0 Estimates of Dispersive Effects in a Bent NLC Main Linac ∗

An alternative being considered for the Next Linear Col-lider (NLC) is not to tunnel in a straight line but to bend the Main Linac into an arc so as to follow an equipotential. We begin here an examination of the effects that this would have on vertical dispersion, with its attendant consequences on synchrotron radiation and emittance growth by looking at two scenarios: a gentle continuous bending of the beam to follow an equipotential surface, and an introduction of sharp bends at a few sites in the linac so as to reduce the maximum sagitta produced. In our first scenario, the Main Linac remains as close as possible to an equipotential surface. Minimalism suggests that we try bending the beam by vertically translating already existing NLC quadrupoles, without introducing new elements or additional magnetic fields. We thus propose that steering be accomplished by precisely aligning all the quads " level " along the equipotential and then raising the vertically defocusing (D) quadrupoles to steer the beam through the centers of the vertically focusing (F) quads. 1 Bending at the D quad locations will minimize the generated dispersion. To estimate the order of magnitude of dispersion produced by such an arrangement, we calculate (a) assuming a periodic sequence of magnets while (b) neglecting the effects of acceleration [1] and (c) keeping only leading terms in the bend angle. Our results will be reasonably correct provided that upstream injection into the Main Linac is redesigned to match the new arrangement. Further details of the calculation and others discussed in this paper are documented elsewhere. [2] Figure 1 shows the physical layout of quadrupoles and identifies the geometric parameters. It is practical to write the vertical offset of the quadrupole relative to the equipotential, d − y sag. In terms of the distance between quadrupoles, L, the local betatron phase advance per cell, µ, and the radius of the earth, R, this offset is d − y sag = L 2 R 1 2 + 1 sin(µ/2) (1) To make a numerical estimate of this offset at the high energy end of the linac, we take L ≈ 19 m, µ ≈ π/2, and R ≈ 6400 km. Eq.(1) then yields d − y sag ≈ 108 µm. The dispersion can be estimated easily using two observations: * Work supported by the U.S. Department of Energy 1 The usual convention is for " …