How many layers are needed?

We want to know how many layers are needed in a certain geometry. Let's assume a 230 MeV beam (the most realistic alternative). The detector should be a bit longer than the range of this beam, let's say five times the range straggling. In that case, a pure beam with no material in front is fully contained.

Use information from DTCToolkit/Output/findManyRangesDegrader.csv, generated by DTCToolkit/Scripts/findManyRangesDegrader.C:

Water phantom degrader	Absorber size	Nominal (physical) range	Nominal (physical) straggling	Inelastic interactions	Energy	Energy straggling
50	3	155.272	1.91	50.93	230.35	0.577

Look at the row with the energy closest to 230 MeV (such as the one above).

In that case, the range is 155.272 mm, with a straggling 1.91 mm. Therefore we need a detector with a length of $155.27+5\times 1.91=164.82\mathrm{m}\mathrm{m}$. The extra length of a single layer (in addition to the here 3 mm degrader) is 435 µm.

$N_{layers}=164.82\mathrm{m}\mathrm{m}/(3\mathrm{m}\mathrm{m}+0.435\mathrm{m}\mathrm{m})\simeq 48$.

So in the case of 3 mm Al absorbers, we need 48 layers to fully stop a pristine beam.