Introduction

When ionising radiation passes through matter, it transfers its energy to the bulk material, which manifests as material heating. Charged particles interact with matter via both nuclear and electrostatic forces and usually deposit their energies over a short path length. On the other hand, electrically neutral particles such as high energy photons and neutrons interact via electro-magnetic and nuclear reactions and can generally travel over a significant distance between interactions [1].

Fission and fusion nuclear reactors are intense sources of various types of radiation, from neutrons, high energy photons to electrons, light and heavy ions. However, owing to the above mentioned reasons, charged particles either lose most of their energy at the location of origin, whereas neutral particles can transfer their energies further away, for instance, to structural or other components. In some cases, components must be kept at cryogenic temperatures, at which the cooling power requirements scale by a factor 1001000 times the heat removal rate owing to the Carnot efficiency of 1.4% and common helium cooling plant efficiencies of between 20% to 35% [2-5]. The heating rate of such devices can range from a few mWg^-1 in low power devices [6] to several Wg^-1 in high power fission [7] and fusion reactors [8] directly due to incident radiation and activation products [9-11], which must be evacuated for stable and safe operation.

When considering neutron and gamma radiation energy deposition, their mechanisms are quite different. Neutrons deposit most of their energy via scattering, which is most effective with light materials. On the other hand, the energy deposition for gamma rays is proportional to some power of the atomic number Z. This implies that gamma radiation is more effective for energy deposition in structural materials commonly used in various nuclear devices than neutrons.

Various particle transport methods are used to quantify the nuclear heating rate and use an effective heating cross section ∑_heat, which is derived from basic nuclear data during the processing stage and is subject to user-specified parameters. The validation of computational schemes is performed by faithfully modelling and reproducing high quality experiments.

In this study, we present the results of two experimental campaigns performed at the JSI TRIGA reactor on nuclear heating measurements in various fission and fusion-relevant materials, and compare them to the calculated heating values using the JSIR2S code [12] by accurate modelling. The heating rates of aluminium, Eurofer97, and tungsten were measured using differential calorimeters based on the CALMOS [13] and CARMEN [14] differential calorimeter designs developed by CEA for the OSIRIS material testing reactor (MTR). The calorimeter design was adapted to lower heating rates and spatial constraints specific to the JSI TRIGA reactor.

In the initial stages of the design, the neutron and gamma heating rate calculations were performed using the MCNP particle transport code [15] in various materials, without considering the self-shielding effect, to asses the expected heating values. Each material sample has unique self-shielding properties and the analysis progressed by including the self-shielding effects by imposing a maximum radiation field attenuation limit of 5%, governing the sample’s size. Each calorimeter was equipped with a four-lead constantan wire heating element, wound inside the alumina pearl and embedded in the calorimeter pedestal, close to the material sample, allowing for the simulation of nuclear heating via electric current injection. The heat transfer was modelled using COMSOL Multiphysics [16] to establish the expected increases in the calorimeter cold and hot spot temperature differences and their time constants with the final design changes [17]. A series of calorimeters with different material samples were constructed, with each undergoing a rigorous calibration procedure, where heating was performed using the embedded electrical heater.

Two experimental campaigns were carried out at the JSI TRIGA reactor [18], the initial one in 2021 at reactor power levels of 100 kW and 250 kW, respectively, with findings reported in [6], where deviations from the expected responses were observed, attributed to non-linear calorimeter calibration responses. In 2022, a second experimental campaign was conducted at a lower reactor power level of 30 kW to minimise non-linear calibration effects.

Both campaigns were reproduced by detailed simulations using the JSIR2S code [12], which couples a modified version of the MCNP 6.1 code [15] with the FISPACT-II inventory code [19] to determine the delayed gamma contribution.

In this paper, both experimental campaigns are briefly described, followed by a description of the modelling steps. The paper concludes with a comparison of the calculated results with the measurements and a proposal for future improvements and developments.

Experiments

Experiments were performed using a custom-designed differential calorimeter at the JSI TRIGA reactor, both of which are described in this section, along with the specifics of individual experimental campaigns.

