I have been looking at the development of the EM shower in a small FMS cell for normally incident photons.

The following figures 1-3 show:

 - Left: transverse components p_x and p_y of the normalised momentum direction vector of the optical photons at their production points

 - Right: angular components θ and ϕ of this momentum vector

Figure 1 is for all optical photons, 2 for optical photons that hit the photocathode, and 3 for the ratio of optical photons that hit to all produced optical photons. The plots are for 10 successive normally incident photons with E=30 GeV.

In figure 1, There is a clear band at θ~0.9; this band corresponds directly to the Cherenkov angle (for n=1.65, θ_cer~0.92). In figure 2, there is some interesting structure in ϕ that reflects the geometry of the cell. Along the central vertical and horizontal axes of the cell, there are peaks in the Cherenkov band. Figure 3 shows additionally that photons produced along these central axes have a higher chance of hitting the photocathode. A lot less photons in the Cherenkov band reach the photocathode than I expected.

Figure 1:

Figure 2:

Figure 3:

Figure 4 shows the production location of the photons in the z direction in cm (the distributions are normalised). Red is for all produced optical photons and blue is for hits. Figure 5 shows the ratio of hits to all produced opt. photons.

The photons that hit the photocathode admit a shower max peak that is shifted ~15% closer to the photocathode than the peak for all produced photons.

Up to 40 cm in the cell, only 4% of the produced photons are detected; this quickly rises to 60% at the end of the cell at 45 cm.

Figure 4:

Figure 5: