1 INTRODUCTION

One of the main specific features of the Tokamak with Reactor Technologies (TRT) project [1] is application of high-temperature superconductors (HTS) in the electromagnetic system (EMS). The HTS allow creating strong toroidal magnetic fields of up to 8 T, which, in turn, allows reaching plasma parameters corresponding to thermonuclear fusion in a compact installation. Such an installation would allow working out key thermonuclear technologies, including new divertor configurations, lithium wall, along with various method of auxiliary heating and maintaining a quasi-stationary current. The installation must also enable the regime of operation with short, about 10 seconds, burning using tritium. In this regime, the thermonuclear-energy yield will exceed energy used by external sources for heating plasma (Q >1). In other words, plasma heating by alpha particles will become dominant.

Using high-temperature superconductors in TRT EMS requires solving a number of problems. Heating of superconductors by ionizing radiation above critical temperature must be prevented, in particular. Therefore, it is necessary to estimate the minimum sufficient efficiency of radiation shielding that can be provided by the vacuum vessel (VV). Helium with temperature varying in the range from 5 to 20 K will be used for cooling the HTS, thus providing a certain time gap to mitigate conductor heating [1].

In this work, we estimated the energy release for the proposed vacuum vessel and EMS, both space-resolved and averaged over the volume of components. These values determine the amount of heat that has to be removed from the EMS elements.

The TRT concept [1] assumes that the total neutron yield with D–D plasma will be at the level of 0.5 × 1018 neutron per second. For plasma containing 1% of tritium, the expected yield will be twice higher, about 1018 [1]. The maximum expected density of neutron flux in D–T plasma equals 2 × 1012 n/(cm2 s).

A simplified model chosen for preliminary analysis of energy release in the vacuum vessel (VV) and TRT EMS elements is illustrated in Fig. 1.

Fig. 1.
figure 1

Simplified 3D model of TRT vacuum vessel (VV) and EMS, including toroidal field coils (TFC), poloidal field coils (PFC), and solenoid.

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The model includes a steel vacuum vessel filled with borated water, toroidal field coils (TFC), poloidal field coils (PFC), and a solenoid. The outer surface of the vacuum vessel is covered by two shielding layers consisting mainly of tungsten and boron carbide. The divertor and in-vessel components facing plasma are not presented in the model.

The simplified model does not contain ports for diagnostic equipment and external heating systems. In reality, the ports will be partially filled. In addition, the space between the vessel and the PFC will also be filled. Therefore, the results of calculation of energy release for the outer segments of the toroidal and poloidal coils along the major radius can substantially differ from real. The calculated heat loads for the outer segments can only be used as the first approximation. At the moment, we are interested in the inner segment of the toroidal coil that is closest to plasma and is thus mostly loaded. The presence or the absence of ports is irrelevant for this segment.

2 THE MODEL AND THE METHOD OF CALCULATION

Calculations were carried out using the MCNP code [2]. A simplified CAD model was transformed into an MCNP model by means of the SuperMC program [3]. The RSICC license was obtained for using the MCNP code, along with training and certification at the NEA/OECD.

We used material specifications from the MCNP ITER model [4] in our MCNP model: pure tungsten (at least 99.7%, Plansee [5]), S316(L)N-IG steel, and boron carbide with natural isotope content [6] with a density of 2.3 g/cm3, which is lower than that offered by Virial LLC (St. Petersburg) [7]. It was assumed that VV water contains 0.8 wt % of boron. In the first variant of the model, shielding layers around vacuum vessel (Fig. 2) consisted of a homogenized composition of steel, tungsten, and boron carbide in proportion determined by thickness and density of the corresponding layers. In subsequent optimized variants of shielding, the inner shielding layer was specified to consist of pure boron carbide, while the outer layer was assumed to be fabricated from tungsten. We used the ENDF/B-VII library of nuclear data [8]. We also calculated variants of using boron with 95% enrichment with the 10В isotope.

Fig. 2.
figure 2

Vacuum vessel dimensions and materials.

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The source configuration was chosen in the form of a toroidal ring located in the equatorial plane of the tokamak (Z = 0 cm) along major radius of R = 215 cm. Such an approximation is acceptable for making preliminary estimates, taking into account that contribution from multiply scattered neutrons to neutron flux on the VV wall is dominant, which will be demonstrated below. Calculations were carried out for the D–D and D–T plasmas, assuming that ion temperature is equal to 10 keV.

