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Samenvatting over 1485 woorden:
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The efficiency of the NeuLAND multiplicity determination is shown in Figs. 6–8. Results were computed for typical neutron energies of 200 MeV, 600 MeV and 1000 MeV, as is commonly done for NeuLAND simulations [8,13] and for NeuLAND configurations of 8 dp, 12 dp, 16 dp, 23 dp and 30 dp. These configurations were chosen, because the configuration with 8 dp is currently (at the publication date of this work) in use, 16 dp have secured funding at present and 30 dp is the design goal (see Section 1). The configurations of 12 dp and 23 dp were added for
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Onderliggende Tekst:
1485 woorden; ca. 7 min.
The efficiency of the NeuLAND multiplicity determination is shown
in Figs. 6–8. Results were computed for typical neutron energies of
200 MeV, 600 MeV and 1000 MeV, as is commonly done for NeuLAND
simulations [8,13] and for NeuLAND configurations of 8 dp, 12 dp,
16 dp, 23 dp and 30 dp. These configurations were chosen, because
the configuration with 8 dp is currently (at the publication date of this
work) in use, 16 dp have secured funding at present and 30 dp is the
design goal (see Section 1). The configurations of 12 dp and 23 dp were
added for upcoming experimental proposals (at the publication date of
this work). The efficiency is shown as a percentage of how often the
correct number of neutrons in the event (that came from the target)
is established. Results are shown as solid lines for the Perfect tracking
algorithm, the TDR algorithm and the DNN algorithm (all discussed in
Section 2). The physics-list uncertainties of the three algorithms are
shown as separate bands (see Section 2). The bands are arbitrarily
placed above 100% in the figures and the band widths represent the 2𝜎
physics-list uncertainties. Note that, as the Perfect tracking algorithm
assigns a shower head to each neutron that produced at least one ‘‘Hit’’
(see Section 2.4), the black curves essentially describe the probability
that all neutrons fired by the particle gun interacted with NeuLAND
and were also detected by NeuLAND.
simulation data. Hence, during an experiment only the solid lines in
Figs. 6–8 will be known.
As can be seen in Figs. 6–8, the TDR and the DNN results (solid
lines) are sometimes higher than the results obtained by the ‘‘Perfect
Tracking’’ algorithm. Since the ‘‘Perfect Tracking’’ algorithm contains
the best possible shower-head identification (see Section 2), this may
seem like a contradiction. However, some events may be ‘accidentally’
assigned the correct multiplicity by either the TDR or the DNN al-
gorithm. In order to understand how this works, consider an event
where four neutrons come from the target. In this case, it is possible
that three neutrons produce ‘‘Hits’’ in NeuLAND and that the fourth
one does not. Subsequently, either the TDR or the DNN algorithm
may wrongly classify the ‘‘Hits’’ produced by three neutrons as a four-
neutron event (consider, for example, the part of the blob above the
cuts in the 3n-figure of Fig. 5). Hence, it is possible for the TDR and
DNN algorithms that the correct multiplicity of the event is found,
while not all neutrons were detected by NeuLAND. For these events
it is impossible to come up with a correct shower head for all neutrons
in the ‘‘Hit’’ selection stage. This phenomenon is designated as ‘false-
positive’ multiplicity assignments. It cannot occur for the ‘‘Perfect
Tracking’’ algorithm, as it only assigns shower heads to neutrons that
are detected (in the sense that they produced scintillator ‘‘Hits’’, see
Section 2). As a result, it is possible that the TDR and DNN algorithms
have a higher multiplicity performance than the ‘‘Perfect Tracking’’
algorithm, as false-positive multiplicity assignments are included. The
dashed lines in Figs. 6–8 give the TDR and DNN result when the
false-positive multiplicity assignments are excluded (These graphs are
designated as the ‘Restricted’ case). However, one should realize that
the computation of the dashed lines in Figs. 6–8 requires the use of the
‘‘Perfect Tracking’’ algorithm (to determine how many neutrons were
actually detected), which means that they can only be computed for
From Figs. 6–8 it can be seen that the problem of false-positive mul-
tiplicity assignments gets relatively smaller as the number of double-
planes increases. This is due to the fact that the probability of neutrons
interacting with NeuLAND increases with the number of dp, which
makes the multiplicity determination more accurate.
