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 [math]\displaystyle{ 155.27 + 5 \times 1.91 = 164.82\ \mathrm{mm} }[/math]. The extra length of a single layer (in addition to the here 3 mm degrader) is 435 µm.

[math]\displaystyle{ N_{layers} = 164.82\ \mathrm{mm} / (3\ \mathrm{mm} + 0.435\ \mathrm{mm}) \simeq 48 }[/math].

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