2.1

Calorimeter

A differential calorimeter sensor for nuclear heating measurements at levels expected in the JSI TRIGA reactor was developed, adapted from the previous CALMOS [13] and CARMEN [14] designs, which were previously used in the OSIRIS reactor. The design is based on a material sample, connected via a thin neck to a heatsink. Thermocouple temperature sensors were placed at each end of the neck. The original designs incorporated cells in a single capsule to form a differential calorimeter: one with a material sample and one serving as a reference. However, the design was updated to a single cell owing to size constraints, with a separate reference sensor with no material sample. Both the reference calorimeter cell and calorimeter cells with the sample material were irradiated at exactly the same position in the central irradiation channel, constrained by the central irradiation channel walls and a bespoke calorimeter cell spacer at the bottom (Sect. 3). During the calorimeter cell replacement, the reactor was shut down and restarted in exactly the same position. Owing to the small sample volume and selection of sample material, no reactivity effects were observed during the calorimeter cell exchange from the reference to the material sample cell.

Nuclear heating was assessed in materials, commonly used in fission and fusion reactors, such as aluminium, graphite, Eurofer97 steel, tungsten, and Nb₃Sn superconductors. As with the previous calorimeter sensor types, the samples were in the form of a hollow cylinder; however, the contact between the material sample and the sensor body was on the inner cylindrical surface of the sample, which allowed for a single calorimeter design accommodating different thicknesses of material samples, as shown in Table 1. The initial assessment of the expected nuclear heating values was performed by calculating both neutron and gamma energy depositions without explicitly modelling the sample material. This was done using the calculated incident neutron and gamma flux, spectrum, and neutron and gamma heating cross sections, neglecting the self-shielding and self-attenuation effects (gamma field depression in the sample thickness) [20]. As expected, the gamma component of the total heating was an order of magnitude greater than the neutron component. Additional calculations were performed to quantify the self-attenuation in the material samples, i.e., to determine the maximal sample outer diameter, which does not significantly perturb or attenuate the incident radiation field and change its underlying heating effect. The attenuation limit was set at 5%, as a compromise between incident field perturbation and energy deposition. In addition to the aforementioned constraints in terms of size, expected heating rate, and perturbation, one of the requirements was to include an electrical heating element for calorimeter calibration. The heating element consisted of a constantan wire wound inside an alumina pearl, which acted as an electric insulator and supported the wire. The wire has four electrical connections for the precise measurement of the injected power via separate voltage and current intensity, independently of the wire resistance variation. In addition to the calibration process, an electrical heater is also necessary for the inference of nuclear heating using the zero method, which is mentioned below. The structural material of the sensor was stainless steel, which has lower thermal conductivity than aluminium. This, combined with the high sensor sensitivity due to the reduced diameter of the pedestal, resulted in a significant temperature stabilization time of approximately 40 min. After establishing the expected heating values, sample material sizes, and other requirements, a calorimeter sensor design was modelled, and the expected temperature profiles and stabilization times were calculated using the COMSOL Multiphysics package [16] to obtain the final sensor design. The results of these analyses are reported in Ref. [17] and the final calorimeter sensor design is shown in Figs. 1 and 2. The manufacturing of the Nb₃Sn superconductor sample was unfortunately not successful because of the unfavorable mechanical properties of the Nb₃Sn material; hence, heating rate measurements with this material were not performed.

Table 1Full-screen View

Radii R₁ and the corresponding sample thicknesses for different materials

Sample material	Sample thickness (mm)	Radius R1 (mm)
Aluminium	2.0	4.4
Eurofer97	1.1	3.5
Tungsten	0.1	2.5

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Fig. 1Full-screen View

(Color online) Schematic view of the calorimeter head with heater and the material sample

Fig. 2Full-screen View

Detailed drawing of the calorimeter sensor used during the experiments. Hot and cold thermocouples are used to measure the temperature difference

Upon manufacturing, the calorimeters were calibrated in a test water tank facility, as shown in Fig. 3, where temperature differences corresponding to injected electrical power were determined, representing the basis for the measurements in the JSI TRIGA reactor by covering the entire expected heating range at different reactor power levels. This procedure yielded two sets of calibration coefficients relating the temperature difference between the hot and cold temperature measurement points: linear, i.e., first-order dependence of the temperature difference to the injected electrical power, valid up to 0.1 W of injected power, and non-linear, 3-order polynomial coefficients, covering the range of 0 W to 0.5 W. Such higher-order dependence is commonly used in calorimetry techniques [21-25]. In this particular case, it stems from the fact that the specific heat capacity depends on the temperature, radiative losses, and changes in thermal contact because the sample material is press-fit to the sample holder. Hence, a 3-order polynomial fit was used.

