It is well known that in a few electromagnetic processes (ionisation and
bremsstrahlung) we need to define a low energy cutoff for the production of
secondary particles. This feature introduces an arbitrary limit between two
models of simulation.
Indeed several physics quantities, like the distribution of the energy released by a charged particle along its trajectory, are independent of that limit. Some others, like the total track length in the shower development or the energy flux across boudaries, may be sensitive to the energy cutoff.
The algorithm described in this note allows:
When a ionising particle is near a boundary, even the delta rays of very low
energy can escape the boundary, reach another part of the detector which could
be a sensitive one, and therefore contribute to the response of the detector.
In conclusion, in many circumstances it is meaningful to create explicitly those
delta rays, even if they have low energy.
With the traditional procedure the only way is to build the and dE/dx tables with the lowest possible tcut. It will generate plenty of delta rays along the full trajectory of the ionising particle, even where this generation is undesirable.
The algorithm we will describe now allows us to keep tcut as high as possible, and to generate low energy delta rays only where they are needed, i.e. near the boundaries. The result can be a drastic improvement of the performance of the simulation, keeping the same quality of physics results as with the lowest cut.
Let us call rcut the range corresponding to default energy threshold tcut. The starting remark is the following: at a given point, if the safety radius is smaller than rcut one has to produce additional delta rays. The energies of these delta rays will correspond to ranges between safety and rcut, since those delta rays can escape a boundary.
In figure 1 a proton of 500 MeV passes through a block
of 5 cm of iron.
The production threshold is rcut = 1 mm, which corresponds to tcut = 1.25 MeV
in iron. Which such a threshold there are no delta rays produced in iron.
In fact, in this picture, 100 protons are superimposed, the multiple scattering
The distribution of the energy deposited in iron is shown in plot 1, with a bigger statistic and multiple scattering included.
In figure 2, protons, with the same energy.
The delta rays production threshold is rcut = 10 micron (tcut = 58 keV).
The delta rays are emitted along the proton trajectory. The distribution
of the vertex position can also be seen in plot 2.
The distribution of the energy deposited in iron is shown in plot 1.
The delta rays created at the end of the block of iron can escape the boundary and travel in the gas behind iron. The energy spectrum of those delta rays when leaving iron is in plot 3: it is the energy flux behind the block of iron.
In figure 3, rcut = 1 mm as in case 1, but the
algorithm described in this note is applied.
The delta rays in iron are not created, except those near the boundaries.
The distribution of the vertex position can also be seen in
plot 2. The energy deposited in iron is in
The energy flux behind the block of iron is shown in plot 3. It is the same as in case 2.
The three cases give the distribution of energy deposit in iron. But only the cases 2 and 3 can simulate the energy flux behind the block of iron. Concerning the performance, in this example, case 3 is about 10 time faster than case 2.