We calculated average values of fluxes and nuclear heat rate for elements of the model filled with materials. Spatial energy distribution of the neutron and gamma ray fields, along with energy release in the area including one of the toroidal field coils, solenoid and crossing poloidal coils, were calculated. The spatial resolution was set equal to 1 cm. The total yield of the neutron source for both variants, the D–D and the D–T ones, was assumed to be equal to 1018 n/s. Calculated parameters for other values of neutron yield or for a mixed D–D + D–T source, can be obtained by using the corresponding linear combination. Statistical errors of calculated quantities were small and did not exceed 0.1%. These errors can be neglected relative to systematic errors caused mainly by using an extremely simplified geometrical model.

3 RESULTS

3.1 D–D Plasma

Results of calculation of energy release in the vacuum vessel and EMS for D–D plasma are presented below (Fig. 3, left). The diagram illustrates the total energy release by neutrons and gamma rays. In the case of D–D plasma, neutrons transfer nearly all energy to vacuum vessel water. Energy release in the toroidal field coils is on the order of several mW/cm3. The inner segment of the toroidal coil in the region close to the equatorial plane of the tokamak experiences the strongest heating, as expected.

Fig. 3.
figure 3

Distribution of energy release, (left) D–D and (right) D–T plasma.

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Distribution of energy release density along major radius in the equatorial plane for inner segments of the VV and TFC is presented in Fig. 4 (D–D, left). Contributions from neutrons and gamma rays are plotted separately. The following layers of the VV and TFC materials are shown (left to right): the first steel layer of the VV body (VV inner), borated water layer closer to plasma (Water), an outer steel layer of the VV body (VV outer), two shielding layers (Sh#1 and Sh#2), a gap, an outer part of the TFC body (TC steel), TFC wires (TC wires), and an inner part of the TFC body (TC steel). In the case of D–D source, the energy release in the 14-cm-thick water layer drops by approximately a factor of 5. Water-layer thickness of 9 cm corresponds to reduction in specific energy release to 1/e of its original value. Energy release in the TFC is illustrated separately in the lower part of the figure. The length corresponding to reduction in energy release to 1/e of its original value equals 17 cm in this case, i.e., it is nearly twice larger than in water. Contribution from gamma rays in energy release in the TFC material is dominant.

Fig. 4.
figure 4

Energy release distribution along major radius: (a) D–D plasma, VV; (b) D–T plasma, VV; (c) D–D plasma, TFC; and (d) D–T plasma, TFC.

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3.2 D–T Plasma

Neutrons penetrate much further in the case of D‒T plasma (Fig. 3, right). In the process, contribution from gamma rays to TFC heating is also larger than in the case of D–D plasma (compare left- and right-hand side diagrams in Fig. 4).

The TFC is subjected to the action of both local gamma rays stemming from photons created in the TFC itself and external gamma rays coming from the VV. To separate contribution from locally created photons to energy release, we conducted a separate calculation in which only gamma quanta appearing in materials of the TFC itself were taken into account. This resulted in reduction in maximum energy release from 38 to 26 mW/cm3 (≈30%). In the process, maximum reduction was observed near the TFC surface facing the VV. However, the average value of specific energy release in entire TFC volume decreased by only 12%. Based on this result, we conclude that contribution of gamma radiation generated in the TFC itself to heating is dominant. Contribution of external photons is comparable but still much lower and only at the VV‑facing surface.

Shielding of TFC from gamma rays from the VV side makes sense only if inhomogeneity of energy release near the surface is of importance. To minimize TFC heating, efforts must be undertaken to suppress the neutron flux itself.

Revisiting Fig. 4 (upper right), it can be seen that, in the case of D–T plasma, given water layer reduces energy release by only a factor of 3 instead of a factor of 5 as was the case with the D–D plasma. This is caused by the fact that the cross section of elastic neutron–proton interaction [9] at energy level of 14 MeV is relatively small (0.68 barn). A 14-cm water layer is insufficient for such neutrons. This is a common problem of compact tokamaks. For example, using a layer of ZrH2 of the same thickness was proposed in [10]. According to calculations [10], ZrH2 is an order of magnitude more efficient in reducing heat release. This approach requires additional analysis for TRT conditions.

The presence of a large amount of hydrogen in the composition of the shielding layer results in return of considerable part of neutrons back into the vacuum vessel. Results of calculation of neutron spectrum as a function of position in the VV and TFC construction are illustrated in Fig. 5. The figure depicts neutron energy distributions averaged over the volume of layers of different materials of the VV and TFC. A cumulative representation of the distribution function was chosen in order to make the fraction of neutrons with specific energy in the total flux more evident. Energy distribution in the inner steel layer of the vacuum vessel (labeled “VV inner steel”) is presented in the upper part of the figure. It can be seen that the fraction of neutrons with energies close to 14 MeV amounts to only one third of the total flux on the VV wall. This fraction drops further as we move deeper into the VV and the TFC.