Fig. 3Full-screen View

(Color online) Calibration water tank with associated measurement and heating equipment

Two different techniques were used to measure nuclear heating.

ΔΔT technique: The temperature difference ΔT_mat between the hot and cold thermocouple is measured in order to determine the heating contribution of the entire sensor equipped with the material sample. Another temperature difference measurement ΔT_ref was performed in the same radiation field using a calorimeter without the sample material (the reference) to determine the heating rate of the calorimeter structure only. The difference is then used to determine the nuclear heating in the actual sample on the basis of the calibration data.

Zero method: The temperature difference ΔT_mat is measured in the calorimeter with the sample material. The reference calorimeter without the sample material is positioned inside the same radiation field, and electrical power is applied to the heater, until ΔT_mat=ΔT_ref is satisfied, at which point the injected electrical power corresponds to nuclear heating in the sample.

It can be observed that the underlying assumption is that both the calorimeter with the sample material and the reference calorimeter are exposed to the same radiation field. This means that the measurement should be performed in the same position and under the same experimental conditions, that is, the same core configuration, control rod position, and duration of the power excursion. The measurements were conducted in an aluminum irradiation channel located at the central (A1) position of the JSI TRIGA reactor core. The channel had custom holes that allowed the ingress of cooling water into the channel, serving as a calorimeter heatsink. An aluminum spacer with a length of 221 mm was manufactured and inserted in the irradiation channel to achieve consistent centering of the sample material at the core mid plane. For consistent positioning in the horizontal plane, the calorimeter sensors were equipped with fins, which centered the sensor inside the irradiation channel and served as an effective heat spreader, maintaining the calorimeter pedestal base at the temperature of the surrounding cooling water.

2.2

JSI TRIGA reactor

The JSI TRIGA reactor is a pool-type reactor with a maximum steady state thermal power of 250 kW. The reactor core is submerged approximately 490 cm below the water surface, as shown in Figs. 4 and 5. It consists of 91 positions in an annular configuration arranged in 6 concentric rings. 4 positions are taken by the control rods, and the rest can be either empty, filled with fuel elements or irradiation positions, which can be dry or filled with water [18]. Two irradiation positions - Triangular channels - occupy three fuel element positions. The in-core irradiation channels are shown schematically in Fig. 6. The core is surrounded by a graphite reflector, which houses a rotary carousel irradiation facility with 40 positions. Aside from the in-core irradiation positions, there are several larger horizontal ports: Tangential, Radial beam, and Radial piercing ports, and 2 two larger ex-core irradiation facilities: the Thermalizing and Thermal columns. The fuel elements are schematically displayed in Fig. 6, consist of a central Zr rod, a homogeneous mixture of fuel and moderator in the U-ZrH form, with graphite reflectors on top and bottom and clad in stainless steel. The reactor core and internal structures around the core are shown schematically in Fig. 7. Two similar reactor core loading patterns were used for the two experiments, as shown in Fig. 8. In both cases, the calorimeter was inserted into the A1 - Central position inside a wet thin-wall irradiation channel (Fig. 6), which has holes on the side, allowing for the exchange of water. Both Triangular channels were inserted during the experiments.

Fig. 4Full-screen View

(Color online) Top view of the JSI TRIGA reactor with Thermal and Thermalizing column, and the horizontal irradiation ports

Fig. 5Full-screen View

(Color online) Side view of the JSI TRIGA reactor, showing the core inside the reactor tank, as well as larger Thermal and Thermalizing column facilities

Fig. 6Full-screen View

(Color online) TRIGA in-core irradiation channels and fuel element

Fig. 7Full-screen View

(Color online) Reactor core and internal structures around the core

Fig. 8Full-screen View

(Color online) Reactor core configuration during the 1 (left) and 2 (right) experimental campaign

Computational modelling

Nuclear heating was modeled using the Monte Carlo particle transport code MCNP [15], for the transport of both prompt and delayed particles, including neutron and photon transport. Electron transport was modelled only inside the sample material, calorimeter body, and irradiation channel, to reduce the computational time but still calculate the energy deposition rate without the Kerma approximation. The ENDF/B-VIII.0 [27] nuclear data libraries [27] were used throughout the modeling.

