EL DETONANTE: ¿CUANDO ESTÁ MIKKEL?

To reduce the amount of the CPU time spent on the simulation of the neutron source, stan-dardise the neutron source, and make the simulated neutron generator positioning more flex-ible, it was decided that the neutron source used in the JET calibration-related calculations would be based on the standard MCNP source definition card (SDEF). Additionally, using this approach multiple source components can be combined to represent the neutron emission from a mixed beam neutron generator. The goal was to produce a neutron source description based on the source components from Table 4.4.

As explained in Section 4.3.1, the ENEA-JSI source subroutine was selected as a ref-erence source and was used for the preparation of the standardised neutron source. Due to the azimuthal symmetry of the generator’s neutron source, only the information about the direction relative to the ion beam and the energy distributions of neutrons as a function of their polar angle was needed.

Two methods of the source description card preparation were tested. First, the method based on the ring detectors provided by the ENEA was tested, and later a different method, based on the ability of MCNP to write out the information about the individual particle histories (PTRAC output file), was developed.

Metod based on the ring detectors

This method for the preparation of the standard MCNP source definition card (SDEF) is based on the neutron spectra estimated by the ring detector tallies surrounding the

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tron source at different emission angles. The method relies on performing the simulation of the neutron production using the MCNP extended by the ENEA-JSI source subroutine in a model where only the target is filled with material while the rest of the geometry is empty.

Ring detector tallies (F5 tally in MCNP) are added to assess the neutron spectra at differ-ent emission angles. The reproduction of the neutron emission properties is achieved by the standard source definition card (SDEF) based on the spectra extracted from these tallies through the analysis of the MCNP output files using an ENEA developed MATLAB script.

The flowchart of the procedure is presented in Figure 4.12. The original procedure used 38 angular bins (36 bins were 5° apart, and two bins 2.5° apart, one in forward and one in backward direction) and energy bins with a 20 keV resolution in the relevant energy region.

The number of angular bins was later increased to 100 (equally spaced in angles) to increase the resolution of the source reproduction.

Some of the limitations of this procedure are:

• The target material always affects the results as it has to be present in the model. The dimensions of the target can be minimised to further reduce this effect.

• The number of ring detectors per simulation is limited to 20 in MCNPX 2.70 and MCNP5 1.40, and to 100 in MCNP5 1.60 and MCNP6. A higher number of angular bins can be achieved by combining the results of multiple simulations where detectors are in different positions.

• The functioning of the ring detectors with the ENEA-JSI source subroutine relies on the modification of another routine, named SRCDX, which is used in simulations where point or ring detector tallies are used. The modified SRCDX subroutine needs to be distributed together with the ENEA-JSI source subroutine and its performance tested to ensure it works properly.

• The production of the source definition based on the same source model but using a different set of energy or angular bins requires the repetition of the MCNP simula-tion(s).

In most cases these limitations are not problematic; however, due to the involvement of the user in the intermediate steps, the possibility of errors made by the user inexperienced in the procedure can be significant. This could be mitigated through automatic generation of modifications to the MCNP input files and MATLAB script based on the required angular and energy bins.

MCNP_otput MATLAB script SDEF.txt

Figure 4.12 A flowchart describing the generation of the source definition card (SDEF) based on the ring detector tallies (in the MCNP_output file) and MATLAB script provided by ENEA.

Method based on the neutron production data

To mitigate the limitations of the method provided by ENEA, a new procedure based on the MCNP’s capability of printing out the particle tracks into a file (PTRAC file) was developed.

To decrease the amount of data, only the particle properties at the time of neutron production events were written to a file. The description of these source events includes the position, energy, direction, and statistical weight of each produced neutron. Once all the information about the produced neutrons was written to the PTRAC file, it had to be extracted. This was performed by a Python script that analysed the file and sorted the particles according to both the cosine of their direction relative to the direction of the ion beam (Y-axis) and according to their energy within this cosine interval. The result of this sorting was the 1D array describing the probability of emission into each cosine interval and the 2D array describing the neutron emission spectrum for each of the cosine intervals. To get a sufficiently detailed description of the neutron emission properties, a large number of neutron production events had to be simulated. Based on the number of angular bins (400, 0.005 wide cosine bins), energy bins (10 keV wide energy bins in appropriate energy interval), and some tests, it was decided that 2 × 10⁸ particles would suffice. This process is schematically described by the left part of the flowchart in Figure 4.13

When extracting data from the PTRAC file, unnecessary rounding errors should be avoided.

MCNP’s PTRAC output file is printed in 5 digits for each of the results, which means that cosine boundaries should be an integer multiple of 1 × 10⁻⁵and energy boundaries an inte-ger multiples of 1 keV for neutron energies above 10 MeV. Due to a relatively large number of the particles, and bins used, both in energy and angle, the sorting was done using the searchsorted function from the NumPy [65] package for scientific computing in Python.

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Source description

Once the information about the neutron emission spectra was obtained through either of the two methods, it was written to a file in an MCNP standard source definition (SDEF) format.

In this format the probabilities for the neutron emission in each of the directions and rela-tive probabilities for emission at different neutron energies are defined. These probabilities correspond to 1D and 2D arrays from data extraction respectively.

The source description of a mixed beam neutron generator was reconstructed as a weighted sum of probabilities for neutron emission based on the information about the relative inten-sity of different neutron source components obtained through the neutron spectrum measure-ment with a diamond detector described in Section 4.3.2 and [63]. In effect this meant that the SDEF distributions for different components were summed into a single SDEF where the intensity of each component was adjusted through their relative intensities (the right part of Figure 4.13).

To make the procedure of combining the source components easier in case of the method based on PTRAC files, the Python script (Python script 1 in Figure 4.13) which produced SDEF files for each of the components also produced another file where the 1D array describ-ing the probability of emission into a cosine interval and the 2D array describdescrib-ing the neutron emission spectra were written in a format simple for reading by another Python script. This second script (Python script 2) combined multiple source components into a single source definition file (SDEF) according to their relative intensities (Figure 4.13). A histogram type description of the neutron source properties was used.

i-th PTRAC Python

Figure 4.13 A schematic description of data extraction and MCNP source definition card preparation based on a PTRAC output file and two Python scripts.