Fig. 5.
figure 5

Cumulative energy distributions of neutron flux density for layers of VV and TFC materials.

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4 ANALYSIS

We performed calculations for variants of using boron with a natural isotope content and with 95% enrichment with 10B in water and the VV shielding layers. The results obtained for D–T plasma are presented in Table 1. Heating is higher in the case of using natural boron but only slightly: the difference does not exceed 8%.

Table 1. Comparison of energy release in TFC wires with enriched and natural boron, mW/cm3
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Figure 6 explains this result. The figure presents distribution of contributions from neutrons and photons to energy release in the TFC wires depending on energy. Calculation was performed for natural boron in this case. It can be seen in the left-hand side that contribution from neutrons with energy close to 14 MeV is substantial, despite the fact that fraction of such neutrons in the flux at this location is small (see the curve labeled “TC copper” corresponding to the middle part of the TFC consisting mainly of copper in Fig. 5). Contribution from gamma rays is also dominated by high-energy photons. It can be seen in the right-hand side of the figure where the energy scale is logarithmic that contribution from particles with energy below 100 keV to energy release is nearly absent.

Fig. 6.
figure 6

Contributions of neutrons and gamma rays with -different energies to energy release in TFC wires (D–T plasma, cumulative distribution).

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As a result of presence of considerable fraction of high-energy neutrons in the neutron flux at the output of the VV, application of boron in shielding layers of the vacuum vessel does not leads to substantial reduction in energy release in the TFC, although it attenuates the flux of the low-energy neutrons. In this situation, natural boron can be used instead of expensive enriched one.

To estimate possibilities to improve shielding, we simulated the variant of the model with an increased amount of water in the VV. The model geometry could not be changed without it being specially agreed upon. Therefore, to obtain a qualitative estimate, we decided to formally increase water density in the model to 2 g/cm3. Specific energy release in the TFC with a double-density water dropped by nearly a factor of 4 and turned out to be closer to values obtained for the D–D plasma relative to the D–T one. Note that the curve representing the dependence of neutron moderation efficiency in the VV on water-layer thickness rises faster than linearly. This means that the amount of water must be sufficient in order for its shielding effect to be substantial, especially in the case of multilayer shielding.

Operation with large volume of water requires solving complex logistical and technical problems. Pools for cooling and storing water, along with radiation-shielded water supply and return systems, will have to be constructed. However, when the water volume is large, the total mass and cost of shielding can be reduced by an order of magnitude due to reduced mass of required steel, boron carbide, and tungsten. Correspondingly, the mass and cost of the radioactive waste will also be lower (radioactive waste can create even larger problems at the end of the system lifetime). Taking waste into account, a refusal from using water as the main neutron shielding element does not eliminate problems but rather postpones them to a later time.

5 CONCLUSIONS

In this work, we calculated the energy release in the vacuum vessel, the toroidal field coil, and other EMS components for a simplified TRT model.

Calculated values of volume-averaged energy release are presented in Table 2. To make an estimate of the total heat release in the TFC, we set its volume equal to 1.08 m3, the value obtained from the simplified 3D model. Heat release in the TFC was found to be equal to 5.5 kW for D–T plasma. Note that we did not take into account the components facing the plasma inside the VV, because it is the VV that represents the major radiation-shielding component in the TRT.

Table 2. Volume-averaged energy release in the TFC, mW/cm3
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Energy release in other EMS elements was also calculated. However, substantial refining of the 3D model is required for more accurate calculations.

Energy release for the case of D–D plasma falls into acceptable range of below 1 mW/cm3. This limit was set by developers of the cooling system of the TRT EMS and is still being discussed: the limit is substantially higher than it proposed for the DEMO reactor (50 µW/cm3) [11] but it is comparable with the value expected for the DTT [12] and SPARC [13] systems. Taking into account that calculation was carried out only for the total neutron yield of 1018 s–1, which is several times higher than the yield expected for the D‒D plasma, this limit will not be reached. In the case of D–T plasma and the same neutron yield, it is necessary to either decrease the discharge time or enhance the shielding, e.g., by increasing the thickness of the water layer in the VV, at least, in the inner segment. It might be necessary to consider a combination with other neutron moderators.