A detailed MCNP model of the JSI TRIGA reactor was used based on the criticality benchmark model [28]. The model was expanded by introducing irradiation channels and verified control rod positions [29] as well as new triangular irradiation channels [30]. Fresh fuel was used. The reactor model core configuration and control rod positions were modified to reflect the configurations used during the experiments. A 3D ray-traced image of the JSI TRIGA MCNP model used in the 2 campaign is displayed in Fig. 9.

Fig. 9Full-screen View

(Color online) Mesh outer boundaries superimposed over MCNP model of reactor core and the calorimeter with Eurofer97 sample from the 2 experimental campaign. 25×25 voxels in X–Y direction, and 50 voxels in Z direction

The calorimeters, including the material samples within, as well as the supporting structures, such as the bottom spacer, connecting cables, and coupler for calorimeter insertion and withdrawal, were modelled in great detail. A 3D ray-traced image of the calorimeter and supporting structures inserted inside the wet thin-wall irradiation channel is displayed in Fig. 10 and 11.

Fig. 10Full-screen View

(Color online) Ray-traced calorimeter MCNP model, side-views

Fig. 11Full-screen View

(Color online) Close-up of the ray-traced calorimeter model: the pedestal and and accompanying components

Two separate simulation steps were performed to model the heating from both prompt and the delayed gamma rays, the latter owing to the decay of fission and activation products. In the first step, calculations were performed in the criticality mode, and the heating due to prompt radiation was calculated inside the sample over a cylindrical mesh corresponding to the sample dimensions. The energy deposition was calculated separately for neutrons, gamma rays in the kerma approximation, and electrons, as well as the total energy deposition using the TMESH functionality of the MCNP code. The effective multiplication factor k_eff and number of neutrons per fission were also obtained for each individual simulation for power normalization using the formulation described in [31]. The reactor power, as measured by the reactor instrumentation [26] was used to normalize the heating level inside the sample at the readout time.

For the simulation and transport of the delayed radiation owing to the decay of fission and activation products, the JSIR2S code was used. The code utilizes the cell-under-voxel approach, where a mesh is superimposed over the model geometry, and each part of the geometry is divided into individual mesh pieces. A 2 cm×2 cm×2 cm mesh was superimposed, spanning the entire reactor core, control rods, and partially encompassing the graphite reflector as shown in Fig. 9. To calculate the volume-averaged fluxes in each cell-under-voxel, volume calculations in the resulting irregular shapes must be performed using the Monte Carlo method, with the target 1σ accuracy set to 1×10^-5 cm³, primarily because of the small size of the calorimeter and its components.

Once the volumes were calculated, another neutron transport simulation was performed in the criticality mode, and the neutron flux was tallied in each of the above mentioned cells-under-voxel in the CCFE-709 energy group structure [32], which was used for subsequent depletion calculations on a per cell-under-voxel basis. The time-dependent total fluxes were modelled in steps closely following the reactor power readout during the experiments: a change in power step was modelled if the reactor power recorded by the instrumentation differed from the last change by more than 0.5%, resulting in several hundred steps, as displayed in Fig. 12. Changes in k_eff and due to different control rod positions and the effects of the sample were also considered for the normalisation of neutron fluxes. This data, along with the material composition of each cell, were used for the depletion calculations using the FISPACT-II code and ENDF/B-VIII.0 nuclear data libraries. Nuclide vectors were calculated at the time of heating measurements during the experiment and were used to construct a custom secondary particle source description, which was used for delayed particle transport calculations and determination of nuclear heating using the same approach as for prompt heating calculations.

Fig. 12Full-screen View

Recorded and modelled reactor power during the 1 campaign’s Eurofer97 sample irradiation

Because the material calorimeter samples were of relatively small size, a comparison of the energy deposition due to incident gamma rays was made under the assumption of charged particle equilibrium (in the kerma approximation) and by the transport and energy deposition of secondary charged particles.

The nuclear heating results owing to delayed radiation were then combined with the results for prompt radiation, scaled to the reactor instrumentation power readout at the measurement times, to obtain the total heating rates. The 1σ statistical uncertainty of the Monte Carlo particle transport tallies was considered for the uncertainty estimate. Further effects, such as the accuracy of reactor power modelling, geometrical model inaccuracies, uncertainties in material definitions, and nuclear data, were not considered in this study.