From Figs. 6–8, we conclude that the DNN performance is higher
than the TDR performance for all studied neutron energies, multiplic-
ities and NeuLAND configurations (except for the 30 dp point in the
3n and 4n cases of the 200 MeV neutron energies). However, in many
situations (mostly the 3n and 4n cases) the difference in performance is
quite small. However, even such a small difference in multiplicity per-
formance has a significant influence on the ‘‘Hit’’ selection performance
due to our choice for handling different multiplicities with different
‘‘Hit’’ selection DNNs (see Section 2).
Another advantage of the new algorithm is that in several cases the
physics-list uncertainties in Figs. 6–8 are smaller for the DNN algorithm
than for the TDR algorithm. The reason for this is that the optimization
of the cuts in Fig. 5, which only relies on two inputs (number of
clusters and total energy deposition), typically results in a very shallow
minimum. On the other hand, the DNN algorithm uses thousands of
inputs and, hence, has a less shallow minimum. A shallow minimum
causes large fluctuations in the final results when some simulation
parameters (like the physics list) are changed.
Figs. 6–8 also reveal some limitations in the use of both the conven-
tional TDR algorithm and the newly developed DNN algorithm. The
first limitation is introduced by the physics-list uncertainties, which
can sometimes be quite significant (especially at a neutron energy
of 200 MeV, see Fig. 6). Hence, accurate multiplicity determination
will not be possible for experimental data unless these physics-list
uncertainties are better understood. This requires both improvements
in the models used in the physics lists as well as accurate benchmarks
against experimental data. As discussed in Section 2.5, event mixing
could also help for this.
As can be seen in Figs. 6–8, the magnitudes of the physics-list
uncertainties are a complicated function of the number of dp. This
is because any error estimate (like the physics-list uncertainty bands)
is influenced by two opposite effects: overlapping particle showers
and the neutron interaction probability. As the number of NeuLAND
dp increases, so does the probability for a neutron to interact with
NeuLAND, which allows for a more accurate multiplicity determina-
tion. On the other hand, having more dp also leads to the particles
showers (produced by the neutrons) to become more complex, and, as
a result, overlap more often. This effect leads to less accuracy in the
determination of the multiplicity. Since both of these effects increase
with the number of dp, one effect may be slightly more dominant for a
certain configuration, while the other effect is slightly more dominant
for another configuration. This results in fluctuations in the magnitude
of the physics-list uncertainties as a function of the number of dp.
The physics-list uncertainties for both the TDR and DNN algorithms
for multiplicity five are relatively large (at all neutron energies). This
is because multiplicity five is the highest multiplicity considered in our
simulations, meaning that any neutron multiplicity above four will be
classified as five. For this reason, multiplicity five suffers from ‘endpoint
fluctuations’, which have a large impact on our estimate of the physics-
list uncertainties. The endpoint fluctuations can be nicely illustrated
with Fig. 5 for the TDR algorithm. Variations in the parameters of
the lower cut in any multiplicity window are partially compensated by
those same variations in the upper cut of that same window (because all
cuts have the same slope). However, this does not happen for multiplic-
ity five, because it does not have an upper cut. Hence, multiplicity five
suffers from larger fluctuations: the endpoint fluctuations. Fortunately,
endpoint fluctuations can be easily avoided by training the algorithms
(both TDR and DNN) up to one multiplicity higher than what is actually
expected in the experiment.
The second limitation of both the conventional TDR algorithm and
the newly-developed DNN algorithm is the number of false-positive
multiplicity assignments. Since not all neutrons from the target are
actually detected for these events, a proper reconstruction of the neu-
tron 4-momenta will not be possible, despite the fact that the correct
multiplicity was found (see next section). The number of false-positive
multiplicity assignments is particularly large for NeuLAND configu-
rations with a smaller number of dp. The severity of this problem
decreases as the number of double-planes increases. From the figures, it
can be seen why a choice of 30 double-planes was made in the original
design.
From the results presented in this section, we conclude that the DNN
algorithm offers advantages over the traditionally-used TDR algorithm,
both in terms of efficiency and in terms of physics-list uncertain-
ties (although the advantages are sometimes small). However, the
(sometimes large) physics-list uncertainties inhibit a good multiplicity
determination, meaning that both model improvements and accurate
benchmarks are needed for the physics list (for all neutron energies,
but particularly for neutron energies around 200 MeV). As discussed in
Section 2.5, event mixing could also help in this. Furthermore, the num-
ber of false-positive multiplicity assignments can, in turn, inhibit a good
shower-head identification, which is why the number of NeuLAND dp
should be as large as possible.
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