam size, enabling a vertical optimal p* of -1 mm, achieving a vertical spot size of -0.3 pm at a divergence of 245 pr, given a vertical emittance of 60 prprn. The decreased spot size gives a luminosity increase by a factor of 2.8 from the geometry alone, and an additional factor of -1.4 from the beam-beam interaction (pinch effect), giving an overall luminosity gain of a factor of approximate x4. II. LIMITING THIRD-ORDER ABERRATIONS. An analysis of the SLC final focus has shown[l] that the dominant vertical aberration is a high order chromaticity, UMti (using the TRANSPORT[S] matrix notation). Using Lie Algebra techniques a complete analysis of the important third(optical) order aberrations has been made in terms of monomials in the Hamiltonian[3]. The monomial corresponding to the afore mentioned chromaticity is y”S’, where y’ is taken to be the phase space coordinate at the IP. In all further discussions, it is assumed that the phase space coordinates (x,x’,y,y’) refer to those at the interaction point. Table 1 gives the results of the analysis (taken from [3]). TRANSPORT Coefficient % of total Monomial notation (meters) a2 ” yw “3466 229.5 86 xjJ”6 “M&3246 817.5 6