Comparison of modelled and measured nuclear heating

In this section, we compare the prompt and delayed heating values obtained from computational modelling with the experimental values.

The heating values obtained by the computations were further divided into individual contributions: prompt neutrons and prompt gamma, as well as the contribution of gamma rays due to the decay of fission and activation products. The nuclear heating values obtained experimentally and by computational modelling and their comparison are graphically presented in Figs. 13 and 14 for the 1st and the 2nd campaign respectively, with numerical values given in Tables S1 and S3 of the Supplementary Materials. The fractions of individual contributions are also reported in Table S2 and S4, respectively. The differences in the modelling frameworks between kerma and dose approximation are presented in Tables S5 and S6, respectively.

Fig. 13Full-screen View

(Color online) Comparison of measured and calculated nuclear heating values for the 1 campaign, performed at reactor power of 100 kW and 250 kW. Values on top of the individual bars represent the total nuclear heating, with black error-bars denoting the 1σ uncertainty. Purple dots and error-bars denote the C/E-1 values and their uncertainties

Fig. 14Full-screen View

(Color online) Comparison of measured and calculated nuclear heating values for the 2 campaign, performed at reactor power of 30 kW. Values on top of the individual bars represent the total nuclear heating, with black error-bars denoting the 1σ uncertainty. Purple dots and error-bars denote the C/E-1 values and their uncertainties

The difference between the simulated and measured nuclear heating is significantly higher for the 1 experimental campaign, where nonlinear calorimeter calibration factors were used to estimate the measured nuclear heating values. The C/E-1 values range between -35% to -28% for aluminium with uncertainty 6%, between -11% to -8% for Eurofer97 with 0.4% uncertainty and between -22% to -18% with 1% uncertainty for tungsten. The discrepancies appear to be much smaller for the second campaign, where special care was taken to irradiate the calorimeter at a sufficiently low power of 30 kW so that the calorimeter response remained in the linear regime. The C/E-1 values here are greatly reduced, being -11.5% with a 3% uncertainty for aluminium, 2.5% with a 0.15% uncertainty for Eurofer 97 and -7.8% with a 1% uncertainty for tungsten.

It is interesting to note that the discrepancy between simulations and measured heating values appears to be systematic, and could be attributed to several reasons:

The computational analysis of the above mentioned uncertainties can be performed by random sampling of both nuclear data within their uncertainties [33], as well as sampling the material composition and model geometry within their uncertainties, known as the total Monte Carlo method. However, such an analysis would be very computationally expensive and beyond the scope of this study.

It can also be noted that although the comparison between the measurements and simulations appears to be within their 1σ uncertainties for the most part, the calculated nuclear heating values are systematically below the measurements, which was not the case in previous analyses of nuclear heating and gamma dose-rates in the JSI TRIGA reactor [12, 34].

Conclusion

We present nuclear heating experiments performed using custom built calorimeter devices, where nuclear heating was measured in aluminum, Eurofer97, and tungsten samples. Two experimental campaigns were performed: the initial one at reactor powers of 100 kW and 250 kW, where the calorimeter responses were determined to be out of the scope of linearity. The second experimental campaign was performed at a much lower reactor power of 30 kW, where the calorimeter response was evaluated to be linear.

Both experimental campaigns were reproduced in great detail, both in terms of model geometry and time-dependent power following. The prompt neutron and gamma radiation were modelled using the MCNP particle transport code, whereas the delayed radiation term was modelled using the JSIR2S code, which coupled the FISPACT-II radioactive inventory calculation code with MCNP.

The agreement between calculated and measured heating values is given, where discrepancies between simulations and measurements for the 1 campaign range between -12% to -8% for Eurofer97 and -21% to -18% for tungsten, while differences of -35% to -28% are observed for aluminum. It is interesting to note that the C/E-1 discrepancy did not increase with an increase in reactor power for Eurofer97 and tungsten, which is the case for aluminum, where the effect of the non-linear response was the most significant.

For the 2 campaign, performed at a reduced reactor power, the discrepancies were much lower, below 12% for aluminum and within 3% for Eurofer97 and tungsten. The calculated heating is in good agreement with the measured heating values within the uncertainty range of the measured values.

Further analysis using the total Monte Carlo method was proposed to identify the source of the systematic discrepancies between the measured and simulated heating values and to identify sensitivity profiles for perturbations of individual simulation parameters.