Due to problems encountered during our first run it seemed desirable to revisit the focusing tube design. There are two primary design constraints, minimize the field gradient at all points on the proton paddle (hopefully reducing field emission), and optimize the cell geometry for proton acceptance. To easily address both goals I have used an electrostatic tracking program (Simion) and realistic beam protons (5000 each run from Alejandro's Monte Carlo) to compare a variety of designs. The figures of merit used were the percentage of protons to hit the detector and the field gradient at the edge of the focusing tube. The plot to the right shows the equipotential surfaces and a few typical trajectories for the current design. What you see is a slice through the center of one of the focusing cells. This plot makes it very clear where the highest gradient regions are.

One should note that the differences between the results I show here and Eric's are primarily due to acceleration voltage. I have run at a variety of voltages and my results match Eric's fairly closely (e.g 88.4% versus ~91% at -35 kV). Note that my results are based on a realistic proton energy distribution which is peaked at the higher energy end of the spectrum. I would attribute the remaining difference to slight changes in geometry. Anyway, my feeling is that with the proposed redesign we will be able to completely eliminate the field emission. Therefore the extra 5% is worth going for. Particularly if we can achieve it without raising the acceleration voltage which is constrained by field emission from the edges of the Quansit Hut. This part of the old design we have little control over, and thus I'd like to run at as low a voltage as possible. If it turns out that this design doesn't solve the problem (We should know in a few weeks) it is trivial to make a plate with no tubes.