Effects of Position and Angle Offsets on NLC Luminosity

We present simulation results for the luminosity reduction due to position and angle offsets in the beams colliding at the NLC interaction point. We look at the nominal NLC-B-500 and NLC-B-1000 designs and also at designs having the vertical beta function doubled at the IP. E ects of position and angle o sets on NLC luminosity K.A. Thompson and T.O.Raubenheimer The purpose of this note is to study the e ect on luminosity of position and angle o sets in the beams colliding at the NLC interaction point. Baseline NLC interaction point design parameters are as given on the NLC website [1] and a previous note [2]; for convenience we redisplay them in Table 1. In this note we shall focus on the NLC-B-500 and NLC-B-1000 designs and variations away from them. The GUINEAPIG beam-beam program [3] is used to simulate the beam-beam interaction. An interesting result of a previous study [2] is that the luminosity (not only the total luminosity, but also the fraction of the luminosity near the nominal energy) is quite insensitive to variations in the vertical beta function If the vertical beta function is increased by a factor of two from the nominal value, for zero-o set collisions one obtains a luminosity degradation of only 10% for NLC-B-500 and 15% for NLC-B-1000. The payo for this luminosity loss is a loosening of tolerances in the nal focus. In addition to quantifying the e ects of o sets on the nominal NLC, another purpose of this note is to compare the e ects of o sets in the relaxed beta function scenario. If the charge is lowered from its nominal value, the disruption will be reduced further. Obviously the overall luminosity will go down when the charge is lowered. But we also wish to check how the luminosity degradation with o set is a ected in the relaxed beta function case. Thus we also examine the case where the charge is reduced from the nominal value of N = 0:95 10 to 0:8 10 (and the vertical beta function is doubled). We show the results of scans in the full vertical o set (in units of the vertical beam size, except for Figures 4 and 12 in which the o set dy is given in nanometers) and scans in the crossing angle y [NOTE: this is the full angle between the beams, not the half-angle]. In all of Figures 1 through 8, the solid curve is for the nominal parameters (NLC-B-500 in Figures 1 through 8, and NLC-B-1000 in Figures 9 through 16), the dashed curve is for the vertical beta function doubled from its nominal value (i.e. y increased to 0.30 mm for NLC-B-1000, and y increased to 0.24 mm for NLC-B-500), and the dotted curve is for doubled vertical beta function and reduced charge (from the nominal value of N = 0:95 10 to 0:8 10). Figures 1 and 9 show the luminosity LD per bunch as the y-o set is varied. Figures 4 and 12 show the same thing, except that the y-o set is plotted in nanometers instead of in units of y. Figures 2 and 10 show the luminosity enhancement factor HD LD=L0 where TABLE 1. NLC IP parameters for baseline designs NLC-A-500 NLC-B-500 NLC-C-500 NLC-A-1000 NLC-B-1000 NLC-C-1000 Ebeam [GeV] 267.5 257.5 250. 523. 504. 489. N [10] 0.75 0.95 1.1 0.75 0.95 1.1 x= y [10 6 m-rad] 4.0/0.06 4.5/0.1 5.0/0.14 4.0/0.06 4.5/0.1 5.0/0.14 x= y [mm] 10/0.1 12/0.12 13/0.2 10/0.125 12/0.15 13/0.2 z [ m] 90. 120. 145. 90. 120. 145. x= y [nm] 276.43/3.39 327.35/4.88 364.50/7.57 197.69/2.71 233.99/3.90 260.62/5.41 L0 [10 33 m ] 4.777 4.496 3.490 8.365 7.870 6.830 Ax=Ay 0.009/0.9 0.010/1.00 0.011/0.725 0.009/0.72 0.01/0.8 0.011/0.725 Dx=Dy 0.094/7.67 0.117/7.87 0.136/6.53 0.094/6.85 0.103/7.03 0.136/6.53 avg 0.14 0.11 0.09 0.39 0.30 0.25 LD [10 33 m ] 6.51 5.84 5.21 12.57 11.36 10.24 HD LD=L0 1.36 1.30 1.49 1.50 1.44 1.50 n 1.08 1.18 1.24 1.39 1.53 1.62 B 4.3% 3.9% 3.7% 9.5% 9.2% 8.7% Num. bunches per train 95 95 95 95 95 95 Repetition rate 120 120 120 120 120 120 LD [cm sec ] 7.42 6.66 5.94 14.33 12.95 11.67