The PB beam line contains four sets of quadrupoles which form two quad-triplets ( see the previous document. PB4Q1 and PB4Q2 form the "flux gathering" quad-triplet while PB6Q1 and PB6Q2 form the "focussing" quad-triplet. The first step is to determine a ratio of field strengths for the two components of each quad-triplet such that they produce equal net focal lengths for both the horizontal and vertical components. This can be done relatively simply using the beam optics program TRANSPORT.
For the PB4 Quad-triplet TRANSPORT can determine the magnet settings required to produce a parallel beam of given momentum from a point source at the primary target. Since the required field strengths scale linearly with momentum then a given PB4Q focussing strength can be expressed in terms of the beam momentum for which a point-to-parallel focuss is achieved.
Similarly, the focussing strength for the PB6 Quad-triplet is expressed as the momentum required for a parallel beam to be focussed to point at the experiment target in PB7.
A large number (81) of TURTLE runs have been generated in which the PB4 and PB6 quads settings were varied over a reasonable range. For each run the number of electrons reaching the PB7 target (assuming no photon production) was determined along with their average momentum. The following plot shows the expected electron yield (electrons striking a 1 inch diamond shaped target per incident primary proton) assuming a 250 GeV secondary momentum tune as a function of the PB4 and PB6 quad settings.
In order to see how well the beam is contained on the target we have plotted the ratio of those electrons which hit the target to the total number which reach the target.
Finally, we have checked to see how the quads affect the beam momentum by plotting the average electron momentum for those electrons hitting the target as a function of the quad settings.
From these plots we have chosen the optimal settings to correspond to PB4Q = 250 to 260 GeV and PB6Q = 225 GeV. This corresponds to an electron yield of about 1.14E-4 ppp with a targetting efficiency of 96% and an average momentum between 235 and 240 GeV.